Portability	portable
Stability	experimental
Maintainer	libraries@haskell.org
Safe Haskell	Trustworthy

Control.Applicative

Contents

Applicative functors
Alternatives
Instances
Utility functions

Description

This module describes a structure intermediate between a functor and a monad (technically, a strong lax monoidal functor). Compared with monads, this interface lacks the full power of the binding operation >>=, but

it has more instances.
it is sufficient for many uses, e.g. context-free parsing, or the Traversable class.
instances can perform analysis of computations before they are executed, and thus produce shared optimizations.

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 parsing work by Doaitse Swierstra.

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.

Synopsis

Applicative functors

class Functor f => Applicative f where

A functor with application, providing operations to

embed pure expressions (pure), and
sequence computations and combine their results (<*>).

A minimal complete definition must include implementations of these functions satisfying 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 other methods have the following default definitions, which may be overridden with equivalent specialized implementations:

      u *> v = pure (const id) <*> u <*> v
      u <* v = pure const <*> u <*> v

As a consequence of these laws, the Functor instance for f will satisfy

      fmap f x = pure f <*> x

If f is also a Monad, it should satisfy pure = return and (<*>) = ap (which implies that pure and <*> satisfy the applicative functor laws).

Methods

pure :: a -> f a

Lift a value.

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

Sequential application.

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

Sequence actions, discarding the value of the first argument.

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

Sequence actions, discarding the value of the second argument.

Instances

Applicative []
Applicative IO
Applicative Maybe
Applicative ReadP
Applicative ReadPrec
Applicative STM
Applicative ZipList
Applicative ((->) a)
Applicative (Either e)
Monoid a => Applicative ((,) a)
Applicative (ST s)
Arrow a => Applicative (ArrowMonad a)
Applicative (ST s)
Monad m => Applicative (WrappedMonad m)
Monoid m => Applicative (Const m)
Arrow a => Applicative (WrappedArrow a b)

Alternatives

class Applicative f => Alternative f where

A monoid on applicative functors.

Minimal complete definition: empty and <|>.

If defined, some and many should be the least solutions of the equations:

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

Methods

empty :: f a

The identity of <|>

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

An associative binary operation

some :: f a -> f [a]

One or more.

many :: f a -> f [a]

Zero or more.

Instances

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

Instances

newtype Const a b

Constructors

Const
Fields getConst :: a

Instances

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

newtype WrappedMonad m a

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

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

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 b

An infix synonym for fmap.

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

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 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.