+{-# LANGUAGE CPP #-}
+
-----------------------------------------------------------------------------
-- |
-- Module : Control.Applicative
-- 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>.
+-- a monad (technically, a strong lax monoidal functor). Compared with
+-- monads, this interface lacks the full power of the binding operation
+-- '>>=', but
+--
+-- * it has more instances.
+--
+-- * it is sufficient for many uses, e.g. context-free parsing, or the
+-- 'Data.Traversable.Traversable' class.
+--
+-- * instances can perform analysis of computations before they are
+-- executed, and thus produce shared optimizations.
--
-- 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.
+-- mostly based on parsing work by Doaitse Swierstra.
--
--- This class is also useful with instances of the
--- 'Data.Traversable.Traversable' class.
+-- 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>.
module Control.Applicative (
- -- * Applicative functors
- Applicative(..),
- -- * Alternatives
- Alternative(..),
- -- * Instances
- Const(..), WrappedMonad(..), WrappedArrow(..), ZipList(..),
- -- * Utility functions
- (<$>), (<$), (<**>),
- liftA, liftA2, liftA3,
- optional,
- ) where
+ -- * Applicative functors
+ Applicative(..),
+ -- * Alternatives
+ Alternative(..),
+ -- * Instances
+ Const(..), WrappedMonad(..), WrappedArrow(..), ZipList(..),
+ -- * Utility functions
+ (<$>), (<$), (<**>),
+ liftA, liftA2, liftA3,
+ optional,
+ ) where
import Prelude hiding (id,(.))
import Control.Category
-import Control.Arrow
- (Arrow(arr, (&&&)), ArrowZero(zeroArrow), ArrowPlus((<+>)))
+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 3 <|>
infixl 4 <*>, <*, *>, <**>
--- | A functor with application.
+-- | A functor with application, providing operations to
+--
+-- * embed pure expressions ('pure'), and
+--
+-- * sequence computations and combine their results ('<*>').
--
--- Instances should satisfy the following laws:
+-- A minimal complete definition must include implementations of these
+-- functions satisfying the following laws:
--
-- [/identity/]
-- @'pure' 'id' '<*>' v = v@
-- [/interchange/]
-- @u '<*>' 'pure' y = 'pure' ('$' y) '<*>' u@
--
--- [/ignore left value/]
--- @u '*>' v = 'pure' ('const' 'id') '<*>' u '<*>' v@
+-- The other methods have the following default definitions, which may
+-- be overridden with equivalent specialized implementations:
--
--- [/ignore right value/]
--- @u '<*' v = 'pure' 'const' '<*>' u '<*>' v@
+-- @
+-- u '*>' v = 'pure' ('const' 'id') '<*>' u '<*>' v
+-- u '<*' v = 'pure' 'const' '<*>' u '<*>' v
+-- @
--
--- The 'Functor' instance should satisfy
+-- As a consequence of these laws, the 'Functor' instance for @f@ will satisfy
--
-- @
-- 'fmap' f x = 'pure' f '<*>' x
-- @
--
--- If @f@ is also a 'Monad', define @'pure' = 'return'@ and @('<*>') = 'ap'@.
---
--- Minimal complete definition: 'pure' and '<*>'.
+-- If @f@ is also a 'Monad', it should satisfy @'pure' = 'return'@ and
+-- @('<*>') = 'ap'@ (which implies that 'pure' and '<*>' satisfy the
+-- applicative functor laws).
class Functor f => Applicative f where
- -- | Lift a value.
- pure :: a -> f a
+ -- | Lift a value.
+ pure :: a -> f a
- -- | Sequential application.
- (<*>) :: f (a -> b) -> f a -> f b
+ -- | Sequential application.
+ (<*>) :: f (a -> b) -> f a -> f b
- -- | Sequence actions, discarding the value of the first argument.
- (*>) :: f a -> f b -> f b
- (*>) = liftA2 (const id)
+ -- | Sequence actions, discarding the value of the first argument.
+ (*>) :: f a -> f b -> f b
+ (*>) = liftA2 (const id)
- -- | Sequence actions, discarding the value of the second argument.
- (<*) :: f a -> f b -> f a
- (<*) = liftA2 const
+ -- | Sequence actions, discarding the value of the second argument.
+ (<*) :: f a -> f b -> f a
+ (<*) = liftA2 const
-- | A monoid on applicative functors.
--
-- Minimal complete definition: 'empty' and '<|>'.
--
--- 'some' and 'many' should be the least solutions of the equations:
+-- If defined, 'some' and 'many' should be the least solutions
+-- of the equations:
--
-- * @some v = (:) '<$>' 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
+ -- | 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
+ 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
+
+#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
#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)
+ 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
+ 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
+ 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
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