{-# LANGUAGE FlexibleInstances #-}

-----------------------------------------------------------------------------
{- |
Module      :  Control.Category.Cont
Description :  Provides a type for Continuation Passing Style development
Copyright   :  (c) Matteo Provenzano 2015

License     :  BSD-style (see the LICENSE file in the distribution)
Maintainer  :  matteo.provenzano@alephdue.com
Stability   :  experimental
Portability :  portable
-}

module Control.Category.Cont (Cont, forget) where

import Prelude hiding (id, (.))
import Control.Category
import Data.Monoid

newtype Cont f g = Cont (f -> g)

instance Category Cont where
    (Cont f) . (Cont g) = Cont (f . g )
    id = Cont id

-- | Identity law:
--
-- prop> Cont f . Cont id = Cont f . id = Cont f = Cont id . f = Cont id . Cont f

-- | Associativity law:
--
-- prop> (Cont f . Cont g) . Cont h = Cont (f . g) . Cont h = Cont (f . g . h) = Cont (f . (g . h)) = Cont f . Cont (g .h) = Cont f . (Cont g . Cont h)

instance Monoid a => Monoid (Cont t (f -> a)) where
    Cont f `mappend` Cont g = Cont $ \h x -> f h x `mappend` g h x
    mempty = Cont $ \h x -> mempty

-- |It 'forgets' the continuation.
forget :: Cont (a -> a) (b -> c) -> b -> c
forget (Cont f) = f id

-- |Apply a function to the continuation.
withCont :: (b -> c) -> Cont (a -> b) (a -> c)
withCont f = Cont $ \g -> f . g

-- |Lift the continuation into a Monad.
lift :: Monad m => Cont (a -> b) (a -> m b)
lift = withCont return