{-# LANGUAGE TypeOperators #-}
{-# LANGUAGE Rank2Types #-}
{-# LANGUAGE DefaultSignatures #-}

-- | Compare to indexed.Control.Comonad.Indexed (IxComonad)
module MHask.Indexed.Comonad where



import MHask.Util

import qualified MHask.Indexed.Functor as MHask
import qualified MHask.Indexed.Copointed as MHask

-- | Indexed version of "MHask.Comonad".
-- Dual of "MHask.Indexed.Monad"
class (MHask.IxCopointed t) => IxComonad t where
  iduplicate :: (Monad m)
    => t i j (t j k m) <~ t i k m
  default iduplicate :: (Monad m, Monad (t j k m))
    => t i j (t j k m) <~ t i k m
  iduplicate = iextend id

  iextend :: (Monad m, Monad n)
    => (m <~ t j k n) -> (t i j m <~ t i k n)
  default iextend ::
    (Monad m, Monad n,
     Monad (t i j m), Monad (t j k n), Monad (t i k n),
     Monad (t i j (t j k n)))
    => (m <~ t j k n) -> (t i j m <~ t i k n)
  iextend f = MHask.imap f ~<~ iduplicate