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-- |
-- Module : Control.Applicative
-- Copyright : Conor McBride and Ross Paterson 2005
-- License : BSD-style (see the LICENSE file in the distribution)
--
-- Maintainer : ross@soi.city.ac.uk
-- 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 Röjemo, 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 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
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