{-# LANGUAGE FlexibleContexts #-}
-----------------------------------------------------------------------------
-- |
-- Module      :  Data.Functor.Alt
-- Copyright   :  (C) 2011 Edward Kmett,
-- License     :  BSD-style (see the file LICENSE)
--
-- Maintainer  :  Edward Kmett <ekmett@gmail.com>
-- Stability   :  provisional
-- Portability :  portable
--
----------------------------------------------------------------------------
module Data.Functor.Alt
  ( Alt(..)
  , module Data.Functor.Apply
  ) where

import Control.Applicative hiding (some, many)
import Control.Arrow
-- import Control.Exception
import Control.Monad
import Control.Monad.Trans.Identity
-- import Control.Monad.Trans.Cont
import Control.Monad.Trans.Error
import Control.Monad.Trans.List
import Control.Monad.Trans.Maybe
import Control.Monad.Trans.Reader
import qualified Control.Monad.Trans.RWS.Strict as Strict
import qualified Control.Monad.Trans.State.Strict as Strict
import qualified Control.Monad.Trans.Writer.Strict as Strict
import qualified Control.Monad.Trans.RWS.Lazy as Lazy
import qualified Control.Monad.Trans.State.Lazy as Lazy
import qualified Control.Monad.Trans.Writer.Lazy as Lazy
import Data.Functor.Apply
import Data.Functor.Bind
import qualified Data.IntMap as IntMap
import Data.IntMap (IntMap)
import Data.Semigroup
import Data.List.NonEmpty (NonEmpty(..))
import Data.Sequence (Seq)
import qualified Data.Map as Map
import Data.Map (Map)
import Data.Monoid
import Prelude hiding (id, (.))

infixl 3 <!> 

-- | Laws:
-- 
-- > <!> is associative:             (a <!> b) <!> c = a <!> (b <!> c)
-- > <$> left-distributes over <!>:  f <$> (a <!> b) = (f <$> a) <!> (f <$> b)
--
-- If extended to an 'Alternative' then '<!>' should equal '<|>'.
--
-- Ideally, an instance of 'Alt' also satisfies the \"left distributon\" law of 
-- MonadPlus with respect to <.>:
--
-- > <.> right-distributes over <!>: (a <!> b) <.> c = (a <.> c) <!> (b <.> c)
-- 
-- But 'Maybe', 'IO', @'Either' a@, @'ErrorT' e m@, and 'STM' satisfy the alternative 
-- \"left catch\" law instead:
-- 
-- > pure a <!> b = pure a
--
-- However, this variation cannot be stated purely in terms of the dependencies of 'Alt'.
--
-- When and if MonadPlus is successfully refactored, this class should also 
-- be refactored to remove these instances.
--
-- The right distributive law should extend in the cases where the a 'Bind' or 'Monad' is
-- provided to yield variations of the right distributive law:
--
-- > (m <!> n) >>- f = (m >>- f) <!> (m >>- f)
-- > (m <!> n) >>= f = (m >>= f) <!> (m >>= f)

class Functor f => Alt f where
  -- | @(<|>)@ without a required @empty@
  (<!>) :: f a -> f a -> f a

  some :: Applicative f => f a -> f [a]
  some v = some_v
    where many_v = some_v <!> pure []
          some_v = (:) <$> v <*> many_v

  many :: Applicative f => f a -> f [a]
  many v = many_v
    where many_v = some_v <!> pure []
          some_v = (:) <$> v <*> many_v


instance Alt (Either a) where
  Left _ <!> b = b
  a      <!> _ = a

-- | This instance does not actually satisfy the (<.>) right distributive law
-- It instead satisfies the "Left-Catch" law
instance Alt IO where
  m <!> n = m `catch` \_ -> n

instance Alt [] where
  (<!>) = (++)

instance Alt Maybe where
  Nothing <!> b = b
  a       <!> _ = a

instance Alt Option where
  (<!>) = (<|>)

instance MonadPlus m => Alt (WrappedMonad m) where
  (<!>) = (<|>)

instance ArrowPlus a => Alt (WrappedArrow a b) where
  (<!>) = (<|>) 

instance Ord k => Alt (Map k) where
  (<!>) = Map.union

instance Alt IntMap where
  (<!>) = IntMap.union

instance Alt Seq where
  (<!>) = mappend

instance Alt NonEmpty where
  (a :| as) <!> ~(b :| bs) = a :| (as ++ b : bs)

instance Alternative f => Alt (WrappedApplicative f) where
  WrapApplicative a <!> WrapApplicative b = WrapApplicative (a <|> b)

instance Alt f => Alt (IdentityT f) where
  IdentityT a <!> IdentityT b = IdentityT (a <!> b)

instance Alt f => Alt (ReaderT e f) where
  ReaderT a <!> ReaderT b = ReaderT $ \e -> a e <!> b e

instance (Bind f, Monad f) => Alt (MaybeT f) where
  MaybeT a <!> MaybeT b = MaybeT $ do
    v <- a
    case v of
      Nothing -> b
      Just _ -> return v
  
instance (Bind f, Monad f) => Alt (ErrorT e f) where
  ErrorT m <!> ErrorT n = ErrorT $ do
    a <- m
    case a of
      Left _ -> n
      Right r -> return (Right r)

instance Apply f => Alt (ListT f) where
  ListT a <!> ListT b = ListT $ (<!>) <$> a <.> b

instance Alt f => Alt (Strict.StateT e f) where
  Strict.StateT m <!> Strict.StateT n = Strict.StateT $ \s -> m s <!> n s
  
instance Alt f => Alt (Lazy.StateT e f) where
  Lazy.StateT m <!> Lazy.StateT n = Lazy.StateT $ \s -> m s <!> n s

instance Alt f => Alt (Strict.WriterT w f) where
  Strict.WriterT m <!> Strict.WriterT n = Strict.WriterT $ m <!> n
  
instance Alt f => Alt (Lazy.WriterT w f) where
  Lazy.WriterT m <!> Lazy.WriterT n = Lazy.WriterT $ m <!> n
  
instance Alt f => Alt (Strict.RWST r w s f) where
  Strict.RWST m <!> Strict.RWST n = Strict.RWST $ \r s -> m r s <!> n r s

instance Alt f => Alt (Lazy.RWST r w s f) where
  Lazy.RWST m <!> Lazy.RWST n = Lazy.RWST $ \r s -> m r s <!> n r s