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Control.Applicative |
Portability | portable
Stability | experimental
Maintainer | ross@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` (`$` y) `<*>` u` The `Functor` instance should satisfy
    	fmap f x = pure f <*> x
If `f` is also a `Monad`, define ``pure` = `return`` and `(`<*>`) = `ap``.
Methods
pure :: a -> f a
Lift a value.
(<*>) :: f (a -> b) -> f a -> f b
Sequential application.
Instances
Applicative IO
Applicative Id
Applicative Maybe
Applicative ZipList
Applicative []
Monoid m => Applicative (Const m)
Monad m => Applicative (WrappedMonad m)
Monoid a => Applicative ((,) a)
Applicative ((->) a)
Arrow a => Applicative (WrappedArrow a b)
Alternatives
class Applicative f => Alternative f where
A monoid on applicative functors.
Methods
empty :: f a
The identity of `<|>`
(<|>) :: f a -> f a -> f a
An associative binary operation
Instances
Alternative Maybe
Alternative []
MonadPlus m => Alternative (WrappedMonad m)
(ArrowZero a, ArrowPlus a) => Alternative (WrappedArrow a b)
Instances
newtype Const a b
Constructors
Const |
getConst :: a |
Instances
Monoid m => Applicative (Const m)
Functor (Const m)
newtype WrappedMonad m a
Constructors
WrapMonad |
unwrapMonad :: (m a) |
Instances
MonadPlus m => Alternative (WrappedMonad m)
Monad m => Applicative (WrappedMonad m)
Monad m => Functor (WrappedMonad m)
newtype WrappedArrow a b c
Constructors
WrapArrow |
unwrapArrow :: (a b c) |
Instances
(ArrowZero a, ArrowPlus a) => Alternative (WrappedArrow a b)
Arrow a => Applicative (WrappedArrow a b)
Arrow a => Functor (WrappedArrow a b)
newtype ZipList a
Lists, but with an `Applicative` functor based on zipping, so that
    f <$> ZipList xs1 <*> ... <*> ZipList xsn = ZipList (zipWithn f xs1 ... xsn)
Constructors
ZipList |
getZipList :: [a] |
Instances
Applicative ZipList
Functor ZipList
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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