constraints 0.10.1 → 0.14.4
raw patch · 13 files changed
Files
- CHANGELOG.markdown +130/−1
- README.markdown +1/−1
- constraints.cabal +41/−27
- src/Data/Constraint.hs +130/−121
- src/Data/Constraint/Char.hs +60/−0
- src/Data/Constraint/Deferrable.hs +21/−75
- src/Data/Constraint/Forall.hs +30/−96
- src/Data/Constraint/Lifting.hs +1/−69
- src/Data/Constraint/Nat.hs +156/−105
- src/Data/Constraint/Symbol.hs +49/−30
- src/Data/Constraint/Unsafe.hs +70/−26
- tests/GH117Spec.hs +34/−0
- tests/GH55Spec.hs +2/−12
CHANGELOG.markdown view
@@ -1,3 +1,132 @@+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.@@ -41,7 +170,7 @@ 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+ * 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
README.markdown view
@@ -1,7 +1,7 @@ constraints =========== -[](https://hackage.haskell.org/package/constraints) [](http://travis-ci.org/ekmett/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.
constraints.cabal view
@@ -1,15 +1,15 @@+cabal-version: 2.4 name: constraints category: Constraints-version: 0.10.1-license: BSD2-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.@@ -17,18 +17,26 @@ This package provides a vocabulary for working with them. build-type: Simple-tested-with: GHC == 7.8.4- , GHC == 7.10.3- , GHC == 8.0.2- , GHC == 8.2.2- , GHC == 8.4.3- , GHC == 8.6.1++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@@ -47,29 +55,34 @@ GADTs build-depends:- base >= 4.7 && < 5,- binary >= 0.7.1 && < 0.9,- deepseq >= 1.3 && < 1.5,- ghc-prim,- hashable >= 1.2 && < 1.3,- mtl >= 2.1.2 && < 2.3,- semigroups >= 0.17 && < 0.19,- transformers >= 0.3.0.0 && < 0.6,- transformers-compat >= 0.5 && < 1+ , 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:+ 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 - if impl(ghc >= 8)+ if impl(ghc >= 9.2) exposed-modules:- Data.Constraint.Nat- Data.Constraint.Symbol+ Data.Constraint.Char - ghc-options: -Wall+ ghc-options: -Wall -Wno-star-is-type test-suite spec type: exitcode-stdio-1.0@@ -77,9 +90,10 @@ 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 >= 4.7 && < 5,- constraints,- hspec >= 2+ , base+ , constraints+ , hspec >= 2
src/Data/Constraint.hs view
@@ -1,33 +1,28 @@-{-# LANGUAGE FunctionalDependencies #-}-{-# LANGUAGE UndecidableInstances #-} {-# LANGUAGE AllowAmbiguousTypes #-}-{-# LANGUAGE ScopedTypeVariables #-}+{-# LANGUAGE CPP #-}+{-# LANGUAGE ConstraintKinds #-} {-# LANGUAGE DeriveDataTypeable #-}-{-# LANGUAGE StandaloneDeriving #-}-{-# LANGUAGE FlexibleInstances #-}+{-# LANGUAGE DerivingStrategies #-} {-# LANGUAGE FlexibleContexts #-}-{-# LANGUAGE ConstraintKinds #-}+{-# LANGUAGE FlexibleInstances #-}+{-# LANGUAGE FunctionalDependencies #-}+{-# LANGUAGE GADTs #-}+{-# LANGUAGE PolyKinds #-}+{-# LANGUAGE QuantifiedConstraints #-}+{-# LANGUAGE Rank2Types #-} {-# LANGUAGE RoleAnnotations #-}-{-# LANGUAGE EmptyDataDecls #-}-{-# LANGUAGE KindSignatures #-}-{-# LANGUAGE TypeOperators #-}-{-# LANGUAGE TypeFamilies #-}+{-# LANGUAGE ScopedTypeVariables #-}+{-# LANGUAGE StandaloneDeriving #-} {-# LANGUAGE Trustworthy #-}-{-# LANGUAGE Rank2Types #-}-{-# LANGUAGE GADTs #-}-{-# LANGUAGE CPP #-}-#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@@ -49,21 +44,26 @@ -- -- 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+ , implied , Bottom(no) , top, bottom -- * Dict is fully faithful@@ -79,20 +79,18 @@ import Control.Monad import Data.Complex import Data.Ratio-#if !MIN_VERSION_base(4,11,0)-import Data.Semigroup-#endif-import Data.Data+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)-#if MIN_VERSION_base(4,8,0) import Numeric.Natural (Natural)-#endif-#if !MIN_VERSION_base(4,8,0)-import Data.Word (Word)-#endif+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@. --@@ -105,16 +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- 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@@ -128,26 +133,64 @@ dictDataType :: DataType dictDataType = mkDataType "Data.Constraint.Dict" [dictConstr]+-} -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. ---withDict :: Dict a -> (a => r) -> r-withDict d r = case d of+-- 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@.@@ -203,28 +246,23 @@ -- library is sensible and can't break any assumptions on the behalf of -- library authors. newtype a :- b = Sub (a => Dict b)- 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@@ -245,12 +283,6 @@ instance a => NFData (a :- b) where rnf (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- -------------------------------------------------------------------------------- -- Constraints form a Category --------------------------------------------------------------------------------@@ -268,10 +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)@@ -423,10 +491,8 @@ 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-#if MIN_VERSION_base(4,8,0) instance Eq a :=> Eq (Const a b) where ins = Sub Dict instance () :=> Eq Natural where ins = Sub Dict-#endif -- Ord instance Class (Eq a) (Ord a) where cls = Sub Dict@@ -446,10 +512,8 @@ 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-#if MIN_VERSION_base(4,8,0) instance Ord a :=> Ord (Const a b) where ins = Sub Dict instance () :=> Ord Natural where ins = Sub Dict-#endif -- Show instance Class () (Show a) where cls = Sub Dict@@ -468,10 +532,8 @@ 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-#if MIN_VERSION_base(4,8,0) instance Show a :=> Show (Const a b) where ins = Sub Dict instance () :=> Show Natural where ins = Sub Dict-#endif -- Read instance Class () (Read a) where cls = Sub Dict@@ -488,10 +550,8 @@ 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-#if MIN_VERSION_base(4,8,0) instance Read a :=> Read (Const a b) where ins = Sub Dict instance () :=> Read Natural where ins = Sub Dict-#endif -- Enum instance Class () (Enum a) where cls = Sub Dict@@ -505,13 +565,9 @@ instance () :=> Enum Double where ins = Sub Dict instance Integral a :=> Enum (Ratio a) where ins = Sub Dict instance () :=> Enum Word where ins = Sub Dict-#if MIN_VERSION_base(4,9,0) instance Enum a :=> Enum (Identity a) where ins = Sub Dict instance Enum a :=> Enum (Const a b) where ins = Sub Dict-#endif-#if MIN_VERSION_base(4,8,0) instance () :=> Enum Natural where ins = Sub Dict-#endif -- Bounded instance Class () (Bounded a) where cls = Sub Dict@@ -522,10 +578,8 @@ 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-#if MIN_VERSION_base(4,9,0) instance Bounded a :=> Bounded (Identity a) where ins = Sub Dict instance Bounded a :=> Bounded (Const a b) where ins = Sub Dict-#endif -- Num instance Class () (Num a) where cls = Sub Dict@@ -536,13 +590,9 @@ 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-#if MIN_VERSION_base(4,9,0) instance Num a :=> Num (Identity a) where ins = Sub Dict instance Num a :=> Num (Const a b) where ins = Sub Dict-#endif-#if MIN_VERSION_base(4,8,0) instance () :=> Num Natural where ins = Sub Dict-#endif -- Real instance Class (Num a, Ord a) (Real a) where cls = Sub Dict@@ -552,26 +602,18 @@ instance () :=> Real Double where ins = Sub Dict instance Integral a :=> Real (Ratio a) where ins = Sub Dict instance () :=> Real Word where ins = Sub Dict-#if MIN_VERSION_base(4,9,0) instance Real a :=> Real (Identity a) where ins = Sub Dict instance Real a :=> Real (Const a b) where ins = Sub Dict-#endif-#if MIN_VERSION_base(4,8,0) instance () :=> Real Natural where ins = Sub Dict-#endif -- 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-#if MIN_VERSION_base(4,9,0) instance Integral a :=> Integral (Identity a) where ins = Sub Dict instance Integral a :=> Integral (Const a b) where ins = Sub Dict-#endif-#if MIN_VERSION_base(4,8,0) instance () :=> Integral Natural where ins = Sub Dict-#endif -- Bits instance Class (Eq a) (Bits a) where cls = Sub Dict@@ -579,13 +621,9 @@ instance () :=> Bits Int where ins = Sub Dict instance () :=> Bits Integer where ins = Sub Dict instance () :=> Bits Word where ins = Sub Dict-#if MIN_VERSION_base(4,9,0) instance Bits a :=> Bits (Identity a) where ins = Sub Dict instance Bits a :=> Bits (Const a b) where ins = Sub Dict-#endif-#if MIN_VERSION_base(4,8,0) instance () :=> Bits Natural where ins = Sub Dict-#endif -- Fractional instance Class (Num a) (Fractional a) where cls = Sub Dict@@ -593,39 +631,31 @@ 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-#if MIN_VERSION_base(4,9,0) instance Fractional a :=> Fractional (Identity a) where ins = Sub Dict instance Fractional a :=> Fractional (Const a b) where ins = Sub Dict-#endif -- 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-#if MIN_VERSION_base(4,9,0) instance Floating a :=> Floating (Identity a) where ins = Sub Dict instance Floating a :=> Floating (Const a b) where ins = Sub Dict-#endif -- 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-#if MIN_VERSION_base(4,9,0) instance RealFrac a :=> RealFrac (Identity a) where ins = Sub Dict instance RealFrac a :=> RealFrac (Const a b) where ins = Sub Dict-#endif -- 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-#if MIN_VERSION_base(4,9,0) instance RealFloat a :=> RealFloat (Identity a) where ins = Sub Dict instance RealFloat a :=> RealFloat (Const a b) where ins = Sub Dict-#endif -- Semigroup instance Class () (Semigroup a) where cls = Sub Dict@@ -635,29 +665,19 @@ 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-#if MIN_VERSION_base(4,9,0) instance Semigroup a :=> Semigroup (Identity a) where ins = Sub Dict-#endif-#if MIN_VERSION_base(4,10,0) instance Semigroup a :=> Semigroup (IO a) where ins = Sub Dict-#endif -- Monoid-#if MIN_VERSION_base(4,11,0) instance Class (Semigroup a) (Monoid a) where cls = Sub Dict-#else-instance Class () (Monoid a) where cls = Sub Dict-#endif 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-#if MIN_VERSION_base(4,9,0) instance Monoid a :=> Monoid (Identity a) where ins = Sub Dict instance Monoid a :=> Monoid (IO a) where ins = Sub Dict-#endif -- Functor instance Class () (Functor f) where cls = Sub Dict@@ -689,11 +709,7 @@ instance MonadPlus m :=> Alternative (WrappedMonad m) where ins = Sub Dict -- Monad-#if MIN_VERSION_base(4,8,0) instance Class (Applicative f) (Monad f) where cls = Sub Dict-#else-instance Class () (Monad f) where cls = Sub Dict-#endif instance () :=> Monad [] where ins = Sub Dict instance () :=> Monad ((->) a) where ins = Sub Dict instance () :=> Monad (Either a) where ins = Sub Dict@@ -701,11 +717,7 @@ instance () :=> Monad Identity where ins = Sub Dict -- MonadPlus-#if MIN_VERSION_base(4,8,0) instance Class (Monad f, Alternative f) (MonadPlus f) where cls = Sub Dict-#else-instance Class (Monad f) (MonadPlus f) where cls = Sub Dict-#endif instance () :=> MonadPlus [] where ins = Sub Dict instance () :=> MonadPlus Maybe where ins = Sub Dict @@ -732,7 +744,4 @@ instance a :=> Monoid (Dict a) where ins = Sub Dict instance a => Monoid (Dict a) where-#if !(MIN_VERSION_base(4,11,0))- mappend = (<>)-#endif 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
@@ -1,42 +1,27 @@-{-# LANGUAGE CPP #-}-{-# LANGUAGE TypeOperators #-}-{-# LANGUAGE GADTs #-}+{-# LANGUAGE AllowAmbiguousTypes #-} {-# LANGUAGE ConstraintKinds #-}-{-# LANGUAGE KindSignatures #-}+{-# LANGUAGE GADTs #-}+{-# LANGUAGE PolyKinds #-} {-# LANGUAGE RankNTypes #-} {-# LANGUAGE ScopedTypeVariables #-}-{-# LANGUAGE DeriveDataTypeable #-}-{-# LANGUAGE PolyKinds #-}--#if __GLASGOW_HASKELL__ >= 800 {-# LANGUAGE TypeApplications #-}-{-# LANGUAGE AllowAmbiguousTypes #-}-{-# LANGUAGE TypeInType #-}-#endif+{-# LANGUAGE TypeOperators #-} ------------------------------------------------------------------------------ -- |--- Module : Data.Constraint.Deferrable--- Copyright : (C) 2015-2016 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-#if __GLASGOW_HASKELL__ >= 800- , defer_- , deferEither_ , (:~~:)(HRefl)-#endif , (:~:)(Refl) ) where @@ -47,90 +32,51 @@ import Data.Typeable (Typeable, cast, typeRep) import Data.Type.Equality ((:~:)(Refl)) -#if __GLASGOW_HASKELL__ >= 800-import GHC.Types (type (~~))-#endif--#if __GLASGOW_HASKELL__ >= 801-import Data.Type.Equality ((:~~:)(HRefl))-#endif+import Data.Type.Equality (type (~~), (:~~:)(HRefl)) -data UnsatisfiedConstraint = UnsatisfiedConstraint String- deriving (Typeable, Show)+newtype UnsatisfiedConstraint = UnsatisfiedConstraint String+ deriving Show instance Exception UnsatisfiedConstraint -- | Allow an attempt at resolution of a constraint at a later time 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 p r proxy. 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--#if __GLASGOW_HASKELL__ >= 800--- | A version of 'defer' that uses visible type application in place of a 'Proxy'.------ Only available on GHC 8.0 or later.-defer_ :: forall p r. Deferrable p => (p => r) -> r-defer_ r = defer @p Proxy r---- | A version of 'deferEither' that uses visible type application in place of a 'Proxy'.------ Only available on GHC 8.0 or later.-deferEither_ :: forall p r. Deferrable p => (p => r) -> Either String r-deferEither_ r = deferEither @p Proxy r-#endif+deferred = Sub $ defer @p Dict -#if __GLASGOW_HASKELL__ >= 800 && __GLASGOW_HASKELL__ < 801--- | Kind heterogeneous propositional equality. Like '(:~:)', @a :~~: b@ is--- inhabited by a terminating value if and only if @a@ is the same type as @b@.------ Only available on GHC 8.0 or later.-data (a :: i) :~~: (b :: j) where- HRefl :: a :~~: a- deriving Typeable-#endif+defer :: forall p r. Deferrable p => (p => r) -> r+defer r = either (throw . UnsatisfiedConstraint) id $ deferEither @p r -showTypeRep :: Typeable t => Proxy t -> String-showTypeRep = show . typeRep+showTypeRep :: forall t. Typeable t => String+showTypeRep = show $ typeRep (Proxy @t) instance Deferrable () where- deferEither _ r = Right r+ 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.-#if __GLASGOW_HASKELL__ >= 800 instance (Typeable k, Typeable (a :: k), Typeable b) => Deferrable (a ~ b) where-#elif __GLASGOW_HASKELL__ == 710-instance (Typeable a, Typeable b) => Deferrable ((a :: *) ~ (b :: *)) where-#else-instance (Typeable a, Typeable b) => Deferrable (a ~ b) where-#endif- deferEither _ r = case cast (Refl :: a :~: a) :: Maybe (a :~: b) of+ deferEither r = case cast (Refl :: a :~: a) :: Maybe (a :~: b) of Just Refl -> Right r Nothing -> Left $- "deferred type equality: type mismatch between `" ++ showTypeRep (Proxy :: Proxy a) ++ "’ and `" ++ showTypeRep (Proxy :: Proxy b) ++ "'"+ "deferred type equality: type mismatch between `" ++ showTypeRep @a ++ "’ and `" ++ showTypeRep @b ++ "'" -#if __GLASGOW_HASKELL__ >= 800 -- | 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+ deferEither r = case cast (HRefl :: a :~~: a) :: Maybe (a :~~: b) of Just HRefl -> Right r Nothing -> Left $- "deferred type equality: type mismatch between `" ++ showTypeRep (Proxy :: Proxy a) ++ "’ and `" ++ showTypeRep (Proxy :: Proxy b) ++ "'"-#endif+ "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
@@ -1,22 +1,21 @@ {-# LANGUAGE CPP #-} {-# LANGUAGE FunctionalDependencies #-}-{-# LANGUAGE MultiParamTypeClasses #-} {-# 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,+-- Copyright : (C) 2011-2021 Edward Kmett, -- (C) 2015 Ørjan Johansen, -- (C) 2016 David Feuer -- License : BSD-style (see the file LICENSE)@@ -26,7 +25,6 @@ -- Portability : non-portable -- -- This module uses a trick to provide quantification over constraints.----------------------------------------------------------------------------- module Data.Constraint.Forall ( Forall, inst@@ -34,89 +32,27 @@ , Forall1, inst1 , ForallT, instT , ForallV, InstV (instV)- , forall+ , 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.- -- - The particular technique used to implement 'Forall' appears to have been- - discovered first by Nicolas Frisby and is- - <https://csks.wordpress.com/2012/10/22/safe-polykinded-universally-quantified-constraints-part-3-of-3/ discussed in some detail>- - on his blog.- -- - However, his discovery did not directly affect the development of this- - module.- -- - 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.- -}---- The `Skolem` type family represents skolem variables; do not export!--- If GHC supports it, these might be made closed with no instances.+class (forall a. p a) => Forall (p :: k -> Constraint)+instance (forall a. p a) => Forall (p :: k -> Constraint) -type family Skolem (p :: k -> Constraint) :: k+-- | Instantiate a quantified @'Forall' p@ constraint at type @a@.+inst :: forall p a. Forall p :- p a+inst = Sub Dict --- The outer `Forall` type family prevents GHC from giving a spurious--- superclass cycle error.--- The inner `Forall_` class prevents the skolem from leaking to the user,--- which would be disastrous.+data Dict1 p where+ Dict1 :: (forall a. p a) => Dict1 p --- | 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)+forallish :: forall p. Dict1 p -> Dict (Forall p)+forallish Dict1 = Dict --- | 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))+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)@@ -143,7 +79,7 @@ instance Forall (Q p t) => ForallT p t -- | Instantiate a quantified @'ForallT' p t@ constraint at types @f@ and @a@.-instT :: forall (p :: k4 -> Constraint) (t :: (k1 -> k2) -> k3 -> k4) (f :: k1 -> k2) (a :: k3). ForallT p t :- p (t f 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@@ -167,25 +103,23 @@ -- | 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+ 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+ 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+ 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+ 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 -forall :: forall p. (forall a. Dict (p a)) -> Dict (Forall p)-forall d = case d :: Dict (p (Skolem p)) of Dict -> Dict
src/Data/Constraint/Lifting.hs view
@@ -3,12 +3,11 @@ {-# 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 ( Lifting(..) , Lifting2(..)@@ -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@@ -50,16 +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 !(MIN_VERSION_base(4,11,0))-import Data.Semigroup-#endif-#if __GLASGOW_HASKELL__ < 710-import Data.Traversable-#endif import GHC.Arr class Lifting p f where@@ -118,7 +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@@ -127,16 +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@@ -199,22 +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@@ -290,24 +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@@ -372,11 +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@@ -385,7 +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@@ -397,28 +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
src/Data/Constraint/Nat.hs view
@@ -1,25 +1,24 @@ {-# LANGUAGE CPP #-} {-# LANGUAGE DataKinds #-}+{-# LANGUAGE MagicHash #-} {-# LANGUAGE PolyKinds #-} {-# LANGUAGE RankNTypes #-} {-# LANGUAGE TypeFamilies #-} {-# LANGUAGE TypeOperators #-}-{-# LANGUAGE KindSignatures #-} {-# LANGUAGE ConstraintKinds #-} {-# LANGUAGE TypeApplications #-} {-# LANGUAGE ScopedTypeVariables #-} {-# LANGUAGE AllowAmbiguousTypes #-} {-# LANGUAGE Trustworthy #-}-#if __GLASGOW_HASKELL__ >= 805+{-# LANGUAGE UndecidableInstances #-} {-# LANGUAGE NoStarIsType #-}-#endif -- | 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- , plusNat, timesNat, powNat, minNat, maxNat, gcdNat, lcmNat, divNat, modNat- , plusZero, timesZero, timesOne, powZero, powOne, maxZero, minZero, gcdZero, gcdOne, lcmZero, lcmOne+ ( 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@@ -38,6 +37,7 @@ , euclideanNat , plusMod, timesMod , modBound+ , log2Pow , dividesDef , timesDiv , eqLe, leEq, leId, leTrans@@ -46,20 +46,27 @@ ) where import Data.Constraint+import Data.Constraint.Unsafe import Data.Proxy-import GHC.TypeLits+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 m = m+ Min m n = If (n <=? m) n m type family Max (m::Nat) (n::Nat) :: Nat where- Max m m = m-#if !(MIN_VERSION_base(4,11,0))-type family Div (m::Nat) (n::Nat) :: Nat where- Div m 1 = m-type family Mod (m::Nat) (n::Nat) :: Nat where- Mod 0 m = 0-#endif+ 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@@ -67,74 +74,100 @@ 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 -magic :: forall n m o. (Integer -> Integer -> Integer) -> (KnownNat n, KnownNat m) :- KnownNat o-magic f = Sub $ unsafeCoerce (Magic Dict) (natVal (Proxy :: Proxy n) `f` natVal (Proxy :: Proxy m))+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 -axiom :: forall a b. Dict (a ~ b)-axiom = unsafeCoerce (Dict :: Dict (a ~ a))+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 b. Dict (a <= b)-axiomLe = axiom+axiomLe :: forall (a :: Nat) (b :: Nat). Dict (a <= b)+axiomLe = unsafeAxiom -eqLe :: (a ~ b) :- (a <= b)+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 axiom+dividesGcd = Sub unsafeAxiom dividesLcm :: forall a b c. (Divides a c, Divides b c) :- Divides (Lcm a b) c-dividesLcm = Sub axiom+dividesLcm = Sub unsafeAxiom gcdCommutes :: forall a b. Dict (Gcd a b ~ Gcd b a)-gcdCommutes = axiom+gcdCommutes = unsafeAxiom lcmCommutes :: forall a b. Dict (Lcm a b ~ Lcm b a)-lcmCommutes = axiom+lcmCommutes = unsafeAxiom gcdZero :: forall a. Dict (Gcd 0 a ~ a)-gcdZero = axiom+gcdZero = unsafeAxiom gcdOne :: forall a. Dict (Gcd 1 a ~ 1)-gcdOne = axiom+gcdOne = unsafeAxiom lcmZero :: forall a. Dict (Lcm 0 a ~ 0)-lcmZero = axiom+lcmZero = unsafeAxiom lcmOne :: forall a. Dict (Lcm 1 a ~ a)-lcmOne = axiom+lcmOne = unsafeAxiom gcdNat :: forall n m. (KnownNat n, KnownNat m) :- KnownNat (Gcd n m)-gcdNat = magic gcd+gcdNat = magicNNN gcd lcmNat :: forall n m. (KnownNat n, KnownNat m) :- KnownNat (Lcm n m)-lcmNat = magic lcm+lcmNat = magicNNN lcm plusNat :: forall n m. (KnownNat n, KnownNat m) :- KnownNat (n + m)-plusNat = magic (+)+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 = magic min+minNat = magicNNN min maxNat :: forall n m. (KnownNat n, KnownNat m) :- KnownNat (Max n m)-maxNat = magic max+maxNat = magicNNN max timesNat :: forall n m. (KnownNat n, KnownNat m) :- KnownNat (n * m)-timesNat = magic (*)+timesNat = magicNNN (*) powNat :: forall n m. (KnownNat n, KnownNat m) :- KnownNat (n ^ m)-powNat = magic (^)+powNat = magicNNN (^) divNat :: forall n m. (KnownNat n, KnownNat m, 1 <= m) :- KnownNat (Div n m)-divNat = Sub $ case magic @n @m div of Sub r -> r+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 magic @n @m mod of Sub r -> r+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 @@ -142,109 +175,124 @@ timesOne = Dict minZero :: forall n. Dict (Min n 0 ~ 0)-minZero = axiom+#if MIN_VERSION_base(4,16,0)+minZero = unsafeAxiom+#else+minZero = Dict+#endif maxZero :: forall n. Dict (Max n 0 ~ n)-maxZero = axiom+#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 axiom+leZero = Sub unsafeAxiom -zeroLe :: forall a. Dict (0 <= a)+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 = axiom+plusMinusInverse1 = unsafeAxiom plusMinusInverse2 :: forall n m. (m <= n) :- (((m + n) - m) ~ n)-plusMinusInverse2 = Sub axiom+plusMinusInverse2 = Sub unsafeAxiom plusMinusInverse3 :: forall n m. (n <= m) :- (((m - n) + n) ~ m)-plusMinusInverse3 = Sub axiom+plusMinusInverse3 = Sub unsafeAxiom plusMonotone1 :: forall a b c. (a <= b) :- (a + c <= b + c)-plusMonotone1 = Sub axiom+plusMonotone1 = Sub unsafeAxiom plusMonotone2 :: forall a b c. (b <= c) :- (a + b <= a + c)-plusMonotone2 = Sub axiom+plusMonotone2 = Sub unsafeAxiom powMonotone1 :: forall a b c. (a <= b) :- ((a^c) <= (b^c))-powMonotone1 = Sub axiom+powMonotone1 = Sub unsafeAxiom powMonotone2 :: forall a b c. (b <= c) :- ((a^b) <= (a^c))-powMonotone2 = Sub axiom+powMonotone2 = Sub unsafeAxiom divMonotone1 :: forall a b c. (a <= b) :- (Div a c <= Div b c)-divMonotone1 = Sub axiom+divMonotone1 = Sub unsafeAxiom divMonotone2 :: forall a b c. (b <= c) :- (Div a c <= Div a b)-divMonotone2 = Sub axiom+divMonotone2 = Sub unsafeAxiom timesMonotone1 :: forall a b c. (a <= b) :- (a * c <= b * c)-timesMonotone1 = Sub axiom+timesMonotone1 = Sub unsafeAxiom timesMonotone2 :: forall a b c. (b <= c) :- (a * b <= a * c)-timesMonotone2 = Sub axiom+timesMonotone2 = Sub unsafeAxiom minMonotone1 :: forall a b c. (a <= b) :- (Min a c <= Min b c)-minMonotone1 = Sub axiom+minMonotone1 = Sub unsafeAxiom minMonotone2 :: forall a b c. (b <= c) :- (Min a b <= Min a c)-minMonotone2 = Sub axiom+minMonotone2 = Sub unsafeAxiom maxMonotone1 :: forall a b c. (a <= b) :- (Max a c <= Max b c)-maxMonotone1 = Sub axiom+maxMonotone1 = Sub unsafeAxiom maxMonotone2 :: forall a b c. (b <= c) :- (Max a b <= Max a c)-maxMonotone2 = Sub axiom+maxMonotone2 = Sub unsafeAxiom powOne :: forall n. Dict ((n ^ 1) ~ n)-powOne = axiom+powOne = unsafeAxiom plusMod :: forall a b c. (1 <= c) :- (Mod (a + b) c ~ Mod (Mod a c + Mod b c) c)-plusMod = Sub axiom+plusMod = Sub unsafeAxiom timesMod :: forall a b c. (1 <= c) :- (Mod (a * b) c ~ Mod (Mod a c * Mod b c) c)-timesMod = Sub axiom+timesMod = Sub unsafeAxiom modBound :: forall m n. (1 <= n) :- (Mod m n <= n)-modBound = Sub axiom+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 axiom+euclideanNat = Sub unsafeAxiom plusCommutes :: forall n m. Dict ((m + n) ~ (n + m))-plusCommutes = axiom+plusCommutes = unsafeAxiom timesCommutes :: forall n m. Dict ((m * n) ~ (n * m))-timesCommutes = axiom+timesCommutes = unsafeAxiom minCommutes :: forall n m. Dict (Min m n ~ Min n m)-minCommutes = axiom+minCommutes = unsafeAxiom maxCommutes :: forall n m. Dict (Max m n ~ Max n m)-maxCommutes = axiom+maxCommutes = unsafeAxiom plusAssociates :: forall m n o. Dict (((m + n) + o) ~ (m + (n + o)))-plusAssociates = axiom+plusAssociates = unsafeAxiom timesAssociates :: forall m n o. Dict (((m * n) * o) ~ (m * (n * o)))-timesAssociates = axiom+timesAssociates = unsafeAxiom minAssociates :: forall m n o. Dict (Min (Min m n) o ~ Min m (Min n o))-minAssociates = axiom+minAssociates = unsafeAxiom maxAssociates :: forall m n o. Dict (Max (Max m n) o ~ Max m (Max n o))-maxAssociates = axiom+maxAssociates = unsafeAxiom gcdAssociates :: forall a b c. Dict (Gcd (Gcd a b) c ~ Gcd a (Gcd b c))-gcdAssociates = axiom+gcdAssociates = unsafeAxiom lcmAssociates :: forall a b c. Dict (Lcm (Lcm a b) c ~ Lcm a (Lcm b c))-lcmAssociates = axiom+lcmAssociates = unsafeAxiom minIsIdempotent :: forall n. Dict (Min n n ~ n) minIsIdempotent = Dict@@ -259,87 +307,90 @@ lcmIsIdempotent = Dict minDistributesOverPlus :: forall n m o. Dict ((n + Min m o) ~ Min (n + m) (n + o))-minDistributesOverPlus = axiom+minDistributesOverPlus = unsafeAxiom minDistributesOverTimes :: forall n m o. Dict ((n * Min m o) ~ Min (n * m) (n * o))-minDistributesOverTimes = axiom+minDistributesOverTimes = unsafeAxiom minDistributesOverPow1 :: forall n m o. Dict ((Min n m ^ o) ~ Min (n ^ o) (m ^ o))-minDistributesOverPow1 = axiom+minDistributesOverPow1 = unsafeAxiom minDistributesOverPow2 :: forall n m o. Dict ((n ^ Min m o) ~ Min (n ^ m) (n ^ o))-minDistributesOverPow2 = axiom+minDistributesOverPow2 = unsafeAxiom minDistributesOverMax :: forall n m o. Dict (Max n (Min m o) ~ Min (Max n m) (Max n o))-minDistributesOverMax = axiom+minDistributesOverMax = unsafeAxiom maxDistributesOverPlus :: forall n m o. Dict ((n + Max m o) ~ Max (n + m) (n + o))-maxDistributesOverPlus = axiom+maxDistributesOverPlus = unsafeAxiom maxDistributesOverTimes :: forall n m o. Dict ((n * Max m o) ~ Max (n * m) (n * o))-maxDistributesOverTimes = axiom+maxDistributesOverTimes = unsafeAxiom maxDistributesOverPow1 :: forall n m o. Dict ((Max n m ^ o) ~ Max (n ^ o) (m ^ o))-maxDistributesOverPow1 = axiom+maxDistributesOverPow1 = unsafeAxiom maxDistributesOverPow2 :: forall n m o. Dict ((n ^ Max m o) ~ Max (n ^ m) (n ^ o))-maxDistributesOverPow2 = axiom+maxDistributesOverPow2 = unsafeAxiom maxDistributesOverMin :: forall n m o. Dict (Min n (Max m o) ~ Max (Min n m) (Min n o))-maxDistributesOverMin = axiom+maxDistributesOverMin = unsafeAxiom plusDistributesOverTimes :: forall n m o. Dict ((n * (m + o)) ~ (n * m + n * o))-plusDistributesOverTimes = axiom+plusDistributesOverTimes = unsafeAxiom timesDistributesOverPow :: forall n m o. Dict ((n ^ (m + o)) ~ (n ^ m * n ^ o))-timesDistributesOverPow = axiom+timesDistributesOverPow = unsafeAxiom timesDistributesOverGcd :: forall n m o. Dict ((n * Gcd m o) ~ Gcd (n * m) (n * o))-timesDistributesOverGcd = axiom+timesDistributesOverGcd = unsafeAxiom timesDistributesOverLcm :: forall n m o. Dict ((n * Lcm m o) ~ Lcm (n * m) (n * o))-timesDistributesOverLcm = axiom+timesDistributesOverLcm = unsafeAxiom plusIsCancellative :: forall n m o. ((n + m) ~ (n + o)) :- (m ~ o)-plusIsCancellative = Sub axiom+plusIsCancellative = Sub unsafeAxiom timesIsCancellative :: forall n m o. (1 <= n, (n * m) ~ (n * o)) :- (m ~ o)-timesIsCancellative = Sub axiom+timesIsCancellative = Sub unsafeAxiom gcdDistributesOverLcm :: forall a b c. Dict (Gcd (Lcm a b) c ~ Lcm (Gcd a c) (Gcd b c))-gcdDistributesOverLcm = axiom+gcdDistributesOverLcm = unsafeAxiom lcmDistributesOverGcd :: forall a b c. Dict (Lcm (Gcd a b) c ~ Gcd (Lcm a c) (Lcm b c))-lcmDistributesOverGcd = axiom+lcmDistributesOverGcd = unsafeAxiom dividesPlus :: (Divides a b, Divides a c) :- Divides a (b + c)-dividesPlus = Sub axiom+dividesPlus = Sub unsafeAxiom -dividesTimes :: (Divides a b, Divides a c) :- Divides a (b * c)-dividesTimes = Sub axiom+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 axiom+dividesMin = Sub unsafeAxiom dividesMax :: (Divides a b, Divides a c) :- Divides a (Max b c)-dividesMax = Sub axiom+dividesMax = Sub unsafeAxiom -dividesDef :: forall a b. Divides a b :- ((a * Div b a) ~ a)-dividesDef = Sub axiom+-- 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 axiom+dividesPow = Sub unsafeAxiom -timesDiv :: forall a b. Dict ((a * Div b a) <= a)-timesDiv = axiom+timesDiv :: forall a b. Dict ((a * Div b a) <= b)+timesDiv = unsafeAxiom -- (<=) is an internal category in the category of constraints. -leId :: forall a. Dict (a <= a)+leId :: forall (a :: Nat). Dict (a <= a) leId = Dict -leEq :: forall a b. (a <= b, b <= a) :- (a ~ b)-leEq = Sub axiom+leEq :: forall (a :: Nat) (b :: Nat). (a <= b, b <= a) :- (a ~ b)+leEq = Sub unsafeAxiom -leTrans :: forall a b c. (b <= c, a <= b) :- (a <= c)+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
@@ -7,11 +7,11 @@ {-# LANGUAGE RankNTypes #-} {-# LANGUAGE DataKinds #-} {-# LANGUAGE PolyKinds #-}+{-# LANGUAGE CPP #-} -- | Utilities for working with 'KnownSymbol' constraints.------ This module is only available on GHC 8.0 or later. module Data.Constraint.Symbol- ( type (++)+ ( type AppendSymbol+ , type (++) , type Take , type Drop , type Length@@ -37,44 +37,63 @@ 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 -type family (++) :: Symbol -> Symbol -> Symbol where+-- | 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-magicNSS f = Sub $ unsafeCoerce (Magic Dict) (fromIntegral (natVal (Proxy :: Proxy n)) `f` symbolVal (Proxy :: Proxy m))+#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-magicSSS f = Sub $ unsafeCoerce (Magic Dict) (symbolVal (Proxy :: Proxy n) `f` symbolVal (Proxy :: Proxy m))+#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-magicSN f = Sub $ unsafeCoerce (Magic Dict) (toInteger (f (symbolVal (Proxy :: Proxy a))))--axiom :: forall a b. Dict (a ~ b)-axiom = unsafeCoerce (Dict :: Dict (a ~ a))+#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 --- axioms and operations+-- operations -appendSymbol :: (KnownSymbol a, KnownSymbol b) :- KnownSymbol (a ++ b)+appendSymbol :: (KnownSymbol a, KnownSymbol b) :- KnownSymbol (AppendSymbol a b) appendSymbol = magicSSS (++) -appendUnit1 :: forall a. Dict (("" ++ a) ~ a)-appendUnit1 = axiom+appendUnit1 :: forall a. Dict (AppendSymbol "" a ~ a)+appendUnit1 = Dict -appendUnit2 :: forall a. Dict ((a ++ "") ~ a)-appendUnit2 = axiom+appendUnit2 :: forall a. Dict (AppendSymbol a "" ~ a)+appendUnit2 = Dict -appendAssociates :: forall a b c. Dict (((a ++ b) ++ c) ~ (a ++ (b ++ c)))-appendAssociates = axiom+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@@ -82,38 +101,38 @@ dropSymbol :: forall n a. (KnownNat n, KnownSymbol a) :- KnownSymbol (Drop n a) dropSymbol = magicNSS drop -takeAppendDrop :: forall n a. Dict (Take n a ++ Drop n a ~ a)-takeAppendDrop = axiom+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 axiom+takeLength = Sub unsafeAxiom take0 :: forall a. Dict (Take 0 a ~ "")-take0 = axiom+take0 = unsafeAxiom takeEmpty :: forall n. Dict (Take n "" ~ "")-takeEmpty = axiom+takeEmpty = unsafeAxiom dropLength :: forall n a. (Length a <= n) :- (Drop n a ~ "")-dropLength = Sub axiom+dropLength = Sub unsafeAxiom drop0 :: forall a. Dict (Drop 0 a ~ a)-drop0 = axiom+drop0 = unsafeAxiom dropEmpty :: forall n. Dict (Drop n "" ~ "")-dropEmpty = axiom+dropEmpty = unsafeAxiom lengthTake :: forall n a. Dict (Length (Take n a) <= n)-lengthTake = axiom+lengthTake = unsafeAxiom lengthDrop :: forall n a. Dict (Length a <= (Length (Drop n a) + n))-lengthDrop = axiom+lengthDrop = unsafeAxiom dropDrop :: forall n m a. Dict (Drop n (Drop m a) ~ Drop (n + m) a)-dropDrop = axiom+dropDrop = unsafeAxiom takeTake :: forall n m a. Dict (Take n (Take m a) ~ Take (Min n m) a)-takeTake = axiom+takeTake = unsafeAxiom
src/Data/Constraint/Unsafe.hs view
@@ -1,4 +1,3 @@-{-# LANGUAGE CPP #-} {-# LANGUAGE ScopedTypeVariables #-} {-# LANGUAGE FlexibleInstances #-} {-# LANGUAGE ConstraintKinds #-}@@ -6,36 +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 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@@ -48,19 +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
@@ -1,22 +1,16 @@-{-# LANGUAGE CPP #-} {-# LANGUAGE DataKinds #-} {-# LANGUAGE GADTs #-} {-# LANGUAGE PolyKinds #-} {-# LANGUAGE ScopedTypeVariables #-}-{-# LANGUAGE TypeOperators #-}--#if __GLASGOW_HASKELL__ >= 800 {-# LANGUAGE TypeApplications #-}-#endif+{-# LANGUAGE TypeOperators #-} module GH55Spec (main, spec) where -import Test.Hspec--#if __GLASGOW_HASKELL__ >= 800 import Data.Constraint import Data.Constraint.Nat import GHC.TypeLits+import Test.Hspec newtype GF (n :: Nat) = GF Integer deriving (Eq, Show) @@ -48,10 +42,6 @@ spec = describe "GH #53" $ it "should normalize Lcm m m" $ z `shouldBe` (GF 0 :: GF (Lcm 5 5))-#else-spec :: Spec-spec = return ()-#endif main :: IO () main = hspec spec