Portability	portable
Stability	experimental
Maintainer	libraries@haskell.org

Control.Applicative

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 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.

Instances

Applicative []
Applicative IO
Applicative Maybe
Applicative STM
Applicative ZipList
Applicative Id
Applicative ((->) a)
Applicative (Either e)
Monoid a => Applicative ((,) a)
Monad m => Applicative (WrappedMonad m)
Monoid m => Applicative (Const m)
Applicative (StateR s)
Applicative (StateL s)
Arrow a => Applicative (WrappedArrow a b)

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:

```
some v = (:) <$> v <*> many v
```
```
many v = some v <|> pure []
```

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

Alternative []
Alternative Maybe
Alternative STM
MonadPlus m => Alternative (WrappedMonad m)
(ArrowZero a, ArrowPlus a) => Alternative (WrappedArrow a b)

Instances

newtype Const a b Source

Constructors

Const
Fields getConst :: a

Instances

Functor (Const m)
Monoid m => Applicative (Const m)

newtype WrappedMonad m a Source

Constructors

WrapMonad
Fields unwrapMonad :: m a

Instances

Monad m => Functor (WrappedMonad m)
Monad m => Applicative (WrappedMonad m)
MonadPlus m => Alternative (WrappedMonad m)

newtype WrappedArrow a b c Source

Constructors

WrapArrow
Fields unwrapArrow :: a b c

Instances

Arrow a => Functor (WrappedArrow a b)
Arrow a => Applicative (WrappedArrow a b)
(ArrowZero a, ArrowPlus a) => Alternative (WrappedArrow a b)

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]

Instances

Functor ZipList
Applicative ZipList

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.