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{-# LANGUAGE TypeFamilies, ConstraintKinds, MultiParamTypeClasses #-}
module Control.RCategory where
import qualified Prelude
import GHC.Prim
infixr 9 .
infixr 1 >>>, <<<
-- | A class for categories.
-- id and (.) must form a monoid.
class RCategory cat where
type RCategoryCtxt cat a b :: Constraint
-- | the identity morphism
id :: RCategoryCtxt cat a a
=> cat a a
-- | morphism composition
(.) :: (RCategoryCtxt cat b c, RCategoryCtxt cat a b, RCategoryCtxt cat a c)
=> cat b c -> cat a b -> cat a c
{-# RULES
"identity/left" forall p .
id . p = p
"identity/right" forall p .
p . id = p
#-}
instance RCategory (->) where
type RCategoryCtxt (->) a a = ()
id = Prelude.id
(.) = (Prelude..)
-- | Right-to-left composition
(<<<) :: (RCategoryCtxt cat a c, RCategoryCtxt cat a b, RCategoryCtxt cat b c, RCategory cat)
=> cat b c -> cat a b -> cat a c
(<<<) = (.)
-- | Left-to-right composition
(>>>) :: (RCategoryCtxt cat a c, RCategoryCtxt cat a b, RCategoryCtxt cat b c, RCategory cat)
=> cat a b -> cat b c -> cat a c
f >>> g = g . f
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