-- 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(..),
- -- * Instances
- WrappedMonad(..), Const(..), ZipList(..),
- -- * Utility functions
- (<$>), (<$), (*>), (<*), (<**>),
- liftA, liftA2, liftA3
- ) where
-
-#ifdef __HADDOCK__
-import Prelude
-#endif
-
-import Control.Monad (liftM, ap)
+ -- * 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((<+>)))
+import Control.Monad (liftM, ap, MonadPlus(..))
import Control.Monad.Instances ()
import Data.Monoid (Monoid(..))
+infixl 3 <|>
infixl 4 <$>, <$
infixl 4 <*>, <*, *>, <**>
-- 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
-- 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
instance Applicative [] where
- pure = return
- (<*>) = ap
+ pure = return
+ (<*>) = ap
+
+instance Alternative [] where
+ 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
+
+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)
+ 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)
-newtype Const a b = Const { getConst :: a }
+instance MonadPlus m => Alternative (WrappedMonad m) where
+ empty = WrapMonad mzero
+ WrapMonad u <|> WrapMonad v = WrapMonad (u `mplus` v)
-instance Functor (Const m) where
- fmap _ (Const v) = Const v
+newtype WrappedArrow a b c = WrapArrow { unwrapArrow :: a b c }
-instance Monoid m => Applicative (Const m) where
- pure _ = Const mempty
- Const f <*> Const v = Const (f `mappend` v)
+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
--
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
-- | 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