{-# LANGUAGE GADTs,TypeSynonymInstances,MultiParamTypeClasses #-}
-----------------------------------------------------------------------------
-- |
-- Module      :  Control.Comonad.Doubled
-- Copyright   :  (C) 2010 Thomas Bereknyei
-- License     :  BSD-style (see the file LICENSE)
--
-- Maintainer  :  Thomas Bereknyei <tomberek@gmail.com>
-- Stability   :  experimental
-- Portability :  portable
--
----------------------------------------------------------------------------
module Comonad2
	( DCopointed(..)
	, DComonad(..)
    , DFunctor(..)
    ,dextendX
    ,(=>>)
	) where

import Data.List (foldl')
    
class (DCopointed g f) => DComonad g f where
    dextend :: (g a b -> f c d) -> g a b -> g c d
   
class (DFunctor g f) => DCopointed g f where
    dextract :: g a b -> f a b
    
class DFunctor g f where
    dmap :: (f a b -> f c d) -> g a b -> g c d
   
dextendX :: DComonad g f => (g a b -> f a b) -> Int -> g a b -> g a b
dextendX f t = foldl' (.) id (take t $ repeat $ dextend f)
--dextendX function times net = (iterate (dextend function) net)!!times

(=>>) :: DComonad g f => g a b-> (g a b-> f a b) -> g a b
(=>>) = flip dextend

{-# RULES
"dextend pextract" 		    dextend dextract = id
"dextract . dextend g" 		forall g. dextract . dextend g = g
"dextend f . dextend g"     forall f g. dextend f.dextend g=dextend (f.dextend g)
    #-}