constraints 0.8 → 0.14.4
raw patch · 14 files changed
Files
- CHANGELOG.markdown +247/−0
- README.markdown +2/−0
- constraints.cabal +53/−19
- src/Data/Constraint.hs +249/−87
- src/Data/Constraint/Char.hs +60/−0
- src/Data/Constraint/Deferrable.hs +44/−28
- src/Data/Constraint/Forall.hs +81/−92
- src/Data/Constraint/Lifting.hs +6/−68
- src/Data/Constraint/Nat.hs +396/−0
- src/Data/Constraint/Symbol.hs +138/−0
- src/Data/Constraint/Unsafe.hs +69/−36
- tests/GH117Spec.hs +34/−0
- tests/GH55Spec.hs +47/−0
- tests/Spec.hs +1/−0
+ CHANGELOG.markdown view
@@ -0,0 +1,247 @@+0.14.4 [2026.01.26]+-------------------+* Depend on `ghc-bignum` instead of `integer-gmp` on recent versions GHC.++0.14.3 [2026.01.10]+-------------------+* Remove unused `ghc-prim` dependency.++0.14.2 [2024.05.12]+-------------------+* Re-export `Log2` from `Data.Constraint.Nat`.+* Add `log2Nat` and `log2Pow` to `Data.Constraint.Nat`.++0.14.1 [2024.04.29]+-------------------+* Remove an unused dependency on the `type-equality` library.++0.14 [2023.10.11]+-----------------+* Drop support for GHCs older than 8.6.+* The `forall` function in `Data.Constraint.Forall` has been renamed to+ `forall_`, since a future version of GHC will make the use of `forall` as+ an identifier an error.+* Implement `Data.Constraint.Forall` using `QuantifiedConstraints`.+* Remove `Lifting` instances for `ErrorT` and `ListT`, which were removed+ in `transformers-0.6.*`.+* Add a `c => Boring (Dict c)` instance.+* Add the `Data.Constraint.Char` module, which contains utilities for working+ with `KnownChar` constraints. This module is only available on GHC 9.2 or+ later.+* Add `unsafeAxiom` to `Data.Constraint.Unsafe`.+* Add `unsafeSChar`, `unsafeSNat`, and `unsafeSSymbol` to+ `Data.Constraint.Unsafe` when building with `base-4.18` (GHC 9.6) or later.++0.13.4 [2022.05.19]+-------------------+* Correct the CPP introduced in `constraints-0.13.3` such that it works when+ building with `mtl-2.3.*` or later combined with `transformers < 0.6`.++0.13.3 [2022.01.31]+-------------------+* Allow building with `transformers-0.6.*` and `mtl-2.3.*`.++0.13.2 [2021.11.10]+-------------------+* Allow building on GHC HEAD.++0.13.1 [2021.10.31]+-------------------+* Allow building with GHC 9.2.++0.13 [2021.02.17]+-----------------+* `Data.Constraint.Symbol` now reexports the `GHC.TypeLits.AppendSymbol` type+ family from recent versions of `base` (or, on old versions of `base`, it+ defines a backwards-compatibile version of `AppendSymbol`). The existing+ `(++)` type family for `Data.Constraint.Symbol` is now a synonym for+ `AppendSymbol`.++ This is technically a breaking change, as `(++)` was previously defined like+ so:++ ```hs+ type family (++) :: Symbol -> Symbol -> Symbol+ ```++ This meant that `(++)` could be partially applied. However, for compatibility+ with the way that `AppendSymbol` is defined, `(++)` is now defined like so:++ ```hs+ type m ++ n = AppendSymbol m n+ ```++ As a result, `(++)` can no longer be partially applied.+* Make the `(++)` type family in `Data.Constraint.Symbol` be `infixr 5`.+* Add `implied :: (a => b) -> (a :- b)` to `Data.Constraint`, which converts+ a quantified constraint into an entailment. This is only available when+ compiled with GHC 8.6 or later.++0.12 [2020.02.03]+-----------------+* Relax the type signature for `divideTimes`:++ ```diff+ -dividesTimes :: (Divides a b, Divides a c) :- Divides a (b * c)+ +dividesTimes :: Divides a b :- Divides a (b * c)+ ```++* Simplify the type signature of `dividesDef`:++ ```diff+ -dividesDef :: forall a b. Divides a b :- ((a * Div b a) ~ b)+ +dividesDef :: forall a b. Divides a b :- (Mod b a ~ 0)+ ```++ The original type of `diviesDef` can be (partially) recovered by defining+ it in terms of the new `dividesDef`:++ ```hs+ dividesDef' :: forall a b. (1 <= a, Divides a b) :- ((a * Div b a) ~ b)+ dividesDef' = Sub $ case (dividesDef @a @b, euclideanNat @a @b) of+ (Sub Dict, Sub Dict) -> Dict+ ```++0.11.2 [2019.09.06]+-------------------+* Depend on the `type-equality` compatibility library so that `(:~~:)` may be+ used when compiling this library with GHC 8.0. This avoids having to redefine+ `(:~~:)` directly in the internals of `constraints` itself.++0.11.1 [2019.08.27]+-------------------+* Make `Data.Constraint.Deferrable.UnsatisfiedConstraint` a newtype.++0.11 [2019.05.10]+-----------------+* Introduce a `HasDict` type class for types that witness evidence of+ constraints, such as `Dict`, `(:-)`, `Coercion`, `(:~:)`, `(:~~:)`, and+ `TypeRep`.+* Generalize the types of `withDict` and `(\\)` to be polymorphic over+ any `HasDict` instance.+* Add `type (⊢) = (:-)`.+* Fix unsafe mistakes in the statements of `dividesDef` and `timesDiv` in+ `Data.Constraint.Nat`.+* Make the implementations of `Min` and `Max` reduce on more inputs in+ `Data.Constraint.Nat`.+* Add `minusNat` and `minusZero` functions to `Data.Constraint.Nat`.+* Support `hashable-1.3.*` and `semigroups-0.19.*`.++0.10.1 [2018.07.02]+-------------------+* Allow building with GHC 8.6.+* Add three axioms about `(+)` and `(-)` to `Data.Constraint.Nat`.++0.10+----+* Adapt to the `Semigroup`–`Monoid` Proposal (introduced in `base-4.11`):+ * Add a `Semigroup` instance for `Dict`+ * Add the appropriate `(:=>)` instances involving `Semigroup`, and change the+ `Class () (Monoid a)` instance to `Class (Semigroup a) (Monoid a)` when+ `base` is recent enough+ * Add the appropriate `Lifting(2)` instances involving `Semigroup`+* `Data.Constraint.Nat` now reexports the `Div` and `Mod` type families from+ `GHC.TypeLits` on `base-4.11` or later+* Fix the type signature of `maxCommutes`+* Export the `no` method of `Bottom`+* Add `NFData` instances for `Dict` and `(:-)`++0.9.1+-----+* Correct an improper use of `unsafeCoerce` in the internals of+ `Data.Constraint.Nat` and `Data.Constraint.Symbol`+* Correctly identify the mismatched types when you defer an unsatisfiable+ equality constraint through `Data.Constraint.Deferrable`+* Re-export the `(:~~:)` defined in `base` from `Data.Constraint.Deferred` with+ GHC 8.2 or later+* Add several new `(:=>)` instances for `Bits`, `Identity`, `Const`, `Natural`,+ `IO`, and `Word`.+* Modernize some existing `Class` and `(:=>)` instances to reflect the fact+ that `Applicative` is now a superclass of `Monad` on recent versions of+ `base`.++0.9+---+* Changes to `Data.Constraint`:+ * Add `strengthen1` and `strengthen2`+* Changes to `Data.Constraint.Deferrable`:+ * Add a `Deferrable ()` instance+ * The `Deferrable (a ~ b)` instance now shows the `TypeRep`s of `a` and `b`+ when a type mismatch error is thrown+ * Add `defer_` and `deferEither_`, counterparts to `defer` and `deferEither`+ which do not require proxy arguments+ * Enable `PolyKinds`. This allows the `Deferrable (a ~ b)` instance to be+ polykinded on all supported versions of GHC _except_ 7.10, where the kinds+ must be `*` due to an old GHC bug+ * Introduce a heterogeneous equality type `(:~~:)`, and use it to define a+ `Deferrable (a ~~ b)` instance on GHC 8.0 or later+* Changes to `Data.Constraint.Forall`:+ * Implement `ForallF` and `ForallT` in terms of `Forall`+ * Add `ForallV` and `InstV` (supporting a variable number of parameters)+ * Add a `forall` combinator+* Introduce `Data.Constraint.Nat` and `Data.Constraint.Symbol`, which contain+ utilities for working with `KnownNat` and `KnownSymbol` constraints,+ respectively. These modules are only available on GHC 8.0 or later.++0.8+-----+* GHC 8 compatibility+* `transformers` 0.5 compatibility+* `binary` 0.8 compatibility+* Dropped support for GHC 7.6 in favor of a nicer Bottom representation.++0.7+---+* Found a nicer encoding of the initial object in the category of constraints using a [nullary constraint](https://ghc.haskell.org/trac/ghc/ticket/7642).++0.6.1+-----+* Remove the need for closed type families from the new `Forall`.++0.6+---+* Completely redesigned `Data.Constraint.Forall`. The old design is unsound and can be abused to define `unsafeCoerce`!+ The new design requires closed type families, so this module now requires GHC 7.8+++0.5.1+-----+* Added `Data.Constraint.Deferrable`.++0.5+-----+* Added `Data.Constraint.Lifting`.++0.4.1.3+-------+* Acknowledge we actually need at least base 4.5++0.4.1.2+-------+* Restore support for building on older GHCs++0.4.1.1+-------+* Minor documentation fixes.++0.4.1+-----+* Added `mapDict` and `unmapDict`.+* Added a lot of documentation.++0.4+---+* `Typeable` and `Data`. The `Data` instance for `(:-)` is a conservative approximation that avoids having to turn (:-) into a cartesian closed category.+ If it becomes a pain point for users, I know how to do that, and have done so in other libraries -- see [hask](http://github.com/ekmett/hask), but I'm hesitant to bring such heavy machinery to bear and it isn't clear how to do it in a way that is compatible with those other libraries.++0.3.5+-----+* Explicit role annotations++0.3.4.1+-------+* Fixed build failures.+* Fixed an unused import warning on older GHCs.++0.3.4+-----+* Added `bottom`
README.markdown view
@@ -1,6 +1,8 @@ constraints =========== +[](https://hackage.haskell.org/package/constraints) [](https://github.com/ekmett/constraints/actions?query=workflow%3AHaskell-CI)+ This package provides data types and classes for manipulating the 'ConstraintKinds' exposed by GHC in 7.4. Contact Information
constraints.cabal view
@@ -1,15 +1,15 @@+cabal-version: 2.4 name: constraints category: Constraints-version: 0.8-license: BSD3-cabal-version: >= 1.10+version: 0.14.4+license: BSD-2-Clause license-file: LICENSE author: Edward A. Kmett maintainer: Edward A. Kmett <ekmett@gmail.com> stability: experimental homepage: http://github.com/ekmett/constraints/ bug-reports: http://github.com/ekmett/constraints/issues-copyright: Copyright (C) 2011-2015 Edward A. Kmett+copyright: Copyright (C) 2011-2021 Edward A. Kmett synopsis: Constraint manipulation description: GHC 7.4 gave us the ability to talk about @ConstraintKinds@. They stopped crashing the compiler in GHC 7.6.@@ -17,12 +17,26 @@ This package provides a vocabulary for working with them. build-type: Simple-tested-with: GHC == 7.6.3, GHC == 7.8.4, GHC == 7.10.1, GHC == 7.10.2++tested-with:+ GHC == 9.14.1+ GHC == 9.12.2+ GHC == 9.10.3+ GHC == 9.8.4+ GHC == 9.6.7+ 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-source-files: README.markdown+ , CHANGELOG.markdown source-repository head type: git- location: git://github.com/ekmett/constraints.git+ location: https://github.com/ekmett/constraints.git library hs-source-dirs: src@@ -41,25 +55,45 @@ GADTs build-depends:- base >= 4.7 && < 5,- binary >= 0.7.3 && < 0.9,- deepseq >= 1.3 && < 1.5,- ghc-prim,- hashable >= 1.2 && < 1.3,- mtl >= 2 && < 2.3,- transformers >= 0.2 && < 0.6,- transformers-compat >= 0.4 && < 1-- if impl(ghc < 7.8)+ , base >= 4.12 && < 5+ , binary >= 0.7.1 && < 0.9+ , boring >= 0.2 && < 0.3+ , deepseq >= 1.3 && < 1.6+ , hashable >= 1.2 && < 1.6+ , mtl >= 2.2 && < 2.4+ , transformers >= 0.5 && < 0.7+ if impl(ghc >= 9.15) build-depends:- newtype >= 0.2 && < 0.3,- tagged >= 0.2 && < 1+ ghc-bignum+ elif impl(ghc < 9.0)+ build-depends:+ integer-gmp exposed-modules: Data.Constraint Data.Constraint.Deferrable Data.Constraint.Forall Data.Constraint.Lifting+ Data.Constraint.Nat+ Data.Constraint.Symbol Data.Constraint.Unsafe - ghc-options: -Wall+ if impl(ghc >= 9.2)+ exposed-modules:+ Data.Constraint.Char++ ghc-options: -Wall -Wno-star-is-type++test-suite spec+ type: exitcode-stdio-1.0+ default-language: Haskell2010+ hs-source-dirs: tests+ main-is: Spec.hs+ other-modules: GH55Spec+ GH117Spec+ ghc-options: -Wall -threaded -rtsopts+ build-tool-depends: hspec-discover:hspec-discover >= 2+ build-depends:+ , base+ , constraints+ , hspec >= 2
src/Data/Constraint.hs view
@@ -1,35 +1,28 @@+{-# LANGUAGE AllowAmbiguousTypes #-}+{-# LANGUAGE CPP #-}+{-# LANGUAGE ConstraintKinds #-}+{-# LANGUAGE DeriveDataTypeable #-}+{-# LANGUAGE DerivingStrategies #-}+{-# LANGUAGE FlexibleContexts #-}+{-# LANGUAGE FlexibleInstances #-} {-# LANGUAGE FunctionalDependencies #-}-{-# LANGUAGE UndecidableInstances #-}+{-# LANGUAGE GADTs #-}+{-# LANGUAGE PolyKinds #-}+{-# LANGUAGE QuantifiedConstraints #-}+{-# LANGUAGE Rank2Types #-}+{-# LANGUAGE RoleAnnotations #-} {-# LANGUAGE ScopedTypeVariables #-} {-# LANGUAGE StandaloneDeriving #-}-{-# LANGUAGE FlexibleInstances #-}-{-# LANGUAGE FlexibleContexts #-}-{-# LANGUAGE ConstraintKinds #-}-{-# LANGUAGE EmptyDataDecls #-}-{-# LANGUAGE KindSignatures #-}-{-# LANGUAGE TypeOperators #-}-{-# LANGUAGE TypeFamilies #-} {-# LANGUAGE Trustworthy #-}-{-# LANGUAGE Rank2Types #-}-{-# LANGUAGE GADTs #-}-{-# LANGUAGE CPP #-}-#if __GLASGOW_HASKELL__ >= 707-{-# LANGUAGE AllowAmbiguousTypes #-}-{-# LANGUAGE DeriveDataTypeable #-}-{-# LANGUAGE RoleAnnotations #-}-#endif-#if __GLASGOW_HASKELL__ >= 800+{-# LANGUAGE TypeFamilies #-}+{-# LANGUAGE TypeOperators #-}+{-# LANGUAGE UndecidableInstances #-} {-# LANGUAGE UndecidableSuperClasses #-}-#endif-#if __GLASGOW_HASKELL__ >= 708 && __GLASGOW_HASKELL__ < 710-{-# LANGUAGE NullaryTypeClasses #-}-#endif------------------------------------------------------------------------------+{-# LANGUAGE UnicodeSyntax #-}+ -- |--- Module : Data.Constraint -- Copyright : (C) 2011-2015 Edward Kmett, -- License : BSD-style (see the file LICENSE)--- -- Maintainer : Edward Kmett <ekmett@gmail.com> -- Stability : experimental -- Portability : non-portable@@ -44,27 +37,34 @@ -- -- The need for this extension was first publicized in the paper ----- <http://research.microsoft.com/pubs/67439/gmap3.pdf Scrap your boilerplate with class: extensible generic functions>+-- <https://www.microsoft.com/en-us/research/wp-content/uploads/2016/07/gmap3.pdf Scrap your boilerplate with class: extensible generic functions> -- -- by Ralf Lämmel and Simon Peyton Jones in 2005, which shoehorned all the -- things they needed into a custom 'Sat' typeclass. -- -- With @ConstraintKinds@ we can put into code a lot of tools for manipulating -- these new types without such awkward workarounds.-----------------------------------------------------------------------------+ module Data.Constraint ( -- * The Kind of Constraints Constraint -- * Dictionary , Dict(Dict)+ , HasDict(..)+ , withDict+ , (\\) -- * Entailment , (:-)(Sub)- , (\\)+ , type (⊢)+ , type (|-)+ , type (&) , weaken1, weaken2, contract+ , strengthen1, strengthen2 , (&&&), (***) , trans, refl- , Bottom+ , implied+ , Bottom(no) , top, bottom -- * Dict is fully faithful , mapDict@@ -73,25 +73,24 @@ , Class(..) , (:=>)(..) ) where-import Control.Monad-#if __GLASGOW_HASKELL__ >= 707-import Control.Category-#endif import Control.Applicative-#if __GLASGOW_HASKELL__ < 710-import Data.Monoid-#endif+import Control.Category+import Control.DeepSeq+import Control.Monad import Data.Complex import Data.Ratio-#if __GLASGOW_HASKELL__ >= 707-import Data.Data-#endif-#if __GLASGOW_HASKELL__ <= 710-import GHC.Prim (Constraint)-#else-import GHC.Types (Constraint)-#endif-import qualified GHC.Prim as Prim+import Data.Data hiding (TypeRep)+import qualified GHC.Exts as Exts (Any)+import GHC.Exts (Constraint)+import Data.Bits (Bits)+import Data.Functor.Identity (Identity)+import Numeric.Natural (Natural)+import Data.Coerce (Coercible)+import Data.Type.Coercion(Coercion(..))+import Data.Type.Equality (type (~~))+import qualified Data.Type.Equality as Hetero+import Type.Reflection (TypeRep, typeRepKind, withTypeable)+import Data.Boring (Boring (..)) -- | Values of type @'Dict' p@ capture a dictionary for a constraint of type @p@. --@@ -104,17 +103,23 @@ -- captures a dictionary that proves we have an: -- -- @--- instance 'Eq' 'Int+-- instance 'Eq' 'Int' -- @ -- -- Pattern matching on the 'Dict' constructor will bring this instance into scope. -- data Dict :: Constraint -> * where Dict :: a => Dict a-#if __GLASGOW_HASKELL__ >= 707- deriving Typeable +deriving stock instance (Typeable p, p) => Data (Dict p)+deriving stock instance Eq (Dict a)+deriving stock instance Ord (Dict a)+deriving stock instance Show (Dict a) +instance c => Boring (Dict c) where+ boring = Dict++{- instance (Typeable p, p) => Data (Dict p) where gfoldl _ z Dict = z Dict toConstr _ = dictConstr@@ -128,14 +133,64 @@ dictDataType :: DataType dictDataType = mkDataType "Data.Constraint.Dict" [dictConstr]-#endif+-} -deriving instance Eq (Dict a)-deriving instance Ord (Dict a)-deriving instance Show (Dict a) +instance NFData (Dict c) where+ rnf Dict = ()++-- | Witnesses that a value of type @e@ contains evidence of the constraint @c@.+--+-- Mainly intended to allow ('\\') to be overloaded, since it's a useful operator.+class HasDict c e | e -> c where+ evidence :: e -> Dict c++instance HasDict a (Dict a) where+ evidence = Prelude.id++instance a => HasDict b (a :- b) where+ evidence (Sub x) = x++instance HasDict (Coercible a b) (Coercion a b) where+ evidence Coercion = Dict++instance HasDict (a ~ b) (a :~: b) where+ evidence Refl = Dict++instance HasDict (a ~~ b) (a Hetero.:~~: b) where+ evidence Hetero.HRefl = Dict++instance HasDict (Typeable k, Typeable a) (TypeRep (a :: k)) where+ evidence tr = withTypeable tr $ withTypeable (typeRepKind tr) Dict++-- | From a 'Dict', takes a value in an environment where the instance+-- witnessed by the 'Dict' is in scope, and evaluates it.+--+-- Essentially a deconstruction of a 'Dict' into its continuation-style+-- form.+--+-- Can also be used to deconstruct an entailment, @a ':-' b@, using a context @a@.+--+-- @+-- withDict :: 'Dict' c -> (c => r) -> r+-- withDict :: a => (a ':-' c) -> (c => r) -> r+-- @+withDict :: HasDict c e => e -> (c => r) -> r+withDict d r = case evidence d of+ Dict -> r++infixl 1 \\ -- required comment++-- | Operator version of 'withDict', with the arguments flipped+(\\) :: HasDict c e => (c => r) -> e -> r+r \\ d = withDict d r+ infixr 9 :-+infixr 9 ⊢ +-- | Type entailment, as written with a single character.+type (⊢) = (:-)+ -- | This is the type of entailment. -- -- @a ':-' b@ is read as @a@ \"entails\" @b@.@@ -152,9 +207,10 @@ -- -- This relationship is captured in the ':-' entailment type here. ----- Since @p ':-' p@ and entailment composes, ':-' forms the arrows of a 'Category'--- of constraints. However, 'Category' only because sufficiently general to support this--- instance in GHC 7.8, so prior to 7.8 this instance is unavailable.+-- Since @p ':-' p@ and entailment composes, ':-' forms the arrows of a+-- 'Category' of constraints. However, 'Category' only became sufficiently+-- general to support this instance in GHC 7.8, so prior to 7.8 this instance+-- is unavailable. -- -- But due to the coherence of instance resolution in Haskell, this 'Category' -- has some very interesting properties. Notably, in the absence of@@ -171,7 +227,7 @@ -- What are the two ways? -- -- Well, we can go from @'Ord' a ':-' 'Eq' a@ via the--- superclass relationship, and them from @'Eq' a ':-' 'Eq' [a]@ via the+-- superclass relationship, and then from @'Eq' a ':-' 'Eq' [a]@ via the -- instance, or we can go from @'Ord' a ':-' 'Ord' [a]@ via the instance -- then from @'Ord' [a] ':-' 'Eq' [a]@ through the superclass relationship -- and this diagram by definition must \"commute\".@@ -190,35 +246,28 @@ -- library is sensible and can't break any assumptions on the behalf of -- library authors. newtype a :- b = Sub (a => Dict b)-#if __GLASGOW_HASKELL__ >= 707- deriving Typeable type role (:-) nominal nominal --- TODO: _proper_ Data for @(p ':-' q)@ requires @(:-)@ to be cartesian _closed_.------ This is admissable, but not present by default---- constraint should be instance (Typeable p, Typeable q, p |- q) => Data (p :- q)-instance (Typeable p, Typeable q, p, q) => Data (p :- q) where- gfoldl _ z (Sub Dict) = z (Sub Dict)- toConstr _ = subConstr+instance (Typeable p, Typeable q, p => q) => Data (p :- q) where+ gfoldl _ z d = z d gunfold _ z c = case constrIndex c of- 1 -> z (Sub Dict)- _ -> error "gunfold"- dataTypeOf _ = subDataType--subConstr :: Constr-subConstr = mkConstr dictDataType "Sub" [] Prefix+ 1 -> z (Sub Dict)+ _ -> error "Data.Data.Data: Data.Constraint.:- constructor out of bounds"+ toConstr _ = subCon+ dataTypeOf _ = subTy -subDataType :: DataType-subDataType = mkDataType "Data.Constraint.:-" [subConstr]+subCon :: Constr+subCon = mkConstr subTy "Sub Dict" [] Prefix+{-# noinline subCon #-}+subTy :: DataType+subTy = mkDataType "Data.Constraint.:-" [subCon]+{-# noinline subTy #-} -- | Possible since GHC 7.8, when 'Category' was made polykinded. instance Category (:-) where id = refl (.) = trans-#endif -- | Assumes 'IncoherentInstances' doesn't exist. instance Eq (a :- b) where@@ -231,11 +280,8 @@ instance Show (a :- b) where showsPrec d _ = showParen (d > 10) $ showString "Sub Dict" -infixl 1 \\ -- required comment---- | Given that @a :- b@, derive something that needs a context @b@, using the context @a@-(\\) :: a => (b => r) -> (a :- b) -> r-r \\ Sub Dict = r+instance a => NFData (a :- b) where+ rnf (Sub Dict) = () -------------------------------------------------------------------------------- -- Constraints form a Category@@ -254,10 +300,46 @@ refl = Sub Dict --------------------------------------------------------------------------------+-- QuantifiedConstraints+--------------------------------------------------------------------------------++-- | Convert a quantified constraint into an entailment.+implied :: forall a b. (a => b) => a :- b+implied = Sub (Dict :: Dict b)++-- | The internal hom for the category of constraints.+--+-- This version can be passed around inside Dict, whereas (a => b) is impredicative+--+-- @+-- foo :: Dict (Ord a => Eq a)+-- foo = Dict+-- @+--+-- fails to typecheck due to the lack of impredicative polymorphism, but+--+-- @+-- foo :: Dict (Ord a |- Eq a)+-- foo = Dict+-- @+--+-- typechecks just fine.++class (p => q) => p |- q+instance (p => q) => p |- q+++-------------------------------------------------------------------------------- -- (,) is a Bifunctor -------------------------------------------------------------------------------- -- | due to the hack for the kind of @(,)@ in the current version of GHC we can't actually+-- make instances for @(,) :: Constraint -> Constraint -> Constraint@, but we can define+-- an equivalent type, that converts back and forth to @(,)@, and lets you hang instances.+class (p,q) => p & q+instance (p,q) => p & q++-- | due to the hack for the kind of @(,)@ in the current version of GHC we can't actually -- make instances for @(,) :: Constraint -> Constraint -> Constraint@, but @(,)@ is a -- bifunctor on the category of constraints. This lets us map over both sides. (***) :: (a :- b) -> (c :- d) -> (a, c) :- (b, d)@@ -279,6 +361,12 @@ weaken2 :: (a, b) :- b weaken2 = Sub Dict +strengthen1 :: Dict b -> a :- c -> a :- (b,c)+strengthen1 d e = unmapDict (const d) &&& e++strengthen2 :: Dict b -> a :- c -> a :- (c,b)+strengthen2 d e = e &&& unmapDict (const d)+ -- | Contracting a constraint / diagonal morphism -- -- The category of constraints is Cartesian. We can reuse information.@@ -305,8 +393,8 @@ top = Sub Dict -- | 'Any' inhabits every kind, including 'Constraint' but is uninhabited, making it impossible to define an instance.-class Prim.Any => Bottom where- no :: Dict a+class Exts.Any => Bottom where+ no :: a -- | -- This demonstrates the law of classical logic <http://en.wikipedia.org/wiki/Principle_of_explosion "ex falso quodlibet">@@ -331,9 +419,7 @@ unmapDict :: (Dict a -> Dict b) -> a :- b unmapDict f = Sub (f Dict) -#if __GLASGOW_HASKELL__ >= 707 type role Dict nominal-#endif -------------------------------------------------------------------------------- -- Reflection@@ -403,6 +489,10 @@ instance (Eq a, Eq b) :=> Eq (Either a b) where ins = Sub Dict instance () :=> Eq (Dict a) where ins = Sub Dict instance () :=> Eq (a :- b) where ins = Sub Dict+instance () :=> Eq Word where ins = Sub Dict+instance Eq a :=> Eq (Identity a) where ins = Sub Dict+instance Eq a :=> Eq (Const a b) where ins = Sub Dict+instance () :=> Eq Natural where ins = Sub Dict -- Ord instance Class (Eq a) (Ord a) where cls = Sub Dict@@ -420,6 +510,10 @@ instance Integral a :=> Ord (Ratio a) where ins = Sub Dict instance () :=> Ord (Dict a) where ins = Sub Dict instance () :=> Ord (a :- b) where ins = Sub Dict+instance () :=> Ord Word where ins = Sub Dict+instance Ord a :=> Ord (Identity a) where ins = Sub Dict+instance Ord a :=> Ord (Const a b) where ins = Sub Dict+instance () :=> Ord Natural where ins = Sub Dict -- Show instance Class () (Show a) where cls = Sub Dict@@ -427,6 +521,7 @@ instance () :=> Show Bool where ins = Sub Dict instance () :=> Show Ordering where ins = Sub Dict instance () :=> Show Char where ins = Sub Dict+instance () :=> Show Int where ins = Sub Dict instance Show a :=> Show (Complex a) where ins = Sub Dict instance Show a :=> Show [a] where ins = Sub Dict instance Show a :=> Show (Maybe a) where ins = Sub Dict@@ -435,6 +530,10 @@ instance (Integral a, Show a) :=> Show (Ratio a) where ins = Sub Dict instance () :=> Show (Dict a) where ins = Sub Dict instance () :=> Show (a :- b) where ins = Sub Dict+instance () :=> Show Word where ins = Sub Dict+instance Show a :=> Show (Identity a) where ins = Sub Dict+instance Show a :=> Show (Const a b) where ins = Sub Dict+instance () :=> Show Natural where ins = Sub Dict -- Read instance Class () (Read a) where cls = Sub Dict@@ -442,12 +541,17 @@ instance () :=> Read Bool where ins = Sub Dict instance () :=> Read Ordering where ins = Sub Dict instance () :=> Read Char where ins = Sub Dict+instance () :=> Read Int where ins = Sub Dict instance Read a :=> Read (Complex a) where ins = Sub Dict instance Read a :=> Read [a] where ins = Sub Dict instance Read a :=> Read (Maybe a) where ins = Sub Dict instance (Read a, Read b) :=> Read (a, b) where ins = Sub Dict instance (Read a, Read b) :=> Read (Either a b) where ins = Sub Dict instance (Integral a, Read a) :=> Read (Ratio a) where ins = Sub Dict+instance () :=> Read Word where ins = Sub Dict+instance Read a :=> Read (Identity a) where ins = Sub Dict+instance Read a :=> Read (Const a b) where ins = Sub Dict+instance () :=> Read Natural where ins = Sub Dict -- Enum instance Class () (Enum a) where cls = Sub Dict@@ -460,6 +564,10 @@ instance () :=> Enum Float where ins = Sub Dict instance () :=> Enum Double where ins = Sub Dict instance Integral a :=> Enum (Ratio a) where ins = Sub Dict+instance () :=> Enum Word where ins = Sub Dict+instance Enum a :=> Enum (Identity a) where ins = Sub Dict+instance Enum a :=> Enum (Const a b) where ins = Sub Dict+instance () :=> Enum Natural where ins = Sub Dict -- Bounded instance Class () (Bounded a) where cls = Sub Dict@@ -469,6 +577,9 @@ instance () :=> Bounded Int where ins = Sub Dict instance () :=> Bounded Char where ins = Sub Dict instance (Bounded a, Bounded b) :=> Bounded (a,b) where ins = Sub Dict+instance () :=> Bounded Word where ins = Sub Dict+instance Bounded a :=> Bounded (Identity a) where ins = Sub Dict+instance Bounded a :=> Bounded (Const a b) where ins = Sub Dict -- Num instance Class () (Num a) where cls = Sub Dict@@ -478,6 +589,10 @@ instance () :=> Num Double where ins = Sub Dict instance RealFloat a :=> Num (Complex a) where ins = Sub Dict instance Integral a :=> Num (Ratio a) where ins = Sub Dict+instance () :=> Num Word where ins = Sub Dict+instance Num a :=> Num (Identity a) where ins = Sub Dict+instance Num a :=> Num (Const a b) where ins = Sub Dict+instance () :=> Num Natural where ins = Sub Dict -- Real instance Class (Num a, Ord a) (Real a) where cls = Sub Dict@@ -486,43 +601,83 @@ instance () :=> Real Float where ins = Sub Dict instance () :=> Real Double where ins = Sub Dict instance Integral a :=> Real (Ratio a) where ins = Sub Dict+instance () :=> Real Word where ins = Sub Dict+instance Real a :=> Real (Identity a) where ins = Sub Dict+instance Real a :=> Real (Const a b) where ins = Sub Dict+instance () :=> Real Natural where ins = Sub Dict -- Integral instance Class (Real a, Enum a) (Integral a) where cls = Sub Dict instance () :=> Integral Int where ins = Sub Dict instance () :=> Integral Integer where ins = Sub Dict+instance () :=> Integral Word where ins = Sub Dict+instance Integral a :=> Integral (Identity a) where ins = Sub Dict+instance Integral a :=> Integral (Const a b) where ins = Sub Dict+instance () :=> Integral Natural where ins = Sub Dict +-- Bits+instance Class (Eq a) (Bits a) where cls = Sub Dict+instance () :=> Bits Bool where ins = Sub Dict+instance () :=> Bits Int where ins = Sub Dict+instance () :=> Bits Integer where ins = Sub Dict+instance () :=> Bits Word where ins = Sub Dict+instance Bits a :=> Bits (Identity a) where ins = Sub Dict+instance Bits a :=> Bits (Const a b) where ins = Sub Dict+instance () :=> Bits Natural where ins = Sub Dict+ -- Fractional instance Class (Num a) (Fractional a) where cls = Sub Dict instance () :=> Fractional Float where ins = Sub Dict instance () :=> Fractional Double where ins = Sub Dict instance RealFloat a :=> Fractional (Complex a) where ins = Sub Dict instance Integral a :=> Fractional (Ratio a) where ins = Sub Dict+instance Fractional a :=> Fractional (Identity a) where ins = Sub Dict+instance Fractional a :=> Fractional (Const a b) where ins = Sub Dict -- Floating instance Class (Fractional a) (Floating a) where cls = Sub Dict instance () :=> Floating Float where ins = Sub Dict instance () :=> Floating Double where ins = Sub Dict instance RealFloat a :=> Floating (Complex a) where ins = Sub Dict+instance Floating a :=> Floating (Identity a) where ins = Sub Dict+instance Floating a :=> Floating (Const a b) where ins = Sub Dict -- RealFrac instance Class (Real a, Fractional a) (RealFrac a) where cls = Sub Dict instance () :=> RealFrac Float where ins = Sub Dict instance () :=> RealFrac Double where ins = Sub Dict instance Integral a :=> RealFrac (Ratio a) where ins = Sub Dict+instance RealFrac a :=> RealFrac (Identity a) where ins = Sub Dict+instance RealFrac a :=> RealFrac (Const a b) where ins = Sub Dict -- RealFloat instance Class (RealFrac a, Floating a) (RealFloat a) where cls = Sub Dict instance () :=> RealFloat Float where ins = Sub Dict instance () :=> RealFloat Double where ins = Sub Dict+instance RealFloat a :=> RealFloat (Identity a) where ins = Sub Dict+instance RealFloat a :=> RealFloat (Const a b) where ins = Sub Dict +-- Semigroup+instance Class () (Semigroup a) where cls = Sub Dict+instance () :=> Semigroup () where ins = Sub Dict+instance () :=> Semigroup Ordering where ins = Sub Dict+instance () :=> Semigroup [a] where ins = Sub Dict+instance Semigroup a :=> Semigroup (Maybe a) where ins = Sub Dict+instance (Semigroup a, Semigroup b) :=> Semigroup (a, b) where ins = Sub Dict+instance Semigroup a :=> Semigroup (Const a b) where ins = Sub Dict+instance Semigroup a :=> Semigroup (Identity a) where ins = Sub Dict+instance Semigroup a :=> Semigroup (IO a) where ins = Sub Dict+ -- Monoid-instance Class () (Monoid a) where cls = Sub Dict+instance Class (Semigroup a) (Monoid a) where cls = Sub Dict instance () :=> Monoid () where ins = Sub Dict instance () :=> Monoid Ordering where ins = Sub Dict instance () :=> Monoid [a] where ins = Sub Dict instance Monoid a :=> Monoid (Maybe a) where ins = Sub Dict instance (Monoid a, Monoid b) :=> Monoid (a, b) where ins = Sub Dict+instance Monoid a :=> Monoid (Const a b) where ins = Sub Dict+instance Monoid a :=> Monoid (Identity a) where ins = Sub Dict+instance Monoid a :=> Monoid (IO a) where ins = Sub Dict -- Functor instance Class () (Functor f) where cls = Sub Dict@@ -533,6 +688,8 @@ instance () :=> Functor ((,) a) where ins = Sub Dict instance () :=> Functor IO where ins = Sub Dict instance Monad m :=> Functor (WrappedMonad m) where ins = Sub Dict+instance () :=> Functor Identity where ins = Sub Dict+instance () :=> Functor (Const a) where ins = Sub Dict -- Applicative instance Class (Functor f) (Applicative f) where cls = Sub Dict@@ -542,6 +699,7 @@ instance () :=> Applicative ((->)a) where ins = Sub Dict instance () :=> Applicative IO where ins = Sub Dict instance Monoid a :=> Applicative ((,)a) where ins = Sub Dict+instance Monoid a :=> Applicative (Const a) where ins = Sub Dict instance Monad m :=> Applicative (WrappedMonad m) where ins = Sub Dict -- Alternative@@ -551,14 +709,15 @@ instance MonadPlus m :=> Alternative (WrappedMonad m) where ins = Sub Dict -- Monad-instance Class () (Monad f) where cls = Sub Dict+instance Class (Applicative f) (Monad f) where cls = Sub Dict instance () :=> Monad [] where ins = Sub Dict instance () :=> Monad ((->) a) where ins = Sub Dict instance () :=> Monad (Either a) where ins = Sub Dict instance () :=> Monad IO where ins = Sub Dict+instance () :=> Monad Identity where ins = Sub Dict -- MonadPlus-instance Class (Monad f) (MonadPlus f) where cls = Sub Dict+instance Class (Monad f, Alternative f) (MonadPlus f) where cls = Sub Dict instance () :=> MonadPlus [] where ins = Sub Dict instance () :=> MonadPlus Maybe where ins = Sub Dict @@ -579,7 +738,10 @@ instance a :=> Read (Dict a) where ins = Sub Dict deriving instance a => Read (Dict a) +instance () :=> Semigroup (Dict a) where ins = Sub Dict+instance Semigroup (Dict a) where+ Dict <> Dict = Dict+ instance a :=> Monoid (Dict a) where ins = Sub Dict instance a => Monoid (Dict a) where- mappend Dict Dict = Dict mempty = Dict
+ src/Data/Constraint/Char.hs view
@@ -0,0 +1,60 @@+{-# LANGUAGE ScopedTypeVariables #-}+{-# LANGUAGE AllowAmbiguousTypes #-}+{-# LANGUAGE TypeApplications #-}+{-# LANGUAGE ConstraintKinds #-}+{-# LANGUAGE TypeOperators #-}+{-# LANGUAGE TypeFamilies #-}+{-# LANGUAGE RankNTypes #-}+{-# LANGUAGE DataKinds #-}+{-# LANGUAGE PolyKinds #-}+{-# LANGUAGE CPP #-}+-- | Utilities for working with 'KnownChar' constraints.+--+-- This module is only available on GHC 9.2 or later.+module Data.Constraint.Char+ ( CharToNat+ , NatToChar+ , charToNat+ , natToChar+ ) where++import Data.Char+import Data.Constraint+import Data.Proxy+import GHC.TypeLits+#if MIN_VERSION_base(4,18,0)+import Data.Constraint.Unsafe+import qualified GHC.TypeNats as TN+#else+import Unsafe.Coerce+#endif++-- implementation details++#if !MIN_VERSION_base(4,18,0)+newtype Magic c = Magic (KnownChar c => Dict (KnownChar c))+#endif++magicCN :: forall c n. (Char -> Int) -> KnownChar c :- KnownNat n+#if MIN_VERSION_base(4,18,0)+magicCN f = Sub $ TN.withKnownNat (unsafeSNat @n (fromIntegral (f (charVal (Proxy @c))))) Dict+#else+magicCN f = Sub $ unsafeCoerce (Magic Dict) (fromIntegral @Int @Natural (f (charVal (Proxy @c))))+#endif++magicNC :: forall n c. (Int -> Char) -> KnownNat n :- KnownChar c+#if MIN_VERSION_base(4,18,0)+magicNC f = Sub $ withKnownChar (unsafeSChar @c (f (fromIntegral (natVal (Proxy @n))))) Dict+#else+magicNC f = Sub $ unsafeCoerce (Magic Dict) (f (fromIntegral (natVal (Proxy @n))))+#endif++-- operations++charToNat :: forall c. KnownChar c :- KnownNat (CharToNat c)+charToNat = magicCN ord++-- NB: 0x10FFFF the maximum value for a Unicode code point. Calling `chr` on+-- anything greater will throw an exception.+natToChar :: forall n. (n <= 0x10FFFF, KnownNat n) :- KnownChar (NatToChar n)+natToChar = Sub $ case magicNC @n @(NatToChar n) chr of Sub r -> r
src/Data/Constraint/Deferrable.hs view
@@ -1,66 +1,82 @@-{-# LANGUAGE TypeOperators #-}-{-# LANGUAGE GADTs #-}+{-# LANGUAGE AllowAmbiguousTypes #-} {-# LANGUAGE ConstraintKinds #-}-{-# LANGUAGE KindSignatures #-}+{-# LANGUAGE GADTs #-}+{-# LANGUAGE PolyKinds #-} {-# LANGUAGE RankNTypes #-} {-# LANGUAGE ScopedTypeVariables #-}-{-# LANGUAGE DeriveDataTypeable #-}+{-# LANGUAGE TypeApplications #-}+{-# LANGUAGE TypeOperators #-} ------------------------------------------------------------------------------ -- |--- Module : Data.Constraint.Deferrable--- Copyright : (C) 2015 Edward Kmett+-- Copyright : (C) 2015-2021 Edward Kmett -- License : BSD-style (see the file LICENSE)--- -- Maintainer : Edward Kmett <ekmett@gmail.com> -- Stability : experimental -- Portability : non-portable -- -- The idea for this trick comes from Dimitrios Vytiniotis.------------------------------------------------------------------------------ module Data.Constraint.Deferrable ( UnsatisfiedConstraint(..) , Deferrable(..) , defer , deferred+ , (:~~:)(HRefl)+ , (:~:)(Refl) ) where import Control.Exception import Control.Monad import Data.Constraint import Data.Proxy-import Data.Typeable (Typeable, cast)+import Data.Typeable (Typeable, cast, typeRep)+import Data.Type.Equality ((:~:)(Refl)) -data UnsatisfiedConstraint = UnsatisfiedConstraint String- deriving (Typeable, Show)+import Data.Type.Equality (type (~~), (:~~:)(HRefl)) +newtype UnsatisfiedConstraint = UnsatisfiedConstraint String+ deriving Show+ instance Exception UnsatisfiedConstraint -- | Allow an attempt at resolution of a constraint at a later time-class Deferrable (p :: Constraint) where+class Deferrable p where -- | Resolve a 'Deferrable' constraint with observable failure.- deferEither :: proxy p -> (p => r) -> Either String r---- | Defer a constraint for later resolution in a context where we want to upgrade failure into an error-defer :: forall proxy p r. Deferrable p => proxy p -> (p => r) -> r-defer _ r = either (throw . UnsatisfiedConstraint) id $ deferEither (Proxy :: Proxy p) r + deferEither :: (p => r) -> Either String r deferred :: forall p. Deferrable p :- p-deferred = Sub $ defer (Proxy :: Proxy p) Dict+deferred = Sub $ defer @p Dict --- We use our own type equality rather than @Data.Type.Equality@ to allow building on GHC 7.6.-data a :~: b where- Refl :: a :~: a- deriving Typeable+defer :: forall p r. Deferrable p => (p => r) -> r+defer r = either (throw . UnsatisfiedConstraint) id $ deferEither @p r -instance (Typeable a, Typeable b) => Deferrable (a ~ b) where- deferEither _ r = case cast (Refl :: a :~: a) :: Maybe (a :~: b) of+showTypeRep :: forall t. Typeable t => String+showTypeRep = show $ typeRep (Proxy @t)++instance Deferrable () where+ deferEither r = Right r++-- | Deferrable homogeneous equality constraints.+--+-- Note that due to a GHC bug (https://ghc.haskell.org/trac/ghc/ticket/10343),+-- using this instance on GHC 7.10 will only work with @*@-kinded types.+instance (Typeable k, Typeable (a :: k), Typeable b) => Deferrable (a ~ b) where+ deferEither r = case cast (Refl :: a :~: a) :: Maybe (a :~: b) of Just Refl -> Right r- Nothing -> Left "deferred type equality: type mismatch"+ Nothing -> Left $+ "deferred type equality: type mismatch between `" ++ showTypeRep @a ++ "’ and `" ++ showTypeRep @b ++ "'" +-- | Deferrable heterogenous equality constraints.+--+-- Only available on GHC 8.0 or later.+instance (Typeable i, Typeable j, Typeable (a :: i), Typeable (b :: j)) => Deferrable (a ~~ b) where+ deferEither r = case cast (HRefl :: a :~~: a) :: Maybe (a :~~: b) of+ Just HRefl -> Right r+ Nothing -> Left $+ "deferred type equality: type mismatch between `" ++ showTypeRep @a ++ "’ and `" ++ showTypeRep @b ++ "'"+ instance (Deferrable a, Deferrable b) => Deferrable (a, b) where- deferEither _ r = join $ deferEither (Proxy :: Proxy a) $ deferEither (Proxy :: Proxy b) r+ deferEither r = join $ deferEither @a $ deferEither @b r instance (Deferrable a, Deferrable b, Deferrable c) => Deferrable (a, b, c) where- deferEither _ r = join $ deferEither (Proxy :: Proxy a) $ join $ deferEither (Proxy :: Proxy b) $ deferEither (Proxy :: Proxy c) r+ deferEither r = join $ deferEither @a $ join $ deferEither @b $ deferEither @c r
src/Data/Constraint/Forall.hs view
@@ -1,21 +1,23 @@ {-# LANGUAGE CPP #-}-{-# LANGUAGE MultiParamTypeClasses #-}+{-# LANGUAGE FunctionalDependencies #-} {-# LANGUAGE UndecidableInstances #-} {-# LANGUAGE ScopedTypeVariables #-} {-# LANGUAGE FlexibleInstances #-} {-# LANGUAGE ConstraintKinds #-} {-# LANGUAGE TypeOperators #-} {-# LANGUAGE TypeFamilies #-}-{-# LANGUAGE Trustworthy #-}+{-# LANGUAGE RankNTypes #-} {-# LANGUAGE PolyKinds #-}-#if __GLASGOW_HASKELL__ >= 800 {-# LANGUAGE UndecidableSuperClasses #-}-#endif------------------------------------------------------------------------------+{-# LANGUAGE Trustworthy #-}+{-# LANGUAGE FlexibleContexts #-}+{-# LANGUAGE QuantifiedConstraints #-}+{-# LANGUAGE GADTs #-}+ -- |--- Module : Data.Constraint.Forall--- Copyright : (C) 2011-2015 Edward Kmett,--- (C) 2015 Ørjan Johansen+-- Copyright : (C) 2011-2021 Edward Kmett,+-- (C) 2015 Ørjan Johansen,+-- (C) 2016 David Feuer -- License : BSD-style (see the file LICENSE) -- -- Maintainer : Edward Kmett <ekmett@gmail.com>@@ -23,114 +25,101 @@ -- Portability : non-portable -- -- This module uses a trick to provide quantification over constraints.----------------------------------------------------------------------------- module Data.Constraint.Forall ( Forall, inst , ForallF, instF , Forall1, inst1 , ForallT, instT+ , ForallV, InstV (instV)+ , forall_ ) where import Data.Constraint import Unsafe.Coerce (unsafeCoerce) -{- The basic trick of this module is to use "skolem" types as test candidates- - for whether a class predicate holds, and if so assume that it holds for all- - types, unsafely coercing the typeclass dictionary.- -- - A previous version of this module used concrete, unexported types as the- - skolems. This turned out to be unsound in the presence of type families.- - There were 3 somewhat distinct issues:- -- - 1. Using closed type families, it is possible to test whether two concrete- - types are equal, even if one of them is not directly importable.- -- - 2. Using just open type families, it is possible to test "at least 2 of- - these n+1 types are equal", thus using the pigeonhole principle to thwart- - any scheme based on having only a finite number of shared skolem types.- -- - 3. Using just pattern matching of types by unification, it is possible- - to extract the skolem types from the application the `Forall p` expands- - to. (Although type families are probably still needed to exploit this.)- -- - András Kovács and Ørjan Johansen independently realized that skolems- - themselves made as type family applications can be used to solve the first- - two problems (and discovered the third problem in the process). As a bonus,- - the resulting code is easy to make polykinded.- -- - Problem 1 is solved by making the type family have no instances, forcing- - GHC to make no assumption about what type a skolem is.- -- - Problem 2 is solved by parametrizing the skolem on the predicate tested- - for. (This is a known trick in predicate logic.)- -- - Problem 3 is solved by making the `Forall p` application expand to a type- - class, and have the *actual* test constraint be a superclass constraint on- - that type class, thus preventing the user directly accessing it.- -- - An unfortunate side effect of the new method is that it tends to trigger- - spurious errors from GHC test for cycles in superclass constraints. András- - Kovács discovered that these can be silenced by yet another use of a type- - family.- -- - David Feuer points out a remaining doubt about the soundness of this scheme:- - GHC *does* know that the skolems created from a single predicate `p` are- - equal. This could in theory apply even if the skolems come from two- - *distinct* invocations of `Forall p`.- -- - However, we don't know any way of bringing two such skolems in contact with- - each other to create an actual exploit. It would seem to require `p` to- - already contain its own skolem, despite there being (hopefully) no way to- - extract it from `Forall p` in order to tie the knot.- -}+class (forall a. p a) => Forall (p :: k -> Constraint)+instance (forall a. p a) => Forall (p :: k -> Constraint) --- the `Skolem*` type families represent skolem variables, do not export!--- if GHC supports it, these might be made closed with no instances.+-- | Instantiate a quantified @'Forall' p@ constraint at type @a@.+inst :: forall p a. Forall p :- p a+inst = Sub Dict -type family Skolem (p :: k -> Constraint) :: k-type family SkolemF (p :: k2 -> Constraint) (f :: k1 -> k2) :: k1-type family SkolemT1 (p :: k3 -> Constraint) (t :: k1 -> k2 -> k3) :: k1-type family SkolemT2 (p :: k3 -> Constraint) (t :: k1 -> k2 -> k3) :: k2+data Dict1 p where+ Dict1 :: (forall a. p a) => Dict1 p --- The outer `Forall*` type families prevent GHC from giving a spurious--- superclass cycle error.--- The inner `Forall*_` classes prevent the skolem from leaking to the user,--- which would be disastrous.+forallish :: forall p. Dict1 p -> Dict (Forall p)+forallish Dict1 = Dict --- | A representation of the quantified constraint @forall a. p a@.-type family Forall (p :: k -> Constraint) :: Constraint-type instance Forall p = Forall_ p-class p (Skolem p) => Forall_ (p :: k -> Constraint)-instance p (Skolem p) => Forall_ (p :: k -> Constraint)+forall_ :: forall p. (forall a. Dict (p a)) -> Dict (Forall p)+forall_ d = forallish (unsafeCoerce d) +-- | Composition for constraints.+class p (f a) => ComposeC (p :: k2 -> Constraint) (f :: k1 -> k2) (a :: k1)+instance p (f a) => ComposeC p f a+ -- | A representation of the quantified constraint @forall a. p (f a)@.-type family ForallF (p :: k2 -> Constraint) (f :: k1 -> k2) :: Constraint-type instance ForallF p f = ForallF_ p f-class p (f (SkolemF p f)) => ForallF_ (p :: k2 -> Constraint) (f :: k1 -> k2)-instance p (f (SkolemF p f)) => ForallF_ (p :: k2 -> Constraint) (f :: k1 -> k2)+class Forall (ComposeC p f) => ForallF (p :: k2 -> Constraint) (f :: k1 -> k2)+instance Forall (ComposeC p f) => ForallF p f -type Forall1 p = Forall p+-- | Instantiate a quantified @'ForallF' p f@ constraint at type @a@.+instF :: forall p f a . ForallF p f :- p (f a)+instF = Sub $+ case inst :: Forall (ComposeC p f) :- ComposeC p f a of+ Sub Dict -> Dict --- | A representation of the quantified constraint @forall f a. p (t f a)@.-type family ForallT (p :: k3 -> Constraint) (t :: k1 -> k2 -> k3) :: Constraint-type instance ForallT p t = ForallT_ p t-class p (t (SkolemT1 p t) (SkolemT2 p t)) => ForallT_ (p :: k3 -> Constraint) (t :: k1 -> k2 -> k3)-instance p (t (SkolemT1 p t) (SkolemT2 p t)) => ForallT_ (p :: k3 -> Constraint) (t :: k1 -> k2 -> k3)+-- Classes building up to ForallT+class p (t a b) => R (p :: k3 -> Constraint) (t :: k1 -> k2 -> k3) (a :: k1) (b :: k2)+instance p (t a b) => R p t a b+class Forall (R p t a) => Q (p :: k3 -> Constraint) (t :: k1 -> k2 -> k3) (a :: k1)+instance Forall (R p t a) => Q p t a --- | Instantiate a quantified @'Forall' p@ constraint at type @a@.-inst :: forall p a. Forall p :- p a-inst = unsafeCoerce (Sub Dict :: Forall p :- p (Skolem p))+-- | A representation of the quantified constraint @forall f a. p (t f a)@.+class Forall (Q p t) => ForallT (p :: k4 -> Constraint) (t :: (k1 -> k2) -> k3 -> k4)+instance Forall (Q p t) => ForallT p t --- | Instantiate a quantified @'ForallF' p f@ constraint at type @a@.-instF :: forall p f a. ForallF p f :- p (f a)-instF = unsafeCoerce (Sub Dict :: ForallF p f :- p (f (SkolemF p f)))+-- | Instantiate a quantified @'ForallT' p t@ constraint at types @f@ and @a@.+instT :: forall k1 k2 k3 k4 (p :: k4 -> Constraint) (t :: (k1 -> k2) -> k3 -> k4) (f :: k1 -> k2) (a :: k3). ForallT p t :- p (t f a)+instT = Sub $+ case inst :: Forall (Q p t) :- Q p t f of { Sub Dict ->+ case inst :: Forall (R p t f) :- R p t f a of+ Sub Dict -> Dict } +type Forall1 p = Forall p -- | Instantiate a quantified constraint on kind @* -> *@. -- This is now redundant since @'inst'@ became polykinded. inst1 :: forall (p :: (* -> *) -> Constraint) (f :: * -> *). Forall p :- p f inst1 = inst --- | Instantiate a quantified @'ForallT' p t@ constraint at types @f@ and @a@.-instT :: forall (p :: k3 -> Constraint) (t :: k1 -> k2 -> k3) (f :: k1) (a :: k2). ForallT p t :- p (t f a)-instT = unsafeCoerce (Sub Dict :: ForallT p t :- p (t (SkolemT1 p t) (SkolemT2 p t)))+-- | A representation of the quantified constraint+-- @forall a1 a2 ... an . p a1 a2 ... an@, supporting a variable number of+-- parameters.+type family ForallV :: k -> Constraint+type instance ForallV = ForallV_++class ForallV' p => ForallV_ (p :: k)+instance ForallV' p => ForallV_ p++-- | Instantiate a quantified @'ForallV' p@ constraint as @c@, where+-- @c ~ p a1 a2 ... an@.+class InstV (p :: k) c | k c -> p where+ type ForallV' (p :: k) :: Constraint+ instV :: ForallV p :- c++instance p ~ c => InstV (p :: Constraint) c where+ type ForallV' (p :: Constraint) = p+ instV = Sub Dict++-- Treating 1 argument specially rather than recursing as a bit of (premature?)+-- optimization+instance p a ~ c => InstV (p :: k -> Constraint) c where+ type ForallV' (p :: k -> Constraint) = Forall p+ instV = Sub $ case inst :: Forall p :- c of+ Sub Dict -> Dict++instance InstV (p a) c => InstV (p :: k1 -> k2 -> k3) c where+ type ForallV' (p :: k1 -> k2 -> k3) = ForallF ForallV p+ instV = Sub $ case instF :: ForallF ForallV p :- ForallV (p a) of+ Sub Dict -> case instV :: ForallV (p a) :- c of+ Sub Dict -> Dict+
src/Data/Constraint/Lifting.hs view
@@ -3,13 +3,12 @@ {-# LANGUAGE TypeFamilies #-} {-# LANGUAGE TypeOperators #-} {-# LANGUAGE ConstraintKinds #-}-{-# LANGUAGE DefaultSignatures #-} {-# LANGUAGE FlexibleInstances #-} {-# LANGUAGE ScopedTypeVariables #-} {-# LANGUAGE MultiParamTypeClasses #-} {-# LANGUAGE PolyKinds #-}-{-# OPTIONS_GHC -fno-warn-deprecations #-}-module Data.Constraint.Lifting ++module Data.Constraint.Lifting ( Lifting(..) , Lifting2(..) ) where@@ -25,10 +24,8 @@ import Control.Monad.IO.Class import Control.Monad.RWS.Class import Control.Monad.Trans.Cont-import Control.Monad.Trans.Error import Control.Monad.Trans.Except import Control.Monad.Trans.Identity-import Control.Monad.Trans.List import Control.Monad.Trans.Maybe import Control.Monad.Trans.Reader import Control.Monad.Trans.RWS.Lazy as Lazy@@ -40,9 +37,6 @@ import Data.Binary import Data.Complex import Data.Constraint-#if __GLASGOW_HASKELL__ < 710-import Data.Foldable-#endif import Data.Functor.Classes import Data.Functor.Compose as Functor import Data.Functor.Identity@@ -50,13 +44,7 @@ import Data.Functor.Reverse as Functor import Data.Functor.Sum as Functor import Data.Hashable-#if __GLASGOW_HASKELL__ < 710-import Data.Monoid-#endif import Data.Ratio-#if __GLASGOW_HASKELL__ < 710-import Data.Traversable-#endif import GHC.Arr class Lifting p f where@@ -77,6 +65,7 @@ instance Lifting Hashable Maybe where lifting = Sub Dict instance Lifting Binary Maybe where lifting = Sub Dict instance Lifting NFData Maybe where lifting = Sub Dict+instance Lifting Semigroup Maybe where lifting = Sub Dict instance Lifting Monoid Maybe where lifting = Sub Dict instance Lifting Eq Ratio where lifting = Sub Dict@@ -85,7 +74,7 @@ instance Lifting Eq Complex where lifting = Sub Dict instance Lifting Read Complex where lifting = Sub Dict instance Lifting Show Complex where lifting = Sub Dict-+instance Lifting Semigroup ((->) a) where lifting = Sub Dict instance Lifting Monoid ((->) a) where lifting = Sub Dict instance Eq a => Lifting Eq (Either a) where lifting = Sub Dict@@ -103,6 +92,7 @@ instance Hashable a => Lifting Hashable ((,) a) where lifting = Sub Dict instance Binary a => Lifting Binary ((,) a) where lifting = Sub Dict instance NFData a => Lifting NFData ((,) a) where lifting = Sub Dict+instance Semigroup a => Lifting Semigroup ((,) a) where lifting = Sub Dict instance Monoid a => Lifting Monoid ((,) a) where lifting = Sub Dict instance Bounded a => Lifting Bounded ((,) a) where lifting = Sub Dict instance Ix a => Lifting Ix ((,) a) where lifting = Sub Dict@@ -113,7 +103,6 @@ instance Applicative f => Lifting Applicative (Compose f) where lifting = Sub Dict instance Alternative f => Lifting Alternative (Compose f) where lifting = Sub Dict -- overconstrained -#if MIN_VERSION_transformers(0,5,0) instance Show1 f => Lifting Show1 (Compose f) where lifting = Sub Dict instance Eq1 f => Lifting Eq1 (Compose f) where lifting = Sub Dict instance Ord1 f => Lifting Ord1 (Compose f) where lifting = Sub Dict@@ -122,16 +111,6 @@ instance (Ord1 f, Ord1 g) => Lifting Ord (Compose f g) where lifting = Sub Dict instance (Read1 f, Read1 g) => Lifting Read (Compose f g) where lifting = Sub Dict instance (Show1 f, Show1 g) => Lifting Show (Compose f g) where lifting = Sub Dict-#else-instance (Functor f, Show1 f) => Lifting Show1 (Compose f) where lifting = Sub Dict-instance (Functor f, Eq1 f) => Lifting Eq1 (Compose f) where lifting = Sub Dict-instance (Functor f, Ord1 f) => Lifting Ord1 (Compose f) where lifting = Sub Dict-instance (Functor f, Read1 f) => Lifting Read1 (Compose f) where lifting = Sub Dict-instance (Functor f, Eq1 f, Eq1 g) => Lifting Eq (Compose f g) where lifting = Sub Dict-instance (Functor f, Ord1 f, Ord1 g) => Lifting Ord (Compose f g) where lifting = Sub Dict-instance (Functor f, Read1 f, Read1 g) => Lifting Read (Compose f g) where lifting = Sub Dict-instance (Functor f, Show1 f, Show1 g) => Lifting Show (Compose f g) where lifting = Sub Dict-#endif instance Functor f => Lifting Functor (Functor.Product f) where lifting = Sub Dict instance Foldable f => Lifting Foldable (Functor.Product f) where lifting = Sub Dict@@ -194,22 +173,6 @@ instance Lifting MonadFix (ReaderT e) where lifting = Sub Dict instance Lifting MonadIO (ReaderT e) where lifting = Sub Dict -instance Lifting Functor (ErrorT e) where lifting = Sub Dict-instance Lifting Foldable (ErrorT e) where lifting = Sub Dict-instance Lifting Traversable (ErrorT e) where lifting = Sub Dict-instance Error e => Lifting Monad (ErrorT e) where lifting = Sub Dict-instance Error e => Lifting MonadFix (ErrorT e) where lifting = Sub Dict-instance Error e => Lifting MonadPlus (ErrorT e) where lifting = Sub Dict -- overconstrained!-instance Error e => Lifting MonadIO (ErrorT e) where lifting = Sub Dict-instance Show e => Lifting Show1 (ErrorT e) where lifting = Sub Dict-instance Eq e => Lifting Eq1 (ErrorT e) where lifting = Sub Dict-instance Ord e => Lifting Ord1 (ErrorT e) where lifting = Sub Dict-instance Read e => Lifting Read1 (ErrorT e) where lifting = Sub Dict-instance (Show e, Show1 m) => Lifting Show (ErrorT e m) where lifting = Sub Dict-instance (Eq e, Eq1 m) => Lifting Eq (ErrorT e m) where lifting = Sub Dict-instance (Ord e, Ord1 m) => Lifting Ord (ErrorT e m) where lifting = Sub Dict-instance (Read e, Read1 m) => Lifting Read (ErrorT e m) where lifting = Sub Dict- instance Lifting Functor (ExceptT e) where lifting = Sub Dict instance Lifting Foldable (ExceptT e) where lifting = Sub Dict instance Lifting Traversable (ExceptT e) where lifting = Sub Dict@@ -285,24 +248,6 @@ instance Ord1 m => Lifting Ord (IdentityT m) where lifting = Sub Dict instance Eq1 m => Lifting Eq (IdentityT m) where lifting = Sub Dict -instance Lifting Functor ListT where lifting = Sub Dict-instance Lifting Applicative ListT where lifting = Sub Dict-instance Lifting Alternative ListT where lifting = Sub Dict -- overconstrained-instance Lifting Monad ListT where lifting = Sub Dict--- instance Lifting MonadFix ListT where lifting = Sub Dict-instance Lifting MonadPlus ListT where lifting = Sub Dict -- overconstrained-instance Lifting Foldable ListT where lifting = Sub Dict-instance Lifting Traversable ListT where lifting = Sub Dict-instance Lifting MonadIO ListT where lifting = Sub Dict-instance Lifting Show1 ListT where lifting = Sub Dict-instance Lifting Read1 ListT where lifting = Sub Dict-instance Lifting Ord1 ListT where lifting = Sub Dict-instance Lifting Eq1 ListT where lifting = Sub Dict-instance Show1 m => Lifting Show (ListT m) where lifting = Sub Dict-instance Read1 m => Lifting Read (ListT m) where lifting = Sub Dict-instance Ord1 m => Lifting Ord (ListT m) where lifting = Sub Dict-instance Eq1 m => Lifting Eq (ListT m) where lifting = Sub Dict- instance Lifting Functor MaybeT where lifting = Sub Dict instance Lifting Monad MaybeT where lifting = Sub Dict -- instance Lifting MonadFix MaybeT where lifting = Sub Dict@@ -367,11 +312,9 @@ instance Lifting Read Identity where lifting = Sub Dict instance Lifting MonadCont MaybeT where lifting = Sub Dict-instance Lifting MonadCont ListT where lifting = Sub Dict instance Lifting MonadCont IdentityT where lifting = Sub Dict instance Monoid w => Lifting MonadCont (Strict.WriterT w) where lifting = Sub Dict instance Monoid w => Lifting MonadCont (Lazy.WriterT w) where lifting = Sub Dict-instance Error e => Lifting MonadCont (ErrorT e) where lifting = Sub Dict instance Lifting MonadCont (ExceptT w) where lifting = Sub Dict instance Lifting MonadCont (Strict.StateT s) where lifting = Sub Dict instance Lifting MonadCont (Lazy.StateT s) where lifting = Sub Dict@@ -380,7 +323,6 @@ instance Monoid w => Lifting MonadCont (Lazy.RWST r w s) where lifting = Sub Dict instance Lifting (MonadError e) MaybeT where lifting = Sub Dict-instance Lifting (MonadError e) ListT where lifting = Sub Dict instance Lifting (MonadError e) IdentityT where lifting = Sub Dict instance Monoid w => Lifting (MonadError e) (Strict.WriterT w) where lifting = Sub Dict instance Monoid w => Lifting (MonadError e) (Lazy.WriterT w) where lifting = Sub Dict@@ -392,28 +334,23 @@ instance Lifting (MonadRWS r w s) MaybeT where lifting = Sub Dict instance Lifting (MonadRWS r w s) IdentityT where lifting = Sub Dict-instance Error e => Lifting (MonadRWS r w s) (ErrorT e) where lifting = Sub Dict instance Lifting (MonadRWS r w s) (ExceptT e) where lifting = Sub Dict instance Lifting (MonadReader r) MaybeT where lifting = Sub Dict-instance Lifting (MonadReader r) ListT where lifting = Sub Dict instance Lifting (MonadReader r) IdentityT where lifting = Sub Dict instance Monoid w => Lifting (MonadReader r) (Strict.WriterT w) where lifting = Sub Dict instance Monoid w => Lifting (MonadReader r) (Lazy.WriterT w) where lifting = Sub Dict instance Lifting (MonadReader r) (Strict.StateT s) where lifting = Sub Dict instance Lifting (MonadReader r) (Lazy.StateT s) where lifting = Sub Dict instance Lifting (MonadReader r) (ExceptT e) where lifting = Sub Dict-instance Error e => Lifting (MonadReader r) (ErrorT e) where lifting = Sub Dict instance Lifting (MonadReader r) (ContT r') where lifting = Sub Dict instance Lifting (MonadState s) MaybeT where lifting = Sub Dict-instance Lifting (MonadState s) ListT where lifting = Sub Dict instance Lifting (MonadState s) IdentityT where lifting = Sub Dict instance Monoid w => Lifting (MonadState s) (Strict.WriterT w) where lifting = Sub Dict instance Monoid w => Lifting (MonadState s) (Lazy.WriterT w) where lifting = Sub Dict instance Lifting (MonadState s) (ReaderT r) where lifting = Sub Dict instance Lifting (MonadState s) (ExceptT e) where lifting = Sub Dict-instance Error e => Lifting (MonadState s) (ErrorT e) where lifting = Sub Dict instance Lifting (MonadState s) (ContT r') where lifting = Sub Dict class Lifting2 p f where@@ -434,6 +371,7 @@ instance Lifting2 Hashable (,) where lifting2 = Sub Dict instance Lifting2 Binary (,) where lifting2 = Sub Dict instance Lifting2 NFData (,) where lifting2 = Sub Dict+instance Lifting2 Semigroup (,) where lifting2 = Sub Dict instance Lifting2 Monoid (,) where lifting2 = Sub Dict instance Lifting2 Bounded (,) where lifting2 = Sub Dict instance Lifting2 Ix (,) where lifting2 = Sub Dict
+ src/Data/Constraint/Nat.hs view
@@ -0,0 +1,396 @@+{-# LANGUAGE CPP #-}+{-# LANGUAGE DataKinds #-}+{-# LANGUAGE MagicHash #-}+{-# LANGUAGE PolyKinds #-}+{-# LANGUAGE RankNTypes #-}+{-# LANGUAGE TypeFamilies #-}+{-# LANGUAGE TypeOperators #-}+{-# LANGUAGE ConstraintKinds #-}+{-# LANGUAGE TypeApplications #-}+{-# LANGUAGE ScopedTypeVariables #-}+{-# LANGUAGE AllowAmbiguousTypes #-}+{-# LANGUAGE Trustworthy #-}+{-# LANGUAGE UndecidableInstances #-}+{-# LANGUAGE NoStarIsType #-}+-- | Utilities for working with 'KnownNat' constraints.+--+-- This module is only available on GHC 8.0 or later.+module Data.Constraint.Nat+ ( Min, Max, Lcm, Gcd, Divides, Div, Mod, Log2+ , plusNat, minusNat, timesNat, powNat, minNat, maxNat, gcdNat, lcmNat, divNat, modNat, log2Nat+ , plusZero, minusZero, timesZero, timesOne, powZero, powOne, maxZero, minZero, gcdZero, gcdOne, lcmZero, lcmOne+ , plusAssociates, timesAssociates, minAssociates, maxAssociates, gcdAssociates, lcmAssociates+ , plusCommutes, timesCommutes, minCommutes, maxCommutes, gcdCommutes, lcmCommutes+ , plusDistributesOverTimes, timesDistributesOverPow, timesDistributesOverGcd, timesDistributesOverLcm+ , minDistributesOverPlus, minDistributesOverTimes, minDistributesOverPow1, minDistributesOverPow2, minDistributesOverMax+ , maxDistributesOverPlus, maxDistributesOverTimes, maxDistributesOverPow1, maxDistributesOverPow2, maxDistributesOverMin+ , gcdDistributesOverLcm, lcmDistributesOverGcd+ , minIsIdempotent, maxIsIdempotent, lcmIsIdempotent, gcdIsIdempotent+ , plusIsCancellative, timesIsCancellative+ , dividesPlus, dividesTimes, dividesMin, dividesMax, dividesPow, dividesGcd, dividesLcm+ , plusMonotone1, plusMonotone2+ , timesMonotone1, timesMonotone2+ , powMonotone1, powMonotone2+ , minMonotone1, minMonotone2+ , maxMonotone1, maxMonotone2+ , divMonotone1, divMonotone2+ , euclideanNat+ , plusMod, timesMod+ , modBound+ , log2Pow+ , dividesDef+ , timesDiv+ , eqLe, leEq, leId, leTrans+ , leZero, zeroLe+ , plusMinusInverse1, plusMinusInverse2, plusMinusInverse3+ ) where++import Data.Constraint+import Data.Constraint.Unsafe+import Data.Proxy+import Data.Type.Bool+import GHC.TypeNats+import qualified Numeric.Natural as Nat++#if MIN_VERSION_base(4,15,0)+import GHC.Num.Natural (naturalLog2)+#else+import GHC.Exts (Int(..))+import GHC.Integer.Logarithms (integerLog2#)+#endif++#if !MIN_VERSION_base(4,18,0)+import Unsafe.Coerce+#endif++type family Min (m::Nat) (n::Nat) :: Nat where+ Min m n = If (n <=? m) n m+type family Max (m::Nat) (n::Nat) :: Nat where+ Max m n = If (n <=? m) m n+type family Gcd (m::Nat) (n::Nat) :: Nat where+ Gcd m m = m+type family Lcm (m::Nat) (n::Nat) :: Nat where+ Lcm m m = m++type Divides n m = n ~ Gcd n m++#if !MIN_VERSION_base(4,18,0)+newtype Magic n = Magic (KnownNat n => Dict (KnownNat n))+#endif++magicNNN :: forall n m o. (Nat.Natural -> Nat.Natural -> Nat.Natural) -> (KnownNat n, KnownNat m) :- KnownNat o+#if MIN_VERSION_base(4,18,0)+magicNNN f = Sub $ withKnownNat @o (unsafeSNat (natVal (Proxy @n) `f` natVal (Proxy @m))) Dict+#else+magicNNN f = Sub $ unsafeCoerce (Magic Dict) (natVal (Proxy @n) `f` natVal (Proxy @m))+#endif++magicNN :: forall n m. (Nat.Natural -> Nat.Natural) -> KnownNat n :- KnownNat m+#if MIN_VERSION_base(4,18,0)+magicNN f = Sub $ withKnownNat @m (unsafeSNat (f (natVal (Proxy @n)))) Dict+#else+magicNN f = Sub $ unsafeCoerce (Magic Dict) (f (natVal (Proxy :: Proxy n)))+#endif++axiomLe :: forall (a :: Nat) (b :: Nat). Dict (a <= b)+axiomLe = unsafeAxiom++eqLe :: forall (a :: Nat) (b :: Nat). (a ~ b) :- (a <= b)+eqLe = Sub Dict++dividesGcd :: forall a b c. (Divides a b, Divides a c) :- Divides a (Gcd b c)+dividesGcd = Sub unsafeAxiom++dividesLcm :: forall a b c. (Divides a c, Divides b c) :- Divides (Lcm a b) c+dividesLcm = Sub unsafeAxiom++gcdCommutes :: forall a b. Dict (Gcd a b ~ Gcd b a)+gcdCommutes = unsafeAxiom++lcmCommutes :: forall a b. Dict (Lcm a b ~ Lcm b a)+lcmCommutes = unsafeAxiom++gcdZero :: forall a. Dict (Gcd 0 a ~ a)+gcdZero = unsafeAxiom++gcdOne :: forall a. Dict (Gcd 1 a ~ 1)+gcdOne = unsafeAxiom++lcmZero :: forall a. Dict (Lcm 0 a ~ 0)+lcmZero = unsafeAxiom++lcmOne :: forall a. Dict (Lcm 1 a ~ a)+lcmOne = unsafeAxiom++gcdNat :: forall n m. (KnownNat n, KnownNat m) :- KnownNat (Gcd n m)+gcdNat = magicNNN gcd++lcmNat :: forall n m. (KnownNat n, KnownNat m) :- KnownNat (Lcm n m)+lcmNat = magicNNN lcm++plusNat :: forall n m. (KnownNat n, KnownNat m) :- KnownNat (n + m)+plusNat = magicNNN (+)++minusNat :: forall n m. (KnownNat n, KnownNat m, m <= n) :- KnownNat (n - m)+minusNat = Sub $ case magicNNN @n @m (-) of Sub r -> r++minNat :: forall n m. (KnownNat n, KnownNat m) :- KnownNat (Min n m)+minNat = magicNNN min++maxNat :: forall n m. (KnownNat n, KnownNat m) :- KnownNat (Max n m)+maxNat = magicNNN max++timesNat :: forall n m. (KnownNat n, KnownNat m) :- KnownNat (n * m)+timesNat = magicNNN (*)++powNat :: forall n m. (KnownNat n, KnownNat m) :- KnownNat (n ^ m)+powNat = magicNNN (^)++divNat :: forall n m. (KnownNat n, KnownNat m, 1 <= m) :- KnownNat (Div n m)+divNat = Sub $ case magicNNN @n @m div of Sub r -> r++modNat :: forall n m. (KnownNat n, KnownNat m, 1 <= m) :- KnownNat (Mod n m)+modNat = Sub $ case magicNNN @n @m mod of Sub r -> r++log2Nat :: forall n. (KnownNat n, 1 <= n) :- KnownNat (Log2 n)+log2Nat = Sub $ case magicNN @n log2 of Sub r -> r+ where+ log2 :: Nat.Natural -> Nat.Natural+#if MIN_VERSION_base(4,15,0)+ log2 n = fromIntegral (naturalLog2 n)+#else+ log2 n = fromIntegral (I# (integerLog2# (toInteger n)))+#endif++plusZero :: forall n. Dict ((n + 0) ~ n)+plusZero = Dict++minusZero :: forall n. Dict ((n - 0) ~ n)+minusZero = Dict++timesZero :: forall n. Dict ((n * 0) ~ 0)+timesZero = Dict++timesOne :: forall n. Dict ((n * 1) ~ n)+timesOne = Dict++minZero :: forall n. Dict (Min n 0 ~ 0)+#if MIN_VERSION_base(4,16,0)+minZero = unsafeAxiom+#else+minZero = Dict+#endif++maxZero :: forall n. Dict (Max n 0 ~ n)+#if MIN_VERSION_base(4,16,0)+maxZero = unsafeAxiom+#else+maxZero = Dict+#endif++powZero :: forall n. Dict ((n ^ 0) ~ 1)+powZero = Dict++leZero :: forall a. (a <= 0) :- (a ~ 0)+leZero = Sub unsafeAxiom++zeroLe :: forall (a :: Nat). Dict (0 <= a)+#if MIN_VERSION_base(4,16,0)+zeroLe = unsafeAxiom+#else+zeroLe = Dict+#endif++plusMinusInverse1 :: forall n m. Dict (((m + n) - n) ~ m)+plusMinusInverse1 = unsafeAxiom++plusMinusInverse2 :: forall n m. (m <= n) :- (((m + n) - m) ~ n)+plusMinusInverse2 = Sub unsafeAxiom++plusMinusInverse3 :: forall n m. (n <= m) :- (((m - n) + n) ~ m)+plusMinusInverse3 = Sub unsafeAxiom++plusMonotone1 :: forall a b c. (a <= b) :- (a + c <= b + c)+plusMonotone1 = Sub unsafeAxiom++plusMonotone2 :: forall a b c. (b <= c) :- (a + b <= a + c)+plusMonotone2 = Sub unsafeAxiom++powMonotone1 :: forall a b c. (a <= b) :- ((a^c) <= (b^c))+powMonotone1 = Sub unsafeAxiom++powMonotone2 :: forall a b c. (b <= c) :- ((a^b) <= (a^c))+powMonotone2 = Sub unsafeAxiom++divMonotone1 :: forall a b c. (a <= b) :- (Div a c <= Div b c)+divMonotone1 = Sub unsafeAxiom++divMonotone2 :: forall a b c. (b <= c) :- (Div a c <= Div a b)+divMonotone2 = Sub unsafeAxiom++timesMonotone1 :: forall a b c. (a <= b) :- (a * c <= b * c)+timesMonotone1 = Sub unsafeAxiom++timesMonotone2 :: forall a b c. (b <= c) :- (a * b <= a * c)+timesMonotone2 = Sub unsafeAxiom++minMonotone1 :: forall a b c. (a <= b) :- (Min a c <= Min b c)+minMonotone1 = Sub unsafeAxiom++minMonotone2 :: forall a b c. (b <= c) :- (Min a b <= Min a c)+minMonotone2 = Sub unsafeAxiom++maxMonotone1 :: forall a b c. (a <= b) :- (Max a c <= Max b c)+maxMonotone1 = Sub unsafeAxiom++maxMonotone2 :: forall a b c. (b <= c) :- (Max a b <= Max a c)+maxMonotone2 = Sub unsafeAxiom++powOne :: forall n. Dict ((n ^ 1) ~ n)+powOne = unsafeAxiom++plusMod :: forall a b c. (1 <= c) :- (Mod (a + b) c ~ Mod (Mod a c + Mod b c) c)+plusMod = Sub unsafeAxiom++timesMod :: forall a b c. (1 <= c) :- (Mod (a * b) c ~ Mod (Mod a c * Mod b c) c)+timesMod = Sub unsafeAxiom++modBound :: forall m n. (1 <= n) :- (Mod m n <= n)+modBound = Sub unsafeAxiom++log2Pow :: forall n. Dict (Log2 (2 ^ n) ~ n)+log2Pow = unsafeAxiom++euclideanNat :: (1 <= c) :- (a ~ (c * Div a c + Mod a c))+euclideanNat = Sub unsafeAxiom++plusCommutes :: forall n m. Dict ((m + n) ~ (n + m))+plusCommutes = unsafeAxiom++timesCommutes :: forall n m. Dict ((m * n) ~ (n * m))+timesCommutes = unsafeAxiom++minCommutes :: forall n m. Dict (Min m n ~ Min n m)+minCommutes = unsafeAxiom++maxCommutes :: forall n m. Dict (Max m n ~ Max n m)+maxCommutes = unsafeAxiom++plusAssociates :: forall m n o. Dict (((m + n) + o) ~ (m + (n + o)))+plusAssociates = unsafeAxiom++timesAssociates :: forall m n o. Dict (((m * n) * o) ~ (m * (n * o)))+timesAssociates = unsafeAxiom++minAssociates :: forall m n o. Dict (Min (Min m n) o ~ Min m (Min n o))+minAssociates = unsafeAxiom++maxAssociates :: forall m n o. Dict (Max (Max m n) o ~ Max m (Max n o))+maxAssociates = unsafeAxiom++gcdAssociates :: forall a b c. Dict (Gcd (Gcd a b) c ~ Gcd a (Gcd b c))+gcdAssociates = unsafeAxiom++lcmAssociates :: forall a b c. Dict (Lcm (Lcm a b) c ~ Lcm a (Lcm b c))+lcmAssociates = unsafeAxiom++minIsIdempotent :: forall n. Dict (Min n n ~ n)+minIsIdempotent = Dict++maxIsIdempotent :: forall n. Dict (Max n n ~ n)+maxIsIdempotent = Dict++gcdIsIdempotent :: forall n. Dict (Gcd n n ~ n)+gcdIsIdempotent = Dict++lcmIsIdempotent :: forall n. Dict (Lcm n n ~ n)+lcmIsIdempotent = Dict++minDistributesOverPlus :: forall n m o. Dict ((n + Min m o) ~ Min (n + m) (n + o))+minDistributesOverPlus = unsafeAxiom++minDistributesOverTimes :: forall n m o. Dict ((n * Min m o) ~ Min (n * m) (n * o))+minDistributesOverTimes = unsafeAxiom++minDistributesOverPow1 :: forall n m o. Dict ((Min n m ^ o) ~ Min (n ^ o) (m ^ o))+minDistributesOverPow1 = unsafeAxiom++minDistributesOverPow2 :: forall n m o. Dict ((n ^ Min m o) ~ Min (n ^ m) (n ^ o))+minDistributesOverPow2 = unsafeAxiom++minDistributesOverMax :: forall n m o. Dict (Max n (Min m o) ~ Min (Max n m) (Max n o))+minDistributesOverMax = unsafeAxiom++maxDistributesOverPlus :: forall n m o. Dict ((n + Max m o) ~ Max (n + m) (n + o))+maxDistributesOverPlus = unsafeAxiom++maxDistributesOverTimes :: forall n m o. Dict ((n * Max m o) ~ Max (n * m) (n * o))+maxDistributesOverTimes = unsafeAxiom++maxDistributesOverPow1 :: forall n m o. Dict ((Max n m ^ o) ~ Max (n ^ o) (m ^ o))+maxDistributesOverPow1 = unsafeAxiom++maxDistributesOverPow2 :: forall n m o. Dict ((n ^ Max m o) ~ Max (n ^ m) (n ^ o))+maxDistributesOverPow2 = unsafeAxiom++maxDistributesOverMin :: forall n m o. Dict (Min n (Max m o) ~ Max (Min n m) (Min n o))+maxDistributesOverMin = unsafeAxiom++plusDistributesOverTimes :: forall n m o. Dict ((n * (m + o)) ~ (n * m + n * o))+plusDistributesOverTimes = unsafeAxiom++timesDistributesOverPow :: forall n m o. Dict ((n ^ (m + o)) ~ (n ^ m * n ^ o))+timesDistributesOverPow = unsafeAxiom++timesDistributesOverGcd :: forall n m o. Dict ((n * Gcd m o) ~ Gcd (n * m) (n * o))+timesDistributesOverGcd = unsafeAxiom++timesDistributesOverLcm :: forall n m o. Dict ((n * Lcm m o) ~ Lcm (n * m) (n * o))+timesDistributesOverLcm = unsafeAxiom++plusIsCancellative :: forall n m o. ((n + m) ~ (n + o)) :- (m ~ o)+plusIsCancellative = Sub unsafeAxiom++timesIsCancellative :: forall n m o. (1 <= n, (n * m) ~ (n * o)) :- (m ~ o)+timesIsCancellative = Sub unsafeAxiom++gcdDistributesOverLcm :: forall a b c. Dict (Gcd (Lcm a b) c ~ Lcm (Gcd a c) (Gcd b c))+gcdDistributesOverLcm = unsafeAxiom++lcmDistributesOverGcd :: forall a b c. Dict (Lcm (Gcd a b) c ~ Gcd (Lcm a c) (Lcm b c))+lcmDistributesOverGcd = unsafeAxiom++dividesPlus :: (Divides a b, Divides a c) :- Divides a (b + c)+dividesPlus = Sub unsafeAxiom++dividesTimes :: Divides a b :- Divides a (b * c)+dividesTimes = Sub unsafeAxiom++dividesMin :: (Divides a b, Divides a c) :- Divides a (Min b c)+dividesMin = Sub unsafeAxiom++dividesMax :: (Divides a b, Divides a c) :- Divides a (Max b c)+dividesMax = Sub unsafeAxiom++-- This `dividesDef` is simpler and more convenient than Divides a b :- ((a * Div b a) ~ b)+-- because the latter can be easily derived via 'euclideanNat', but not vice versa.++dividesDef :: forall a b. Divides a b :- (Mod b a ~ 0)+dividesDef = Sub unsafeAxiom++dividesPow :: (1 <= n, Divides a b) :- Divides a (b^n)+dividesPow = Sub unsafeAxiom++timesDiv :: forall a b. Dict ((a * Div b a) <= b)+timesDiv = unsafeAxiom++-- (<=) is an internal category in the category of constraints.++leId :: forall (a :: Nat). Dict (a <= a)+leId = Dict++leEq :: forall (a :: Nat) (b :: Nat). (a <= b, b <= a) :- (a ~ b)+leEq = Sub unsafeAxiom++leTrans :: forall (a :: Nat) (b :: Nat) (c :: Nat). (b <= c, a <= b) :- (a <= c)+leTrans = Sub (axiomLe @a @c)
+ src/Data/Constraint/Symbol.hs view
@@ -0,0 +1,138 @@+{-# LANGUAGE ScopedTypeVariables #-}+{-# LANGUAGE AllowAmbiguousTypes #-}+{-# LANGUAGE TypeApplications #-}+{-# LANGUAGE ConstraintKinds #-}+{-# LANGUAGE TypeOperators #-}+{-# LANGUAGE TypeFamilies #-}+{-# LANGUAGE RankNTypes #-}+{-# LANGUAGE DataKinds #-}+{-# LANGUAGE PolyKinds #-}+{-# LANGUAGE CPP #-}+-- | Utilities for working with 'KnownSymbol' constraints.+module Data.Constraint.Symbol+ ( type AppendSymbol+ , type (++)+ , type Take+ , type Drop+ , type Length+ , appendSymbol+ , appendUnit1+ , appendUnit2+ , appendAssociates+ , takeSymbol+ , dropSymbol+ , takeAppendDrop+ , lengthSymbol+ , takeLength+ , take0+ , takeEmpty+ , dropLength+ , drop0+ , dropEmpty+ , lengthTake+ , lengthDrop+ , dropDrop+ , takeTake+ ) where++import Data.Constraint+import Data.Constraint.Nat+import Data.Constraint.Unsafe+import Data.Proxy+import GHC.TypeLits+#if MIN_VERSION_base(4,18,0)+import qualified GHC.TypeNats as TN+#else+import Unsafe.Coerce+#endif++-- | An infix synonym for 'AppendSymbol'.+type (m :: Symbol) ++ (n :: Symbol) = AppendSymbol m n+infixr 5 ++++type family Take :: Nat -> Symbol -> Symbol where+type family Drop :: Nat -> Symbol -> Symbol where+type family Length :: Symbol -> Nat where++-- implementation details++#if !MIN_VERSION_base(4,18,0)+newtype Magic n = Magic (KnownSymbol n => Dict (KnownSymbol n))+#endif++magicNSS :: forall n m o. (Int -> String -> String) -> (KnownNat n, KnownSymbol m) :- KnownSymbol o+#if MIN_VERSION_base(4,18,0)+magicNSS f = Sub $ withKnownSymbol (unsafeSSymbol @o (fromIntegral (natVal (Proxy @n)) `f` symbolVal (Proxy @m))) Dict+#else+magicNSS f = Sub $ unsafeCoerce (Magic Dict) (fromIntegral (natVal (Proxy @n)) `f` symbolVal (Proxy @m))+#endif++magicSSS :: forall n m o. (String -> String -> String) -> (KnownSymbol n, KnownSymbol m) :- KnownSymbol o+#if MIN_VERSION_base(4,18,0)+magicSSS f = Sub $ withKnownSymbol (unsafeSSymbol @o (symbolVal (Proxy @n) `f` symbolVal (Proxy @m))) Dict+#else+magicSSS f = Sub $ unsafeCoerce (Magic Dict) (symbolVal (Proxy @n) `f` symbolVal (Proxy @m))+#endif++magicSN :: forall a n. (String -> Int) -> KnownSymbol a :- KnownNat n+#if MIN_VERSION_base(4,18,0)+magicSN f = Sub $ TN.withKnownNat (unsafeSNat @n (fromIntegral (f (symbolVal (Proxy :: Proxy a))))) Dict+#else+magicSN f = Sub $ unsafeCoerce (Magic Dict) (toInteger (f (symbolVal (Proxy @a))))+#endif++-- operations++appendSymbol :: (KnownSymbol a, KnownSymbol b) :- KnownSymbol (AppendSymbol a b)+appendSymbol = magicSSS (++)++appendUnit1 :: forall a. Dict (AppendSymbol "" a ~ a)+appendUnit1 = Dict++appendUnit2 :: forall a. Dict (AppendSymbol a "" ~ a)+appendUnit2 = Dict++appendAssociates :: forall a b c. Dict (AppendSymbol (AppendSymbol a b) c ~ AppendSymbol a (AppendSymbol b c))+appendAssociates = unsafeAxiom++takeSymbol :: forall n a. (KnownNat n, KnownSymbol a) :- KnownSymbol (Take n a)+takeSymbol = magicNSS take++dropSymbol :: forall n a. (KnownNat n, KnownSymbol a) :- KnownSymbol (Drop n a)+dropSymbol = magicNSS drop++takeAppendDrop :: forall n a. Dict (AppendSymbol (Take n a) (Drop n a) ~ a)+takeAppendDrop = unsafeAxiom++lengthSymbol :: forall a. KnownSymbol a :- KnownNat (Length a)+lengthSymbol = magicSN length++takeLength :: forall n a. (Length a <= n) :- (Take n a ~ a)+takeLength = Sub unsafeAxiom++take0 :: forall a. Dict (Take 0 a ~ "")+take0 = unsafeAxiom++takeEmpty :: forall n. Dict (Take n "" ~ "")+takeEmpty = unsafeAxiom++dropLength :: forall n a. (Length a <= n) :- (Drop n a ~ "")+dropLength = Sub unsafeAxiom++drop0 :: forall a. Dict (Drop 0 a ~ a)+drop0 = unsafeAxiom++dropEmpty :: forall n. Dict (Drop n "" ~ "")+dropEmpty = unsafeAxiom++lengthTake :: forall n a. Dict (Length (Take n a) <= n)+lengthTake = unsafeAxiom++lengthDrop :: forall n a. Dict (Length a <= (Length (Drop n a) + n))+lengthDrop = unsafeAxiom++dropDrop :: forall n m a. Dict (Drop n (Drop m a) ~ Drop (n + m) a)+dropDrop = unsafeAxiom++takeTake :: forall n m a. Dict (Take n (Take m a) ~ Take (Min n m) a)+takeTake = unsafeAxiom
src/Data/Constraint/Unsafe.hs view
@@ -1,4 +1,3 @@-{-# LANGUAGE CPP #-} {-# LANGUAGE ScopedTypeVariables #-} {-# LANGUAGE FlexibleInstances #-} {-# LANGUAGE ConstraintKinds #-}@@ -6,47 +5,48 @@ {-# LANGUAGE Rank2Types #-} {-# LANGUAGE GADTs #-} {-# LANGUAGE Unsafe #-}-#if __GLASGOW_HASKELL__ >= 800+{-# LANGUAGE CPP #-} {-# OPTIONS_GHC -fno-warn-redundant-constraints #-}-#endif------------------------------------------------------------------------------+ -- |--- Module : Data.Constraint.Unsafe--- Copyright : (C) 2011-2015 Edward Kmett+-- Copyright : (C) 2011-2021 Edward Kmett -- License : BSD-style (see the file LICENSE)--- -- Maintainer : Edward Kmett <ekmett@gmail.com> -- Stability : experimental -- Portability : non-portable -------------------------------------------------------------------------------+-- Unsafe utilities used throughout @constraints@. As the names suggest, these+-- functions are unsafe in general and can cause your program to segfault if+-- used improperly. Handle with care.+ module Data.Constraint.Unsafe ( Coercible+ , unsafeAxiom , unsafeCoerceConstraint , unsafeDerive , unsafeUnderive- -- * Sugar- , unsafeApplicative- , unsafeAlternative++#if MIN_VERSION_base(4,18,0)+ -- * Unsafely creating @GHC.TypeLits@ singleton values+ , unsafeSChar+ , unsafeSNat+ , unsafeSSymbol+#endif ) where -import Control.Applicative-import Control.Monad+import Data.Coerce import Data.Constraint import Unsafe.Coerce -#if __GLASGOW_HASKELL__ >= 708--import Data.Coerce--#else--import Control.Newtype--type Coercible = Newtype-+#if MIN_VERSION_base(4,18,0)+import GHC.TypeLits (SChar, SNat, SSymbol)+import Numeric.Natural (Natural) #endif +-- | Unsafely create a dictionary for any constraint.+unsafeAxiom :: Dict c+unsafeAxiom = unsafeCoerce (Dict :: Dict ())+ -- | Coerce a dictionary unsafely from one type to another unsafeCoerceConstraint :: a :- b unsafeCoerceConstraint = unsafeCoerce refl@@ -59,19 +59,52 @@ unsafeUnderive :: Coercible n o => (o -> n) -> t n :- t o unsafeUnderive _ = unsafeCoerceConstraint +#if MIN_VERSION_base(4,18,0)+-- NB: if https://gitlab.haskell.org/ghc/ghc/-/issues/23478 were implemented,+-- then we could avoid using 'unsafeCoerce' in the definitions below. --- | Construct an Applicative instance from a Monad-unsafeApplicative :: forall m a. Monad m => (Applicative m => m a) -> m a-#if __GLASGOW_HASKELL__ < 710-unsafeApplicative m = m \\ trans (unsafeCoerceConstraint :: Applicative (WrappedMonad m) :- Applicative m) ins-#else-unsafeApplicative m = m-#endif+-- | Unsafely create an 'SChar' value directly from a 'Char'. Use this function+-- with care:+--+-- * The 'Char' value must match the 'Char' @c@ encoded in the return type+-- @'SChar' c@.+--+-- * Be wary of using this function to create multiple values of type+-- @'SChar' T@, where @T@ is a type family that does not reduce (e.g.,+-- @Any@ from "GHC.Exts"). If you do, GHC is liable to optimize away one of+-- the values and replace it with the other during a common subexpression+-- elimination pass. If the two values have different underlying 'Char'+-- values, this could be disastrous.+unsafeSChar :: Char -> SChar c+unsafeSChar = unsafeCoerce --- | Construct an Alternative instance from a MonadPlus-unsafeAlternative :: forall m a. MonadPlus m => (Alternative m => m a) -> m a-#if __GLASGOW_HASKELL__ < 710-unsafeAlternative m = m \\ trans (unsafeCoerceConstraint :: Alternative (WrappedMonad m) :- Alternative m) ins-#else-unsafeAlternative m = m+-- | Unsafely create an 'SNat' value directly from a 'Natural'. Use this+-- function with care:+--+-- * The 'Natural' value must match the 'Nat' @n@ encoded in the return type+-- @'SNat' n@.+--+-- * Be wary of using this function to create multiple values of type+-- @'SNat' T@, where @T@ is a type family that does not reduce (e.g.,+-- @Any@ from "GHC.Exts"). If you do, GHC is liable to optimize away one of+-- the values and replace it with the other during a common subexpression+-- elimination pass. If the two values have different underlying 'Natural'+-- values, this could be disastrous.+unsafeSNat :: Natural -> SNat n+unsafeSNat = unsafeCoerce++-- | Unsafely create an 'SSymbol' value directly from a 'String'. Use this+-- function with care:+--+-- * The 'String' value must match the 'Symbol' @s@ encoded in the return type+-- @'SSymbol' s@.+--+-- * Be wary of using this function to create multiple values of type+-- @'SSymbol' T@, where @T@ is a type family that does not reduce (e.g.,+-- @Any@ from "GHC.Exts"). If you do, GHC is liable to optimize away one of+-- the values and replace it with the other during a common subexpression+-- elimination pass. If the two values have different underlying 'String'+-- values, this could be disastrous.+unsafeSSymbol :: String -> SSymbol s+unsafeSSymbol = unsafeCoerce #endif
+ tests/GH117Spec.hs view
@@ -0,0 +1,34 @@+{-# LANGUAGE CPP #-}+{-# LANGUAGE DataKinds #-}+{-# LANGUAGE GADTs #-}+{-# LANGUAGE ScopedTypeVariables #-}+{-# LANGUAGE TypeApplications #-}++module GH117Spec (main, spec) where++import Test.Hspec++#if __GLASGOW_HASKELL__ >= 902+import Data.Constraint+import Data.Constraint.Char+import Data.Proxy+import GHC.TypeLits++spec :: Spec+spec =+ describe "GH #117" $ do+ it "should evaluate `charToNat @'a'` to 97" $+ case charToNat @'a' of+ Sub (Dict :: Dict (KnownNat n)) ->+ natVal (Proxy @n) `shouldBe` 97+ it "should evaluate `natToChar @97` to 'a'" $+ case natToChar @97 of+ Sub (Dict :: Dict (KnownChar c)) ->+ charVal (Proxy @c) `shouldBe` 'a'+#else+spec :: Spec+spec = return ()+#endif++main :: IO ()+main = hspec spec
+ tests/GH55Spec.hs view
@@ -0,0 +1,47 @@+{-# LANGUAGE DataKinds #-}+{-# LANGUAGE GADTs #-}+{-# LANGUAGE PolyKinds #-}+{-# LANGUAGE ScopedTypeVariables #-}+{-# LANGUAGE TypeApplications #-}+{-# LANGUAGE TypeOperators #-}++module GH55Spec (main, spec) where++import Data.Constraint+import Data.Constraint.Nat+import GHC.TypeLits+import Test.Hspec++newtype GF (n :: Nat) = GF Integer deriving (Eq, Show)++instance KnownNat n => Num (GF n) where+ xf@(GF a) + GF b = GF $ (a+b) `mod` (natVal xf)+ xf@(GF a) - GF b = GF $ (a-b) `mod` (natVal xf)+ xf@(GF a) * GF b = GF $ (a*b) `mod` (natVal xf)+ abs = id+ signum xf@(GF a) | a==0 = xf+ | otherwise = GF 1+ fromInteger = GF++x :: GF 5+x = GF 3++y :: GF 5+y = GF 4++foo :: (KnownNat m, KnownNat n) => GF m -> GF n -> GF (Lcm m n)+foo m@(GF a) n@(GF b) = GF $ (a*b) `mod` (lcm (natVal m) (natVal n))++bar :: (KnownNat m) => GF m -> GF m -> GF m+bar (a :: GF m) b = foo a b - foo b a \\ Sub @() (lcmIsIdempotent @m) \\ lcmNat @m @m++z :: GF 5+z = bar x y++spec :: Spec+spec = describe "GH #53" $+ it "should normalize Lcm m m" $+ z `shouldBe` (GF 0 :: GF (Lcm 5 5))++main :: IO ()+main = hspec spec
+ tests/Spec.hs view
@@ -0,0 +1,1 @@+{-# OPTIONS_GHC -F -pgmF hspec-discover #-}