Indexed.hs

-----------------------------------------------------------------------------
-- |
-- Module      :  Control.Applicative.Indexed
-- 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)
--
----------------------------------------------------------------------------
module Control.Applicative.Indexed 
	( module Control.Applicative
	, module Control.Functor.Pointed.Indexed
	, IxApplicative(..)
	) where

import Control.Applicative
import Control.Functor.Pointed.Indexed

class IxPointed m => IxApplicative m where
	iap :: m i j (a -> b) -> m j k a -> m i k b

instance (Pointed m, Applicative m) => IxApplicative (LiftIx m) where
	iap f m = LiftIx (lowerIx f <*> lowerIx m)

instance IxApplicative m => Applicative (LowerIx m i) where
	pure = LowerIx . ireturn
	f <*> m = LowerIx (liftIx f `iap` liftIx m)