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Showing content from http://hackage.haskell.org/packages/archive/base/4.5.0.0/doc/html/src/Control-Applicative.html below:

Control/Applicative.hs

module Control.Applicative (
    
    Applicative(..),
    
    Alternative(..),
    
    Const(..), WrappedMonad(..), WrappedArrow(..), ZipList(..),
    
    (<$>), (<$), (<**>),
    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 ()
#ifndef __NHC__
import Control.Monad.ST.Safe (ST)
import qualified Control.Monad.ST.Lazy.Safe as Lazy (ST)
#endif
import Data.Functor ((<$>), (<$))
import Data.Monoid (Monoid(..))

#ifdef __GLASGOW_HASKELL__
import GHC.Conc (STM, retry, orElse)
#endif

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








































class Functor f => Applicative f where
    
    pure :: a -> f a

    
    (<*>) :: f (a -> b) -> f a -> f b

    
    (*>) :: f a -> f b -> f b
    (*>) = liftA2 (const id)

    
    (<*) :: f a -> f b -> f a
    (<*) = liftA2 const











class Applicative f => Alternative f where
    
    empty :: f a
    
    (<|>) :: f a -> f a -> f a

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

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



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

#ifndef __NHC__
instance Applicative (ST s) where
    pure = return
    (<*>) = ap

instance Applicative (Lazy.ST s) where
    pure = return
    (<*>) = ap
#endif

#ifdef __GLASGOW_HASKELL__
instance Applicative STM where
    pure = return
    (<*>) = ap

instance Alternative STM where
    empty = retry
    (<|>) = orElse
#endif

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)

instance Applicative (Either e) where
    pure          = Right
    Left  e <*> _ = Left e
    Right f <*> r = fmap f r



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)





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)




(<**>) :: Applicative f => f a -> f (a -> b) -> f b
(<**>) = liftA2 (flip ($))



liftA :: Applicative f => (a -> b) -> f a -> f b
liftA f a = pure f <*> a


liftA2 :: Applicative f => (a -> b -> c) -> f a -> f b -> f c
liftA2 f a b = f <$> a <*> b


liftA3 :: Applicative f => (a -> b -> c -> d) -> f a -> f b -> f c -> f d
liftA3 f a b c = f <$> a <*> b <*> c


optional :: Alternative f => f a -> f (Maybe a)
optional v = Just <$> v <|> pure Nothing

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