    -----------------------------------------------------------------------------
    -- |
    -- Module      :  Control.Applicative
    -- Copyright   :  Conor McBride and Ross Paterson 2005
    -- License     :  BSD-style (see the LICENSE file in the distribution)
    --
    -- Maintainer  :  libraries@haskell.org
    -- 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, some, many
            ) where

    import Prelude hiding (id,(.))
    import qualified Prelude

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

    infixl 3 <|>
    infixl 4 <$>, <$
    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@
    --
    -- The 'Functor' instance should satisfy
    --
    -- @
    --      'fmap' f x = 'pure' f '<*>' x
    -- @
    --
    -- If @f@ is also a 'Monad', define @'pure' = 'return'@ and @('<*>') = 'ap'@.

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

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

    -- | A monoid on applicative functors.
    class Applicative f => Alternative f where
            -- | The identity of '<|>'
            empty :: f a
            -- | An associative binary operation
            (<|>) :: f a -> f a -> f a

    -- 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 synonym for 'fmap'.
    (<$>) :: Functor f => (a -> b) -> f a -> f b
    f <$> a = fmap f a

    -- | Replace the value.
    (<$) :: Functor f => a -> f b -> f a
    (<$) = (<$>) . const

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

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

    -- | 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

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

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