Relude.Applicative

This module contains reexports of Applicative and related functional. Additionally, it provides convenient combinators to work with Applicative.

Reexports

Main data types and functions reexported from Control.Applicative.

class Applicative f => Alternative (f :: Type -> Type) where

A monoid on applicative functors.

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

• some v = (:) <$> v <*> many v

• many v = some v <|> pure []

Minimal complete definition

empty, (<|>)

Methods

empty :: f a

The identity of <|>

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

An associative binary operation

some :: f a -> f [a]

One or more.

many :: f a -> f [a]

Zero or more.

Instances

Alternative ZipList

Since: base-4.11.0.0

Defined in Control.Applicative

Methods

empty :: ZipList a

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

some :: ZipList a -> ZipList [a]

many :: ZipList a -> ZipList [a]

Alternative STM

Takes the first non-retrying STM action.

Since: base-4.8.0.0

Defined in GHC.Conc.Sync

Methods

empty :: STM a

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

some :: STM a -> STM [a]

many :: STM a -> STM [a]

Alternative P

Since: base-4.5.0.0

Defined in Text.ParserCombinators.ReadP

Methods

empty :: P a

(<|>) :: P a -> P a -> P a

some :: P a -> P [a]

many :: P a -> P [a]

Alternative ReadP

Since: base-4.6.0.0

Defined in Text.ParserCombinators.ReadP

Methods

empty :: ReadP a

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

some :: ReadP a -> ReadP [a]

many :: ReadP a -> ReadP [a]

Alternative ReadPrec

Since: base-4.6.0.0

Defined in Text.ParserCombinators.ReadPrec

Methods

empty :: ReadPrec a

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

some :: ReadPrec a -> ReadPrec [a]

many :: ReadPrec a -> ReadPrec [a]

Alternative Seq

Since: containers-0.5.4

Defined in Data.Sequence.Internal

Methods

empty :: Seq a

(<|>) :: Seq a -> Seq a -> Seq a

some :: Seq a -> Seq [a]

many :: Seq a -> Seq [a]

Alternative IO

Takes the first non-throwing IO action's result. empty throws an exception.

Since: base-4.9.0.0

Defined in GHC.Base

Methods

empty :: IO a

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

some :: IO a -> IO [a]

many :: IO a -> IO [a]

Alternative Maybe

Picks the leftmost Just value, or, alternatively, Nothing.

Since: base-2.1

Defined in GHC.Base

Methods

empty :: Maybe a

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

some :: Maybe a -> Maybe [a]

many :: Maybe a -> Maybe [a]

Alternative List

Combines lists by concatenation, starting from the empty list.

Since: base-2.1

Defined in GHC.Base

Methods

empty :: [a]

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

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

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

MonadPlus m => Alternative (WrappedMonad m)

Since: base-2.1

Defined in Control.Applicative

Methods

empty :: WrappedMonad m a

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

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

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

ArrowPlus a => Alternative (ArrowMonad a)

Since: base-4.6.0.0

Defined in Control.Arrow

Methods

empty :: ArrowMonad a a0

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

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

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

Alternative (Proxy :: Type -> Type)

Since: base-4.9.0.0

Defined in Data.Proxy

Methods

empty :: Proxy a

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

some :: Proxy a -> Proxy [a]

many :: Proxy a -> Proxy [a]

Alternative (U1 :: Type -> Type)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

empty :: U1 a

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

some :: U1 a -> U1 [a]

many :: U1 a -> U1 [a]

(Functor m, Monad m) => Alternative (MaybeT m)

Defined in Control.Monad.Trans.Maybe

Methods

empty :: MaybeT m a

(<|>) :: MaybeT m a -> MaybeT m a -> MaybeT m a

some :: MaybeT m a -> MaybeT m [a]

many :: MaybeT m a -> MaybeT m [a]

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

Since: base-2.1

Defined in Control.Applicative

Methods

empty :: WrappedArrow a b a0

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

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

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

Alternative m => Alternative (Kleisli m a)

Since: base-4.14.0.0

Defined in Control.Arrow

Methods

empty :: Kleisli m a a0

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

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

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

Alternative f => Alternative (Ap f)

Since: base-4.12.0.0

Defined in Data.Monoid

Methods

empty :: Ap f a

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

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

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

Alternative f => Alternative (Alt f)

Since: base-4.8.0.0

Defined in Data.Semigroup.Internal

Methods

empty :: Alt f a

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

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

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

(Generic1 f, Alternative (Rep1 f)) => Alternative (Generically1 f)

Since: base-4.17.0.0

Defined in GHC.Generics

Methods

empty :: Generically1 f a

(<|>) :: Generically1 f a -> Generically1 f a -> Generically1 f a

some :: Generically1 f a -> Generically1 f [a]

many :: Generically1 f a -> Generically1 f [a]

Alternative f => Alternative (Rec1 f)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

empty :: Rec1 f a

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

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

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

(Monoid w, Functor m, MonadPlus m) => Alternative (AccumT w m)

Defined in Control.Monad.Trans.Accum

Methods

empty :: AccumT w m a

(<|>) :: AccumT w m a -> AccumT w m a -> AccumT w m a

some :: AccumT w m a -> AccumT w m [a]

many :: AccumT w m a -> AccumT w m [a]

(Functor m, Monad m, Monoid e) => Alternative (ExceptT e m)

Defined in Control.Monad.Trans.Except

Methods

empty :: ExceptT e m a

(<|>) :: ExceptT e m a -> ExceptT e m a -> ExceptT e m a

some :: ExceptT e m a -> ExceptT e m [a]

many :: ExceptT e m a -> ExceptT e m [a]

Alternative m => Alternative (IdentityT m)

Defined in Control.Monad.Trans.Identity

Methods

empty :: IdentityT m a

(<|>) :: IdentityT m a -> IdentityT m a -> IdentityT m a

some :: IdentityT m a -> IdentityT m [a]

many :: IdentityT m a -> IdentityT m [a]

Alternative m => Alternative (ReaderT r m)

Defined in Control.Monad.Trans.Reader

Methods

empty :: ReaderT r m a

(<|>) :: ReaderT r m a -> ReaderT r m a -> ReaderT r m a

some :: ReaderT r m a -> ReaderT r m [a]

many :: ReaderT r m a -> ReaderT r m [a]

(Functor m, MonadPlus m) => Alternative (SelectT r m)

Defined in Control.Monad.Trans.Select

Methods

empty :: SelectT r m a

(<|>) :: SelectT r m a -> SelectT r m a -> SelectT r m a

some :: SelectT r m a -> SelectT r m [a]

many :: SelectT r m a -> SelectT r m [a]

(Functor m, MonadPlus m) => Alternative (StateT s m)

Defined in Control.Monad.Trans.State.Lazy

Methods

empty :: StateT s m a

(<|>) :: StateT s m a -> StateT s m a -> StateT s m a

some :: StateT s m a -> StateT s m [a]

many :: StateT s m a -> StateT s m [a]

(Functor m, MonadPlus m) => Alternative (StateT s m)

Defined in Control.Monad.Trans.State.Strict

Methods

empty :: StateT s m a

(<|>) :: StateT s m a -> StateT s m a -> StateT s m a

some :: StateT s m a -> StateT s m [a]

many :: StateT s m a -> StateT s m [a]

(Functor m, MonadPlus m) => Alternative (WriterT w m)

Defined in Control.Monad.Trans.Writer.CPS

Methods

empty :: WriterT w m a

(<|>) :: WriterT w m a -> WriterT w m a -> WriterT w m a

some :: WriterT w m a -> WriterT w m [a]

many :: WriterT w m a -> WriterT w m [a]

(Monoid w, Alternative m) => Alternative (WriterT w m)

Defined in Control.Monad.Trans.Writer.Lazy

Methods

empty :: WriterT w m a

(<|>) :: WriterT w m a -> WriterT w m a -> WriterT w m a

some :: WriterT w m a -> WriterT w m [a]

many :: WriterT w m a -> WriterT w m [a]

(Monoid w, Alternative m) => Alternative (WriterT w m)

Defined in Control.Monad.Trans.Writer.Strict

Methods

empty :: WriterT w m a

(<|>) :: WriterT w m a -> WriterT w m a -> WriterT w m a

some :: WriterT w m a -> WriterT w m [a]

many :: WriterT w m a -> WriterT w m [a]

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

Since: base-4.9.0.0

Defined in Data.Functor.Product

Methods

empty :: Product f g a

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

some :: Product f g a -> Product f g [a]

many :: Product f g a -> Product f g [a]

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

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

empty :: (f :*: g) a

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

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

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

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

Since: base-4.9.0.0

Defined in Data.Functor.Compose

Methods

empty :: Compose f g a

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

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

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

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

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

empty :: (f :.: g) a

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

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

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

Alternative f => Alternative (M1 i c f)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

empty :: M1 i c f a

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

some :: M1 i c f a -> M1 i c f [a]

many :: M1 i c f a -> M1 i c f [a]

(Functor m, MonadPlus m) => Alternative (RWST r w s m)

Defined in Control.Monad.Trans.RWS.CPS

Methods

empty :: RWST r w s m a

(<|>) :: RWST r w s m a -> RWST r w s m a -> RWST r w s m a

some :: RWST r w s m a -> RWST r w s m [a]

many :: RWST r w s m a -> RWST r w s m [a]

(Monoid w, Functor m, MonadPlus m) => Alternative (RWST r w s m)

Defined in Control.Monad.Trans.RWS.Lazy

Methods

empty :: RWST r w s m a

(<|>) :: RWST r w s m a -> RWST r w s m a -> RWST r w s m a

some :: RWST r w s m a -> RWST r w s m [a]

many :: RWST r w s m a -> RWST r w s m [a]

(Monoid w, Functor m, MonadPlus m) => Alternative (RWST r w s m)

Defined in Control.Monad.Trans.RWS.Strict

Methods

empty :: RWST r w s m a

(<|>) :: RWST r w s m a -> RWST r w s m a -> RWST r w s m a

some :: RWST r w s m a -> RWST r w s m [a]

many :: RWST r w s m a -> RWST r w s m [a]

class Functor f => Applicative (f :: Type -> Type) where

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:

• u *> v = (id <$ u) <*> v

• u <* v = liftA2 const u v

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

If f is also a Monad, it should satisfy

• pure = return

• m1 <*> m2 = m1 >>= (\x1 -> m2 >>= (\x2 -> return (x1 x2)))

• (*>) = (>>)

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

Minimal complete definition

pure, ((<*>) | liftA2)

Methods

pure :: a -> f a

Lift a value.

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

Sequential application.

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

Example

Used in combination with (<$>), (<*>) can be used to build a record.

>>> data MyState = MyState {arg1 :: Foo, arg2 :: Bar, arg3 :: Baz}

>>> produceFoo :: Applicative f => f Foo

>>> produceBar :: Applicative f => f Bar
>>> produceBaz :: Applicative f => f Baz

>>> mkState :: Applicative f => f MyState
>>> mkState = MyState <$> produceFoo <*> produceBar <*> produceBaz

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

Lift a binary function to actions.

Some functors support an implementation of liftA2 that is more efficient than the default one. In particular, if fmap is an expensive operation, it is likely better to use liftA2 than to fmap over the structure and then use <*>.

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

Example

>>> liftA2 (,) (Just 3) (Just 5)
Just (3,5)

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

Sequence actions, discarding the value of the first argument.

Examples

If used in conjunction with the Applicative instance for Maybe, you can chain Maybe computations, with a possible "early return" in case of Nothing.

>>> Just 2 *> Just 3
Just 3

>>> Nothing *> Just 3
Nothing

Of course a more interesting use case would be to have effectful computations instead of just returning pure values.

>>> import Data.Char
>>> import Text.ParserCombinators.ReadP
>>> let p = string "my name is " *> munch1 isAlpha <* eof
>>> readP_to_S p "my name is Simon"
[("Simon","")]

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

Sequence actions, discarding the value of the second argument.

Instances

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

Defined in Control.Applicative

Methods

pure :: a -> ZipList a

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

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

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

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

Applicative Complex

Since: base-4.9.0.0

Defined in Data.Complex

Methods

pure :: a -> Complex a

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

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

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

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

Applicative Identity

Since: base-4.8.0.0

Defined in Data.Functor.Identity

Methods

pure :: a -> Identity a

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

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

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

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

Applicative First

Since: base-4.8.0.0

Defined in Data.Monoid

Methods

pure :: a -> First a

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

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

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

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

Applicative Last

Since: base-4.8.0.0

Defined in Data.Monoid

Methods

pure :: a -> Last a

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

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

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

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

Applicative Down

Since: base-4.11.0.0

Defined in Data.Ord

Methods

pure :: a -> Down a

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

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

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

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

Applicative First

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

pure :: a -> First a

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

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

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

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

Applicative Last

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

pure :: a -> Last a

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

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

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

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

Applicative Max

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

pure :: a -> Max a

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

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

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

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

Applicative Min

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

pure :: a -> Min a

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

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

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

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

Applicative Dual

Since: base-4.8.0.0

Defined in Data.Semigroup.Internal

Methods

pure :: a -> Dual a

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

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

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

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

Applicative Product

Since: base-4.8.0.0

Defined in Data.Semigroup.Internal

Methods

pure :: a -> Product a

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

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

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

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

Applicative Sum

Since: base-4.8.0.0

Defined in Data.Semigroup.Internal

Methods

pure :: a -> Sum a

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

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

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

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

Applicative NonEmpty

Since: base-4.9.0.0

Defined in GHC.Base

Methods

pure :: a -> NonEmpty a

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

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

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

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

Applicative STM

Since: base-4.8.0.0

Defined in GHC.Conc.Sync

Methods

pure :: a -> STM a

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

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

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

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

Applicative Par1

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

pure :: a -> Par1 a

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

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

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

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

Applicative P

Since: base-4.5.0.0

Defined in Text.ParserCombinators.ReadP

Methods

pure :: a -> P a

(<*>) :: P (a -> b) -> P a -> P b

liftA2 :: (a -> b -> c) -> P a -> P b -> P c

(*>) :: P a -> P b -> P b

(<*) :: P a -> P b -> P a

Applicative ReadP

Since: base-4.6.0.0

Defined in Text.ParserCombinators.ReadP

Methods

pure :: a -> ReadP a

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

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

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

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

Applicative ReadPrec

Since: base-4.6.0.0

Defined in Text.ParserCombinators.ReadPrec

Methods

pure :: a -> ReadPrec a

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

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

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

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

Applicative Put

Defined in Data.ByteString.Builder.Internal

Methods

pure :: a -> Put a

(<*>) :: Put (a -> b) -> Put a -> Put b

liftA2 :: (a -> b -> c) -> Put a -> Put b -> Put c

(*>) :: Put a -> Put b -> Put b

(<*) :: Put a -> Put b -> Put a

Applicative Seq

Since: containers-0.5.4

Defined in Data.Sequence.Internal

Methods

pure :: a -> Seq a

(<*>) :: Seq (a -> b) -> Seq a -> Seq b

liftA2 :: (a -> b -> c) -> Seq a -> Seq b -> Seq c

(*>) :: Seq a -> Seq b -> Seq b

(<*) :: Seq a -> Seq b -> Seq a

Applicative Tree

Defined in Data.Tree

Methods

pure :: a -> Tree a

(<*>) :: Tree (a -> b) -> Tree a -> Tree b

liftA2 :: (a -> b -> c) -> Tree a -> Tree b -> Tree c

(*>) :: Tree a -> Tree b -> Tree b

(<*) :: Tree a -> Tree b -> Tree a

Applicative IO

Since: base-2.1

Defined in GHC.Base

Methods

pure :: a -> IO a

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

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

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

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

Applicative Q

Defined in Language.Haskell.TH.Syntax

Methods

pure :: a -> Q a

(<*>) :: Q (a -> b) -> Q a -> Q b

liftA2 :: (a -> b -> c) -> Q a -> Q b -> Q c

(*>) :: Q a -> Q b -> Q b

(<*) :: Q a -> Q b -> Q a

Applicative Maybe

Since: base-2.1

Defined in GHC.Base

Methods

pure :: a -> Maybe a

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

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

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

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

Applicative Solo

Since: base-4.15

Defined in GHC.Base

Methods

pure :: a -> Solo a

(<*>) :: Solo (a -> b) -> Solo a -> Solo b

liftA2 :: (a -> b -> c) -> Solo a -> Solo b -> Solo c

(*>) :: Solo a -> Solo b -> Solo b

(<*) :: Solo a -> Solo b -> Solo a

Applicative List

Since: base-2.1

Defined in GHC.Base

Methods

pure :: a -> [a]

(<*>) :: [a -> b] -> [a] -> [b]

liftA2 :: (a -> b -> c) -> [a] -> [b] -> [c]

(*>) :: [a] -> [b] -> [b]

(<*) :: [a] -> [b] -> [a]

Monad m => Applicative (WrappedMonad m)

Since: base-2.1

Defined in Control.Applicative

Methods

pure :: a -> WrappedMonad m a

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

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

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

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

Arrow a => Applicative (ArrowMonad a)

Since: base-4.6.0.0

Defined in Control.Arrow

Methods

pure :: a0 -> ArrowMonad a a0

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

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

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

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

Applicative (Either e)

Since: base-3.0

Defined in Data.Either

Methods

pure :: a -> Either e a

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

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

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

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

Applicative (Proxy :: Type -> Type)

Since: base-4.7.0.0

Defined in Data.Proxy

Methods

pure :: a -> Proxy a

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

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

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

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

Applicative (U1 :: Type -> Type)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

pure :: a -> U1 a

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

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

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

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

(Functor m, Monad m) => Applicative (MaybeT m)

Defined in Control.Monad.Trans.Maybe

Methods

pure :: a -> MaybeT m a

(<*>) :: MaybeT m (a -> b) -> MaybeT m a -> MaybeT m b

liftA2 :: (a -> b -> c) -> MaybeT m a -> MaybeT m b -> MaybeT m c

(*>) :: MaybeT m a -> MaybeT m b -> MaybeT m b

(<*) :: MaybeT m a -> MaybeT m b -> MaybeT m a

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

Defined in GHC.Base

Methods

pure :: a0 -> (a, a0)

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

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

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

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

Arrow a => Applicative (WrappedArrow a b)

Since: base-2.1

Defined in Control.Applicative

Methods

pure :: a0 -> WrappedArrow a b a0

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

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

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

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

Applicative m => Applicative (Kleisli m a)

Since: base-4.14.0.0

Defined in Control.Arrow

Methods

pure :: a0 -> Kleisli m a a0

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

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

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

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

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

Since: base-2.0.1

Defined in Data.Functor.Const

Methods

pure :: a -> Const m a

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

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

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

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

Applicative f => Applicative (Ap f)

Since: base-4.12.0.0

Defined in Data.Monoid

Methods

pure :: a -> Ap f a

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

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

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

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

Applicative f => Applicative (Alt f)

Since: base-4.8.0.0

Defined in Data.Semigroup.Internal

Methods

pure :: a -> Alt f a

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

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

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

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

(Generic1 f, Applicative (Rep1 f)) => Applicative (Generically1 f)

Since: base-4.17.0.0

Defined in GHC.Generics

Methods

pure :: a -> Generically1 f a

(<*>) :: Generically1 f (a -> b) -> Generically1 f a -> Generically1 f b

liftA2 :: (a -> b -> c) -> Generically1 f a -> Generically1 f b -> Generically1 f c

(*>) :: Generically1 f a -> Generically1 f b -> Generically1 f b

(<*) :: Generically1 f a -> Generically1 f b -> Generically1 f a

Applicative f => Applicative (Rec1 f)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

pure :: a -> Rec1 f a

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

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

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

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

(Applicative f, Monad f) => Applicative (WhenMissing f x)

Equivalent to ReaderT k (ReaderT x (MaybeT f)).

Since: containers-0.5.9

Defined in Data.IntMap.Internal

Methods

pure :: a -> WhenMissing f x a

(<*>) :: WhenMissing f x (a -> b) -> WhenMissing f x a -> WhenMissing f x b

liftA2 :: (a -> b -> c) -> WhenMissing f x a -> WhenMissing f x b -> WhenMissing f x c

(*>) :: WhenMissing f x a -> WhenMissing f x b -> WhenMissing f x b

(<*) :: WhenMissing f x a -> WhenMissing f x b -> WhenMissing f x a

(Monoid w, Functor m, Monad m) => Applicative (AccumT w m)

Defined in Control.Monad.Trans.Accum

Methods

pure :: a -> AccumT w m a

(<*>) :: AccumT w m (a -> b) -> AccumT w m a -> AccumT w m b

liftA2 :: (a -> b -> c) -> AccumT w m a -> AccumT w m b -> AccumT w m c

(*>) :: AccumT w m a -> AccumT w m b -> AccumT w m b

(<*) :: AccumT w m a -> AccumT w m b -> AccumT w m a

(Functor m, Monad m) => Applicative (ExceptT e m)

Defined in Control.Monad.Trans.Except

Methods

pure :: a -> ExceptT e m a

(<*>) :: ExceptT e m (a -> b) -> ExceptT e m a -> ExceptT e m b

liftA2 :: (a -> b -> c) -> ExceptT e m a -> ExceptT e m b -> ExceptT e m c

(*>) :: ExceptT e m a -> ExceptT e m b -> ExceptT e m b

(<*) :: ExceptT e m a -> ExceptT e m b -> ExceptT e m a

Applicative m => Applicative (IdentityT m)

Defined in Control.Monad.Trans.Identity

Methods

pure :: a -> IdentityT m a

(<*>) :: IdentityT m (a -> b) -> IdentityT m a -> IdentityT m b

liftA2 :: (a -> b -> c) -> IdentityT m a -> IdentityT m b -> IdentityT m c

(*>) :: IdentityT m a -> IdentityT m b -> IdentityT m b

(<*) :: IdentityT m a -> IdentityT m b -> IdentityT m a

Applicative m => Applicative (ReaderT r m)

Defined in Control.Monad.Trans.Reader

Methods

pure :: a -> ReaderT r m a

(<*>) :: ReaderT r m (a -> b) -> ReaderT r m a -> ReaderT r m b

liftA2 :: (a -> b -> c) -> ReaderT r m a -> ReaderT r m b -> ReaderT r m c

(*>) :: ReaderT r m a -> ReaderT r m b -> ReaderT r m b

(<*) :: ReaderT r m a -> ReaderT r m b -> ReaderT r m a

(Functor m, Monad m) => Applicative (SelectT r m)

Defined in Control.Monad.Trans.Select

Methods

pure :: a -> SelectT r m a

(<*>) :: SelectT r m (a -> b) -> SelectT r m a -> SelectT r m b

liftA2 :: (a -> b -> c) -> SelectT r m a -> SelectT r m b -> SelectT r m c

(*>) :: SelectT r m a -> SelectT r m b -> SelectT r m b

(<*) :: SelectT r m a -> SelectT r m b -> SelectT r m a

(Functor m, Monad m) => Applicative (StateT s m)

Defined in Control.Monad.Trans.State.Lazy

Methods

pure :: a -> StateT s m a

(<*>) :: StateT s m (a -> b) -> StateT s m a -> StateT s m b

liftA2 :: (a -> b -> c) -> StateT s m a -> StateT s m b -> StateT s m c

(*>) :: StateT s m a -> StateT s m b -> StateT s m b

(<*) :: StateT s m a -> StateT s m b -> StateT s m a

(Functor m, Monad m) => Applicative (StateT s m)

Defined in Control.Monad.Trans.State.Strict

Methods

pure :: a -> StateT s m a

(<*>) :: StateT s m (a -> b) -> StateT s m a -> StateT s m b

liftA2 :: (a -> b -> c) -> StateT s m a -> StateT s m b -> StateT s m c

(*>) :: StateT s m a -> StateT s m b -> StateT s m b

(<*) :: StateT s m a -> StateT s m b -> StateT s m a

(Functor m, Monad m) => Applicative (WriterT w m)

Defined in Control.Monad.Trans.Writer.CPS

Methods

pure :: a -> WriterT w m a

(<*>) :: WriterT w m (a -> b) -> WriterT w m a -> WriterT w m b

liftA2 :: (a -> b -> c) -> WriterT w m a -> WriterT w m b -> WriterT w m c

(*>) :: WriterT w m a -> WriterT w m b -> WriterT w m b

(<*) :: WriterT w m a -> WriterT w m b -> WriterT w m a

(Monoid w, Applicative m) => Applicative (WriterT w m)

Defined in Control.Monad.Trans.Writer.Lazy

Methods

pure :: a -> WriterT w m a

(<*>) :: WriterT w m (a -> b) -> WriterT w m a -> WriterT w m b

liftA2 :: (a -> b -> c) -> WriterT w m a -> WriterT w m b -> WriterT w m c

(*>) :: WriterT w m a -> WriterT w m b -> WriterT w m b

(<*) :: WriterT w m a -> WriterT w m b -> WriterT w m a

(Monoid w, Applicative m) => Applicative (WriterT w m)

Defined in Control.Monad.Trans.Writer.Strict

Methods

pure :: a -> WriterT w m a

(<*>) :: WriterT w m (a -> b) -> WriterT w m a -> WriterT w m b

liftA2 :: (a -> b -> c) -> WriterT w m a -> WriterT w m b -> WriterT w m c

(*>) :: WriterT w m a -> WriterT w m b -> WriterT w m b

(<*) :: WriterT w m a -> WriterT w m b -> WriterT w m a

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

Since: base-4.14.0.0

Defined in GHC.Base

Methods

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

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

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

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

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

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

Since: base-4.9.0.0

Defined in Data.Functor.Product

Methods

pure :: a -> Product f g a

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

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

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

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

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

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

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

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

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

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

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

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

Since: base-4.12.0.0

Defined in GHC.Generics

Methods

pure :: a -> K1 i c a

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

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

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

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

(Monad f, Applicative f) => Applicative (WhenMatched f x y)

Equivalent to ReaderT Key (ReaderT x (ReaderT y (MaybeT f)))

Since: containers-0.5.9

Defined in Data.IntMap.Internal

Methods

pure :: a -> WhenMatched f x y a

(<*>) :: WhenMatched f x y (a -> b) -> WhenMatched f x y a -> WhenMatched f x y b

liftA2 :: (a -> b -> c) -> WhenMatched f x y a -> WhenMatched f x y b -> WhenMatched f x y c

(*>) :: WhenMatched f x y a -> WhenMatched f x y b -> WhenMatched f x y b

(<*) :: WhenMatched f x y a -> WhenMatched f x y b -> WhenMatched f x y a

(Applicative f, Monad f) => Applicative (WhenMissing f k x)

Equivalent to ReaderT k (ReaderT x (MaybeT f)) .

Since: containers-0.5.9

Defined in Data.Map.Internal

Methods

pure :: a -> WhenMissing f k x a

(<*>) :: WhenMissing f k x (a -> b) -> WhenMissing f k x a -> WhenMissing f k x b

liftA2 :: (a -> b -> c) -> WhenMissing f k x a -> WhenMissing f k x b -> WhenMissing f k x c

(*>) :: WhenMissing f k x a -> WhenMissing f k x b -> WhenMissing f k x b

(<*) :: WhenMissing f k x a -> WhenMissing f k x b -> WhenMissing f k x a

Applicative (ContT r m)

Defined in Control.Monad.Trans.Cont

Methods

pure :: a -> ContT r m a

(<*>) :: ContT r m (a -> b) -> ContT r m a -> ContT r m b

liftA2 :: (a -> b -> c) -> ContT r m a -> ContT r m b -> ContT r m c

(*>) :: ContT r m a -> ContT r m b -> ContT r m b

(<*) :: ContT r m a -> ContT r m b -> ContT r m a

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

Since: base-4.14.0.0

Defined in GHC.Base

Methods

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

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

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

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

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

Applicative ((->) r)

Since: base-2.1

Defined in GHC.Base

Methods

pure :: a -> r -> a

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

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

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

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

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

Since: base-4.9.0.0

Defined in Data.Functor.Compose

Methods

pure :: a -> Compose f g a

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

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

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

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

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

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

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

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

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

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

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

Applicative f => Applicative (M1 i c f)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

pure :: a -> M1 i c f a

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

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

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

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

(Monad f, Applicative f) => Applicative (WhenMatched f k x y)

Equivalent to ReaderT k (ReaderT x (ReaderT y (MaybeT f)))

Since: containers-0.5.9

Defined in Data.Map.Internal

Methods

pure :: a -> WhenMatched f k x y a

(<*>) :: WhenMatched f k x y (a -> b) -> WhenMatched f k x y a -> WhenMatched f k x y b

liftA2 :: (a -> b -> c) -> WhenMatched f k x y a -> WhenMatched f k x y b -> WhenMatched f k x y c

(*>) :: WhenMatched f k x y a -> WhenMatched f k x y b -> WhenMatched f k x y b

(<*) :: WhenMatched f k x y a -> WhenMatched f k x y b -> WhenMatched f k x y a

(Functor m, Monad m) => Applicative (RWST r w s m)

Defined in Control.Monad.Trans.RWS.CPS

Methods

pure :: a -> RWST r w s m a

(<*>) :: RWST r w s m (a -> b) -> RWST r w s m a -> RWST r w s m b

liftA2 :: (a -> b -> c) -> RWST r w s m a -> RWST r w s m b -> RWST r w s m c

(*>) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m b

(<*) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m a

(Monoid w, Functor m, Monad m) => Applicative (RWST r w s m)

Defined in Control.Monad.Trans.RWS.Lazy

Methods

pure :: a -> RWST r w s m a

(<*>) :: RWST r w s m (a -> b) -> RWST r w s m a -> RWST r w s m b

liftA2 :: (a -> b -> c) -> RWST r w s m a -> RWST r w s m b -> RWST r w s m c

(*>) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m b

(<*) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m a

(Monoid w, Functor m, Monad m) => Applicative (RWST r w s m)

Defined in Control.Monad.Trans.RWS.Strict

Methods

pure :: a -> RWST r w s m a

(<*>) :: RWST r w s m (a -> b) -> RWST r w s m a -> RWST r w s m b

liftA2 :: (a -> b -> c) -> RWST r w s m a -> RWST r w s m b -> RWST r w s m c

(*>) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m b

(<*) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m a

newtype Const a (b :: k)

The Const functor.

Constructors

Const

Fields

• getConst :: a

Instances

Generic1 (Const a :: k -> Type)

Defined in Data.Functor.Const

Associated Types

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

Methods

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

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

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

Since: base-4.10.0.0

Defined in Data.Bifoldable

Methods

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

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

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

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

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

Since: base-4.8.0.0

Defined in Data.Bifunctor

Methods

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

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

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

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

Since: base-4.10.0.0

Defined in Data.Bitraversable

Methods

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

NFData2 (Const :: Type -> Type -> Type)

Since: deepseq-1.4.3.0

Defined in Control.DeepSeq

Methods

liftRnf2 :: (a -> ()) -> (b -> ()) -> Const a b -> ()

Hashable2 (Const :: Type -> Type -> Type)

Defined in Data.Hashable.Class

Methods

liftHashWithSalt2 :: (Int -> a -> Int) -> (Int -> b -> Int) -> Int -> Const a b -> Int

Foldable (Const m :: Type -> Type)

Since: base-4.7.0.0

Defined in Data.Functor.Const

Methods

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

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

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

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

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

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

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

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

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

toList :: Const m a -> [a]

null :: Const m a -> Bool

length :: Const m a -> Int

elem :: Eq a => a -> Const m a -> Bool

maximum :: Ord a => Const m a -> a

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

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

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

Contravariant (Const a :: Type -> Type)

Defined in Data.Functor.Contravariant

Methods

contramap :: (a' -> a0) -> Const a a0 -> Const a a'

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

Traversable (Const m :: Type -> Type)

Since: base-4.7.0.0

Defined in Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> Const m a -> f (Const m b)

sequenceA :: Applicative f => Const m (f a) -> f (Const m a)

mapM :: Monad m0 => (a -> m0 b) -> Const m a -> m0 (Const m b)

sequence :: Monad m0 => Const m (m0 a) -> m0 (Const m a)

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

Since: base-2.0.1

Defined in Data.Functor.Const

Methods

pure :: a -> Const m a

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

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

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

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

Functor (Const m :: Type -> Type)

Since: base-2.1

Defined in Data.Functor.Const

Methods

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

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

NFData a => NFData1 (Const a :: Type -> Type)

Since: deepseq-1.4.3.0

Defined in Control.DeepSeq

Methods

liftRnf :: (a0 -> ()) -> Const a a0 -> ()

Hashable a => Hashable1 (Const a :: Type -> Type)

Defined in Data.Hashable.Class

Methods

liftHashWithSalt :: (Int -> a0 -> Int) -> Int -> Const a a0 -> Int

(Typeable k, Data a, Typeable b) => Data (Const a b)

Since: base-4.10.0.0

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)

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

toConstr :: Const a b -> Constr

dataTypeOf :: Const a b -> DataType

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

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

gmapT :: (forall b0. Data b0 => b0 -> b0) -> Const a b -> Const a b

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

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

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

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

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Const a b -> m (Const a b)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Const a b -> m (Const a b)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Const a b -> m (Const a b)

IsString a => IsString (Const a b)

Since: base-4.9.0.0

Defined in Data.String

Methods

fromString :: String -> Const a b

Storable a => Storable (Const a b)

Since: base-4.9.0.0

Defined in Data.Functor.Const

Methods

sizeOf :: Const a b -> Int

alignment :: Const a b -> Int

peekElemOff :: Ptr (Const a b) -> Int -> IO (Const a b)

pokeElemOff :: Ptr (Const a b) -> Int -> Const a b -> IO ()

peekByteOff :: Ptr b0 -> Int -> IO (Const a b)

pokeByteOff :: Ptr b0 -> Int -> Const a b -> IO ()

peek :: Ptr (Const a b) -> IO (Const a b)

poke :: Ptr (Const a b) -> Const a b -> IO ()

Monoid a => Monoid (Const a b)

Since: base-4.9.0.0

Defined in Data.Functor.Const

Methods

mempty :: Const a b

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

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

Semigroup a => Semigroup (Const a b)

Since: base-4.9.0.0

Defined in Data.Functor.Const

Methods

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

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

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

Bits a => Bits (Const a b)

Since: base-4.9.0.0

Defined in Data.Functor.Const

Methods

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

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

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

complement :: Const a b -> Const a b

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

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

zeroBits :: Const a b

bit :: Int -> Const a b

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

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

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

testBit :: Const a b -> Int -> Bool

bitSizeMaybe :: Const a b -> Maybe Int

bitSize :: Const a b -> Int

isSigned :: Const a b -> Bool

shiftL :: Const a b -> Int -> Const a b

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

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

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

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

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

popCount :: Const a b -> Int

FiniteBits a => FiniteBits (Const a b)

Since: base-4.9.0.0

Defined in Data.Functor.Const

Methods

finiteBitSize :: Const a b -> Int

countLeadingZeros :: Const a b -> Int

countTrailingZeros :: Const a b -> Int

Bounded a => Bounded (Const a b)

Since: base-4.9.0.0

Defined in Data.Functor.Const

Methods

minBound :: Const a b

maxBound :: Const a b

Enum a => Enum (Const a b)

Since: base-4.9.0.0

Defined in Data.Functor.Const

Methods

succ :: Const a b -> Const a b

pred :: Const a b -> Const a b

toEnum :: Int -> Const a b

fromEnum :: Const a b -> Int

enumFrom :: Const a b -> [Const a b]

enumFromThen :: Const a b -> Const a b -> [Const a b]

enumFromTo :: Const a b -> Const a b -> [Const a b]

enumFromThenTo :: Const a b -> Const a b -> Const a b -> [Const a b]

Floating a => Floating (Const a b)

Since: base-4.9.0.0

Defined in Data.Functor.Const

Methods

pi :: Const a b

exp :: Const a b -> Const a b

log :: Const a b -> Const a b

sqrt :: Const a b -> Const a b

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

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

sin :: Const a b -> Const a b

cos :: Const a b -> Const a b

tan :: Const a b -> Const a b

asin :: Const a b -> Const a b

acos :: Const a b -> Const a b

atan :: Const a b -> Const a b

sinh :: Const a b -> Const a b

cosh :: Const a b -> Const a b

tanh :: Const a b -> Const a b

asinh :: Const a b -> Const a b

acosh :: Const a b -> Const a b

atanh :: Const a b -> Const a b

log1p :: Const a b -> Const a b

expm1 :: Const a b -> Const a b

log1pexp :: Const a b -> Const a b

log1mexp :: Const a b -> Const a b

RealFloat a => RealFloat (Const a b)

Since: base-4.9.0.0

Defined in Data.Functor.Const

Methods

floatRadix :: Const a b -> Integer

floatDigits :: Const a b -> Int

floatRange :: Const a b -> (Int, Int)

decodeFloat :: Const a b -> (Integer, Int)

encodeFloat :: Integer -> Int -> Const a b

exponent :: Const a b -> Int

significand :: Const a b -> Const a b

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

isNaN :: Const a b -> Bool

isInfinite :: Const a b -> Bool

isDenormalized :: Const a b -> Bool

isNegativeZero :: Const a b -> Bool

isIEEE :: Const a b -> Bool

atan2 :: Const a b -> Const a b -> Const a b

Generic (Const a b)

Defined in Data.Functor.Const

Associated Types

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

Methods

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

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

Ix a => Ix (Const a b)

Since: base-4.9.0.0

Defined in Data.Functor.Const

Methods

range :: (Const a b, Const a b) -> [Const a b]

index :: (Const a b, Const a b) -> Const a b -> Int

unsafeIndex :: (Const a b, Const a b) -> Const a b -> Int

inRange :: (Const a b, Const a b) -> Const a b -> Bool

rangeSize :: (Const a b, Const a b) -> Int

unsafeRangeSize :: (Const a b, Const a b) -> Int

Num a => Num (Const a b)

Since: base-4.9.0.0

Defined in Data.Functor.Const

Methods

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

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

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

negate :: Const a b -> Const a b

abs :: Const a b -> Const a b

signum :: Const a b -> Const a b

fromInteger :: Integer -> Const a b

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

Defined in Data.Functor.Const

Methods

readsPrec :: Int -> ReadS (Const a b)

readList :: ReadS [Const a b]

readPrec :: ReadPrec (Const a b)

readListPrec :: ReadPrec [Const a b]

Fractional a => Fractional (Const a b)

Since: base-4.9.0.0

Defined in Data.Functor.Const

Methods

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

recip :: Const a b -> Const a b

fromRational :: Rational -> Const a b

Integral a => Integral (Const a b)

Since: base-4.9.0.0

Defined in Data.Functor.Const

Methods

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

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

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

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

quotRem :: Const a b -> Const a b -> (Const a b, Const a b)

divMod :: Const a b -> Const a b -> (Const a b, Const a b)

toInteger :: Const a b -> Integer

Real a => Real (Const a b)

Since: base-4.9.0.0

Defined in Data.Functor.Const

Methods

toRational :: Const a b -> Rational

RealFrac a => RealFrac (Const a b)

Since: base-4.9.0.0

Defined in Data.Functor.Const

Methods

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

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

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

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

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

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

Defined in Data.Functor.Const

Methods

showsPrec :: Int -> Const a b -> ShowS

show :: Const a b -> String

showList :: [Const a b] -> ShowS

NFData a => NFData (Const a b)

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: Const a b -> ()

Eq a => Eq (Const a b)

Since: base-4.9.0.0

Defined in Data.Functor.Const

Methods

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

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

Ord a => Ord (Const a b)

Since: base-4.9.0.0

Defined in Data.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

Hashable a => Hashable (Const a b)

Defined in Data.Hashable.Class

Methods

hashWithSalt :: Int -> Const a b -> Int

hash :: Const a b -> Int

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

Since: base-4.9.0.0

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)

Since: base-4.9.0.0

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 ZipList a

Lists, but with an Applicative functor based on zipping.

Constructors

ZipList

Fields

• getZipList :: [a]

Instances

Foldable ZipList

Since: base-4.9.0.0

Defined in Control.Applicative

Methods

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

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

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

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

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

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

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

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

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

toList :: ZipList a -> [a]

null :: ZipList a -> Bool

length :: ZipList a -> Int

elem :: Eq a => a -> ZipList a -> Bool

maximum :: Ord a => ZipList a -> a

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

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

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

Traversable ZipList

Since: base-4.9.0.0

Defined in Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> ZipList a -> f (ZipList b)

sequenceA :: Applicative f => ZipList (f a) -> f (ZipList a)

mapM :: Monad m => (a -> m b) -> ZipList a -> m (ZipList b)

sequence :: Monad m => ZipList (m a) -> m (ZipList a)

Alternative ZipList

Since: base-4.11.0.0

Defined in Control.Applicative

Methods

empty :: ZipList a

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

some :: ZipList a -> ZipList [a]

many :: ZipList a -> ZipList [a]

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

Defined in Control.Applicative

Methods

pure :: a -> ZipList a

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

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

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

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

Functor ZipList

Since: base-2.1

Defined in Control.Applicative

Methods

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

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

NFData1 ZipList

Since: deepseq-1.4.3.0

Defined in Control.DeepSeq

Methods

liftRnf :: (a -> ()) -> ZipList a -> ()

Generic1 ZipList

Defined in Control.Applicative

Associated Types

type Rep1 ZipList :: k -> Type

Methods

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

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

Data a => Data (ZipList a)

Since: base-4.14.0.0

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)

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

toConstr :: ZipList a -> Constr

dataTypeOf :: ZipList a -> DataType

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

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

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

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

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

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

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

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

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

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

Generic (ZipList a)

Defined in Control.Applicative

Associated Types

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

Methods

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

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

IsList (ZipList a)

Since: base-4.15.0.0

Defined in GHC.IsList

Associated Types

type Item (ZipList a)

Methods

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

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

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

Read a => Read (ZipList a)

Since: base-4.7.0.0

Defined in Control.Applicative

Methods

readsPrec :: Int -> ReadS (ZipList a)

readList :: ReadS [ZipList a]

readPrec :: ReadPrec (ZipList a)

readListPrec :: ReadPrec [ZipList a]

Show a => Show (ZipList a)

Since: base-4.7.0.0

Defined in Control.Applicative

Methods

showsPrec :: Int -> ZipList a -> ShowS

show :: ZipList a -> String

showList :: [ZipList a] -> ShowS

NFData a => NFData (ZipList a)

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: ZipList a -> ()

Eq a => Eq (ZipList a)

Since: base-4.7.0.0

Defined in Control.Applicative

Methods

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

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

Ord a => Ord (ZipList a)

Since: base-4.7.0.0

Defined in Control.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

type Rep1 ZipList

Since: base-4.7.0.0

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 List)))

type Rep (ZipList a)

Since: base-4.7.0.0

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)

Defined in GHC.IsList

type Item (ZipList a) = a

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

Lift a ternary function to actions.

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

One or none.

It is useful for modelling any computation that is allowed to fail.

Examples

Using the Alternative instance of Control.Monad.Except, the following functions:

>>> import Control.Monad.Except

>>> canFail = throwError "it failed" :: Except String Int
>>> final = return 42                :: Except String Int

Can be combined by allowing the first function to fail:

>>> runExcept $ canFail *> final
Left "it failed"
>>> runExcept $ optional canFail *> final
Right 42

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

A variant of <*> with the arguments reversed.

Combinators

pass :: Applicative f => f ()

Shorter alias for pure ().

>>> pass :: Maybe ()
Just ()

Useful shortcut when need an empty action:

printJust :: Maybe Int -> IO ()
printJust mInt = case mInt of
    Just i -> putStrLn $ "Number: " ++ show i
    Nothing -> pass

appliedTo :: Applicative f => f a -> f (a -> b) -> f b

Named version of the <**> operator, which is <*> but flipped. It is helpful for chaining applicative operations in forward applications using &.

>>> Just (+ 1) & appliedTo (Just 2)
Just 3
>>> Just (+) & appliedTo (Just 1) & appliedTo (Just 2)
Just 3
>>> Nothing & appliedTo (Just 2)
Nothing

Since: 0.5.0