effectful generalised hylomorphism

ghyloM.hs

ghyloM
  :: forall w f m n a b. (Comonad w, Traversable f, Monad m, Monad n)
  => (forall x. f (w x) -> w (f x))
  -> (forall x. m (f x) -> f (m x))
  -> (forall x. w (n x) -> n (w x))
  -> (forall x. m (n x) -> n (m x))
  -> (f (w b) -> n b)
  -> (a -> n (f (m a)))
  -> a
  -> n b
ghyloM distfw distmf distwn distmn fwalg fmcoalg = fmap extract . go . pure
  where
    go :: m a -> n (w b)
    go = join . fmap j . distmn . fmap fmcoalg
    h :: f (w (w b)) -> n (w b)
    h = distwn . fmap fwalg . distfw
    i :: m (m a) -> n (w (w b))
    i = fmap duplicate . go . join
    j :: m (f (m a)) -> n (w b)
    j = join . fmap h . traverse i . distmf