| Copyright | Conor McBride and Ross Paterson 2005 |
|---|---|
| License | BSD-style (see the LICENSE file in the distribution) |
| Maintainer | libraries@haskell.org |
| Stability | experimental |
| Portability | portable |
| Safe Haskell | Trustworthy |
| Language | Haskell2010 |
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
Traversableclass. - 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.
- class Functor f => Applicative f where
- class Applicative f => Alternative f where
- 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 (a -> b) -> f b
- liftA :: Applicative f => (a -> b) -> f a -> f b
- liftA3 :: Applicative f => (a -> b -> c -> d) -> f a -> f b -> f c -> f d
- optional :: Alternative f => f a -> f (Maybe a)
Applicative functors
class Functor f => Applicative f where #
A functor with application, providing operations to
A minimal complete definition must include implementations of pure
and of either <*> or liftA2. If it defines both, then they must behave
the same as their default definitions:
(
<*>) = liftA2 idliftA2 f x y = f <$> x <*> y
Further, any definition must satisfy the following:
- identity
pureid<*>v = v- composition
pure(.)<*>u<*>v<*>w = u<*>(v<*>w)- homomorphism
puref<*>purex =pure(f x)- interchange
u
<*>purey =pure($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
It may be useful to note that supposing
forall x y. p (q x y) = f x . g y
it follows from the above that
liftA2p (liftA2q u v) =liftA2f u .liftA2g v
If f is also a Monad, it should satisfy
(which implies that pure and <*> satisfy the applicative functor laws).
Methods
Lift a value.
(<*>) :: f (a -> b) -> f a -> f b infixl 4 #
Sequential application.
A few functors support an implementation of <*> that is more
efficient than the default one.
liftA2 :: (a -> b -> c) -> f a -> f b -> f c #
Lift a binary function to actions.
Some functors support an implementation of liftA2 that is more
efficient than the default one. In particular, if fmap is an
expensive operation, it is likely better to use liftA2 than to
fmap over the structure and then use <*>.
(*>) :: f a -> f b -> f b infixl 4 #
Sequence actions, discarding the value of the first argument.
(<*) :: f a -> f b -> f a infixl 4 #
Sequence actions, discarding the value of the second argument.
Instances
| Applicative [] # | Since: 2.1 |
| Applicative Maybe # | Since: 2.1 |
| Applicative IO # | Since: 2.1 |
| Applicative Par1 # | Since: 4.9.0.0 |
| Applicative ReadP # | Since: 4.6.0.0 |
| Applicative ReadPrec # | Since: 4.6.0.0 |
| Applicative Last # | |
| Applicative First # | |
| Applicative Product # | Since: 4.8.0.0 |
| Applicative Sum # | Since: 4.8.0.0 |
| Applicative Dual # | Since: 4.8.0.0 |
| Applicative STM # | Since: 4.8.0.0 |
| Applicative Identity # | Since: 4.8.0.0 |
| Applicative ZipList # | f '<$>' 'ZipList' xs1 '<*>' ... '<*>' 'ZipList' xsN
|
| Applicative NonEmpty # | Since: 4.9.0.0 |
| Applicative Option # | Since: 4.9.0.0 |
| Applicative Last # | Since: 4.9.0.0 |
| Applicative First # | Since: 4.9.0.0 |
| Applicative Max # | Since: 4.9.0.0 |
| Applicative Min # | Since: 4.9.0.0 |
| Applicative Complex # | Since: 4.9.0.0 |
| Applicative (Either e) # | Since: 3.0 |
| Applicative (U1 *) # | Since: 4.9.0.0 |
| Monoid a => Applicative ((,) a) # | For tuples, the ("hello ", (+15)) <*> ("world!", 2002)
("hello world!",2017)Since: 2.1 |
| Applicative (ST s) # | Since: 4.4.0.0 |
| Applicative (Proxy *) # | Since: 4.7.0.0 |
| Arrow a => Applicative (ArrowMonad a) # | Since: 4.6.0.0 |
| Monad m => Applicative (WrappedMonad m) # | Since: 2.1 |
| Applicative (ST s) # | Since: 2.1 |
| Applicative f => Applicative (Rec1 * f) # | Since: 4.9.0.0 |
| Applicative f => Applicative (Alt * f) # | |
| Monoid m => Applicative (Const * m) # | Since: 2.0.1 |
| Arrow a => Applicative (WrappedArrow a b) # | Since: 2.1 |
| Applicative ((->) LiftedRep LiftedRep a) # | Since: 2.1 |
| (Applicative f, Applicative g) => Applicative ((:*:) * f g) # | Since: 4.9.0.0 |
| (Applicative f, Applicative g) => Applicative (Product * f g) # | Since: 4.9.0.0 |
| Applicative f => Applicative (M1 * i c f) # | Since: 4.9.0.0 |
| (Applicative f, Applicative g) => Applicative ((:.:) * * f g) # | Since: 4.9.0.0 |
| (Applicative f, Applicative g) => Applicative (Compose * * f g) # | Since: 4.9.0.0 |
Alternatives
class Applicative f => Alternative f where #
A monoid on applicative functors.
If defined, some and many should be the least solutions
of the equations:
Methods
The identity of <|>
(<|>) :: f a -> f a -> f a infixl 3 #
An associative binary operation
One or more.
Zero or more.
Instances
| Alternative [] # | Since: 2.1 |
| Alternative Maybe # | Since: 2.1 |
| Alternative IO # | Since: 4.9.0.0 |
| Alternative ReadP # | Since: 4.6.0.0 |
| Alternative ReadPrec # | Since: 4.6.0.0 |
| Alternative STM # | Since: 4.8.0.0 |
| Alternative Option # | Since: 4.9.0.0 |
| Alternative (U1 *) # | Since: 4.9.0.0 |
| Alternative (Proxy *) # | Since: 4.9.0.0 |
| ArrowPlus a => Alternative (ArrowMonad a) # | Since: 4.6.0.0 |
| MonadPlus m => Alternative (WrappedMonad m) # | Since: 2.1 |
| Alternative f => Alternative (Rec1 * f) # | Since: 4.9.0.0 |
| Alternative f => Alternative (Alt * f) # | |
| (ArrowZero a, ArrowPlus a) => Alternative (WrappedArrow a b) # | Since: 2.1 |
| (Alternative f, Alternative g) => Alternative ((:*:) * f g) # | Since: 4.9.0.0 |
| (Alternative f, Alternative g) => Alternative (Product * f g) # | Since: 4.9.0.0 |
| Alternative f => Alternative (M1 * i c f) # | Since: 4.9.0.0 |
| (Alternative f, Applicative g) => Alternative ((:.:) * * f g) # | Since: 4.9.0.0 |
| (Alternative f, Applicative g) => Alternative (Compose * * f g) # | Since: 4.9.0.0 |
Instances
The Const functor.
Instances
| Generic1 k (Const k a) # | |
| Show2 (Const *) # | Since: 4.9.0.0 |
| Read2 (Const *) # | Since: 4.9.0.0 |
| Ord2 (Const *) # | Since: 4.9.0.0 |
| Eq2 (Const *) # | Since: 4.9.0.0 |
| Bifunctor (Const *) # | Since: 4.8.0.0 |
| Bifoldable (Const *) # | Since: 4.10.0.0 |
| Bitraversable (Const *) # | Since: 4.10.0.0 |
| Functor (Const * m) # | Since: 2.1 |
| Monoid m => Applicative (Const * m) # | Since: 2.0.1 |
| Foldable (Const * m) # | Since: 4.7.0.0 |
| Traversable (Const * m) # | Since: 4.7.0.0 |
| Show a => Show1 (Const * a) # | Since: 4.9.0.0 |
| Read a => Read1 (Const * a) # | Since: 4.9.0.0 |
| Ord a => Ord1 (Const * a) # | Since: 4.9.0.0 |
| Eq a => Eq1 (Const * a) # | Since: 4.9.0.0 |
| Bounded a => Bounded (Const k a b) # | |
| Enum a => Enum (Const k a b) # | |
| Eq a => Eq (Const k a b) # | |
| Floating a => Floating (Const k a b) # | |
| Fractional a => Fractional (Const k a b) # | |
| Integral a => Integral (Const k a b) # | |
| (Typeable * k3, Data a, Typeable k3 b) => Data (Const k3 a b) # | Since: 4.10.0.0 |
| Num a => Num (Const k a b) # | |
| Ord a => Ord (Const k a b) # | |
| Read a => Read (Const k a b) # | This instance would be equivalent to the derived instances of the
Since: 4.8.0.0 |
| Real a => Real (Const k a b) # | |
| RealFloat a => RealFloat (Const k a b) # | |
| RealFrac a => RealFrac (Const k a b) # | |
| Show a => Show (Const k a b) # | This instance would be equivalent to the derived instances of the
Since: 4.8.0.0 |
| Ix a => Ix (Const k a b) # | |
| IsString a => IsString (Const * a b) # | Since: 4.9.0.0 |
| Generic (Const k a b) # | |
| Semigroup a => Semigroup (Const k a b) # | Since: 4.9.0.0 |
| Monoid a => Monoid (Const k a b) # | |
| FiniteBits a => FiniteBits (Const k a b) # | |
| Bits a => Bits (Const k a b) # | |
| Storable a => Storable (Const k a b) # | |
| type Rep1 k (Const k a) # | |
| type Rep (Const k a b) # | |
newtype WrappedMonad m a #
Constructors
| WrapMonad | |
Fields
| |
Instances
| Monad m => Monad (WrappedMonad m) # | |
| Monad m => Functor (WrappedMonad m) # | Since: 2.1 |
| Monad m => Applicative (WrappedMonad m) # | Since: 2.1 |
| MonadPlus m => Alternative (WrappedMonad m) # | Since: 2.1 |
| Generic1 * (WrappedMonad m) # | |
| Generic (WrappedMonad m a) # | |
| type Rep1 * (WrappedMonad m) # | |
| type Rep (WrappedMonad m a) # | |
newtype WrappedArrow a b c #
Constructors
| WrapArrow | |
Fields
| |
Instances
| Generic1 * (WrappedArrow a b) # | |
| Arrow a => Functor (WrappedArrow a b) # | Since: 2.1 |
| Arrow a => Applicative (WrappedArrow a b) # | Since: 2.1 |
| (ArrowZero a, ArrowPlus a) => Alternative (WrappedArrow a b) # | Since: 2.1 |
| Generic (WrappedArrow a b c) # | |
| type Rep1 * (WrappedArrow a b) # | |
| type Rep (WrappedArrow a b c) # | |
Lists, but with an Applicative functor based on zipping.
Constructors
| ZipList | |
Fields
| |
Instances
| Functor ZipList # | |
| Applicative ZipList # | f '<$>' 'ZipList' xs1 '<*>' ... '<*>' 'ZipList' xsN
|
| Foldable ZipList # | |
| Traversable ZipList # | Since: 4.9.0.0 |
| Eq a => Eq (ZipList a) # | |
| Ord a => Ord (ZipList a) # | |
| Read a => Read (ZipList a) # | |
| Show a => Show (ZipList a) # | |
| Generic (ZipList a) # | |
| Generic1 * ZipList # | |
| type Rep (ZipList a) # | |
| type Rep1 * ZipList # | |
Utility functions
(<$>) :: Functor f => (a -> b) -> f a -> f b infixl 4 #
An infix synonym for fmap.
The name of this operator is an allusion to $.
Note the similarities between their types:
($) :: (a -> b) -> a -> b (<$>) :: Functor f => (a -> b) -> f a -> f b
Whereas $ is function application, <$> is function
application lifted over a Functor.
Examples
Convert from a Maybe IntMaybe Stringshow:
>>>show <$> NothingNothing>>>show <$> Just 3Just "3"
Convert from an Either Int IntEither IntString using show:
>>>show <$> Left 17Left 17>>>show <$> Right 17Right "17"
Double each element of a list:
>>>(*2) <$> [1,2,3][2,4,6]
Apply even to the second element of a pair:
>>>even <$> (2,2)(2,True)
(<**>) :: Applicative f => f a -> f (a -> b) -> f b infixl 4 #
A variant of <*> with the arguments reversed.
liftA :: Applicative f => (a -> b) -> f a -> f b #
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.