{-# LANGUAGE CPP #-}
-----------------------------------------------------------------------------
-- |
-- Module      :  Control.Comonad.Trans.Store.Lazy
-- Copyright   :  (C) 2008-2011 Edward Kmett
-- License     :  BSD-style (see the file LICENSE)
--
-- Maintainer  :  Edward Kmett <ekmett@gmail.com>
-- Stability   :  provisional
-- Portability :  portable
--
-- The lazy store (state-in-context/costate) comonad transformer is subject to the laws:
-- 
-- > x = seek (pos x) x
-- > y = pos (seek y x)
-- > seek y x = seek y (seek z x)
--
-- Thanks go to Russell O'Connor and Daniel Peebles for their help formulating 
-- and proving the laws for this comonad transformer.
----------------------------------------------------------------------------
module Control.Comonad.Trans.Store.Lazy
  ( 
  -- * The Store comonad
    Store, store, runStore
  -- * The Store comonad transformer
  , StoreT(..), runStoreT
  -- * Operations
  , pos
  , seek, seeks
  , peek, peeks
  ) where

import Control.Applicative
import Control.Comonad
import Control.Comonad.Hoist.Class
import Control.Comonad.Trans.Class
import Data.Functor.Identity
import Data.Functor.Apply
import Data.Semigroup

#ifdef __GLASGOW_HASKELL__
import Data.Typeable
instance (Typeable s, Typeable1 w) => Typeable1 (StoreT s w) where
  typeOf1 dswa = mkTyConApp storeTTyCon [typeOf (s dswa), typeOf1 (w dswa)]
    where
      s :: StoreT s w a -> s
      s = undefined
      w :: StoreT s w a -> w a
      w = undefined

instance (Typeable s, Typeable1 w, Typeable a) => Typeable (StoreT s w a) where
  typeOf = typeOfDefault

storeTTyCon :: TyCon
storeTTyCon = mkTyCon "Control.Comonad.Trans.Store.Lazy.StoreT"
{-# NOINLINE storeTTyCon #-}
#endif

type Store s = StoreT s Identity

store :: (s -> a) -> s -> Store s a 
store f s = StoreT (Identity f) s

runStore :: Store s a -> (s -> a, s)
runStore ~(StoreT (Identity f) s) = (f, s)

data StoreT s w a = StoreT (w (s -> a)) s

runStoreT :: StoreT s w a -> (w (s -> a), s)
runStoreT ~(StoreT wf s) = (wf, s)

instance Functor w => Functor (StoreT s w) where
  fmap f ~(StoreT wf s) = StoreT (fmap (f .) wf) s

instance (Apply w, Semigroup s) => Apply (StoreT s w) where
  ~(StoreT ff m) <.> ~(StoreT fa n) = StoreT ((<*>) <$> ff <.> fa) (m <> n)

instance (Applicative w, Semigroup s, Monoid s) => Applicative (StoreT s w) where
  pure a = StoreT (pure (const a)) mempty
  ~(StoreT ff m) <*> ~(StoreT fa n) = StoreT ((<*>) <$> ff <*> fa) (m `mappend` n)

instance Extend w => Extend (StoreT s w) where
  duplicate ~(StoreT wf s) = StoreT (extend StoreT wf) s
  extend f ~(StoreT wf s) = StoreT (extend (\wf' s' -> f (StoreT wf' s')) wf) s

instance Comonad w => Comonad (StoreT s w) where
  extract ~(StoreT wf s) = extract wf s

instance ComonadTrans (StoreT s) where
  lower ~(StoreT f s) = fmap ($s) f

instance ComonadHoist (StoreT s) where
  cohoist ~(StoreT f s) = StoreT (Identity (extract f)) s

-- | Read the current position
pos :: StoreT s w a -> s
pos (StoreT _ s) = s

-- | Seek to an absolute location
--
-- > seek s = peek s . duplicate
seek :: Comonad w => s -> StoreT s w a -> StoreT s w a 
seek s ~(StoreT f _) = StoreT f s

-- | Seek to a relative location
--
-- > seeks f = peeks f . duplicate
seeks :: Comonad w => (s -> s) -> StoreT s w a -> StoreT s w a
seeks f ~(StoreT g s) = StoreT g (f s)

-- | Peek at a value at a given absolute location
--
-- > peek x . extend (peek y) = peek y
peek :: Comonad w => s -> StoreT s w a -> a
peek s (StoreT g _) = extract g s

-- | Peek at a value at a given relative location
peeks :: Comonad w => (s -> s) -> StoreT s w a -> a
peeks f ~(StoreT g s) = extract g (f s)