profunctor.hs

import Control.Monad

class Profunctor p where
  dimap :: (a -> b) -> (c -> d) -> p b c -> p a d

  -- lmap :: (a -> b) -> p b c -> p a c
  -- rmap :: (c -> d) -> p b c -> p b d

instance Profunctor (->) where
  -- dimap :: (a -> b) -> (c -> d) -> (->) b c -> (->) a d
  dimap ab cd bc = cd . bc . ab

newtype Kleisli m b c = Kleisli { runKleisli :: b -> m c }

instance Monad m => Profunctor (Kleisli m) where
  -- dimap :: (a -> b) -> (c -> d) -> Kleisli m b c -> Kleisli m a d
  dimap ab cd (Kleisli bmc) =
    Kleisli (liftM cd . bmc . ab)