gistfile1.hs

{-#LANGUAGE PolyKinds, TypeFamilies, TypeOperators, ConstraintKinds, UndecidableInstances, FlexibleInstances, FunctionalDependencies, MultiParamTypeClasses, TypeOperators, KindSignatures #-}
import qualified Prelude ((.), id, String)
import Data.Proxy
import GHC.Exts
import GHC.TypeLits

class SmallCategory cat where
    name :: Proxy cat -> Prelude.String
    id ::(Objects cat a, CategoryMorphism cat morph) => morph a a
    type Objects cat :: a ->  Constraint 
--    type Morph cat :: a -> a -> b 
class CategoryMorphism cat morph | cat -> morph, morph -> cat where
    (.) :: (Objects cat a, Objects cat b, Objects cat c) => b `morph` c -> a `morph` b -> a `morph` c

instance SmallCategory "Hask" where
    id = Prelude.id
    name Proxy = "Hask"
    type Objects "Hask" = Vacuous "Hask"
--    type Morph "Hask" = (->)
instance CategoryMorphism "Hask" (->) where
    (.) = (Prelude..)