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

Contents

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 theTraversable 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, seeApplicative Programming with Effects, by Conor McBride and Ross Paterson.

Synopsis

classFunctor f =>Applicative fwhere
- pure :: a -> f a
- (<*>) :: f (a -> b) -> f a -> f b
- liftA2 :: (a -> b -> c) -> f a -> f b -> f c
- (*>) :: f a -> f b -> f b
- (<*) :: f a -> f b -> f a
classApplicative f =>Alternative fwhere
- empty :: f a
- (<|>) :: f a -> f a -> f a
- some :: f a -> f [a]
- many :: f a -> f [a]
newtypeConst a b =Const {
- getConst :: a
}
newtypeWrappedMonad m a =WrapMonad {
- unwrapMonad :: m a
}
newtypeWrappedArrow a b c =WrapArrow {
- unwrapArrow :: a b c
}
newtypeZipList 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

classFunctor f =>Applicative fwhereSource #

A functor with application, providing operations to

embed pure expressions (pure), and
sequence computations and combine their results (<*> andliftA2).

A minimal complete definition must include implementations ofpure and of either<*> orliftA2. If it defines both, then they must behave the same as their default definitions:

(<*>) =liftA2id

liftA2 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

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 = (id<$ u)<*> v
```
```
u<* v =liftA2const u v
```

As a consequence of these laws, theFunctor instance forf will satisfy

```
fmap f x =pure f<*> x
```

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

liftA2 p (liftA2 q u v) =liftA2 f u .liftA2 g v

Iff is also aMonad, it should satisfy

```
pure =return
```
```
(<*>) =ap
```
```
(*>) = (>>)
```

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

Minimal complete definition

pure, ((<*>) |liftA2)

Methods

pure :: a -> f aSource #

Lift a value.

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

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 cSource #

Lift a binary function to actions.

Some functors support an implementation ofliftA2 that is more efficient than the default one. In particular, iffmap is an expensive operation, it is likely better to useliftA2 than tofmap over the structure and then use<*>.

(*>) :: f a -> f b -> f binfixl 4Source #

Sequence actions, discarding the value of the first argument.

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

Sequence actions, discarding the value of the second argument.

Instances

Applicative []Source #	Since: 2.1
Instance details Defined inGHC.Base Methods pure :: a -> [a]Source # (<>) :: [a -> b] -> [a] -> [b]Source # liftA2 :: (a -> b -> c) -> [a] -> [b] -> [c]Source # (>) :: [a] -> [b] -> [b]Source # (<*) :: [a] -> [b] -> [a]Source #
Applicative MaybeSource #	Since: 2.1
Instance details Defined inGHC.Base Methods pure :: a ->Maybe aSource # (<>) ::Maybe (a -> b) ->Maybe a ->Maybe bSource # liftA2 :: (a -> b -> c) ->Maybe a ->Maybe b ->Maybe cSource # (>) ::Maybe a ->Maybe b ->Maybe bSource # (<*) ::Maybe a ->Maybe b ->Maybe aSource #
Applicative IOSource #	Since: 2.1
Instance details Defined inGHC.Base Methods pure :: a ->IO aSource # (<>) ::IO (a -> b) ->IO a ->IO bSource # liftA2 :: (a -> b -> c) ->IO a ->IO b ->IO cSource # (>) ::IO a ->IO b ->IO bSource # (<*) ::IO a ->IO b ->IO aSource #
Applicative Par1Source #	Since: 4.9.0.0
Instance details Defined inGHC.Generics Methods pure :: a ->Par1 aSource # (<>) ::Par1 (a -> b) ->Par1 a ->Par1 bSource # liftA2 :: (a -> b -> c) ->Par1 a ->Par1 b ->Par1 cSource # (>) ::Par1 a ->Par1 b ->Par1 bSource # (<*) ::Par1 a ->Par1 b ->Par1 aSource #
Applicative NonEmptySource #	Since: 4.9.0.0
Instance details Defined inGHC.Base Methods pure :: a ->NonEmpty aSource # (<>) ::NonEmpty (a -> b) ->NonEmpty a ->NonEmpty bSource # liftA2 :: (a -> b -> c) ->NonEmpty a ->NonEmpty b ->NonEmpty cSource # (>) ::NonEmpty a ->NonEmpty b ->NonEmpty bSource # (<*) ::NonEmpty a ->NonEmpty b ->NonEmpty aSource #
Applicative ReadPSource #	Since: 4.6.0.0
Instance details Defined inText.ParserCombinators.ReadP Methods pure :: a ->ReadP aSource # (<>) ::ReadP (a -> b) ->ReadP a ->ReadP bSource # liftA2 :: (a -> b -> c) ->ReadP a ->ReadP b ->ReadP cSource # (>) ::ReadP a ->ReadP b ->ReadP bSource # (<*) ::ReadP a ->ReadP b ->ReadP aSource #
Applicative ReadPrecSource #	Since: 4.6.0.0
Instance details Defined inText.ParserCombinators.ReadPrec Methods pure :: a ->ReadPrec aSource # (<>) ::ReadPrec (a -> b) ->ReadPrec a ->ReadPrec bSource # liftA2 :: (a -> b -> c) ->ReadPrec a ->ReadPrec b ->ReadPrec cSource # (>) ::ReadPrec a ->ReadPrec b ->ReadPrec bSource # (<*) ::ReadPrec a ->ReadPrec b ->ReadPrec aSource #
Applicative DownSource #	Since: 4.11.0.0
Instance details Defined inData.Ord Methods pure :: a ->Down aSource # (<>) ::Down (a -> b) ->Down a ->Down bSource # liftA2 :: (a -> b -> c) ->Down a ->Down b ->Down cSource # (>) ::Down a ->Down b ->Down bSource # (<*) ::Down a ->Down b ->Down aSource #
Applicative ProductSource #	Since: 4.8.0.0
Instance details Defined inData.Semigroup.Internal Methods pure :: a ->Product aSource # (<>) ::Product (a -> b) ->Product a ->Product bSource # liftA2 :: (a -> b -> c) ->Product a ->Product b ->Product cSource # (>) ::Product a ->Product b ->Product bSource # (<*) ::Product a ->Product b ->Product aSource #
Applicative SumSource #	Since: 4.8.0.0
Instance details Defined inData.Semigroup.Internal Methods pure :: a ->Sum aSource # (<>) ::Sum (a -> b) ->Sum a ->Sum bSource # liftA2 :: (a -> b -> c) ->Sum a ->Sum b ->Sum cSource # (>) ::Sum a ->Sum b ->Sum bSource # (<*) ::Sum a ->Sum b ->Sum aSource #
Applicative DualSource #	Since: 4.8.0.0
Instance details Defined inData.Semigroup.Internal Methods pure :: a ->Dual aSource # (<>) ::Dual (a -> b) ->Dual a ->Dual bSource # liftA2 :: (a -> b -> c) ->Dual a ->Dual b ->Dual cSource # (>) ::Dual a ->Dual b ->Dual bSource # (<*) ::Dual a ->Dual b ->Dual aSource #
Applicative LastSource #	Since: 4.8.0.0
Instance details Defined inData.Monoid Methods pure :: a ->Last aSource # (<>) ::Last (a -> b) ->Last a ->Last bSource # liftA2 :: (a -> b -> c) ->Last a ->Last b ->Last cSource # (>) ::Last a ->Last b ->Last bSource # (<*) ::Last a ->Last b ->Last aSource #
Applicative FirstSource #	Since: 4.8.0.0
Instance details Defined inData.Monoid Methods pure :: a ->First aSource # (<>) ::First (a -> b) ->First a ->First bSource # liftA2 :: (a -> b -> c) ->First a ->First b ->First cSource # (>) ::First a ->First b ->First bSource # (<*) ::First a ->First b ->First aSource #
Applicative STMSource #	Since: 4.8.0.0
Instance details Defined inGHC.Conc.Sync Methods pure :: a ->STM aSource # (<>) ::STM (a -> b) ->STM a ->STM bSource # liftA2 :: (a -> b -> c) ->STM a ->STM b ->STM cSource # (>) ::STM a ->STM b ->STM bSource # (<*) ::STM a ->STM b ->STM aSource #
Applicative IdentitySource #	Since: 4.8.0.0
Instance details Defined inData.Functor.Identity Methods pure :: a ->Identity aSource # (<>) ::Identity (a -> b) ->Identity a ->Identity bSource # liftA2 :: (a -> b -> c) ->Identity a ->Identity b ->Identity cSource # (>) ::Identity a ->Identity b ->Identity bSource # (<*) ::Identity a ->Identity b ->Identity aSource #
Applicative ZipListSource #	f '<$>' 'ZipList' xs1 '<>' ... '<>' 'ZipList' xsN = 'ZipList' (zipWithN f xs1 ... xsN) where`zipWithN` refers to the`zipWith` function of the appropriate arity (`zipWith`,`zipWith3`,`zipWith4`, ...). For example: (\a b c -> stimes c [a, b]) <$> ZipList "abcd" <> ZipList "567" <> ZipList [1..] = ZipList (zipWith3 (\a b c -> stimes c [a, b]) "abcd" "567" [1..]) = ZipList {getZipList = ["a5","b6b6","c7c7c7"]} Since: 2.1
Instance details Defined inControl.Applicative Methods pure :: a ->ZipList aSource # (<>) ::ZipList (a -> b) ->ZipList a ->ZipList bSource # liftA2 :: (a -> b -> c) ->ZipList a ->ZipList b ->ZipList cSource # (>) ::ZipList a ->ZipList b ->ZipList bSource # (<*) ::ZipList a ->ZipList b ->ZipList aSource #
Applicative OptionSource #	Since: 4.9.0.0
Instance details Defined inData.Semigroup Methods pure :: a ->Option aSource # (<>) ::Option (a -> b) ->Option a ->Option bSource # liftA2 :: (a -> b -> c) ->Option a ->Option b ->Option cSource # (>) ::Option a ->Option b ->Option bSource # (<*) ::Option a ->Option b ->Option aSource #
Applicative LastSource #	Since: 4.9.0.0
Instance details Defined inData.Semigroup Methods pure :: a ->Last aSource # (<>) ::Last (a -> b) ->Last a ->Last bSource # liftA2 :: (a -> b -> c) ->Last a ->Last b ->Last cSource # (>) ::Last a ->Last b ->Last bSource # (<*) ::Last a ->Last b ->Last aSource #
Applicative FirstSource #	Since: 4.9.0.0
Instance details Defined inData.Semigroup Methods pure :: a ->First aSource # (<>) ::First (a -> b) ->First a ->First bSource # liftA2 :: (a -> b -> c) ->First a ->First b ->First cSource # (>) ::First a ->First b ->First bSource # (<*) ::First a ->First b ->First aSource #
Applicative MaxSource #	Since: 4.9.0.0
Instance details Defined inData.Semigroup Methods pure :: a ->Max aSource # (<>) ::Max (a -> b) ->Max a ->Max bSource # liftA2 :: (a -> b -> c) ->Max a ->Max b ->Max cSource # (>) ::Max a ->Max b ->Max bSource # (<*) ::Max a ->Max b ->Max aSource #
Applicative MinSource #	Since: 4.9.0.0
Instance details Defined inData.Semigroup Methods pure :: a ->Min aSource # (<>) ::Min (a -> b) ->Min a ->Min bSource # liftA2 :: (a -> b -> c) ->Min a ->Min b ->Min cSource # (>) ::Min a ->Min b ->Min bSource # (<*) ::Min a ->Min b ->Min aSource #
Applicative ComplexSource #	Since: 4.9.0.0
Instance details Defined inData.Complex Methods pure :: a ->Complex aSource # (<>) ::Complex (a -> b) ->Complex a ->Complex bSource # liftA2 :: (a -> b -> c) ->Complex a ->Complex b ->Complex cSource # (>) ::Complex a ->Complex b ->Complex bSource # (<*) ::Complex a ->Complex b ->Complex aSource #
Applicative (Either e)Source #	Since: 3.0
Instance details Defined inData.Either Methods pure :: a ->Either e aSource # (<>) ::Either e (a -> b) ->Either e a ->Either e bSource # liftA2 :: (a -> b -> c) ->Either e a ->Either e b ->Either e cSource # (>) ::Either e a ->Either e b ->Either e bSource # (<*) ::Either e a ->Either e b ->Either e aSource #
Applicative (U1 ::Type ->Type)Source #	Since: 4.9.0.0
Instance details Defined inGHC.Generics Methods pure :: a ->U1 aSource # (<>) ::U1 (a -> b) ->U1 a ->U1 bSource # liftA2 :: (a -> b -> c) ->U1 a ->U1 b ->U1 cSource # (>) ::U1 a ->U1 b ->U1 bSource # (<*) ::U1 a ->U1 b ->U1 aSource #
Monoid a =>Applicative ((,) a)Source #	For tuples, the`Monoid` constraint on`a` determines how the first values merge. For example,`String`s concatenate: ("hello ", (+15)) <> ("world!", 2002)("hello world!",2017) Since: 2.1*
Instance details Defined inGHC.Base Methods pure :: a0 -> (a, a0)Source # (<>) :: (a, a0 -> b) -> (a, a0) -> (a, b)Source # liftA2 :: (a0 -> b -> c) -> (a, a0) -> (a, b) -> (a, c)Source # (>) :: (a, a0) -> (a, b) -> (a, b)Source # (<*) :: (a, a0) -> (a, b) -> (a, a0)Source #
Applicative (ST s)Source #	Since: 4.4.0.0
Instance details Defined inGHC.ST Methods pure :: a ->ST s aSource # (<>) ::ST s (a -> b) ->ST s a ->ST s bSource # liftA2 :: (a -> b -> c) ->ST s a ->ST s b ->ST s cSource # (>) ::ST s a ->ST s b ->ST s bSource # (<*) ::ST s a ->ST s b ->ST s aSource #
Applicative (Proxy ::Type ->Type)Source #	Since: 4.7.0.0
Instance details Defined inData.Proxy Methods pure :: a ->Proxy aSource # (<>) ::Proxy (a -> b) ->Proxy a ->Proxy bSource # liftA2 :: (a -> b -> c) ->Proxy a ->Proxy b ->Proxy cSource # (>) ::Proxy a ->Proxy b ->Proxy bSource # (<*) ::Proxy a ->Proxy b ->Proxy aSource #
Arrow a =>Applicative (ArrowMonad a)Source #	Since: 4.6.0.0
Instance details Defined inControl.Arrow Methods pure :: a0 ->ArrowMonad a a0Source # (<>) ::ArrowMonad a (a0 -> b) ->ArrowMonad a a0 ->ArrowMonad a bSource # liftA2 :: (a0 -> b -> c) ->ArrowMonad a a0 ->ArrowMonad a b ->ArrowMonad a cSource # (>) ::ArrowMonad a a0 ->ArrowMonad a b ->ArrowMonad a bSource # (<*) ::ArrowMonad a a0 ->ArrowMonad a b ->ArrowMonad a a0Source #
Monad m =>Applicative (WrappedMonad m)Source #	Since: 2.1
Instance details Defined inControl.Applicative Methods pure :: a ->WrappedMonad m aSource # (<>) ::WrappedMonad m (a -> b) ->WrappedMonad m a ->WrappedMonad m bSource # liftA2 :: (a -> b -> c) ->WrappedMonad m a ->WrappedMonad m b ->WrappedMonad m cSource # (>) ::WrappedMonad m a ->WrappedMonad m b ->WrappedMonad m bSource # (<*) ::WrappedMonad m a ->WrappedMonad m b ->WrappedMonad m aSource #
Applicative (ST s)Source #	Since: 2.1
Instance details Defined inControl.Monad.ST.Lazy.Imp Methods pure :: a ->ST s aSource # (<>) ::ST s (a -> b) ->ST s a ->ST s bSource # liftA2 :: (a -> b -> c) ->ST s a ->ST s b ->ST s cSource # (>) ::ST s a ->ST s b ->ST s bSource # (<*) ::ST s a ->ST s b ->ST s aSource #
Applicative f =>Applicative (Rec1 f)Source #	Since: 4.9.0.0
Instance details Defined inGHC.Generics Methods pure :: a ->Rec1 f aSource # (<>) ::Rec1 f (a -> b) ->Rec1 f a ->Rec1 f bSource # liftA2 :: (a -> b -> c) ->Rec1 f a ->Rec1 f b ->Rec1 f cSource # (>) ::Rec1 f a ->Rec1 f b ->Rec1 f bSource # (<*) ::Rec1 f a ->Rec1 f b ->Rec1 f aSource #
Applicative f =>Applicative (Alt f)Source #	Since: 4.8.0.0
Instance details Defined inData.Semigroup.Internal Methods pure :: a ->Alt f aSource # (<>) ::Alt f (a -> b) ->Alt f a ->Alt f bSource # liftA2 :: (a -> b -> c) ->Alt f a ->Alt f b ->Alt f cSource # (>) ::Alt f a ->Alt f b ->Alt f bSource # (<*) ::Alt f a ->Alt f b ->Alt f aSource #
Applicative f =>Applicative (Ap f)Source #	Since: 4.12.0.0
Instance details Defined inData.Monoid Methods pure :: a ->Ap f aSource # (<>) ::Ap f (a -> b) ->Ap f a ->Ap f bSource # liftA2 :: (a -> b -> c) ->Ap f a ->Ap f b ->Ap f cSource # (>) ::Ap f a ->Ap f b ->Ap f bSource # (<*) ::Ap f a ->Ap f b ->Ap f aSource #
Monoid m =>Applicative (Const m ::Type ->Type)Source #	Since: 2.0.1
Instance details Defined inData.Functor.Const Methods pure :: a ->Const m aSource # (<>) ::Const m (a -> b) ->Const m a ->Const m bSource # liftA2 :: (a -> b -> c) ->Const m a ->Const m b ->Const m cSource # (>) ::Const m a ->Const m b ->Const m bSource # (<*) ::Const m a ->Const m b ->Const m aSource #
Arrow a =>Applicative (WrappedArrow a b)Source #	Since: 2.1
Instance details Defined inControl.Applicative Methods pure :: a0 ->WrappedArrow a b a0Source # (<>) ::WrappedArrow a b (a0 -> b0) ->WrappedArrow a b a0 ->WrappedArrow a b b0Source # liftA2 :: (a0 -> b0 -> c) ->WrappedArrow a b a0 ->WrappedArrow a b b0 ->WrappedArrow a b cSource # (>) ::WrappedArrow a b a0 ->WrappedArrow a b b0 ->WrappedArrow a b b0Source # (<*) ::WrappedArrow a b a0 ->WrappedArrow a b b0 ->WrappedArrow a b a0Source #
Applicative ((->) a ::Type ->Type)Source #	Since: 2.1
Instance details Defined inGHC.Base Methods pure :: a0 -> a -> a0Source # (<>) :: (a -> (a0 -> b)) -> (a -> a0) -> a -> bSource # liftA2 :: (a0 -> b -> c) -> (a -> a0) -> (a -> b) -> a -> cSource # (>) :: (a -> a0) -> (a -> b) -> a -> bSource # (<*) :: (a -> a0) -> (a -> b) -> a -> a0Source #
Monoid c =>Applicative (K1 i c ::Type ->Type)Source #	Since: 4.12.0.0
Instance details Defined inGHC.Generics Methods pure :: a ->K1 i c aSource # (<>) ::K1 i c (a -> b) ->K1 i c a ->K1 i c bSource # liftA2 :: (a -> b -> c0) ->K1 i c a ->K1 i c b ->K1 i c c0Source # (>) ::K1 i c a ->K1 i c b ->K1 i c bSource # (<*) ::K1 i c a ->K1 i c b ->K1 i c aSource #
(Applicative f,Applicative g) =>Applicative (f:*: g)Source #	Since: 4.9.0.0
Instance details Defined inGHC.Generics Methods pure :: a -> (f:: g) aSource # (<>) :: (f:: g) (a -> b) -> (f:: g) a -> (f:: g) bSource # liftA2 :: (a -> b -> c) -> (f:: g) a -> (f:: g) b -> (f:: g) cSource # (>) :: (f:: g) a -> (f:: g) b -> (f:: g) bSource # (<) :: (f:: g) a -> (f:: g) b -> (f:: g) aSource #
(Applicative f,Applicative g) =>Applicative (Product f g)Source #	Since: 4.9.0.0
Instance details Defined inData.Functor.Product Methods pure :: a ->Product f g aSource # (<>) ::Product f g (a -> b) ->Product f g a ->Product f g bSource # liftA2 :: (a -> b -> c) ->Product f g a ->Product f g b ->Product f g cSource # (>) ::Product f g a ->Product f g b ->Product f g bSource # (<*) ::Product f g a ->Product f g b ->Product f g aSource #
Applicative f =>Applicative (M1 i c f)Source #	Since: 4.9.0.0
Instance details Defined inGHC.Generics Methods pure :: a ->M1 i c f aSource # (<>) ::M1 i c f (a -> b) ->M1 i c f a ->M1 i c f bSource # liftA2 :: (a -> b -> c0) ->M1 i c f a ->M1 i c f b ->M1 i c f c0Source # (>) ::M1 i c f a ->M1 i c f b ->M1 i c f bSource # (<*) ::M1 i c f a ->M1 i c f b ->M1 i c f aSource #
(Applicative f,Applicative g) =>Applicative (f:.: g)Source #	Since: 4.9.0.0
Instance details Defined inGHC.Generics Methods pure :: a -> (f:.: g) aSource # (<>) :: (f:.: g) (a -> b) -> (f:.: g) a -> (f:.: g) bSource # liftA2 :: (a -> b -> c) -> (f:.: g) a -> (f:.: g) b -> (f:.: g) cSource # (>) :: (f:.: g) a -> (f:.: g) b -> (f:.: g) bSource # (<*) :: (f:.: g) a -> (f:.: g) b -> (f:.: g) aSource #
(Applicative f,Applicative g) =>Applicative (Compose f g)Source #	Since: 4.9.0.0
Instance details Defined inData.Functor.Compose Methods pure :: a ->Compose f g aSource # (<>) ::Compose f g (a -> b) ->Compose f g a ->Compose f g bSource # liftA2 :: (a -> b -> c) ->Compose f g a ->Compose f g b ->Compose f g cSource # (>) ::Compose f g a ->Compose f g b ->Compose f g bSource # (<*) ::Compose f g a ->Compose f g b ->Compose f g aSource #

Alternatives

classApplicative f =>Alternative fwhereSource #

A monoid on applicative functors.

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

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

Minimal complete definition

empty,(<|>)

Methods

empty :: f aSource #

The identity of<|>

(<|>) :: f a -> f a -> f ainfixl 3Source #

An associative binary operation

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

One or more.

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

Zero or more.

Instances

Alternative []Source #	Since: 2.1
Instance details Defined inGHC.Base Methods empty :: [a]Source # (<\|>) :: [a] -> [a] -> [a]Source # some :: [a] -> [[a]]Source # many :: [a] -> [[a]]Source #
Alternative MaybeSource #	Since: 2.1
Instance details Defined inGHC.Base Methods empty ::Maybe aSource # (<\|>) ::Maybe a ->Maybe a ->Maybe aSource # some ::Maybe a ->Maybe [a]Source # many ::Maybe a ->Maybe [a]Source #
Alternative IOSource #	Since: 4.9.0.0
Instance details Defined inGHC.Base Methods empty ::IO aSource # (<\|>) ::IO a ->IO a ->IO aSource # some ::IO a ->IO [a]Source # many ::IO a ->IO [a]Source #
Alternative ReadPSource #	Since: 4.6.0.0
Instance details Defined inText.ParserCombinators.ReadP Methods empty ::ReadP aSource # (<\|>) ::ReadP a ->ReadP a ->ReadP aSource # some ::ReadP a ->ReadP [a]Source # many ::ReadP a ->ReadP [a]Source #
Alternative ReadPrecSource #	Since: 4.6.0.0
Instance details Defined inText.ParserCombinators.ReadPrec Methods empty ::ReadPrec aSource # (<\|>) ::ReadPrec a ->ReadPrec a ->ReadPrec aSource # some ::ReadPrec a ->ReadPrec [a]Source # many ::ReadPrec a ->ReadPrec [a]Source #
Alternative STMSource #	Since: 4.8.0.0
Instance details Defined inGHC.Conc.Sync Methods empty ::STM aSource # (<\|>) ::STM a ->STM a ->STM aSource # some ::STM a ->STM [a]Source # many ::STM a ->STM [a]Source #
Alternative ZipListSource #	Since: 4.11.0.0
Instance details Defined inControl.Applicative Methods empty ::ZipList aSource # (<\|>) ::ZipList a ->ZipList a ->ZipList aSource # some ::ZipList a ->ZipList [a]Source # many ::ZipList a ->ZipList [a]Source #
Alternative OptionSource #	Since: 4.9.0.0
Instance details Defined inData.Semigroup Methods empty ::Option aSource # (<\|>) ::Option a ->Option a ->Option aSource # some ::Option a ->Option [a]Source # many ::Option a ->Option [a]Source #
Alternative (U1 ::Type ->Type)Source #	Since: 4.9.0.0
Instance details Defined inGHC.Generics Methods empty ::U1 aSource # (<\|>) ::U1 a ->U1 a ->U1 aSource # some ::U1 a ->U1 [a]Source # many ::U1 a ->U1 [a]Source #
Alternative (Proxy ::Type ->Type)Source #	Since: 4.9.0.0
Instance details Defined inData.Proxy Methods empty ::Proxy aSource # (<\|>) ::Proxy a ->Proxy a ->Proxy aSource # some ::Proxy a ->Proxy [a]Source # many ::Proxy a ->Proxy [a]Source #
ArrowPlus a =>Alternative (ArrowMonad a)Source #	Since: 4.6.0.0
Instance details Defined inControl.Arrow Methods empty ::ArrowMonad a a0Source # (<\|>) ::ArrowMonad a a0 ->ArrowMonad a a0 ->ArrowMonad a a0Source # some ::ArrowMonad a a0 ->ArrowMonad a [a0]Source # many ::ArrowMonad a a0 ->ArrowMonad a [a0]Source #
MonadPlus m =>Alternative (WrappedMonad m)Source #	Since: 2.1
Instance details Defined inControl.Applicative Methods empty ::WrappedMonad m aSource # (<\|>) ::WrappedMonad m a ->WrappedMonad m a ->WrappedMonad m aSource # some ::WrappedMonad m a ->WrappedMonad m [a]Source # many ::WrappedMonad m a ->WrappedMonad m [a]Source #
Alternative f =>Alternative (Rec1 f)Source #	Since: 4.9.0.0
Instance details Defined inGHC.Generics Methods empty ::Rec1 f aSource # (<\|>) ::Rec1 f a ->Rec1 f a ->Rec1 f aSource # some ::Rec1 f a ->Rec1 f [a]Source # many ::Rec1 f a ->Rec1 f [a]Source #
Alternative f =>Alternative (Alt f)Source #	Since: 4.8.0.0
Instance details Defined inData.Semigroup.Internal Methods empty ::Alt f aSource # (<\|>) ::Alt f a ->Alt f a ->Alt f aSource # some ::Alt f a ->Alt f [a]Source # many ::Alt f a ->Alt f [a]Source #
Alternative f =>Alternative (Ap f)Source #	Since: 4.12.0.0
Instance details Defined inData.Monoid Methods empty ::Ap f aSource # (<\|>) ::Ap f a ->Ap f a ->Ap f aSource # some ::Ap f a ->Ap f [a]Source # many ::Ap f a ->Ap f [a]Source #
(ArrowZero a,ArrowPlus a) =>Alternative (WrappedArrow a b)Source #	Since: 2.1
Instance details Defined inControl.Applicative Methods empty ::WrappedArrow a b a0Source # (<\|>) ::WrappedArrow a b a0 ->WrappedArrow a b a0 ->WrappedArrow a b a0Source # some ::WrappedArrow a b a0 ->WrappedArrow a b [a0]Source # many ::WrappedArrow a b a0 ->WrappedArrow a b [a0]Source #
(Alternative f,Alternative g) =>Alternative (f:*: g)Source #	Since: 4.9.0.0
Instance details Defined inGHC.Generics Methods empty :: (f:: g) aSource # (<\|>) :: (f:: g) a -> (f:: g) a -> (f:: g) aSource # some :: (f:: g) a -> (f:: g) [a]Source # many :: (f:: g) a -> (f:: g) [a]Source #
(Alternative f,Alternative g) =>Alternative (Product f g)Source #	Since: 4.9.0.0
Instance details Defined inData.Functor.Product Methods empty ::Product f g aSource # (<\|>) ::Product f g a ->Product f g a ->Product f g aSource # some ::Product f g a ->Product f g [a]Source # many ::Product f g a ->Product f g [a]Source #
Alternative f =>Alternative (M1 i c f)Source #	Since: 4.9.0.0
Instance details Defined inGHC.Generics Methods empty ::M1 i c f aSource # (<\|>) ::M1 i c f a ->M1 i c f a ->M1 i c f aSource # some ::M1 i c f a ->M1 i c f [a]Source # many ::M1 i c f a ->M1 i c f [a]Source #
(Alternative f,Applicative g) =>Alternative (f:.: g)Source #	Since: 4.9.0.0
Instance details Defined inGHC.Generics Methods empty :: (f:.: g) aSource # (<\|>) :: (f:.: g) a -> (f:.: g) a -> (f:.: g) aSource # some :: (f:.: g) a -> (f:.: g) [a]Source # many :: (f:.: g) a -> (f:.: g) [a]Source #
(Alternative f,Applicative g) =>Alternative (Compose f g)Source #	Since: 4.9.0.0
Instance details Defined inData.Functor.Compose Methods empty ::Compose f g aSource # (<\|>) ::Compose f g a ->Compose f g a ->Compose f g aSource # some ::Compose f g a ->Compose f g [a]Source # many ::Compose f g a ->Compose f g [a]Source #

Instances

newtypeConst a bSource #

TheConst functor.

Constructors

Const
Fields getConst :: a

Instances

Generic1 (Const a :: k ->Type)Source #
Instance details Defined inData.Functor.Const Associated Types typeRep1 (Const a) :: k ->Type Source # Methods from1 ::Const a a0 ->Rep1 (Const a) a0Source # to1 ::Rep1 (Const a) a0 ->Const a a0Source #
Show2 (Const ::Type ->Type ->Type)Source #	Since: 4.9.0.0
Instance details Defined inData.Functor.Classes Methods liftShowsPrec2 :: (Int -> a ->ShowS) -> ([a] ->ShowS) -> (Int -> b ->ShowS) -> ([b] ->ShowS) ->Int ->Const a b ->ShowS Source # liftShowList2 :: (Int -> a ->ShowS) -> ([a] ->ShowS) -> (Int -> b ->ShowS) -> ([b] ->ShowS) -> [Const a b] ->ShowS Source #
Read2 (Const ::Type ->Type ->Type)Source #	Since: 4.9.0.0
Instance details Defined inData.Functor.Classes Methods liftReadsPrec2 :: (Int ->ReadS a) ->ReadS [a] -> (Int ->ReadS b) ->ReadS [b] ->Int ->ReadS (Const a b)Source # liftReadList2 :: (Int ->ReadS a) ->ReadS [a] -> (Int ->ReadS b) ->ReadS [b] ->ReadS [Const a b]Source # liftReadPrec2 ::ReadPrec a ->ReadPrec [a] ->ReadPrec b ->ReadPrec [b] ->ReadPrec (Const a b)Source # liftReadListPrec2 ::ReadPrec a ->ReadPrec [a] ->ReadPrec b ->ReadPrec [b] ->ReadPrec [Const a b]Source #
Ord2 (Const ::Type ->Type ->Type)Source #	Since: 4.9.0.0
Instance details Defined inData.Functor.Classes Methods liftCompare2 :: (a -> b ->Ordering) -> (c -> d ->Ordering) ->Const a c ->Const b d ->Ordering Source #
Eq2 (Const ::Type ->Type ->Type)Source #	Since: 4.9.0.0
Instance details Defined inData.Functor.Classes Methods liftEq2 :: (a -> b ->Bool) -> (c -> d ->Bool) ->Const a c ->Const b d ->Bool Source #
Bifunctor (Const ::Type ->Type ->Type)Source #	Since: 4.8.0.0
Instance details Defined inData.Bifunctor Methods bimap :: (a -> b) -> (c -> d) ->Const a c ->Const b dSource # first :: (a -> b) ->Const a c ->Const b cSource # second :: (b -> c) ->Const a b ->Const a cSource #
Bifoldable (Const ::Type ->Type ->Type)Source #	Since: 4.10.0.0
Instance details Defined inData.Bifoldable Methods bifold ::Monoid m =>Const m m -> mSource # bifoldMap ::Monoid m => (a -> m) -> (b -> m) ->Const a b -> mSource # bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c ->Const a b -> cSource # bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c ->Const a b -> cSource #
Bitraversable (Const ::Type ->Type ->Type)Source #	Since: 4.10.0.0
Instance details Defined inData.Bitraversable Methods bitraverse ::Applicative f => (a -> f c) -> (b -> f d) ->Const a b -> f (Const c d)Source #
Functor (Const m ::Type ->Type)Source #	Since: 2.1
Instance details Defined inData.Functor.Const Methods fmap :: (a -> b) ->Const m a ->Const m bSource # (<$) :: a ->Const m b ->Const m aSource #
Monoid m =>Applicative (Const m ::Type ->Type)Source #	Since: 2.0.1
Instance details Defined inData.Functor.Const Methods pure :: a ->Const m aSource # (<>) ::Const m (a -> b) ->Const m a ->Const m bSource # liftA2 :: (a -> b -> c) ->Const m a ->Const m b ->Const m cSource # (>) ::Const m a ->Const m b ->Const m bSource # (<*) ::Const m a ->Const m b ->Const m aSource #
Foldable (Const m ::Type ->Type)Source #	Since: 4.7.0.0
Instance details Defined inData.Functor.Const Methods fold ::Monoid m0 =>Const m m0 -> m0Source # foldMap ::Monoid m0 => (a -> m0) ->Const m a -> m0Source # foldr :: (a -> b -> b) -> b ->Const m a -> bSource # foldr' :: (a -> b -> b) -> b ->Const m a -> bSource # foldl :: (b -> a -> b) -> b ->Const m a -> bSource # foldl' :: (b -> a -> b) -> b ->Const m a -> bSource # foldr1 :: (a -> a -> a) ->Const m a -> aSource # foldl1 :: (a -> a -> a) ->Const m a -> aSource # toList ::Const m a -> [a]Source # null ::Const m a ->Bool Source # length ::Const m a ->Int Source # elem ::Eq a => a ->Const m a ->Bool Source # maximum ::Ord a =>Const m a -> aSource # minimum ::Ord a =>Const m a -> aSource # sum ::Num a =>Const m a -> aSource # product ::Num a =>Const m a -> aSource #
Traversable (Const m ::Type ->Type)Source #	Since: 4.7.0.0
Instance details Defined inData.Traversable Methods traverse ::Applicative f => (a -> f b) ->Const m a -> f (Const m b)Source # sequenceA ::Applicative f =>Const m (f a) -> f (Const m a)Source # mapM ::Monad m0 => (a -> m0 b) ->Const m a -> m0 (Const m b)Source # sequence ::Monad m0 =>Const m (m0 a) -> m0 (Const m a)Source #
Show a =>Show1 (Const a ::Type ->Type)Source #	Since: 4.9.0.0
Instance details Defined inData.Functor.Classes Methods liftShowsPrec :: (Int -> a0 ->ShowS) -> ([a0] ->ShowS) ->Int ->Const a a0 ->ShowS Source # liftShowList :: (Int -> a0 ->ShowS) -> ([a0] ->ShowS) -> [Const a a0] ->ShowS Source #
Read a =>Read1 (Const a ::Type ->Type)Source #	Since: 4.9.0.0
Instance details Defined inData.Functor.Classes Methods liftReadsPrec :: (Int ->ReadS a0) ->ReadS [a0] ->Int ->ReadS (Const a a0)Source # liftReadList :: (Int ->ReadS a0) ->ReadS [a0] ->ReadS [Const a a0]Source # liftReadPrec ::ReadPrec a0 ->ReadPrec [a0] ->ReadPrec (Const a a0)Source # liftReadListPrec ::ReadPrec a0 ->ReadPrec [a0] ->ReadPrec [Const a a0]Source #
Ord a =>Ord1 (Const a ::Type ->Type)Source #	Since: 4.9.0.0
Instance details Defined inData.Functor.Classes Methods liftCompare :: (a0 -> b ->Ordering) ->Const a a0 ->Const a b ->Ordering Source #
Eq a =>Eq1 (Const a ::Type ->Type)Source #	Since: 4.9.0.0
Instance details Defined inData.Functor.Classes Methods liftEq :: (a0 -> b ->Bool) ->Const a a0 ->Const a b ->Bool Source #
Contravariant (Const a ::Type ->Type)Source #
Instance details Defined inData.Functor.Contravariant Methods contramap :: (a0 -> b) ->Const a b ->Const a a0Source # (>$) :: b ->Const a b ->Const a a0Source #
Bounded a =>Bounded (Const a b)Source #	Since: 4.9.0.0
Instance details Defined inData.Functor.Const Methods minBound ::Const a bSource # maxBound ::Const a bSource #
Enum a =>Enum (Const a b)Source #	Since: 4.9.0.0
Instance details Defined inData.Functor.Const Methods succ ::Const a b ->Const a bSource # pred ::Const a b ->Const a bSource # toEnum ::Int ->Const a bSource # fromEnum ::Const a b ->Int Source # enumFrom ::Const a b -> [Const a b]Source # enumFromThen ::Const a b ->Const a b -> [Const a b]Source # enumFromTo ::Const a b ->Const a b -> [Const a b]Source # enumFromThenTo ::Const a b ->Const a b ->Const a b -> [Const a b]Source #
Eq a =>Eq (Const a b)Source #	Since: 4.9.0.0
Instance details Defined inData.Functor.Const Methods (==) ::Const a b ->Const a b ->Bool # (/=) ::Const a b ->Const a b ->Bool #
Floating a =>Floating (Const a b)Source #	Since: 4.9.0.0
Instance details Defined inData.Functor.Const Methods pi ::Const a bSource # exp ::Const a b ->Const a bSource # log ::Const a b ->Const a bSource # sqrt ::Const a b ->Const a bSource # (**) ::Const a b ->Const a b ->Const a bSource # logBase ::Const a b ->Const a b ->Const a bSource # sin ::Const a b ->Const a bSource # cos ::Const a b ->Const a bSource # tan ::Const a b ->Const a bSource # asin ::Const a b ->Const a bSource # acos ::Const a b ->Const a bSource # atan ::Const a b ->Const a bSource # sinh ::Const a b ->Const a bSource # cosh ::Const a b ->Const a bSource # tanh ::Const a b ->Const a bSource # asinh ::Const a b ->Const a bSource # acosh ::Const a b ->Const a bSource # atanh ::Const a b ->Const a bSource # log1p ::Const a b ->Const a bSource # expm1 ::Const a b ->Const a bSource # log1pexp ::Const a b ->Const a bSource # log1mexp ::Const a b ->Const a bSource #
Fractional a =>Fractional (Const a b)Source #	Since: 4.9.0.0
Instance details Defined inData.Functor.Const Methods (/) ::Const a b ->Const a b ->Const a bSource # recip ::Const a b ->Const a bSource # fromRational ::Rational ->Const a bSource #
Integral a =>Integral (Const a b)Source #	Since: 4.9.0.0
Instance details Defined inData.Functor.Const Methods quot ::Const a b ->Const a b ->Const a bSource # rem ::Const a b ->Const a b ->Const a bSource # div ::Const a b ->Const a b ->Const a bSource # mod ::Const a b ->Const a b ->Const a bSource # quotRem ::Const a b ->Const a b -> (Const a b,Const a b)Source # divMod ::Const a b ->Const a b -> (Const a b,Const a b)Source # toInteger ::Const a b ->Integer Source #
(Typeable k,Data a,Typeable b) =>Data (Const a b)Source #	Since: 4.10.0.0
Instance details Defined inData.Data Methods gfoldl :: (forall d b0.Data d => c (d -> b0) -> d -> c b0) -> (forall g. g -> c g) ->Const a b -> c (Const a b)Source # gunfold :: (forall b0 r.Data b0 => c (b0 -> r) -> c r) -> (forall r. r -> c r) ->Constr -> c (Const a b)Source # toConstr ::Const a b ->Constr Source # dataTypeOf ::Const a b ->DataType Source # dataCast1 ::Typeable t => (forall d.Data d => c (t d)) ->Maybe (c (Const a b))Source # dataCast2 ::Typeable t => (forall d e. (Data d,Data e) => c (t d e)) ->Maybe (c (Const a b))Source # gmapT :: (forall b0.Data b0 => b0 -> b0) ->Const a b ->Const a bSource # gmapQl :: (r -> r' -> r) -> r -> (forall d.Data d => d -> r') ->Const a b -> rSource # gmapQr :: (r' -> r -> r) -> r -> (forall d.Data d => d -> r') ->Const a b -> rSource # gmapQ :: (forall d.Data d => d -> u) ->Const a b -> [u]Source # gmapQi ::Int -> (forall d.Data d => d -> u) ->Const a b -> uSource # gmapM ::Monad m => (forall d.Data d => d -> m d) ->Const a b -> m (Const a b)Source # gmapMp ::MonadPlus m => (forall d.Data d => d -> m d) ->Const a b -> m (Const a b)Source # gmapMo ::MonadPlus m => (forall d.Data d => d -> m d) ->Const a b -> m (Const a b)Source #
Num a =>Num (Const a b)Source #	Since: 4.9.0.0
Instance details Defined inData.Functor.Const Methods (+) ::Const a b ->Const a b ->Const a bSource # (-) ::Const a b ->Const a b ->Const a bSource # (*) ::Const a b ->Const a b ->Const a bSource # negate ::Const a b ->Const a bSource # abs ::Const a b ->Const a bSource # signum ::Const a b ->Const a bSource # fromInteger ::Integer ->Const a bSource #
Ord a =>Ord (Const a b)Source #	Since: 4.9.0.0
Instance details Defined inData.Functor.Const Methods compare ::Const a b ->Const a b ->Ordering # (<) ::Const a b ->Const a b ->Bool # (<=) ::Const a b ->Const a b ->Bool # (>) ::Const a b ->Const a b ->Bool # (>=) ::Const a b ->Const a b ->Bool # max ::Const a b ->Const a b ->Const a b# min ::Const a b ->Const a b ->Const a b#
Read a =>Read (Const a b)Source #	This instance would be equivalent to the derived instances of the`Const` newtype if the`runConst` field were removed Since: 4.8.0.0
Instance details Defined inData.Functor.Const Methods readsPrec ::Int ->ReadS (Const a b)Source # readList ::ReadS [Const a b]Source # readPrec ::ReadPrec (Const a b)Source # readListPrec ::ReadPrec [Const a b]Source #
Real a =>Real (Const a b)Source #	Since: 4.9.0.0
Instance details Defined inData.Functor.Const Methods toRational ::Const a b ->Rational Source #
RealFloat a =>RealFloat (Const a b)Source #	Since: 4.9.0.0
Instance details Defined inData.Functor.Const Methods floatRadix ::Const a b ->Integer Source # floatDigits ::Const a b ->Int Source # floatRange ::Const a b -> (Int,Int)Source # decodeFloat ::Const a b -> (Integer,Int)Source # encodeFloat ::Integer ->Int ->Const a bSource # exponent ::Const a b ->Int Source # significand ::Const a b ->Const a bSource # scaleFloat ::Int ->Const a b ->Const a bSource # isNaN ::Const a b ->Bool Source # isInfinite ::Const a b ->Bool Source # isDenormalized ::Const a b ->Bool Source # isNegativeZero ::Const a b ->Bool Source # isIEEE ::Const a b ->Bool Source # atan2 ::Const a b ->Const a b ->Const a bSource #
RealFrac a =>RealFrac (Const a b)Source #	Since: 4.9.0.0
Instance details Defined inData.Functor.Const Methods properFraction ::Integral b0 =>Const a b -> (b0,Const a b)Source # truncate ::Integral b0 =>Const a b -> b0Source # round ::Integral b0 =>Const a b -> b0Source # ceiling ::Integral b0 =>Const a b -> b0Source # floor ::Integral b0 =>Const a b -> b0Source #
Show a =>Show (Const a b)Source #	This instance would be equivalent to the derived instances of the`Const` newtype if the`runConst` field were removed Since: 4.8.0.0
Instance details Defined inData.Functor.Const Methods showsPrec ::Int ->Const a b ->ShowS Source # show ::Const a b ->String Source # showList :: [Const a b] ->ShowS Source #
Ix a =>Ix (Const a b)Source #	Since: 4.9.0.0
Instance details Defined inData.Functor.Const Methods range :: (Const a b,Const a b) -> [Const a b]Source # index :: (Const a b,Const a b) ->Const a b ->Int Source # unsafeIndex :: (Const a b,Const a b) ->Const a b ->Int inRange :: (Const a b,Const a b) ->Const a b ->Bool Source # rangeSize :: (Const a b,Const a b) ->Int Source # unsafeRangeSize :: (Const a b,Const a b) ->Int
IsString a =>IsString (Const a b)Source #	Since: 4.9.0.0
Instance details Defined inData.String Methods fromString ::String ->Const a bSource #
Generic (Const a b)Source #
Instance details Defined inData.Functor.Const Associated Types typeRep (Const a b) ::Type ->Type Source # Methods from ::Const a b ->Rep (Const a b) xSource # to ::Rep (Const a b) x ->Const a bSource #
Semigroup a =>Semigroup (Const a b)Source #	Since: 4.9.0.0
Instance details Defined inData.Functor.Const Methods (<>) ::Const a b ->Const a b ->Const a bSource # sconcat ::NonEmpty (Const a b) ->Const a bSource # stimes ::Integral b0 => b0 ->Const a b ->Const a bSource #
Monoid a =>Monoid (Const a b)Source #	Since: 4.9.0.0
Instance details Defined inData.Functor.Const Methods mempty ::Const a bSource # mappend ::Const a b ->Const a b ->Const a bSource # mconcat :: [Const a b] ->Const a bSource #
FiniteBits a =>FiniteBits (Const a b)Source #	Since: 4.9.0.0
Instance details Defined inData.Functor.Const Methods finiteBitSize ::Const a b ->Int Source # countLeadingZeros ::Const a b ->Int Source # countTrailingZeros ::Const a b ->Int Source #
Bits a =>Bits (Const a b)Source #	Since: 4.9.0.0
Instance details Defined inData.Functor.Const Methods (.&.) ::Const a b ->Const a b ->Const a bSource # (.\|.) ::Const a b ->Const a b ->Const a bSource # xor ::Const a b ->Const a b ->Const a bSource # complement ::Const a b ->Const a bSource # shift ::Const a b ->Int ->Const a bSource # rotate ::Const a b ->Int ->Const a bSource # zeroBits ::Const a bSource # bit ::Int ->Const a bSource # setBit ::Const a b ->Int ->Const a bSource # clearBit ::Const a b ->Int ->Const a bSource # complementBit ::Const a b ->Int ->Const a bSource # testBit ::Const a b ->Int ->Bool Source # bitSizeMaybe ::Const a b ->Maybe Int Source # bitSize ::Const a b ->Int Source # isSigned ::Const a b ->Bool Source # shiftL ::Const a b ->Int ->Const a bSource # unsafeShiftL ::Const a b ->Int ->Const a bSource # shiftR ::Const a b ->Int ->Const a bSource # unsafeShiftR ::Const a b ->Int ->Const a bSource # rotateL ::Const a b ->Int ->Const a bSource # rotateR ::Const a b ->Int ->Const a bSource # popCount ::Const a b ->Int Source #
Storable a =>Storable (Const a b)Source #	Since: 4.9.0.0
Instance details Defined inData.Functor.Const Methods sizeOf ::Const a b ->Int Source # alignment ::Const a b ->Int Source # peekElemOff ::Ptr (Const a b) ->Int ->IO (Const a b)Source # pokeElemOff ::Ptr (Const a b) ->Int ->Const a b ->IO ()Source # peekByteOff ::Ptr b0 ->Int ->IO (Const a b)Source # pokeByteOff ::Ptr b0 ->Int ->Const a b ->IO ()Source # peek ::Ptr (Const a b) ->IO (Const a b)Source # poke ::Ptr (Const a b) ->Const a b ->IO ()Source #
typeRep1 (Const a :: k ->Type)Source #	Since: 4.9.0.0
Instance details Defined inData.Functor.Const typeRep1 (Const a :: k ->Type) =D1 (MetaData "Const" "Data.Functor.Const" "base"True) (C1 (MetaCons "Const"PrefixI True) (S1 (MetaSel (Just "getConst")NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))
typeRep (Const a b)Source #	Since: 4.9.0.0
Instance details Defined inData.Functor.Const typeRep (Const a b) =D1 (MetaData "Const" "Data.Functor.Const" "base"True) (C1 (MetaCons "Const"PrefixI True) (S1 (MetaSel (Just "getConst")NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))

newtypeWrappedMonad m aSource #

Constructors

WrapMonad
Fields unwrapMonad :: m a

Instances

Monad m =>Monad (WrappedMonad m)Source #	Since: 4.7.0.0
Instance details Defined inControl.Applicative Methods (>>=) ::WrappedMonad m a -> (a ->WrappedMonad m b) ->WrappedMonad m bSource # (>>) ::WrappedMonad m a ->WrappedMonad m b ->WrappedMonad m bSource # return :: a ->WrappedMonad m aSource # fail ::String ->WrappedMonad m aSource #
Monad m =>Functor (WrappedMonad m)Source #	Since: 2.1
Instance details Defined inControl.Applicative Methods fmap :: (a -> b) ->WrappedMonad m a ->WrappedMonad m bSource # (<$) :: a ->WrappedMonad m b ->WrappedMonad m aSource #
Monad m =>Applicative (WrappedMonad m)Source #	Since: 2.1
Instance details Defined inControl.Applicative Methods pure :: a ->WrappedMonad m aSource # (<>) ::WrappedMonad m (a -> b) ->WrappedMonad m a ->WrappedMonad m bSource # liftA2 :: (a -> b -> c) ->WrappedMonad m a ->WrappedMonad m b ->WrappedMonad m cSource # (>) ::WrappedMonad m a ->WrappedMonad m b ->WrappedMonad m bSource # (<*) ::WrappedMonad m a ->WrappedMonad m b ->WrappedMonad m aSource #
MonadPlus m =>Alternative (WrappedMonad m)Source #	Since: 2.1
Instance details Defined inControl.Applicative Methods empty ::WrappedMonad m aSource # (<\|>) ::WrappedMonad m a ->WrappedMonad m a ->WrappedMonad m aSource # some ::WrappedMonad m a ->WrappedMonad m [a]Source # many ::WrappedMonad m a ->WrappedMonad m [a]Source #
Generic1 (WrappedMonad m ::Type ->Type)Source #
Instance details Defined inControl.Applicative Associated Types typeRep1 (WrappedMonad m) :: k ->Type Source # Methods from1 ::WrappedMonad m a ->Rep1 (WrappedMonad m) aSource # to1 ::Rep1 (WrappedMonad m) a ->WrappedMonad m aSource #
Generic (WrappedMonad m a)Source #
Instance details Defined inControl.Applicative Associated Types typeRep (WrappedMonad m a) ::Type ->Type Source # Methods from ::WrappedMonad m a ->Rep (WrappedMonad m a) xSource # to ::Rep (WrappedMonad m a) x ->WrappedMonad m aSource #
typeRep1 (WrappedMonad m ::Type ->Type)Source #	Since: 4.7.0.0
Instance details Defined inControl.Applicative typeRep1 (WrappedMonad m ::Type ->Type) =D1 (MetaData "WrappedMonad" "Control.Applicative" "base"True) (C1 (MetaCons "WrapMonad"PrefixI True) (S1 (MetaSel (Just "unwrapMonad")NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec1 m)))
typeRep (WrappedMonad m a)Source #	Since: 4.7.0.0
Instance details Defined inControl.Applicative typeRep (WrappedMonad m a) =D1 (MetaData "WrappedMonad" "Control.Applicative" "base"True) (C1 (MetaCons "WrapMonad"PrefixI True) (S1 (MetaSel (Just "unwrapMonad")NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (m a))))

newtypeWrappedArrow a b cSource #

Constructors

WrapArrow
Fields unwrapArrow :: a b c

Instances

Generic1 (WrappedArrow a b ::Type ->Type)Source #
Instance details Defined inControl.Applicative Associated Types typeRep1 (WrappedArrow a b) :: k ->Type Source # Methods from1 ::WrappedArrow a b a0 ->Rep1 (WrappedArrow a b) a0Source # to1 ::Rep1 (WrappedArrow a b) a0 ->WrappedArrow a b a0Source #
Arrow a =>Functor (WrappedArrow a b)Source #	Since: 2.1
Instance details Defined inControl.Applicative Methods fmap :: (a0 -> b0) ->WrappedArrow a b a0 ->WrappedArrow a b b0Source # (<$) :: a0 ->WrappedArrow a b b0 ->WrappedArrow a b a0Source #
Arrow a =>Applicative (WrappedArrow a b)Source #	Since: 2.1
Instance details Defined inControl.Applicative Methods pure :: a0 ->WrappedArrow a b a0Source # (<>) ::WrappedArrow a b (a0 -> b0) ->WrappedArrow a b a0 ->WrappedArrow a b b0Source # liftA2 :: (a0 -> b0 -> c) ->WrappedArrow a b a0 ->WrappedArrow a b b0 ->WrappedArrow a b cSource # (>) ::WrappedArrow a b a0 ->WrappedArrow a b b0 ->WrappedArrow a b b0Source # (<*) ::WrappedArrow a b a0 ->WrappedArrow a b b0 ->WrappedArrow a b a0Source #
(ArrowZero a,ArrowPlus a) =>Alternative (WrappedArrow a b)Source #	Since: 2.1
Instance details Defined inControl.Applicative Methods empty ::WrappedArrow a b a0Source # (<\|>) ::WrappedArrow a b a0 ->WrappedArrow a b a0 ->WrappedArrow a b a0Source # some ::WrappedArrow a b a0 ->WrappedArrow a b [a0]Source # many ::WrappedArrow a b a0 ->WrappedArrow a b [a0]Source #
Generic (WrappedArrow a b c)Source #
Instance details Defined inControl.Applicative Associated Types typeRep (WrappedArrow a b c) ::Type ->Type Source # Methods from ::WrappedArrow a b c ->Rep (WrappedArrow a b c) xSource # to ::Rep (WrappedArrow a b c) x ->WrappedArrow a b cSource #
typeRep1 (WrappedArrow a b ::Type ->Type)Source #	Since: 4.7.0.0
Instance details Defined inControl.Applicative typeRep1 (WrappedArrow a b ::Type ->Type) =D1 (MetaData "WrappedArrow" "Control.Applicative" "base"True) (C1 (MetaCons "WrapArrow"PrefixI True) (S1 (MetaSel (Just "unwrapArrow")NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec1 (a b))))
typeRep (WrappedArrow a b c)Source #	Since: 4.7.0.0
Instance details Defined inControl.Applicative typeRep (WrappedArrow a b c) =D1 (MetaData "WrappedArrow" "Control.Applicative" "base"True) (C1 (MetaCons "WrapArrow"PrefixI True) (S1 (MetaSel (Just "unwrapArrow")NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (a b c))))

newtypeZipList aSource #

Lists, but with anApplicative functor based on zipping.

Constructors

ZipList
Fields getZipList :: [a]

Instances

Functor ZipListSource #	Since: 2.1
Instance details Defined inControl.Applicative Methods fmap :: (a -> b) ->ZipList a ->ZipList bSource # (<$) :: a ->ZipList b ->ZipList aSource #
Applicative ZipListSource #	f '<$>' 'ZipList' xs1 '<>' ... '<>' 'ZipList' xsN = 'ZipList' (zipWithN f xs1 ... xsN) where`zipWithN` refers to the`zipWith` function of the appropriate arity (`zipWith`,`zipWith3`,`zipWith4`, ...). For example: (\a b c -> stimes c [a, b]) <$> ZipList "abcd" <> ZipList "567" <> ZipList [1..] = ZipList (zipWith3 (\a b c -> stimes c [a, b]) "abcd" "567" [1..]) = ZipList {getZipList = ["a5","b6b6","c7c7c7"]} Since: 2.1
Instance details Defined inControl.Applicative Methods pure :: a ->ZipList aSource # (<>) ::ZipList (a -> b) ->ZipList a ->ZipList bSource # liftA2 :: (a -> b -> c) ->ZipList a ->ZipList b ->ZipList cSource # (>) ::ZipList a ->ZipList b ->ZipList bSource # (<*) ::ZipList a ->ZipList b ->ZipList aSource #
Foldable ZipListSource #	Since: 4.9.0.0
Instance details Defined inControl.Applicative Methods fold ::Monoid m =>ZipList m -> mSource # foldMap ::Monoid m => (a -> m) ->ZipList a -> mSource # foldr :: (a -> b -> b) -> b ->ZipList a -> bSource # foldr' :: (a -> b -> b) -> b ->ZipList a -> bSource # foldl :: (b -> a -> b) -> b ->ZipList a -> bSource # foldl' :: (b -> a -> b) -> b ->ZipList a -> bSource # foldr1 :: (a -> a -> a) ->ZipList a -> aSource # foldl1 :: (a -> a -> a) ->ZipList a -> aSource # toList ::ZipList a -> [a]Source # null ::ZipList a ->Bool Source # length ::ZipList a ->Int Source # elem ::Eq a => a ->ZipList a ->Bool Source # maximum ::Ord a =>ZipList a -> aSource # minimum ::Ord a =>ZipList a -> aSource # sum ::Num a =>ZipList a -> aSource # product ::Num a =>ZipList a -> aSource #
Traversable ZipListSource #	Since: 4.9.0.0
Instance details Defined inData.Traversable Methods traverse ::Applicative f => (a -> f b) ->ZipList a -> f (ZipList b)Source # sequenceA ::Applicative f =>ZipList (f a) -> f (ZipList a)Source # mapM ::Monad m => (a -> m b) ->ZipList a -> m (ZipList b)Source # sequence ::Monad m =>ZipList (m a) -> m (ZipList a)Source #
Alternative ZipListSource #	Since: 4.11.0.0
Instance details Defined inControl.Applicative Methods empty ::ZipList aSource # (<\|>) ::ZipList a ->ZipList a ->ZipList aSource # some ::ZipList a ->ZipList [a]Source # many ::ZipList a ->ZipList [a]Source #
Eq a =>Eq (ZipList a)Source #	Since: 4.7.0.0
Instance details Defined inControl.Applicative Methods (==) ::ZipList a ->ZipList a ->Bool # (/=) ::ZipList a ->ZipList a ->Bool #
Ord a =>Ord (ZipList a)Source #	Since: 4.7.0.0
Instance details Defined inControl.Applicative Methods compare ::ZipList a ->ZipList a ->Ordering # (<) ::ZipList a ->ZipList a ->Bool # (<=) ::ZipList a ->ZipList a ->Bool # (>) ::ZipList a ->ZipList a ->Bool # (>=) ::ZipList a ->ZipList a ->Bool # max ::ZipList a ->ZipList a ->ZipList a# min ::ZipList a ->ZipList a ->ZipList a#
Read a =>Read (ZipList a)Source #	Since: 4.7.0.0
Instance details Defined inControl.Applicative Methods readsPrec ::Int ->ReadS (ZipList a)Source # readList ::ReadS [ZipList a]Source # readPrec ::ReadPrec (ZipList a)Source # readListPrec ::ReadPrec [ZipList a]Source #
Show a =>Show (ZipList a)Source #	Since: 4.7.0.0
Instance details Defined inControl.Applicative Methods showsPrec ::Int ->ZipList a ->ShowS Source # show ::ZipList a ->String Source # showList :: [ZipList a] ->ShowS Source #
Generic (ZipList a)Source #
Instance details Defined inControl.Applicative Associated Types typeRep (ZipList a) ::Type ->Type Source # Methods from ::ZipList a ->Rep (ZipList a) xSource # to ::Rep (ZipList a) x ->ZipList aSource #
Generic1 ZipListSource #
Instance details Defined inControl.Applicative Associated Types typeRep1 ZipList :: k ->Type Source # Methods from1 ::ZipList a ->Rep1 ZipList aSource # to1 ::Rep1 ZipList a ->ZipList aSource #
typeRep (ZipList a)Source #	Since: 4.7.0.0
Instance details Defined inControl.Applicative typeRep (ZipList a) =D1 (MetaData "ZipList" "Control.Applicative" "base"True) (C1 (MetaCons "ZipList"PrefixI True) (S1 (MetaSel (Just "getZipList")NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 [a])))
typeRep1 ZipListSource #	Since: 4.7.0.0
Instance details Defined inControl.Applicative typeRep1 ZipList =D1 (MetaData "ZipList" "Control.Applicative" "base"True) (C1 (MetaCons "ZipList"PrefixI True) (S1 (MetaSel (Just "getZipList")NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec1 [])))

Utility functions

(<$>) ::Functor f => (a -> b) -> f a -> f binfixl 4Source #

An infix synonym forfmap.

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 aFunctor.

Examples

Expand

Convert from aMaybeInt to aMaybeString usingshow:

>>>show <$> NothingNothing>>>show <$> Just 3Just "3"

Convert from anEitherIntInt to anEitherIntString usingshow:

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

Double each element of a list:

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

Applyeven to the second element of a pair:

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

(<$) ::Functor f => a -> f b -> f ainfixl 4Source #

Replace all locations in the input with the same value. The default definition isfmap .const, but this may be overridden with a more efficient version.

(<**>) ::Applicative f => f a -> f (a -> b) -> f binfixl 4Source #

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 forfmap in aFunctor instance.

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.

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Applicative functors

Alternatives

Instances

Utility functions

Examples