base-4.3.1.0: Basic libraries

Portabilityportable
Stabilityexperimental
Maintainer[email protected]

Control.Applicative

Contents

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 Data.Traversable.Traversable class.

Synopsis

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
ignore left value
u *> v = pure (const id) <*> u <*> v
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 Monad, define pure = return and (<*>) = ap.

Minimal complete definition: pure and <*>.

Methods

pure :: a -> f aSource

Lift a value.

(<*>) :: f (a -> b) -> f a -> f bSource

Sequential application.

(*>) :: f a -> f b -> f bSource

Sequence actions, discarding the value of the first argument.

(<*) :: f a -> f b -> f aSource

Sequence actions, discarding the value of the second argument.

Alternatives

class Applicative f => Alternative f whereSource

A monoid on applicative functors.

Minimal complete definition: empty and <|>.

some and many should be the least solutions of the equations:

Methods

empty :: f aSource

The identity of <|>

(<|>) :: f a -> f a -> f aSource

An associative binary operation

some :: f a -> f [a]Source

One or more.

many :: f a -> f [a]Source

Zero or more.

Instances

newtype Const a b Source

Constructors

Const 

Fields

getConst :: a
 

Instances

newtype WrappedMonad m a Source

Constructors

WrapMonad 

Fields

unwrapMonad :: m a
 

newtype WrappedArrow a b c Source

Constructors

WrapArrow 

Fields

unwrapArrow :: a b c
 

newtype ZipList a Source

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

f <$> ZipList xs1 <*> ... <*> ZipList xsn = ZipList (zipWithn f xs1 ... xsn)

Constructors

ZipList 

Fields

getZipList :: [a]
 

Utility functions

(<$>) :: Functor f => (a -> b) -> f a -> f bSource

An infix synonym for fmap.

(<$) :: Functor f => a -> f b -> f aSource

Replace all locations in the input with the same value. The default definition is fmap . const, but this may be overridden with a more efficient version.

(<**>) :: 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.