Haskell/Profunctor

profunctor.hs

class Profunctor p where
  dimap :: (a -> b) -> (c -> d) -> p b c -> p a d
  dimap f g = lmap f . rmap g
  lmap :: (a -> b) -> p b c -> p a c
  lmap f = dimap f id
  rmap :: (b -> c) -> p a b -> p a c
  rmap = dimap id

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