Haskell Hierarchical Libraries (base package)Source codeContentsIndex
Control.Applicative
Portabilityportable
Stabilityexperimental
Maintainerross@soi.city.ac.uk
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 where

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

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 b
A synonym for fmap.
(<$) :: Functor f => a -> f b -> f a
Replace the value.
(*>) :: Applicative f => f a -> f b -> f b
Sequence actions, discarding the value of the first argument.
(<*) :: Applicative f => f a -> f b -> f a
Sequence actions, discarding the value of the second argument.
(<**>) :: Applicative f => f a -> f (a -> b) -> f b
A variant of <*> with the arguments reversed.
liftA :: Applicative f => (a -> b) -> f a -> f b
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 c
Lift a binary function to actions.
liftA3 :: Applicative f => (a -> b -> c -> d) -> f a -> f b -> f c -> f d
Lift a ternary function to actions.
optional :: Alternative f => f a -> f (Maybe a)
One or none.
some :: Alternative f => f a -> f [a]
One or more.
many :: Alternative f => f a -> f [a]
Zero or more.
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