+{-# LANGUAGE CPP #-}
+
-----------------------------------------------------------------------------
-- |
-- 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
+-- 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 Röjemo, because
-- 'Data.Traversable.Traversable' class.
module Control.Applicative (
- -- * Applicative functors
- Applicative(..),
- -- * Instances
- WrappedMonad(..), Const(..), ZipList(..),
- -- * Utility functions
- (<$), (*>), (<*), (<**>),
- liftA, liftA2, liftA3
- ) where
-
-#ifdef __HADDOCK__
-import Prelude
-#endif
+ -- * Applicative functors
+ Applicative(..),
+ -- * Alternatives
+ Alternative(..),
+ -- * Instances
+ Const(..), WrappedMonad(..), WrappedArrow(..), ZipList(..),
+ -- * Utility functions
+ (<$>), (<$), (<**>),
+ liftA, liftA2, liftA3,
+ optional,
+ ) where
+
+import Prelude hiding (id,(.))
-import Control.Monad (liftM, ap)
+import Control.Category
+import Control.Arrow (Arrow(arr, (&&&)), ArrowZero(zeroArrow), ArrowPlus((<+>)))
+import Control.Monad (liftM, ap, MonadPlus(..))
+import Control.Monad.Instances ()
+#ifndef __NHC__
+import Control.Monad.ST (ST)
+import qualified Control.Monad.ST.Lazy as Lazy (ST)
+#endif
+import Data.Functor ((<$>), (<$))
import Data.Monoid (Monoid(..))
-infixl 4 <$>, <$
+#ifdef __GLASGOW_HASKELL__
+import GHC.Conc (STM, retry, orElse)
+#endif
+
+infixl 3 <|>
infixl 4 <*>, <*, *>, <**>
-- | A functor with application.
-- 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@
--
--- [/pure application/]
--- @f '<$>' v = 'pure' f '<*>' v@
+-- [/ignore left value/]
+-- @u '*>' v = 'pure' ('const' 'id') '<*>' u '<*>' v@
--
--- Minimal complete definition: 'pure' and '<*>'.
+-- [/ignore right value/]
+-- @u '<*' v = 'pure' 'const' '<*>' u '<*>' v@
+--
+-- The 'Functor' instance should satisfy
+--
+-- @
+-- 'fmap' f x = 'pure' f '<*>' x
+-- @
--
--- If @f@ is also a 'Functor', define @('<$>') = 'fmap'@.
--- If it is also a 'Monad', define @'pure' = 'return'@ and @('<*>') = 'ap'@.
+-- If @f@ is also a 'Monad', define @'pure' = 'return'@ and @('<*>') = 'ap'@.
+--
+-- Minimal complete definition: 'pure' and '<*>'.
-class Applicative f where
- -- | Lift a value.
- pure :: a -> f a
+class Functor f => Applicative f where
+ -- | Lift a value.
+ pure :: a -> f a
- -- | Sequential application.
- (<*>) :: f (a -> b) -> f a -> f b
+ -- | Sequential application.
+ (<*>) :: f (a -> b) -> f a -> f b
- -- | Map a function over an action.
- (<$>) :: (a -> b) -> f a -> f b
- f <$> v = pure f <*> v
+ -- | Sequence actions, discarding the value of the first argument.
+ (*>) :: f a -> f b -> f b
+ (*>) = liftA2 (const id)
+
+ -- | Sequence actions, discarding the value of the second argument.
+ (<*) :: f a -> f b -> f a
+ (<*) = liftA2 const
+
+-- | A monoid on applicative functors.
+--
+-- Minimal complete definition: 'empty' and '<|>'.
+--
+-- 'some' and 'many' should be the least solutions of the equations:
+--
+-- * @some v = (:) '<$>' v '<*>' many v@
+--
+-- * @many v = some v '<|>' 'pure' []@
+class Applicative f => Alternative f where
+ -- | The identity of '<|>'
+ empty :: f a
+ -- | An associative binary operation
+ (<|>) :: f a -> f a -> f a
+
+ -- | One or more.
+ some :: f a -> f [a]
+ some v = some_v
+ where
+ many_v = some_v <|> pure []
+ some_v = (:) <$> v <*> many_v
+
+ -- | Zero or more.
+ many :: f a -> f [a]
+ many v = many_v
+ where
+ many_v = some_v <|> pure []
+ some_v = (:) <$> v <*> many_v
-- instances for Prelude types
instance Applicative Maybe where
- pure = return
- (<*>) = ap
+ pure = return
+ (<*>) = ap
+
+instance Alternative Maybe where
+ empty = Nothing
+ Nothing <|> p = p
+ Just x <|> _ = Just x
instance Applicative [] where
- pure = return
- (<*>) = ap
+ pure = return
+ (<*>) = ap
+
+instance Alternative [] where
+ empty = []
+ (<|>) = (++)
instance Applicative IO where
- pure = return
- (<*>) = ap
+ pure = return
+ (<*>) = ap
+
+#ifndef __NHC__
+instance Applicative (ST s) where
+ pure = return
+ (<*>) = ap
+
+instance Applicative (Lazy.ST s) where
+ pure = return
+ (<*>) = ap
+#endif
+
+#ifdef __GLASGOW_HASKELL__
+instance Applicative STM where
+ pure = return
+ (<*>) = ap
+
+instance Alternative STM where
+ empty = retry
+ (<|>) = orElse
+#endif
instance Applicative ((->) a) where
- pure = const
- (<*>) f g x = f x (g x)
+ pure = const
+ (<*>) f g x = f x (g x)
+
+instance Monoid a => Applicative ((,) a) where
+ pure x = (mempty, x)
+ (u, f) <*> (v, x) = (u `mappend` v, f x)
+
+instance Applicative (Either e) where
+ pure = Right
+ Left e <*> _ = Left e
+ Right f <*> r = fmap f r
-- new instances
+newtype Const a b = Const { getConst :: a }
+
+instance Functor (Const m) where
+ fmap _ (Const v) = Const v
+
+instance Monoid m => Applicative (Const m) where
+ pure _ = Const mempty
+ Const f <*> Const v = Const (f `mappend` v)
+
newtype WrappedMonad m a = WrapMonad { unwrapMonad :: m a }
+instance Monad m => Functor (WrappedMonad m) where
+ fmap f (WrapMonad v) = WrapMonad (liftM f v)
+
instance Monad m => Applicative (WrappedMonad m) where
- pure = WrapMonad . return
- WrapMonad f <*> WrapMonad v = WrapMonad (f `ap` v)
- f <$> WrapMonad v = WrapMonad (liftM f 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 Monoid m => Applicative (Const m) where
- pure _ = Const mempty
- Const f <*> Const v = Const (f `mappend` v)
- _ <$> Const v = Const v
+newtype WrappedArrow a b c = WrapArrow { unwrapArrow :: a b c }
+
+instance Arrow a => Functor (WrappedArrow a b) where
+ fmap f (WrapArrow a) = WrapArrow (a >>> arr f)
+
+instance Arrow a => Applicative (WrappedArrow a b) where
+ pure x = WrapArrow (arr (const x))
+ WrapArrow f <*> WrapArrow v = WrapArrow (f &&& v >>> arr (uncurry id))
+
+instance (ArrowZero a, ArrowPlus a) => Alternative (WrappedArrow a b) where
+ empty = WrapArrow zeroArrow
+ WrapArrow u <|> WrapArrow v = WrapArrow (u <+> v)
-- | Lists, but with an 'Applicative' functor based on zipping, so that
--
--
newtype ZipList a = ZipList { getZipList :: [a] }
+instance Functor ZipList where
+ fmap f (ZipList xs) = ZipList (map f xs)
+
instance Applicative ZipList where
- pure x = ZipList (repeat x)
- ZipList fs <*> ZipList xs = ZipList (zipWith id fs xs)
- f <$> ZipList xs = ZipList (map f xs)
+ pure x = ZipList (repeat x)
+ ZipList fs <*> ZipList xs = ZipList (zipWith id fs xs)
-- extra functions
--- | Replace the value.
-(<$) :: Applicative f => a -> f b -> f a
-(<$) = (<$>) . const
-
--- | Sequence actions, discarding the value of the first argument.
-(*>) :: Applicative f => f a -> f b -> f b
-(*>) = liftA2 (const id)
-
--- | Sequence actions, discarding the value of the second argument.
-(<*) :: Applicative f => f a -> f b -> f a
-(<*) = liftA2 const
-
-- | A variant of '<*>' with the arguments reversed.
(<**>) :: Applicative f => f a -> f (a -> b) -> f b
(<**>) = liftA2 (flip ($))
--- | A synonym for '<$>'.
+-- | Lift a function to actions.
+-- This function may be used as a value for `fmap` in a `Functor` instance.
liftA :: Applicative f => (a -> b) -> f a -> f b
-liftA f a = f <$> a
+liftA f a = pure f <*> a
-- | Lift a binary function to actions.
liftA2 :: Applicative f => (a -> b -> c) -> f a -> f b -> f c
-- | 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
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