Functor Results

RB.hs

{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE FunctionalDependencies #-}

module RB where

import Data.Functor.Contravariant 
newtype O f g e = Comp { deComp :: f (g e) }

newtype Square f a = Square { unSquare :: f (f a) }

instance Contravariant f => Functor (Square f) where
  fmap f = Square . contramap (contramap f) . unSquare

instance (Contravariant f, Contravariant g) => Functor (O f g) where
  fmap f = Comp . contramap (contramap f) . deComp

class Coyo f a where
  coyoneda :: (b -> a) -> f a -> f b

class Yon f a where
  yoneda :: (a -> b) -> f b

instance (Functor f, Contravariant g) => Coyo (O f g) (g a) where
  coyoneda f = Comp . fmap (contramap f) . deComp

instance (Contravariant f, Functor g) => Coyo (O f g) (g a) where
  coyoneda f = Comp . contramap (fmap f) . deComp

instance (Functor f, Functor g) => Yon (O f g) (g a) where
  yoneda f = Comp . fmap (fmap f) . deComp

instance (Contravariant f, Contravariant g) => Yon (O f g) (g a) where
  yoneda f = Comp . contramap (contramap f) . deComp

newtype Product f g a = Product (f a, g a)
newtype Coproduct f g a = Coproduct (Either (f a) (g a))