Control.Applicative

Copyright Conor McBride and Ross Paterson 2005
License BSD-style (see the LICENSE file in the distribution)
Maintainer [email protected]
Stability experimental
Portability portable
Safe Haskell Trustworthy
Language Haskell2010

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.

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 (<*> and liftA2).

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 id
liftA2 f x y = f <$> x <*> y

Further, any definition must satisfy the following:

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

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

If f is also a Monad, it should satisfy

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

Minimal complete definition

pure, ((<*>) | liftA2)

Methods

pure :: a -> f a Source

Lift a value.

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

Sequential application.

A few functors support an implementation of <*> that is more efficient than the default one.

Using ApplicativeDo: 'fs <*> as' can be understood as the do expression

do f <- fs
   a <- as
   pure (f a)

liftA2 :: (a -> b -> c) -> f a -> f b -> f c Source

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 <*>.

This became a typeclass method in 4.10.0.0. Prior to that, it was a function defined in terms of <*> and fmap.

Using ApplicativeDo: 'liftA2 f as bs' can be understood as the do expression

do a <- as
   b <- bs
   pure (f a b)

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

Sequence actions, discarding the value of the first argument.

'as *> bs' can be understood as the do expression

do as
   bs

This is a tad complicated for our ApplicativeDo extension which will give it a Monad constraint. For an Applicative constraint we write it of the form

do _ <- as
   b <- bs
   pure b

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

Sequence actions, discarding the value of the second argument.

Using ApplicativeDo: 'as <* bs' can be understood as the do expression

do a <- as
   bs
   pure a
Instances
Instances details
Applicative []

Since: base-2.1
Instance details

Defined in GHC.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 Maybe

Since: base-2.1
Instance details

Defined in GHC.Base

Methods

pure :: a -> Maybe a Source

(<*>) :: Maybe (a -> b) -> Maybe a -> Maybe b Source

liftA2 :: (a -> b -> c) -> Maybe a -> Maybe b -> Maybe c Source

(*>) :: Maybe a -> Maybe b -> Maybe b Source

(<*) :: Maybe a -> Maybe b -> Maybe a Source

Applicative IO

Since: base-2.1
Instance details

Defined in GHC.Base

Methods

pure :: a -> IO a Source

(<*>) :: IO (a -> b) -> IO a -> IO b Source

liftA2 :: (a -> b -> c) -> IO a -> IO b -> IO c Source

(*>) :: IO a -> IO b -> IO b Source

(<*) :: IO a -> IO b -> IO a Source

Applicative Par1

Since: base-4.9.0.0
Instance details

Defined in GHC.Generics

Methods

pure :: a -> Par1 a Source

(<*>) :: Par1 (a -> b) -> Par1 a -> Par1 b Source

liftA2 :: (a -> b -> c) -> Par1 a -> Par1 b -> Par1 c Source

(*>) :: Par1 a -> Par1 b -> Par1 b Source

(<*) :: Par1 a -> Par1 b -> Par1 a Source

Applicative NonEmpty

Since: base-4.9.0.0
Instance details

Defined in GHC.Base

Methods

pure :: a -> NonEmpty a Source

(<*>) :: NonEmpty (a -> b) -> NonEmpty a -> NonEmpty b Source

liftA2 :: (a -> b -> c) -> NonEmpty a -> NonEmpty b -> NonEmpty c Source

(*>) :: NonEmpty a -> NonEmpty b -> NonEmpty b Source

(<*) :: NonEmpty a -> NonEmpty b -> NonEmpty a Source

Applicative NoIO

Since: base-4.8.0.0
Instance details

Defined in GHC.GHCi

Methods

pure :: a -> NoIO a Source

(<*>) :: NoIO (a -> b) -> NoIO a -> NoIO b Source

liftA2 :: (a -> b -> c) -> NoIO a -> NoIO b -> NoIO c Source

(*>) :: NoIO a -> NoIO b -> NoIO b Source

(<*) :: NoIO a -> NoIO b -> NoIO a Source

Applicative ReadP

Since: base-4.6.0.0
Instance details

Defined in Text.ParserCombinators.ReadP

Methods

pure :: a -> ReadP a Source

(<*>) :: ReadP (a -> b) -> ReadP a -> ReadP b Source

liftA2 :: (a -> b -> c) -> ReadP a -> ReadP b -> ReadP c Source

(*>) :: ReadP a -> ReadP b -> ReadP b Source

(<*) :: ReadP a -> ReadP b -> ReadP a Source

Applicative ReadPrec

Since: base-4.6.0.0
Instance details

Defined in Text.ParserCombinators.ReadPrec

Methods

pure :: a -> ReadPrec a Source

(<*>) :: ReadPrec (a -> b) -> ReadPrec a -> ReadPrec b Source

liftA2 :: (a -> b -> c) -> ReadPrec a -> ReadPrec b -> ReadPrec c Source

(*>) :: ReadPrec a -> ReadPrec b -> ReadPrec b Source

(<*) :: ReadPrec a -> ReadPrec b -> ReadPrec a Source

Applicative Down

Since: base-4.11.0.0
Instance details

Defined in Data.Ord

Methods

pure :: a -> Down a Source

(<*>) :: Down (a -> b) -> Down a -> Down b Source

liftA2 :: (a -> b -> c) -> Down a -> Down b -> Down c Source

(*>) :: Down a -> Down b -> Down b Source

(<*) :: Down a -> Down b -> Down a Source

Applicative Product

Since: base-4.8.0.0
Instance details

Defined in Data.Semigroup.Internal

Methods

pure :: a -> Product a Source

(<*>) :: Product (a -> b) -> Product a -> Product b Source

liftA2 :: (a -> b -> c) -> Product a -> Product b -> Product c Source

(*>) :: Product a -> Product b -> Product b Source

(<*) :: Product a -> Product b -> Product a Source

Applicative Sum

Since: base-4.8.0.0
Instance details

Defined in Data.Semigroup.Internal

Methods

pure :: a -> Sum a Source

(<*>) :: Sum (a -> b) -> Sum a -> Sum b Source

liftA2 :: (a -> b -> c) -> Sum a -> Sum b -> Sum c Source

(*>) :: Sum a -> Sum b -> Sum b Source

(<*) :: Sum a -> Sum b -> Sum a Source

Applicative Dual

Since: base-4.8.0.0
Instance details

Defined in Data.Semigroup.Internal

Methods

pure :: a -> Dual a Source

(<*>) :: Dual (a -> b) -> Dual a -> Dual b Source

liftA2 :: (a -> b -> c) -> Dual a -> Dual b -> Dual c Source

(*>) :: Dual a -> Dual b -> Dual b Source

(<*) :: Dual a -> Dual b -> Dual a Source

Applicative Last

Since: base-4.8.0.0
Instance details

Defined in Data.Monoid

Methods

pure :: a -> Last a Source

(<*>) :: Last (a -> b) -> Last a -> Last b Source

liftA2 :: (a -> b -> c) -> Last a -> Last b -> Last c Source

(*>) :: Last a -> Last b -> Last b Source

(<*) :: Last a -> Last b -> Last a Source

Applicative First

Since: base-4.8.0.0
Instance details

Defined in Data.Monoid

Methods

pure :: a -> First a Source

(<*>) :: First (a -> b) -> First a -> First b Source

liftA2 :: (a -> b -> c) -> First a -> First b -> First c Source

(*>) :: First a -> First b -> First b Source

(<*) :: First a -> First b -> First a Source

Applicative STM

Since: base-4.8.0.0
Instance details

Defined in GHC.Conc.Sync

Methods

pure :: a -> STM a Source

(<*>) :: STM (a -> b) -> STM a -> STM b Source

liftA2 :: (a -> b -> c) -> STM a -> STM b -> STM c Source

(*>) :: STM a -> STM b -> STM b Source

(<*) :: STM a -> STM b -> STM a Source

Applicative Identity

Since: base-4.8.0.0
Instance details

Defined in Data.Functor.Identity

Methods

pure :: a -> Identity a Source

(<*>) :: Identity (a -> b) -> Identity a -> Identity b Source

liftA2 :: (a -> b -> c) -> Identity a -> Identity b -> Identity c Source

(*>) :: Identity a -> Identity b -> Identity b Source

(<*) :: Identity a -> Identity b -> Identity a Source

Applicative ZipList 
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: base-2.1
Instance details

Defined in Control.Applicative

Methods

pure :: a -> ZipList a Source

(<*>) :: ZipList (a -> b) -> ZipList a -> ZipList b Source

liftA2 :: (a -> b -> c) -> ZipList a -> ZipList b -> ZipList c Source

(*>) :: ZipList a -> ZipList b -> ZipList b Source

(<*) :: ZipList a -> ZipList b -> ZipList a Source

Applicative Option

Since: base-4.9.0.0
Instance details

Defined in Data.Semigroup

Methods

pure :: a -> Option a Source

(<*>) :: Option (a -> b) -> Option a -> Option b Source

liftA2 :: (a -> b -> c) -> Option a -> Option b -> Option c Source

(*>) :: Option a -> Option b -> Option b Source

(<*) :: Option a -> Option b -> Option a Source

Applicative Last

Since: base-4.9.0.0
Instance details

Defined in Data.Semigroup

Methods

pure :: a -> Last a Source

(<*>) :: Last (a -> b) -> Last a -> Last b Source

liftA2 :: (a -> b -> c) -> Last a -> Last b -> Last c Source

(*>) :: Last a -> Last b -> Last b Source

(<*) :: Last a -> Last b -> Last a Source

Applicative First

Since: base-4.9.0.0
Instance details

Defined in Data.Semigroup

Methods

pure :: a -> First a Source

(<*>) :: First (a -> b) -> First a -> First b Source

liftA2 :: (a -> b -> c) -> First a -> First b -> First c Source

(*>) :: First a -> First b -> First b Source

(<*) :: First a -> First b -> First a Source

Applicative Max

Since: base-4.9.0.0
Instance details

Defined in Data.Semigroup

Methods

pure :: a -> Max a Source

(<*>) :: Max (a -> b) -> Max a -> Max b Source

liftA2 :: (a -> b -> c) -> Max a -> Max b -> Max c Source

(*>) :: Max a -> Max b -> Max b Source

(<*) :: Max a -> Max b -> Max a Source

Applicative Min

Since: base-4.9.0.0
Instance details

Defined in Data.Semigroup

Methods

pure :: a -> Min a Source

(<*>) :: Min (a -> b) -> Min a -> Min b Source

liftA2 :: (a -> b -> c) -> Min a -> Min b -> Min c Source

(*>) :: Min a -> Min b -> Min b Source

(<*) :: Min a -> Min b -> Min a Source

Applicative Complex

Since: base-4.9.0.0
Instance details

Defined in Data.Complex

Methods

pure :: a -> Complex a Source

(<*>) :: Complex (a -> b) -> Complex a -> Complex b Source

liftA2 :: (a -> b -> c) -> Complex a -> Complex b -> Complex c Source

(*>) :: Complex a -> Complex b -> Complex b Source

(<*) :: Complex a -> Complex b -> Complex a Source

Applicative (Either e)

Since: base-3.0
Instance details

Defined in Data.Either

Methods

pure :: a -> Either e a Source

(<*>) :: Either e (a -> b) -> Either e a -> Either e b Source

liftA2 :: (a -> b -> c) -> Either e a -> Either e b -> Either e c Source

(*>) :: Either e a -> Either e b -> Either e b Source

(<*) :: Either e a -> Either e b -> Either e a Source

Applicative (U1 :: Type -> Type)

Since: base-4.9.0.0
Instance details

Defined in GHC.Generics

Methods

pure :: a -> U1 a Source

(<*>) :: U1 (a -> b) -> U1 a -> U1 b Source

liftA2 :: (a -> b -> c) -> U1 a -> U1 b -> U1 c Source

(*>) :: U1 a -> U1 b -> U1 b Source

(<*) :: U1 a -> U1 b -> U1 a Source

Monoid a => Applicative ((,) a)

For tuples, the Monoid constraint on a determines how the first values merge. For example, Strings concatenate:

("hello ", (+15)) <*> ("world!", 2002)
("hello world!",2017)

Since: base-2.1
Instance details

Defined in GHC.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)

Since: base-4.4.0.0
Instance details

Defined in GHC.ST

Methods

pure :: a -> ST s a Source

(<*>) :: ST s (a -> b) -> ST s a -> ST s b Source

liftA2 :: (a -> b -> c) -> ST s a -> ST s b -> ST s c Source

(*>) :: ST s a -> ST s b -> ST s b Source

(<*) :: ST s a -> ST s b -> ST s a Source

Applicative (Proxy :: Type -> Type)

Since: base-4.7.0.0
Instance details

Defined in Data.Proxy

Methods

pure :: a -> Proxy a Source

(<*>) :: Proxy (a -> b) -> Proxy a -> Proxy b Source

liftA2 :: (a -> b -> c) -> Proxy a -> Proxy b -> Proxy c Source

(*>) :: Proxy a -> Proxy b -> Proxy b Source

(<*) :: Proxy a -> Proxy b -> Proxy a Source

Arrow a => Applicative (ArrowMonad a)

Since: base-4.6.0.0
Instance details

Defined in Control.Arrow

Methods

pure :: a0 -> ArrowMonad a a0 Source

(<*>) :: ArrowMonad a (a0 -> b) -> ArrowMonad a a0 -> ArrowMonad a b Source

liftA2 :: (a0 -> b -> c) -> ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a c Source

(*>) :: ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a b Source

(<*) :: ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a a0 Source

Monad m => Applicative (WrappedMonad m)

Since: base-2.1
Instance details

Defined in Control.Applicative

Methods

pure :: a -> WrappedMonad m a Source

(<*>) :: WrappedMonad m (a -> b) -> WrappedMonad m a -> WrappedMonad m b Source

liftA2 :: (a -> b -> c) -> WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m c Source

(*>) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m b Source

(<*) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m a Source

Applicative (ST s)

Since: base-2.1
Instance details

Defined in Control.Monad.ST.Lazy.Imp

Methods

pure :: a -> ST s a Source

(<*>) :: ST s (a -> b) -> ST s a -> ST s b Source

liftA2 :: (a -> b -> c) -> ST s a -> ST s b -> ST s c Source

(*>) :: ST s a -> ST s b -> ST s b Source

(<*) :: ST s a -> ST s b -> ST s a Source

Applicative f => Applicative (Rec1 f)

Since: base-4.9.0.0
Instance details

Defined in GHC.Generics

Methods

pure :: a -> Rec1 f a Source

(<*>) :: Rec1 f (a -> b) -> Rec1 f a -> Rec1 f b Source

liftA2 :: (a -> b -> c) -> Rec1 f a -> Rec1 f b -> Rec1 f c Source

(*>) :: Rec1 f a -> Rec1 f b -> Rec1 f b Source

(<*) :: Rec1 f a -> Rec1 f b -> Rec1 f a Source

(Monoid a, Monoid b) => Applicative ((,,) a b)

Since: base-4.14.0.0
Instance details

Defined in GHC.Base

Methods

pure :: a0 -> (a, b, a0) Source

(<*>) :: (a, b, a0 -> b0) -> (a, b, a0) -> (a, b, b0) Source

liftA2 :: (a0 -> b0 -> c) -> (a, b, a0) -> (a, b, b0) -> (a, b, c) Source

(*>) :: (a, b, a0) -> (a, b, b0) -> (a, b, b0) Source

(<*) :: (a, b, a0) -> (a, b, b0) -> (a, b, a0) Source

Applicative f => Applicative (Alt f)

Since: base-4.8.0.0
Instance details

Defined in Data.Semigroup.Internal

Methods

pure :: a -> Alt f a Source

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

liftA2 :: (a -> b -> c) -> Alt f a -> Alt f b -> Alt f c Source

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

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

Applicative f => Applicative (Ap f)

Since: base-4.12.0.0
Instance details

Defined in Data.Monoid

Methods

pure :: a -> Ap f a Source

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

liftA2 :: (a -> b -> c) -> Ap f a -> Ap f b -> Ap f c Source

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

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

Monoid m => Applicative (Const m :: Type -> Type)

Since: base-2.0.1
Instance details

Defined in Data.Functor.Const

Methods

pure :: a -> Const m a Source

(<*>) :: Const m (a -> b) -> Const m a -> Const m b Source

liftA2 :: (a -> b -> c) -> Const m a -> Const m b -> Const m c Source

(*>) :: Const m a -> Const m b -> Const m b Source

(<*) :: Const m a -> Const m b -> Const m a Source

Applicative m => Applicative (Kleisli m a)

Since: base-4.14.0.0
Instance details

Defined in Control.Arrow

Methods

pure :: a0 -> Kleisli m a a0 Source

(<*>) :: Kleisli m a (a0 -> b) -> Kleisli m a a0 -> Kleisli m a b Source

liftA2 :: (a0 -> b -> c) -> Kleisli m a a0 -> Kleisli m a b -> Kleisli m a c Source

(*>) :: Kleisli m a a0 -> Kleisli m a b -> Kleisli m a b Source

(<*) :: Kleisli m a a0 -> Kleisli m a b -> Kleisli m a a0 Source

Arrow a => Applicative (WrappedArrow a b)

Since: base-2.1
Instance details

Defined in Control.Applicative

Methods

pure :: a0 -> WrappedArrow a b a0 Source

(<*>) :: WrappedArrow a b (a0 -> b0) -> WrappedArrow a b a0 -> WrappedArrow a b b0 Source

liftA2 :: (a0 -> b0 -> c) -> WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b c Source

(*>) :: WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b b0 Source

(<*) :: WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0 Source

Applicative ((->) r :: Type -> Type)

Since: base-2.1
Instance details

Defined in GHC.Base

Methods

pure :: a -> r -> a Source

(<*>) :: (r -> (a -> b)) -> (r -> a) -> r -> b Source

liftA2 :: (a -> b -> c) -> (r -> a) -> (r -> b) -> r -> c Source

(*>) :: (r -> a) -> (r -> b) -> r -> b Source

(<*) :: (r -> a) -> (r -> b) -> r -> a Source

Monoid c => Applicative (K1 i c :: Type -> Type)

Since: base-4.12.0.0
Instance details

Defined in GHC.Generics

Methods

pure :: a -> K1 i c a Source

(<*>) :: K1 i c (a -> b) -> K1 i c a -> K1 i c b Source

liftA2 :: (a -> b -> c0) -> K1 i c a -> K1 i c b -> K1 i c c0 Source

(*>) :: K1 i c a -> K1 i c b -> K1 i c b Source

(<*) :: K1 i c a -> K1 i c b -> K1 i c a Source

(Applicative f, Applicative g) => Applicative (f :*: g)

Since: base-4.9.0.0
Instance details

Defined in GHC.Generics

Methods

pure :: a -> (f :*: g) a Source

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

liftA2 :: (a -> b -> c) -> (f :*: g) a -> (f :*: g) b -> (f :*: g) c Source

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

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

(Monoid a, Monoid b, Monoid c) => Applicative ((,,,) a b c)

Since: base-4.14.0.0
Instance details

Defined in GHC.Base

Methods

pure :: a0 -> (a, b, c, a0) Source

(<*>) :: (a, b, c, a0 -> b0) -> (a, b, c, a0) -> (a, b, c, b0) Source

liftA2 :: (a0 -> b0 -> c0) -> (a, b, c, a0) -> (a, b, c, b0) -> (a, b, c, c0) Source

(*>) :: (a, b, c, a0) -> (a, b, c, b0) -> (a, b, c, b0) Source

(<*) :: (a, b, c, a0) -> (a, b, c, b0) -> (a, b, c, a0) Source

(Applicative f, Applicative g) => Applicative (Product f g)

Since: base-4.9.0.0
Instance details

Defined in Data.Functor.Product

Methods

pure :: a -> Product f g a Source

(<*>) :: Product f g (a -> b) -> Product f g a -> Product f g b Source

liftA2 :: (a -> b -> c) -> Product f g a -> Product f g b -> Product f g c Source

(*>) :: Product f g a -> Product f g b -> Product f g b Source

(<*) :: Product f g a -> Product f g b -> Product f g a Source

Applicative f => Applicative (M1 i c f)

Since: base-4.9.0.0
Instance details

Defined in GHC.Generics

Methods

pure :: a -> M1 i c f a Source

(<*>) :: M1 i c f (a -> b) -> M1 i c f a -> M1 i c f b Source

liftA2 :: (a -> b -> c0) -> M1 i c f a -> M1 i c f b -> M1 i c f c0 Source

(*>) :: M1 i c f a -> M1 i c f b -> M1 i c f b Source

(<*) :: M1 i c f a -> M1 i c f b -> M1 i c f a Source

(Applicative f, Applicative g) => Applicative (f :.: g)

Since: base-4.9.0.0
Instance details

Defined in GHC.Generics

Methods

pure :: a -> (f :.: g) a Source

(<*>) :: (f :.: g) (a -> b) -> (f :.: g) a -> (f :.: g) b Source

liftA2 :: (a -> b -> c) -> (f :.: g) a -> (f :.: g) b -> (f :.: g) c Source

(*>) :: (f :.: g) a -> (f :.: g) b -> (f :.: g) b Source

(<*) :: (f :.: g) a -> (f :.: g) b -> (f :.: g) a Source

(Applicative f, Applicative g) => Applicative (Compose f g)

Since: base-4.9.0.0
Instance details

Defined in Data.Functor.Compose

Methods

pure :: a -> Compose f g a Source

(<*>) :: Compose f g (a -> b) -> Compose f g a -> Compose f g b Source

liftA2 :: (a -> b -> c) -> Compose f g a -> Compose f g b -> Compose f g c Source

(*>) :: Compose f g a -> Compose f g b -> Compose f g b Source

(<*) :: Compose f g a -> Compose f g b -> Compose f g a Source

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:

Minimal complete definition

empty, (<|>)

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
Instances details
Alternative []

Since: base-2.1
Instance details

Defined in GHC.Base

Methods

empty :: [a] Source

(<|>) :: [a] -> [a] -> [a] Source

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

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

Alternative Maybe

Since: base-2.1
Instance details

Defined in GHC.Base

Methods

empty :: Maybe a Source

(<|>) :: Maybe a -> Maybe a -> Maybe a Source

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

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

Alternative IO

Since: base-4.9.0.0
Instance details

Defined in GHC.Base

Methods

empty :: IO a Source

(<|>) :: IO a -> IO a -> IO a Source

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

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

Alternative ReadP

Since: base-4.6.0.0
Instance details

Defined in Text.ParserCombinators.ReadP

Methods

empty :: ReadP a Source

(<|>) :: ReadP a -> ReadP a -> ReadP a Source

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

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

Alternative ReadPrec

Since: base-4.6.0.0
Instance details

Defined in Text.ParserCombinators.ReadPrec

Methods

empty :: ReadPrec a Source

(<|>) :: ReadPrec a -> ReadPrec a -> ReadPrec a Source

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

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

Alternative STM

Since: base-4.8.0.0
Instance details

Defined in GHC.Conc.Sync

Methods

empty :: STM a Source

(<|>) :: STM a -> STM a -> STM a Source

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

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

Alternative ZipList

Since: base-4.11.0.0
Instance details

Defined in Control.Applicative

Methods

empty :: ZipList a Source

(<|>) :: ZipList a -> ZipList a -> ZipList a Source

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

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

Alternative Option

Since: base-4.9.0.0
Instance details

Defined in Data.Semigroup

Methods

empty :: Option a Source

(<|>) :: Option a -> Option a -> Option a Source

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

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

Alternative (U1 :: Type -> Type)

Since: base-4.9.0.0
Instance details

Defined in GHC.Generics

Methods

empty :: U1 a Source

(<|>) :: U1 a -> U1 a -> U1 a Source

some :: U1 a -> U1 [a] Source

many :: U1 a -> U1 [a] Source

Alternative (Proxy :: Type -> Type)

Since: base-4.9.0.0
Instance details

Defined in Data.Proxy

Methods

empty :: Proxy a Source

(<|>) :: Proxy a -> Proxy a -> Proxy a Source

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

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

ArrowPlus a => Alternative (ArrowMonad a)

Since: base-4.6.0.0
Instance details

Defined in Control.Arrow

Methods

empty :: ArrowMonad a a0 Source

(<|>) :: ArrowMonad a a0 -> ArrowMonad a a0 -> ArrowMonad a a0 Source

some :: ArrowMonad a a0 -> ArrowMonad a [a0] Source

many :: ArrowMonad a a0 -> ArrowMonad a [a0] Source

MonadPlus m => Alternative (WrappedMonad m)

Since: base-2.1
Instance details

Defined in Control.Applicative

Methods

empty :: WrappedMonad m a Source

(<|>) :: WrappedMonad m a -> WrappedMonad m a -> WrappedMonad m a Source

some :: WrappedMonad m a -> WrappedMonad m [a] Source

many :: WrappedMonad m a -> WrappedMonad m [a] Source

Alternative f => Alternative (Rec1 f)

Since: base-4.9.0.0
Instance details

Defined in GHC.Generics

Methods

empty :: Rec1 f a Source

(<|>) :: Rec1 f a -> Rec1 f a -> Rec1 f a Source

some :: Rec1 f a -> Rec1 f [a] Source

many :: Rec1 f a -> Rec1 f [a] Source

Alternative f => Alternative (Alt f)

Since: base-4.8.0.0
Instance details

Defined in Data.Semigroup.Internal

Methods

empty :: Alt f a Source

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

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

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

Alternative f => Alternative (Ap f)

Since: base-4.12.0.0
Instance details

Defined in Data.Monoid

Methods

empty :: Ap f a Source

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

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

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

Alternative m => Alternative (Kleisli m a)

Since: base-4.14.0.0
Instance details

Defined in Control.Arrow

Methods

empty :: Kleisli m a a0 Source

(<|>) :: Kleisli m a a0 -> Kleisli m a a0 -> Kleisli m a a0 Source

some :: Kleisli m a a0 -> Kleisli m a [a0] Source

many :: Kleisli m a a0 -> Kleisli m a [a0] Source

(ArrowZero a, ArrowPlus a) => Alternative (WrappedArrow a b)

Since: base-2.1
Instance details

Defined in Control.Applicative

Methods

empty :: WrappedArrow a b a0 Source

(<|>) :: WrappedArrow a b a0 -> WrappedArrow a b a0 -> WrappedArrow a b a0 Source

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)

Since: base-4.9.0.0
Instance details

Defined in GHC.Generics

Methods

empty :: (f :*: g) a Source

(<|>) :: (f :*: g) a -> (f :*: g) a -> (f :*: g) a Source

some :: (f :*: g) a -> (f :*: g) [a] Source

many :: (f :*: g) a -> (f :*: g) [a] Source

(Alternative f, Alternative g) => Alternative (Product f g)

Since: base-4.9.0.0
Instance details

Defined in Data.Functor.Product

Methods

empty :: Product f g a Source

(<|>) :: Product f g a -> Product f g a -> Product f g a Source

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)

Since: base-4.9.0.0
Instance details

Defined in GHC.Generics

Methods

empty :: M1 i c f a Source

(<|>) :: M1 i c f a -> M1 i c f a -> M1 i c f a Source

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)

Since: base-4.9.0.0
Instance details

Defined in GHC.Generics

Methods

empty :: (f :.: g) a Source

(<|>) :: (f :.: g) a -> (f :.: g) a -> (f :.: g) a Source

some :: (f :.: g) a -> (f :.: g) [a] Source

many :: (f :.: g) a -> (f :.: g) [a] Source

(Alternative f, Applicative g) => Alternative (Compose f g)

Since: base-4.9.0.0
Instance details

Defined in Data.Functor.Compose

Methods

empty :: Compose f g a Source

(<|>) :: Compose f g a -> Compose f g a -> Compose f g a Source

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

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

Instances

newtype Const a b Source

The Const functor.

Constructors

Const

Fields

Instances
Instances details
Generic1 (Const a :: k -> Type)

Since: base-4.9.0.0
Instance details

Defined in Data.Functor.Const

Associated Types

type Rep1 (Const a) :: k -> Type Source

Methods

from1 :: forall (a0 :: k0). Const a a0 -> Rep1 (Const a) a0 Source

to1 :: forall (a0 :: k0). Rep1 (Const a) a0 -> Const a a0 Source

Show2 (Const :: Type -> Type -> Type)

Since: base-4.9.0.0
Instance details

Defined in Data.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)

Since: base-4.9.0.0
Instance details

Defined in Data.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)

Since: base-4.9.0.0
Instance details

Defined in Data.Functor.Classes

Methods

liftCompare2 :: (a -> b -> Ordering) -> (c -> d -> Ordering) -> Const a c -> Const b d -> Ordering Source

Eq2 (Const :: Type -> Type -> Type)

Since: base-4.9.0.0
Instance details

Defined in Data.Functor.Classes

Methods

liftEq2 :: (a -> b -> Bool) -> (c -> d -> Bool) -> Const a c -> Const b d -> Bool Source

Bifunctor (Const :: Type -> Type -> Type)

Since: base-4.8.0.0
Instance details

Defined in Data.Bifunctor

Methods

bimap :: (a -> b) -> (c -> d) -> Const a c -> Const b d Source

first :: (a -> b) -> Const a c -> Const b c Source

second :: (b -> c) -> Const a b -> Const a c Source

Bifoldable (Const :: Type -> Type -> Type)

Since: base-4.10.0.0
Instance details

Defined in Data.Bifoldable

Methods

bifold :: Monoid m => Const m m -> m Source

bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> Const a b -> m Source

bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> Const a b -> c Source

bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> Const a b -> c Source

Bitraversable (Const :: Type -> Type -> Type)

Since: base-4.10.0.0
Instance details

Defined in Data.Bitraversable

Methods

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

Functor (Const m :: Type -> Type)

Since: base-2.1
Instance details

Defined in Data.Functor.Const

Methods

fmap :: (a -> b) -> Const m a -> Const m b Source

(<$) :: a -> Const m b -> Const m a Source

Monoid m => Applicative (Const m :: Type -> Type)

Since: base-2.0.1
Instance details

Defined in Data.Functor.Const

Methods

pure :: a -> Const m a Source

(<*>) :: Const m (a -> b) -> Const m a -> Const m b Source

liftA2 :: (a -> b -> c) -> Const m a -> Const m b -> Const m c Source

(*>) :: Const m a -> Const m b -> Const m b Source

(<*) :: Const m a -> Const m b -> Const m a Source

Foldable (Const m :: Type -> Type)

Since: base-4.7.0.0
Instance details

Defined in Data.Functor.Const

Methods

fold :: Monoid m0 => Const m m0 -> m0 Source

foldMap :: Monoid m0 => (a -> m0) -> Const m a -> m0 Source

foldMap' :: Monoid m0 => (a -> m0) -> Const m a -> m0 Source

foldr :: (a -> b -> b) -> b -> Const m a -> b Source

foldr' :: (a -> b -> b) -> b -> Const m a -> b Source

foldl :: (b -> a -> b) -> b -> Const m a -> b Source

foldl' :: (b -> a -> b) -> b -> Const m a -> b Source

foldr1 :: (a -> a -> a) -> Const m a -> a Source

foldl1 :: (a -> a -> a) -> Const m a -> a Source

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 -> a Source

minimum :: Ord a => Const m a -> a Source

sum :: Num a => Const m a -> a Source

product :: Num a => Const m a -> a Source

Traversable (Const m :: Type -> Type)

Since: base-4.7.0.0
Instance details

Defined in Data.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)

Since: base-4.9.0.0
Instance details

Defined in Data.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)

Since: base-4.9.0.0
Instance details

Defined in Data.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)

Since: base-4.9.0.0
Instance details

Defined in Data.Functor.Classes

Methods

liftCompare :: (a0 -> b -> Ordering) -> Const a a0 -> Const a b -> Ordering Source

Eq a => Eq1 (Const a :: Type -> Type)

Since: base-4.9.0.0
Instance details

Defined in Data.Functor.Classes

Methods

liftEq :: (a0 -> b -> Bool) -> Const a a0 -> Const a b -> Bool Source

Contravariant (Const a :: Type -> Type)
Instance details

Defined in Data.Functor.Contravariant

Methods

contramap :: (a0 -> b) -> Const a b -> Const a a0 Source

(>$) :: b -> Const a b -> Const a a0 Source

Bounded a => Bounded (Const a b)

Since: base-4.9.0.0
Instance details

Defined in Data.Functor.Const

Methods

minBound :: Const a b Source

maxBound :: Const a b Source

Enum a => Enum (Const a b)

Since: base-4.9.0.0
Instance details

Defined in Data.Functor.Const

Methods

succ :: Const a b -> Const a b Source

pred :: Const a b -> Const a b Source

toEnum :: Int -> Const a b Source

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)

Since: base-4.9.0.0
Instance details

Defined in Data.Functor.Const

Methods

(==) :: Const a b -> Const a b -> Bool Source

(/=) :: Const a b -> Const a b -> Bool Source

Floating a => Floating (Const a b)

Since: base-4.9.0.0
Instance details

Defined in Data.Functor.Const

Methods

pi :: Const a b Source

exp :: Const a b -> Const a b Source

log :: Const a b -> Const a b Source

sqrt :: Const a b -> Const a b Source

(**) :: Const a b -> Const a b -> Const a b Source

logBase :: Const a b -> Const a b -> Const a b Source

sin :: Const a b -> Const a b Source

cos :: Const a b -> Const a b Source

tan :: Const a b -> Const a b Source

asin :: Const a b -> Const a b Source

acos :: Const a b -> Const a b Source

atan :: Const a b -> Const a b Source

sinh :: Const a b -> Const a b Source

cosh :: Const a b -> Const a b Source

tanh :: Const a b -> Const a b Source

asinh :: Const a b -> Const a b Source

acosh :: Const a b -> Const a b Source

atanh :: Const a b -> Const a b Source

log1p :: Const a b -> Const a b Source

expm1 :: Const a b -> Const a b Source

log1pexp :: Const a b -> Const a b Source

log1mexp :: Const a b -> Const a b Source

Fractional a => Fractional (Const a b)

Since: base-4.9.0.0
Instance details

Defined in Data.Functor.Const

Methods

(/) :: Const a b -> Const a b -> Const a b Source

recip :: Const a b -> Const a b Source

fromRational :: Rational -> Const a b Source

Integral a => Integral (Const a b)

Since: base-4.9.0.0
Instance details

Defined in Data.Functor.Const

Methods

quot :: Const a b -> Const a b -> Const a b Source

rem :: Const a b -> Const a b -> Const a b Source

div :: Const a b -> Const a b -> Const a b Source

mod :: Const a b -> Const a b -> Const a b Source

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)

Since: base-4.10.0.0
Instance details

Defined in Data.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 b Source

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Const a b -> r Source

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Const a b -> r Source

gmapQ :: (forall d. Data d => d -> u) -> Const a b -> [u] Source

gmapQi :: Int -> (forall d. Data d => d -> u) -> Const a b -> u Source

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)

Since: base-4.9.0.0
Instance details

Defined in Data.Functor.Const

Methods

(+) :: Const a b -> Const a b -> Const a b Source

(-) :: Const a b -> Const a b -> Const a b Source

(*) :: Const a b -> Const a b -> Const a b Source

negate :: Const a b -> Const a b Source

abs :: Const a b -> Const a b Source

signum :: Const a b -> Const a b Source

fromInteger :: Integer -> Const a b Source

Ord a => Ord (Const a b)

Since: base-4.9.0.0
Instance details

Defined in Data.Functor.Const

Methods

compare :: Const a b -> Const a b -> Ordering Source

(<) :: Const a b -> Const a b -> Bool Source

(<=) :: Const a b -> Const a b -> Bool Source

(>) :: Const a b -> Const a b -> Bool Source

(>=) :: Const a b -> Const a b -> Bool Source

max :: Const a b -> Const a b -> Const a b Source

min :: Const a b -> Const a b -> Const a b Source

Read a => Read (Const a b)

This instance would be equivalent to the derived instances of the Const newtype if the getConst field were removed

Since: base-4.8.0.0
Instance details

Defined in Data.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)

Since: base-4.9.0.0
Instance details

Defined in Data.Functor.Const

Methods

toRational :: Const a b -> Rational Source

RealFloat a => RealFloat (Const a b)

Since: base-4.9.0.0
Instance details

Defined in Data.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 b Source

exponent :: Const a b -> Int Source

significand :: Const a b -> Const a b Source

scaleFloat :: Int -> Const a b -> Const a b Source

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 b Source

RealFrac a => RealFrac (Const a b)

Since: base-4.9.0.0
Instance details

Defined in Data.Functor.Const

Methods

properFraction :: Integral b0 => Const a b -> (b0, Const a b) Source

truncate :: Integral b0 => Const a b -> b0 Source

round :: Integral b0 => Const a b -> b0 Source

ceiling :: Integral b0 => Const a b -> b0 Source

floor :: Integral b0 => Const a b -> b0 Source

Show a => Show (Const a b)

This instance would be equivalent to the derived instances of the Const newtype if the getConst field were removed

Since: base-4.8.0.0
Instance details

Defined in Data.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)

Since: base-4.9.0.0
Instance details

Defined in Data.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 Source

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 Source

IsString a => IsString (Const a b)

Since: base-4.9.0.0
Instance details

Defined in Data.String

Methods

fromString :: String -> Const a b Source

Generic (Const a b)

Since: base-4.9.0.0
Instance details

Defined in Data.Functor.Const

Associated Types

type Rep (Const a b) :: Type -> Type Source

Methods

from :: Const a b -> Rep (Const a b) x Source

to :: Rep (Const a b) x -> Const a b Source

Semigroup a => Semigroup (Const a b)

Since: base-4.9.0.0
Instance details

Defined in Data.Functor.Const

Methods

(<>) :: Const a b -> Const a b -> Const a b Source

sconcat :: NonEmpty (Const a b) -> Const a b Source

stimes :: Integral b0 => b0 -> Const a b -> Const a b Source

Monoid a => Monoid (Const a b)

Since: base-4.9.0.0
Instance details

Defined in Data.Functor.Const

Methods

mempty :: Const a b Source

mappend :: Const a b -> Const a b -> Const a b Source

mconcat :: [Const a b] -> Const a b Source

FiniteBits a => FiniteBits (Const a b)

Since: base-4.9.0.0
Instance details

Defined in Data.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)

Since: base-4.9.0.0
Instance details

Defined in Data.Functor.Const

Methods

(.&.) :: Const a b -> Const a b -> Const a b Source

(.|.) :: Const a b -> Const a b -> Const a b Source

xor :: Const a b -> Const a b -> Const a b Source

complement :: Const a b -> Const a b Source

shift :: Const a b -> Int -> Const a b Source

rotate :: Const a b -> Int -> Const a b Source

zeroBits :: Const a b Source

bit :: Int -> Const a b Source

setBit :: Const a b -> Int -> Const a b Source

clearBit :: Const a b -> Int -> Const a b Source

complementBit :: Const a b -> Int -> Const a b Source

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 b Source

unsafeShiftL :: Const a b -> Int -> Const a b Source

shiftR :: Const a b -> Int -> Const a b Source

unsafeShiftR :: Const a b -> Int -> Const a b Source

rotateL :: Const a b -> Int -> Const a b Source

rotateR :: Const a b -> Int -> Const a b Source

popCount :: Const a b -> Int Source

Storable a => Storable (Const a b)

Since: base-4.9.0.0
Instance details

Defined in Data.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

type Rep1 (Const a :: k -> Type)
Instance details

Defined in Data.Functor.Const

type Rep1 (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)))
type Rep (Const a b)
Instance details

Defined in Data.Functor.Const

type Rep (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)))

newtype WrappedMonad m a Source

Constructors

WrapMonad

Fields

Instances
Instances details
Monad m => Monad (WrappedMonad m)

Since: base-4.7.0.0
Instance details

Defined in Control.Applicative

Methods

(>>=) :: WrappedMonad m a -> (a -> WrappedMonad m b) -> WrappedMonad m b Source

(>>) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m b Source

return :: a -> WrappedMonad m a Source

Monad m => Functor (WrappedMonad m)

Since: base-2.1
Instance details

Defined in Control.Applicative

Methods

fmap :: (a -> b) -> WrappedMonad m a -> WrappedMonad m b Source

(<$) :: a -> WrappedMonad m b -> WrappedMonad m a Source

Monad m => Applicative (WrappedMonad m)

Since: base-2.1
Instance details

Defined in Control.Applicative

Methods

pure :: a -> WrappedMonad m a Source

(<*>) :: WrappedMonad m (a -> b) -> WrappedMonad m a -> WrappedMonad m b Source

liftA2 :: (a -> b -> c) -> WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m c Source

(*>) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m b Source

(<*) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m a Source

MonadPlus m => Alternative (WrappedMonad m)

Since: base-2.1
Instance details

Defined in Control.Applicative

Methods

empty :: WrappedMonad m a Source

(<|>) :: WrappedMonad m a -> WrappedMonad m a -> WrappedMonad m a Source

some :: WrappedMonad m a -> WrappedMonad m [a] Source

many :: WrappedMonad m a -> WrappedMonad m [a] Source

Generic1 (WrappedMonad m :: Type -> Type)

Since: base-4.7.0.0
Instance details

Defined in Control.Applicative

Associated Types

type Rep1 (WrappedMonad m) :: k -> Type Source

Methods

from1 :: forall (a :: k). WrappedMonad m a -> Rep1 (WrappedMonad m) a Source

to1 :: forall (a :: k). Rep1 (WrappedMonad m) a -> WrappedMonad m a Source

(Typeable m, Typeable a, Data (m a)) => Data (WrappedMonad m a)

Since: base-4.14.0.0
Instance details

Defined in Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> WrappedMonad m a -> c (WrappedMonad m a) Source

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (WrappedMonad m a) Source

toConstr :: WrappedMonad m a -> Constr Source

dataTypeOf :: WrappedMonad m a -> DataType Source

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (WrappedMonad m a)) Source

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (WrappedMonad m a)) Source

gmapT :: (forall b. Data b => b -> b) -> WrappedMonad m a -> WrappedMonad m a Source

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> WrappedMonad m a -> r Source

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> WrappedMonad m a -> r Source

gmapQ :: (forall d. Data d => d -> u) -> WrappedMonad m a -> [u] Source

gmapQi :: Int -> (forall d. Data d => d -> u) -> WrappedMonad m a -> u Source

gmapM :: Monad m0 => (forall d. Data d => d -> m0 d) -> WrappedMonad m a -> m0 (WrappedMonad m a) Source

gmapMp :: MonadPlus m0 => (forall d. Data d => d -> m0 d) -> WrappedMonad m a -> m0 (WrappedMonad m a) Source

gmapMo :: MonadPlus m0 => (forall d. Data d => d -> m0 d) -> WrappedMonad m a -> m0 (WrappedMonad m a) Source

Generic (WrappedMonad m a)

Since: base-4.7.0.0
Instance details

Defined in Control.Applicative

Associated Types

type Rep (WrappedMonad m a) :: Type -> Type Source

Methods

from :: WrappedMonad m a -> Rep (WrappedMonad m a) x Source

to :: Rep (WrappedMonad m a) x -> WrappedMonad m a Source

type Rep1 (WrappedMonad m :: Type -> Type)
Instance details

Defined in Control.Applicative

type Rep1 (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)))
type Rep (WrappedMonad m a)
Instance details

Defined in Control.Applicative

type Rep (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))))

newtype WrappedArrow a b c Source

Constructors

WrapArrow

Fields

Instances
Instances details
Generic1 (WrappedArrow a b :: Type -> Type)

Since: base-4.7.0.0
Instance details

Defined in Control.Applicative

Associated Types

type Rep1 (WrappedArrow a b) :: k -> Type Source

Methods

from1 :: forall (a0 :: k). WrappedArrow a b a0 -> Rep1 (WrappedArrow a b) a0 Source

to1 :: forall (a0 :: k). Rep1 (WrappedArrow a b) a0 -> WrappedArrow a b a0 Source

Arrow a => Functor (WrappedArrow a b)

Since: base-2.1
Instance details

Defined in Control.Applicative

Methods

fmap :: (a0 -> b0) -> WrappedArrow a b a0 -> WrappedArrow a b b0 Source

(<$) :: a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0 Source

Arrow a => Applicative (WrappedArrow a b)

Since: base-2.1
Instance details

Defined in Control.Applicative

Methods

pure :: a0 -> WrappedArrow a b a0 Source

(<*>) :: WrappedArrow a b (a0 -> b0) -> WrappedArrow a b a0 -> WrappedArrow a b b0 Source

liftA2 :: (a0 -> b0 -> c) -> WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b c Source

(*>) :: WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b b0 Source

(<*) :: WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0 Source

(ArrowZero a, ArrowPlus a) => Alternative (WrappedArrow a b)

Since: base-2.1
Instance details

Defined in Control.Applicative

Methods

empty :: WrappedArrow a b a0 Source

(<|>) :: WrappedArrow a b a0 -> WrappedArrow a b a0 -> WrappedArrow a b a0 Source

some :: WrappedArrow a b a0 -> WrappedArrow a b [a0] Source

many :: WrappedArrow a b a0 -> WrappedArrow a b [a0] Source

(Typeable a, Typeable b, Typeable c, Data (a b c)) => Data (WrappedArrow a b c)

Since: base-4.14.0.0
Instance details

Defined in Data.Data

Methods

gfoldl :: (forall d b0. Data d => c0 (d -> b0) -> d -> c0 b0) -> (forall g. g -> c0 g) -> WrappedArrow a b c -> c0 (WrappedArrow a b c) Source

gunfold :: (forall b0 r. Data b0 => c0 (b0 -> r) -> c0 r) -> (forall r. r -> c0 r) -> Constr -> c0 (WrappedArrow a b c) Source

toConstr :: WrappedArrow a b c -> Constr Source

dataTypeOf :: WrappedArrow a b c -> DataType Source

dataCast1 :: Typeable t => (forall d. Data d => c0 (t d)) -> Maybe (c0 (WrappedArrow a b c)) Source

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c0 (t d e)) -> Maybe (c0 (WrappedArrow a b c)) Source

gmapT :: (forall b0. Data b0 => b0 -> b0) -> WrappedArrow a b c -> WrappedArrow a b c Source

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> WrappedArrow a b c -> r Source

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> WrappedArrow a b c -> r Source

gmapQ :: (forall d. Data d => d -> u) -> WrappedArrow a b c -> [u] Source

gmapQi :: Int -> (forall d. Data d => d -> u) -> WrappedArrow a b c -> u Source

gmapM :: Monad m => (forall d. Data d => d -> m d) -> WrappedArrow a b c -> m (WrappedArrow a b c) Source

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> WrappedArrow a b c -> m (WrappedArrow a b c) Source

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> WrappedArrow a b c -> m (WrappedArrow a b c) Source

Generic (WrappedArrow a b c)

Since: base-4.7.0.0
Instance details

Defined in Control.Applicative

Associated Types

type Rep (WrappedArrow a b c) :: Type -> Type Source

Methods

from :: WrappedArrow a b c -> Rep (WrappedArrow a b c) x Source

to :: Rep (WrappedArrow a b c) x -> WrappedArrow a b c Source

type Rep1 (WrappedArrow a b :: Type -> Type)
Instance details

Defined in Control.Applicative

type Rep1 (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))))
type Rep (WrappedArrow a b c)
Instance details

Defined in Control.Applicative

type Rep (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))))

newtype ZipList a Source

Lists, but with an Applicative functor based on zipping.

Constructors

ZipList

Fields

Instances
Instances details
Functor ZipList

Since: base-2.1
Instance details

Defined in Control.Applicative

Methods

fmap :: (a -> b) -> ZipList a -> ZipList b Source

(<$) :: a -> ZipList b -> ZipList a Source

Applicative ZipList 
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: base-2.1
Instance details

Defined in Control.Applicative

Methods

pure :: a -> ZipList a Source

(<*>) :: ZipList (a -> b) -> ZipList a -> ZipList b Source

liftA2 :: (a -> b -> c) -> ZipList a -> ZipList b -> ZipList c Source

(*>) :: ZipList a -> ZipList b -> ZipList b Source

(<*) :: ZipList a -> ZipList b -> ZipList a Source

Foldable ZipList

Since: base-4.9.0.0
Instance details

Defined in Control.Applicative

Methods

fold :: Monoid m => ZipList m -> m Source

foldMap :: Monoid m => (a -> m) -> ZipList a -> m Source

foldMap' :: Monoid m => (a -> m) -> ZipList a -> m Source

foldr :: (a -> b -> b) -> b -> ZipList a -> b Source

foldr' :: (a -> b -> b) -> b -> ZipList a -> b Source

foldl :: (b -> a -> b) -> b -> ZipList a -> b Source

foldl' :: (b -> a -> b) -> b -> ZipList a -> b Source

foldr1 :: (a -> a -> a) -> ZipList a -> a Source

foldl1 :: (a -> a -> a) -> ZipList a -> a Source

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 -> a Source

minimum :: Ord a => ZipList a -> a Source

sum :: Num a => ZipList a -> a Source

product :: Num a => ZipList a -> a Source

Traversable ZipList

Since: base-4.9.0.0
Instance details

Defined in Data.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 ZipList

Since: base-4.11.0.0
Instance details

Defined in Control.Applicative

Methods

empty :: ZipList a Source

(<|>) :: ZipList a -> ZipList a -> ZipList a Source

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

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

IsList (ZipList a)

Since: base-4.15.0.0
Instance details

Defined in GHC.Exts

Associated Types

type Item (ZipList a) Source

Methods

fromList :: [Item (ZipList a)] -> ZipList a Source

fromListN :: Int -> [Item (ZipList a)] -> ZipList a Source

toList :: ZipList a -> [Item (ZipList a)] Source

Eq a => Eq (ZipList a)

Since: base-4.7.0.0
Instance details

Defined in Control.Applicative

Methods

(==) :: ZipList a -> ZipList a -> Bool Source

(/=) :: ZipList a -> ZipList a -> Bool Source

Data a => Data (ZipList a)

Since: base-4.14.0.0
Instance details

Defined in Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> ZipList a -> c (ZipList a) Source

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (ZipList a) Source

toConstr :: ZipList a -> Constr Source

dataTypeOf :: ZipList a -> DataType Source

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (ZipList a)) Source

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (ZipList a)) Source

gmapT :: (forall b. Data b => b -> b) -> ZipList a -> ZipList a Source

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> ZipList a -> r Source

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> ZipList a -> r Source

gmapQ :: (forall d. Data d => d -> u) -> ZipList a -> [u] Source

gmapQi :: Int -> (forall d. Data d => d -> u) -> ZipList a -> u Source

gmapM :: Monad m => (forall d. Data d => d -> m d) -> ZipList a -> m (ZipList a) Source

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> ZipList a -> m (ZipList a) Source

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> ZipList a -> m (ZipList a) Source

Ord a => Ord (ZipList a)

Since: base-4.7.0.0
Instance details

Defined in Control.Applicative

Methods

compare :: ZipList a -> ZipList a -> Ordering Source

(<) :: ZipList a -> ZipList a -> Bool Source

(<=) :: ZipList a -> ZipList a -> Bool Source

(>) :: ZipList a -> ZipList a -> Bool Source

(>=) :: ZipList a -> ZipList a -> Bool Source

max :: ZipList a -> ZipList a -> ZipList a Source

min :: ZipList a -> ZipList a -> ZipList a Source

Read a => Read (ZipList a)

Since: base-4.7.0.0
Instance details

Defined in Control.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)

Since: base-4.7.0.0
Instance details

Defined in Control.Applicative

Methods

showsPrec :: Int -> ZipList a -> ShowS Source

show :: ZipList a -> String Source

showList :: [ZipList a] -> ShowS Source

Generic (ZipList a)

Since: base-4.7.0.0
Instance details

Defined in Control.Applicative

Associated Types

type Rep (ZipList a) :: Type -> Type Source

Methods

from :: ZipList a -> Rep (ZipList a) x Source

to :: Rep (ZipList a) x -> ZipList a Source

Generic1 ZipList

Since: base-4.7.0.0
Instance details

Defined in Control.Applicative

Associated Types

type Rep1 ZipList :: k -> Type Source

Methods

from1 :: forall (a :: k). ZipList a -> Rep1 ZipList a Source

to1 :: forall (a :: k). Rep1 ZipList a -> ZipList a Source

type Rep (ZipList a)
Instance details

Defined in Control.Applicative

type Rep (ZipList a) = D1 ('MetaData "ZipList" "Control.Applicative" "base" 'True) (C1 ('MetaCons "ZipList" 'PrefixI 'True) (S1 ('MetaSel ('Just "getZipList") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 [a])))
type Item (ZipList a)
Instance details

Defined in GHC.Exts

type Item (ZipList a) = a
type Rep1 ZipList
Instance details

Defined in Control.Applicative

type Rep1 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 b infixl 4 Source

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
Expand

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 infixl 4 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.

Using ApplicativeDo: 'a <$ bs' can be understood as the do expression

do bs
   pure a

with an inferred Functor constraint.

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

A variant of <*> with the arguments reversed.

Using ApplicativeDo: 'as <**> fs' can be understood as the do expression

do a <- as
   f <- fs
   pure (f a)

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.

| Using ApplicativeDo: 'liftA f as' can be understood as the do expression

do a <- as
   pure (f a)

with an inferred Functor constraint, weaker than Applicative.

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

Lift a ternary function to actions.

Using ApplicativeDo: 'liftA3 f as bs cs' can be understood as the do expression

do a <- as
   b <- bs
   c <- cs
   pure (f a b c)

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

One or none.

© The University of Glasgow and others
Licensed under a BSD-style license (see top of the page).
https://downloads.haskell.org/~ghc/8.10.2/docs/html/libraries/base-4.14.1.0/Control-Applicative.html