Control/Category.hs

{-# LANGUAGE Trustworthy #-}
{-# LANGUAGE GADTs #-}
{-# LANGUAGE NoImplicitPrelude #-}
{-# LANGUAGE PolyKinds #-}
{-# OPTIONS_GHC -Wno-inline-rule-shadowing #-}
 -- The RULES for the methods of class Category may never fire
 -- e.g. identity/left, identity/right, association; see #10528

-----------------------------------------------------------------------------
-- |
-- Module : Control.Category
-- Copyright : (c) Ashley Yakeley 2007
-- License : BSD-style (see the LICENSE file in the distribution)
--
-- Maintainer : ashley@semantic.org
-- Stability : experimental
-- Portability : portable

-- https://gitlab.haskell.org/ghc/ghc/issues/1773

module Control.Category where

import qualified GHC.Base (id,(.))
import Data.Type.Coercion
import Data.Type.Equality
import Data.Coerce (coerce)

infixr 9 .
infixr 1 >>>, <<<

-- | A class for categories. Instances should satisfy the laws
--
-- [Right identity] @f '.' 'id' = f@
-- [Left identity] @'id' '.' f = f@
-- [Associativity] @f '.' (g '.' h) = (f '.' g) '.' h@
--
class Category cat where
 -- | the identity morphism
 id :: cat a a

 -- | morphism composition
 (.) :: cat b c -> cat a b -> cat a c

{-# RULES
"identity/left" forall p .
 id . p = p
"identity/right" forall p .
 p . id = p
"association" forall p q r .
 (p . q) . r = p . (q . r)
 #-}

-- | @since 3.0
instance Category (->) where
 id = GHC.Base.id
 (.) = (GHC.Base..)

-- | @since 4.7.0.0
instance Category (:~:) where
 id = Refl
 Refl . Refl = Refl

-- | @since 4.10.0.0
instance Category (:~~:) where
 id = HRefl
 HRefl . HRefl = HRefl

-- | @since 4.7.0.0
instance Category Coercion where
 id = Coercion
 (.) Coercion = coerce

-- | Right-to-left composition
(<<<) :: Category cat => cat b c -> cat a b -> cat a c
(<<<) = (.)

-- | Left-to-right composition
(>>>) :: Category cat => cat a b -> cat b c -> cat a c
f >>> g = g . f