base-4.8.1.0: Basic libraries

Control.Applicative

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.

Synopsis

# Applicative functors

class Functor f => Applicative f where Source

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:

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

If f is also a Monad, it should satisfy

(which implies that pure and <*> satisfy the applicative functor laws).

Minimal complete definition

Methods

pure :: a -> f a Source

Lift a value.

(<*>) :: f (a -> b) -> f a -> f b infixl 4 Source

Sequential application.

(*>) :: f a -> f b -> f b infixl 4 Source

Sequence actions, discarding the value of the first argument.

(<*) :: f a -> f b -> f a infixl 4 Source

Sequence actions, discarding the value of the second argument.

Instances

 Applicative ((->) a) Monoid a => Applicative ((,) a) Arrow a => Applicative (ArrowMonad a) Monad m => Applicative (WrappedMonad m) Monoid m => Applicative (Const m) Applicative f => Applicative (Alt * f) Arrow a => Applicative (WrappedArrow a b)

# Alternatives

class Applicative f => Alternative f where Source

A monoid on applicative functors.

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

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

Minimal complete definition

Methods

empty :: f a Source

The identity of <|>

(<|>) :: f a -> f a -> f a infixl 3 Source

An associative binary operation

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

One or more.

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

Zero or more.

Instances

 Alternative f => Alternative (Alt * f) (ArrowZero a, ArrowPlus a) => Alternative (WrappedArrow a b)

# Instances

newtype Const a b Source

Constructors

 Const FieldsgetConst :: a

Instances

 Functor (Const m) Monoid m => Applicative (Const m) Eq a => Eq (Const a b) Ord a => Ord (Const a b) Read a => Read (Const a b) Show a => Show (Const a b) Generic (Const a b) Monoid a => Monoid (Const a b) type Rep1 (Const a) type Rep (Const a b)

Constructors

Instances

newtype WrappedArrow a b c Source

Constructors

 WrapArrow FieldsunwrapArrow :: a b c

Instances

 Arrow a => Functor (WrappedArrow a b) Arrow a => Applicative (WrappedArrow a b) Generic1 (WrappedArrow a b) (ArrowZero a, ArrowPlus a) => Alternative (WrappedArrow a b) Generic (WrappedArrow a b c) type Rep1 (WrappedArrow a b) type Rep (WrappedArrow 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 FieldsgetZipList :: [a]

Instances

 Eq a => Eq (ZipList a) Ord a => Ord (ZipList a) Read a => Read (ZipList a) Show a => Show (ZipList a) type Rep1 ZipList type Rep (ZipList a)

# Utility functions

(<\$>) :: Functor f => (a -> b) -> f a -> f b infixl 4 Source

An infix synonym for fmap.

#### Examples

Convert from a Maybe Int to a Maybe String using show:

>>> show <\$> Nothing
Nothing
>>> show <\$> Just 3
Just "3"

Convert from an Either Int Int to an Either Int String using show:

>>> show <\$> Left 17
Left 17
>>> show <\$> Right 17
Right "17"

Double each element of a list:

>>> (*2) <\$> [1,2,3]
[2,4,6]

Apply even to the second element of a pair:

>>> even <\$> (2,2)
(2,True)

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

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 infixl 4 Source

A variant of <*> with the arguments reversed.

liftA :: Applicative f => (a -> b) -> f a -> f b Source

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 Source

Lift a binary function to actions.

liftA3 :: Applicative f => (a -> b -> c -> d) -> f a -> f b -> f c -> f d Source

Lift a ternary function to actions.

optional :: Alternative f => f a -> f (Maybe a) Source

One or none.