{-# LANGUAGE Trustworthy #-}
{-# LANGUAGE GADTs #-}
{-# LANGUAGE NoImplicitPrelude #-}
{-# LANGUAGE PolyKinds #-}
{-# OPTIONS_GHC -Wno-inline-rule-shadowing #-}
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 >>>, <<<
class Category cat where
id :: cat a a
(.) :: 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)
#-}
instance Category (->) where
id = GHC.Base.id
(.) = (GHC.Base..)
instance Category (:~:) where
id = Refl
Refl . Refl = Refl
instance Category (:~~:) where
id = HRefl
HRefl . HRefl = HRefl
instance Category Coercion where
id = Coercion
(.) Coercion = coerce
(<<<) :: Category cat => cat b c -> cat a b -> cat a c
(<<<) = (.)
(>>>) :: Category cat => cat a b -> cat b c -> cat a c
f >>> g = g . f