-----------------------------------------------------------------------------
-- |
-- Module      :  Control.Applicative
-- Copyright   :  Conor McBride and Ross Paterson 2005
-- License     :  BSD-style (see the LICENSE file in the distribution)
--
-- Maintainer  :  [email protected]
-- Stability   :  experimental
-- Portability :  portable
--
-- This module describes a structure intermediate between a functor and
-- a monad: it provides pure expressions and sequencing, but no binding.
-- (Technically, a strong lax monoidal functor.)  For more details, see
-- /Applicative Programming with Effects/,
-- by Conor McBride and Ross Paterson, online at
-- <http://www.soi.city.ac.uk/~ross/papers/Applicative.html>.
--
-- This interface was introduced for parsers by Niklas R&#xF6;jemo, because
-- it admits more sharing than the monadic interface.  The names here are
-- mostly based on recent parsing work by Doaitse Swierstra.
--
-- This class is also useful with instances of the
-- 'Data.Traversable.Traversable' class.

module Control.Applicative (
        -- * Applicative functors
        Applicative(..),
        -- * Alternatives
        Alternative(..),
        -- * Instances
        Const(..), WrappedMonad(..), WrappedArrow(..), ZipList(..),
        -- * Utility functions
        (<$>), (<$), (<**>),
        liftA, liftA2, liftA3,
        optional,
        ) where

import Prelude hiding (id,(.))

import Control.Category
import Control.Arrow
        (Arrow(arr, (&&&)), ArrowZero(zeroArrow), ArrowPlus((<+>)))
import Control.Monad (liftM, ap, MonadPlus(..))
import Control.Monad.Instances ()
import Data.Functor ((<$>), (<$))
import Data.Monoid (Monoid(..))

infixl 3 <|>
infixl 4 <*>, <*, *>, <**>

-- | A functor with application.
--
-- Instances should satisfy the following laws:
--
-- [/identity/]
--      @'pure' 'id' '<*>' v = v@
--
-- [/composition/]
--      @'pure' (.) '<*>' u '<*>' v '<*>' w = u '<*>' (v '<*>' w)@
--
-- [/homomorphism/]
--      @'pure' f '<*>' 'pure' x = 'pure' (f x)@
--
-- [/interchange/]
--      @u '<*>' 'pure' y = 'pure' ('$' y) '<*>' u@
--
-- [/ignore left value/]
--      @u '*>' v = 'pure' ('const' 'id') '<*>' u '<*>' v@
--
-- [/ignore right value/]
--      @u '<*' v = 'pure' 'const' '<*>' u '<*>' v@
--
-- The 'Functor' instance should satisfy
--
-- @
--      'fmap' f x = 'pure' f '<*>' x
-- @
--
-- If @f@ is also a 'Monad', define @'pure' = 'return'@ and @('<*>') = 'ap'@.
--
-- Minimal complete definition: 'pure' and '<*>'.

class Functor f => Applicative f where
        -- | Lift a value.
        pure :: a -> f a

        -- | Sequential application.
        (<*>) :: f (a -> b) -> f a -> f b

	-- | Sequence actions, discarding the value of the first argument.
	(*>) :: f a -> f b -> f b
	(*>) = liftA2 (const id)

	-- | Sequence actions, discarding the value of the second argument.
	(<*) :: f a -> f b -> f a
	(<*) = liftA2 const

-- | A monoid on applicative functors.
--
-- Minimal complete definition: 'empty' and '<|>'.
--
-- 'some' and 'many' should be the least solutions of the equations:
--
-- * @some v = (:) '<$>' v '<*>' many v@
--
-- * @many v = some v '<|>' 'pure' []@
class Applicative f => Alternative f where
        -- | The identity of '<|>'
        empty :: f a
        -- | An associative binary operation
        (<|>) :: f a -> f a -> f a

	-- | One or more.
	some :: f a -> f [a]
	some v = some_v
	  where many_v = some_v <|> pure []
		some_v = (:) <$> v <*> many_v

	-- | Zero or more.
	many :: f a -> f [a]
	many v = many_v
	  where many_v = some_v <|> pure []
		some_v = (:) <$> v <*> many_v

-- instances for Prelude types

instance Applicative Maybe where
        pure = return
        (<*>) = ap

instance Alternative Maybe where
        empty = Nothing
        Nothing <|> p = p
        Just x <|> _ = Just x

instance Applicative [] where
        pure = return
        (<*>) = ap

instance Alternative [] where
        empty = []
        (<|>) = (++)

instance Applicative IO where
        pure = return
        (<*>) = ap

instance Applicative ((->) a) where
        pure = const
        (<*>) f g x = f x (g x)

instance Monoid a => Applicative ((,) a) where
        pure x = (mempty, x)
        (u, f) <*> (v, x) = (u `mappend` v, f x)

-- new instances

newtype Const a b = Const { getConst :: a }

instance Functor (Const m) where
        fmap _ (Const v) = Const v

instance Monoid m => Applicative (Const m) where
        pure _ = Const mempty
        Const f <*> Const v = Const (f `mappend` v)

newtype WrappedMonad m a = WrapMonad { unwrapMonad :: m a }

instance Monad m => Functor (WrappedMonad m) where
        fmap f (WrapMonad v) = WrapMonad (liftM f v)

instance Monad m => Applicative (WrappedMonad m) where
        pure = WrapMonad . return
        WrapMonad f <*> WrapMonad v = WrapMonad (f `ap` v)

instance MonadPlus m => Alternative (WrappedMonad m) where
        empty = WrapMonad mzero
        WrapMonad u <|> WrapMonad v = WrapMonad (u `mplus` v)

newtype WrappedArrow a b c = WrapArrow { unwrapArrow :: a b c }

instance Arrow a => Functor (WrappedArrow a b) where
        fmap f (WrapArrow a) = WrapArrow (a >>> arr f)

instance Arrow a => Applicative (WrappedArrow a b) where
        pure x = WrapArrow (arr (const x))
        WrapArrow f <*> WrapArrow v = WrapArrow (f &&& v >>> arr (uncurry id))

instance (ArrowZero a, ArrowPlus a) => Alternative (WrappedArrow a b) where
        empty = WrapArrow zeroArrow
        WrapArrow u <|> WrapArrow v = WrapArrow (u <+> v)

-- | Lists, but with an 'Applicative' functor based on zipping, so that
--
-- @f '<$>' 'ZipList' xs1 '<*>' ... '<*>' 'ZipList' xsn = 'ZipList' (zipWithn f xs1 ... xsn)@
--
newtype ZipList a = ZipList { getZipList :: [a] }

instance Functor ZipList where
        fmap f (ZipList xs) = ZipList (map f xs)

instance Applicative ZipList where
        pure x = ZipList (repeat x)
        ZipList fs <*> ZipList xs = ZipList (zipWith id fs xs)

-- extra functions

-- | A variant of '<*>' with the arguments reversed.
(<**>) :: Applicative f => f a -> f (a -> b) -> f b
(<**>) = liftA2 (flip ($))

-- | Lift a function to actions.
-- This function may be used as a value for `fmap` in a `Functor` instance.
liftA :: Applicative f => (a -> b) -> f a -> f b
liftA f a = pure f <*> a

-- | Lift a binary function to actions.
liftA2 :: Applicative f => (a -> b -> c) -> f a -> f b -> f c
liftA2 f a b = f <$> a <*> b

-- | Lift a ternary function to actions.
liftA3 :: Applicative f => (a -> b -> c -> d) -> f a -> f b -> f c -> f d
liftA3 f a b c = f <$> a <*> b <*> c

-- | One or none.
optional :: Alternative f => f a -> f (Maybe a)
optional v = Just <$> v <|> pure Nothing