-- Yoneda --------------------------------------------------------------
newtype Yoneda f a = Yoneda { runYoneda :: forall b. ((a -> b) -> f b) }

instance Functor (Yoneda f) where
  fmap f y = Yoneda (\ab -> runYoneda y (ab . f))

toYoneda :: Functor f => f a -> Yoneda f a
toYoneda fa = Yoneda (\f -> fmap f fa)

fromYoneda :: Yoneda f a -> f a
fromYoneda y = runYoneda y id

-- Coyoneda -----------------------------------------
data CoYoneda f a = forall b . CoYoneda (b -> a) (f b)

instance Functor (CoYoneda f) where
  fmap f (CoYoneda mp fb) = CoYoneda (f . mp) fb

toCoYoneda :: f a -> CoYoneda f a
toCoYoneda fa = CoYoneda id fa

fromCoYoneda :: Functor f => CoYoneda f a -> f a
fromCoYoneda (CoYoneda mp fb) = fmap mp fb