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{-# LANGUAGE TypeFamilies, ConstraintKinds, MultiParamTypeClasses
#-}
module Control.RCategory where
import qualified Prelude
import GHC.Prim
infixr 9 .
infixr 1 >>>, <<<
class RCategory cat where
type RCategoryCtxt cat a b :: Constraint
id :: RCategoryCtxt cat a a => cat a a
(.) ::
(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..)
(<<<) ::
(RCategoryCtxt cat a c, RCategoryCtxt cat a b,
RCategoryCtxt cat b c, RCategory cat) =>
cat b c -> cat a b -> cat a c
(<<<) = (.)
(>>>) ::
(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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