Covariant and contravariant functors

example.hs

-- Covariate functor
class Fun f where
  fun :: (a -> b) -> f a -> f b

-- Contravariate functor
class Con f where
  con :: (b -> a) -> f a -> f b

-- Function parameterized over input type 'i'
newtype Fin o i = Fin (i -> o)

-- Function parameterized over output type 'o'
newtype Fou i o = Fou (i -> o)

instance Fun (Fou i) where
  -- (a -> b) -> Fou i a  -> Fou i b
  -- (a -> b) -> (i -> a) -> (i -> b)
  fun ab (Fou ia) = Fou (\i -> ab (ia i)) -- Fou ib

instance Con (Fin o) where
  -- (b -> a) -> Fin o a  -> Fin o b
  -- (b -> a) -> (a -> o) -> (b -> o)
  con ba (Fin ao) = Fin (\b -> ao (ba b))

-- instance Con Ord where
--   -- (b -> a) -> Ord a -> Ord b
--   con ba o = Ord { compare b1 b2 = o.compare (ba b1) (ba b2)
--                  , b1 <= b2      = (o.<=)    (ba b1) (ba b2)
--                  , ...
--                  }