-- Copyright : Conor McBride and Ross Paterson 2005
-- License : BSD-style (see the LICENSE file in the distribution)
--
--- Maintainer : ross@soi.city.ac.uk
+-- Maintainer : libraries@haskell.org
-- Stability : experimental
-- Portability : portable
--
-- '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
+ -- * Applicative functors
+ Applicative(..),
+ -- * Alternatives
+ Alternative(..),
+ -- * Instances
+ Const(..), WrappedMonad(..), WrappedArrow(..), ZipList(..),
+ -- * Utility functions
+ (<$>), (<$), (*>), (<*), (<**>),
+ liftA, liftA2, liftA3,
+ optional, some, many
+ ) where
import Prelude hiding (id,(.))
import Control.Category
import Control.Arrow
- (Arrow(arr, (&&&)), ArrowZero(zeroArrow), ArrowPlus((<+>)))
+ (Arrow(arr, (&&&)), ArrowZero(zeroArrow), ArrowPlus((<+>)))
import Control.Monad (liftM, ap, MonadPlus(..))
import Control.Monad.Instances ()
import Data.Monoid (Monoid(..))
-- Instances should satisfy the following laws:
--
-- [/identity/]
--- @'pure' 'id' '<*>' v = v@
+-- @'pure' 'id' '<*>' v = v@
--
-- [/composition/]
--- @'pure' (.) '<*>' u '<*>' v '<*>' w = u '<*>' (v '<*>' w)@
+-- @'pure' (.) '<*>' u '<*>' v '<*>' w = u '<*>' (v '<*>' w)@
--
-- [/homomorphism/]
--- @'pure' f '<*>' 'pure' x = 'pure' (f x)@
+-- @'pure' f '<*>' 'pure' x = 'pure' (f x)@
--
-- [/interchange/]
--- @u '<*>' 'pure' y = 'pure' ('$' y) '<*>' u@
+-- @u '<*>' 'pure' y = 'pure' ('$' y) '<*>' u@
--
-- The 'Functor' instance should satisfy
--
-- @
--- 'fmap' f x = 'pure' f '<*>' x
+-- '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
+ -- | Lift a value.
+ pure :: a -> f a
-- | Sequential application.
- (<*>) :: f (a -> b) -> f a -> f b
+ (<*>) :: 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
+ -- | 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
+ pure = return
+ (<*>) = ap
instance Alternative Maybe where
- empty = Nothing
- Nothing <|> p = p
- Just x <|> _ = Just x
+ empty = Nothing
+ Nothing <|> p = p
+ Just x <|> _ = Just x
instance Applicative [] where
- pure = return
- (<*>) = ap
+ pure = return
+ (<*>) = ap
instance Alternative [] where
- empty = []
- (<|>) = (++)
+ empty = []
+ (<|>) = (++)
instance Applicative IO where
- pure = return
- (<*>) = ap
+ pure = return
+ (<*>) = ap
instance Applicative ((->) a) where
- pure = const
- (<*>) f g x = f x (g x)
+ 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)
+ 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
+ fmap _ (Const v) = Const v
instance Monoid m => Applicative (Const m) where
- pure _ = Const mempty
- Const f <*> Const v = Const (f `mappend` v)
+ 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)
+ 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)
+ 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)
+ 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)
+ 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))
+ 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)
+ empty = WrapArrow zeroArrow
+ WrapArrow u <|> WrapArrow v = WrapArrow (u <+> v)
-- | Lists, but with an 'Applicative' functor based on zipping, so that
--
newtype ZipList a = ZipList { getZipList :: [a] }
instance Functor ZipList where
- fmap f (ZipList xs) = ZipList (map f xs)
+ 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)
+ pure x = ZipList (repeat x)
+ ZipList fs <*> ZipList xs = ZipList (zipWith id fs xs)
-- extra functions
some :: Alternative f => f a -> f [a]
some v = some_v
where many_v = some_v <|> pure []
- some_v = (:) <$> v <*> many_v
+ some_v = (:) <$> 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 = (:) <$> v <*> many_v
+ some_v = (:) <$> v <*> many_v
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