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{-# 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 Trac #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

-- http://ghc.haskell.org/trac/ghc/ticket/1773

module Control.Category where

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

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

-- | A class for categories. Instances should satisfy the laws

-- @ -- f '.' 'id' = f -- (right identity) -- 'id' '.' f = f -- (left identity) -- f '.' (g '.' h) = (f '.' g) '.' h -- (associativity) -- @ class Category cat where -- | the identity morphism id :: cat a a

-- | morphism composition
([.](Control.Category.html#.)) :: [cat](#local-6989586621679176050) [b](#local-6989586621679176052) [c](#local-6989586621679176053) -> [cat](#local-6989586621679176050) [a](#local-6989586621679176054) [b](#local-6989586621679176052) -> [cat](#local-6989586621679176050) [a](#local-6989586621679176054) [c](#local-6989586621679176053)

{-# 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