-- 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
module Control.Applicative (
-- * Applicative functors
Applicative(..),
+ -- * Alternatives
+ Alternative(..),
-- * Instances
- WrappedMonad(..), Const(..), ZipList(..),
+ Const(..), WrappedMonad(..), WrappedArrow(..), ZipList(..),
-- * Utility functions
- (<$), (*>), (<*), (<**>),
- liftA, liftA2, liftA3
+ (<$>), (<$), (*>), (<*), (<**>),
+ liftA, liftA2, liftA3,
+ optional, some, many
) where
#ifdef __HADDOCK__
import Prelude
#endif
-import Control.Monad (liftM, ap)
+import Control.Arrow
+ (Arrow(arr, (>>>), (&&&)), ArrowZero(zeroArrow), ArrowPlus((<+>)))
+import Control.Monad (liftM, ap, MonadPlus(..))
+import Control.Monad.Instances ()
import Data.Monoid (Monoid(..))
+infixl 3 <|>
infixl 4 <$>, <$
infixl 4 <*>, <*, *>, <**>
-- [/interchange/]
-- @u '<*>' 'pure' y = 'pure' ('$' y) '<*>' u@
--
--- [/pure application/]
--- @f '<$>' v = 'pure' f '<*>' v@
+-- The 'Functor' instance should satisfy
--
--- Minimal complete definition: 'pure' and '<*>'.
+-- @
+-- 'fmap' f x = 'pure' f '<*>' x
+-- @
--
--- If @f@ is also a 'Functor', define @('<$>') = 'fmap'@.
--- If it is also a 'Monad', define @'pure' = 'return'@ and @('<*>') = 'ap'@.
+-- If @f@ is also a 'Monad', define @'pure' = 'return'@ and @('<*>') = 'ap'@.
-class Applicative f where
+class Functor f => Applicative f where
-- | Lift a value.
pure :: a -> f a
-- | Sequential application.
(<*>) :: f (a -> b) -> f a -> f b
- -- | Map a function over an action.
- (<$>) :: (a -> b) -> f a -> f b
- f <$> v = pure f <*> v
+-- | A monoid on applicative functors.
+class Applicative f => Alternative f where
+ -- | The identity of '<|>'
+ empty :: f a
+ -- | An associative binary operation
+ (<|>) :: f a -> f a -> f a
-- instances for Prelude types
pure = return
(<*>) = ap
+instance Alternative Maybe where
+ empty = Nothing
+ Nothing <|> p = p
+ Just x <|> _ = Just x
+
instance Applicative [] where
pure = return
(<*>) = ap
+instance Alternative [] where
+ empty = []
+ (<|>) = (++)
+
instance Applicative IO where
pure = return
(<*>) = ap
pure = const
(<*>) f g x = f x (g x)
+instance Monoid a => Applicative ((,) a) where
+ pure x = (mempty, x)
+ (u, f) <*> (v, x) = (u `mappend` v, f x)
+
-- new instances
+newtype Const a b = Const { getConst :: a }
+
+instance Functor (Const m) where
+ fmap _ (Const v) = Const v
+
+instance Monoid m => Applicative (Const m) where
+ pure _ = Const mempty
+ Const f <*> Const v = Const (f `mappend` v)
+
newtype WrappedMonad m a = WrapMonad { unwrapMonad :: m a }
+instance Monad m => Functor (WrappedMonad m) where
+ fmap f (WrapMonad v) = WrapMonad (liftM f v)
+
instance Monad m => Applicative (WrappedMonad m) where
pure = WrapMonad . return
WrapMonad f <*> WrapMonad v = WrapMonad (f `ap` v)
- f <$> WrapMonad v = WrapMonad (liftM f 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)
-- extra functions
+-- | A synonym for 'fmap'.
+(<$>) :: Functor f => (a -> b) -> f a -> f b
+f <$> a = fmap f a
+
-- | Replace the value.
-(<$) :: Applicative f => a -> f b -> f a
+(<$) :: Functor f => a -> f b -> f a
(<$) = (<$>) . const
-- | Sequence actions, discarding the value of the first argument.
(<**>) :: 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 <$> v <|> pure Nothing
+
+-- | One or more.
+some :: Alternative f => f a -> f [a]
+some v = some_v
+ where many_v = some_v <|> pure []
+ some_v = (:) <$> 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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