base-3.0.2.0: Basic librariesSource codeContentsIndex
Control.Applicative
Portabilityportable
Stabilityexperimental
Maintainerlibraries@haskell.org
Contents
Applicative functors
Alternatives
Instances
Utility functions
Description

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 it admits more sharing than the monadic interface. The names here are mostly based on recent parsing work by Doaitse Swierstra.

This class is also useful with instances of the Traversable class.

Synopsis
class Functor f => Applicative f where
pure :: a -> f a
(<*>) :: f (a -> b) -> f a -> f b
class Applicative f => Alternative f where
empty :: f a
(<|>) :: f a -> f a -> f a
newtype Const a b = Const {
getConst :: a
}
newtype WrappedMonad m a = WrapMonad {
unwrapMonad :: (m a)
}
newtype WrappedArrow a b c = WrapArrow {
unwrapArrow :: (a b c)
}
newtype ZipList a = ZipList {
getZipList :: [a]
}
(<$>) :: Functor f => (a -> b) -> f a -> f b
(<$) :: Functor f => a -> f b -> f a
(*>) :: Applicative f => f a -> f b -> f b
(<*) :: Applicative f => f a -> f b -> f a
(<**>) :: Applicative f => f a -> f (a -> b) -> f b
liftA :: Applicative f => (a -> b) -> f a -> f b
liftA2 :: Applicative f => (a -> b -> c) -> f a -> f b -> f c
liftA3 :: Applicative f => (a -> b -> c -> d) -> f a -> f b -> f c -> f d
optional :: Alternative f => f a -> f (Maybe a)
some :: Alternative f => f a -> f [a]
many :: Alternative f => f a -> f [a]
Applicative functors
class Functor f => Applicative f whereSource

A functor with application.

Instances should satisfy the following laws:

identity
pure id <*> v = v
composition
pure (.) <*> u <*> v <*> w = u <*> (v <*> w)
homomorphism
pure f <*> pure x = pure (f x)
interchange
u <*> pure y = pure ($ y) <*> u

The Functor instance should satisfy 

	fmap f x = pure f <*> x

If f is also a Monad, define pure = return and (<*>) = ap.

Methods
pure :: a -> f aSource
Lift a value.
(<*>) :: f (a -> b) -> f a -> f bSource
Sequential application.
show/hide Instances
Alternatives
class Applicative f => Alternative f whereSource
A monoid on applicative functors.
Methods
empty :: f aSource
The identity of <|>
(<|>) :: f a -> f a -> f aSource
An associative binary operation
show/hide Instances
Instances
newtype Const a bSource
Constructors
Const
getConst :: a
show/hide Instances
newtype WrappedMonad m aSource
Constructors
WrapMonad
unwrapMonad :: (m a)
show/hide Instances
newtype WrappedArrow a b cSource
Constructors
WrapArrow
unwrapArrow :: (a b c)
show/hide Instances
newtype ZipList aSource

Lists, but with an Applicative functor based on zipping, so that 

f <$> ZipList xs1 <*> ... <*> ZipList xsn = ZipList (zipWithn f xs1 ... xsn)
Constructors
ZipList
getZipList :: [a]
show/hide Instances
Utility functions
(<$>) :: Functor f => (a -> b) -> f a -> f bSource
A synonym for fmap.
(<$) :: Functor f => a -> f b -> f aSource
Replace the value.
(*>) :: Applicative f => f a -> f b -> f bSource
Sequence actions, discarding the value of the first argument.
(<*) :: Applicative f => f a -> f b -> f aSource
Sequence actions, discarding the value of the second argument.
(<**>) :: Applicative f => f a -> f (a -> b) -> f bSource
A variant of <*> with the arguments reversed.
liftA :: Applicative f => (a -> b) -> f a -> f bSource
Lift a function to actions. This function may be used as a value for fmap in a Functor instance.
liftA2 :: Applicative f => (a -> b -> c) -> f a -> f b -> f cSource
Lift a binary function to actions.
liftA3 :: Applicative f => (a -> b -> c -> d) -> f a -> f b -> f c -> f dSource
Lift a ternary function to actions.
optional :: Alternative f => f a -> f (Maybe a)Source
One or none.
some :: Alternative f => f a -> f [a]Source
One or more.
many :: Alternative f => f a -> f [a]Source
Zero or more.
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