```{-# OPTIONS_GHC -fglasgow-exts #-}
-----------------------------------------------------------------------------
-- |
-- Module      :  Control.Morphism.Postpro
-- Copyright   :  (C) 2008 Edward Kmett
-- License     :  BSD-style (see the file LICENSE)
--
-- Maintainer  :  Edward Kmett <ekmett@gmail.com>
-- Stability   :  experimental
-- Portability :  non-portable (rank-2 polymorphism)
--
-- See Maarten Fokkinga''s PhD Dissertation for postpro. g_postpro is
-- an obvious generalization.
----------------------------------------------------------------------------
module Control.Morphism.Postpro
( postpro
, g_postpro
, bipostpro
, g_bipostpro
) where

import Control.Functor
import Control.Functor.Algebra
import Control.Functor.Extras
import Control.Functor.Fix
import Control.Morphism.Ana

-- prepro f e = x where x = f . fmap (x . cata (InF . e)) . outF
postpro :: Functor f => Coalgebra f c -> (f :~> f) -> c -> FixF f
postpro g e = x where x = InF . fmap (ana (e . outF) . x) . g

-- | Generalized postpromorphisms
g_postpro :: (Functor f, Monad m) => Dist m f -> GCoalgebra f m a -> (f :~> f) -> a -> FixF f
g_postpro k g e = a . return where a = InF . fmap (ana (e . outF) . a . join) . k . liftM g

bipostpro :: Bifunctor f Hask Hask Hask => Coalgebra (f a) c -> (f a :~> f a) -> c -> Fix f a
bipostpro g e = x where x = InB . bimap id (biana (e . outB) . x) . g

g_bipostpro :: (Bifunctor f Hask Hask Hask, Monad m) => Dist m (f a) -> GCoalgebra (f a) m c -> (f a :~> f a) -> c -> Fix f a
g_bipostpro k g e = a . return where a = InB . bimap id (biana (e . outB) . a . join) . k . liftM g
```