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/Haskell 8

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

Applicative functors
Alternatives
Instances
Utility functions

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:

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

(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.

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 <*>.

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

Sequence actions, discarding the value of the first argument.

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

Sequence actions, discarding the value of the second argument.

Instances

Applicative []	Since: 2.1
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: 2.1
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: 2.1
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: 4.9.0.0
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 ReadP	Since: 4.6.0.0
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: 4.6.0.0
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 Last
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
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 Product	Since: 4.8.0.0
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: 4.8.0.0
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: 4.8.0.0
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 STM	Since: 4.8.0.0
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: 4.8.0.0
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: 2.1
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 NonEmpty	Since: 4.9.0.0
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 Option	Since: 4.9.0.0
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: 4.9.0.0
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: 4.9.0.0
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: 4.9.0.0
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: 4.9.0.0
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: 4.9.0.0
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: 3.0
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 *)	Since: 4.9.0.0
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, `String`s concatenate: ("hello ", (+15)) <*> ("world!", 2002) ("hello world!",2017) Since: 2.1
Methods pure :: a -> (a, a) Source (<>) :: (a, a -> b) -> (a, a) -> (a, b) Source liftA2 :: (a -> b -> c) -> (a, a) -> (a, b) -> (a, c) Source (>) :: (a, a) -> (a, b) -> (a, b) Source (<*) :: (a, a) -> (a, b) -> (a, a) Source
Applicative (ST s)	Since: 4.4.0.0
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 *)	Since: 4.7.0.0
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: 4.6.0.0
Methods pure :: a -> ArrowMonad a a Source (<>) :: ArrowMonad a (a -> b) -> ArrowMonad a a -> ArrowMonad a b Source liftA2 :: (a -> b -> c) -> ArrowMonad a a -> ArrowMonad a b -> ArrowMonad a c Source (>) :: ArrowMonad a a -> ArrowMonad a b -> ArrowMonad a b Source (<*) :: ArrowMonad a a -> ArrowMonad a b -> ArrowMonad a a Source
Monad m => Applicative (WrappedMonad m)	Since: 2.1
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: 2.1
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: 4.9.0.0
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
Applicative f => Applicative (Alt * f)
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
Monoid m => Applicative (Const * m)	Since: 2.0.1
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
Arrow a => Applicative (WrappedArrow a b)	Since: 2.1
Methods pure :: a -> WrappedArrow a b a Source (<>) :: WrappedArrow a b (a -> b) -> WrappedArrow a b a -> WrappedArrow a b b Source liftA2 :: (a -> b -> c) -> WrappedArrow a b a -> WrappedArrow a b b -> WrappedArrow a b c Source (>) :: WrappedArrow a b a -> WrappedArrow a b b -> WrappedArrow a b b Source (<*) :: WrappedArrow a b a -> WrappedArrow a b b -> WrappedArrow a b a Source
Applicative ((->) LiftedRep LiftedRep a)	Since: 2.1
Methods pure :: a -> (LiftedRep -> LiftedRep) a a Source (<>) :: (LiftedRep -> LiftedRep) a (a -> b) -> (LiftedRep -> LiftedRep) a a -> (LiftedRep -> LiftedRep) a b Source liftA2 :: (a -> b -> c) -> (LiftedRep -> LiftedRep) a a -> (LiftedRep -> LiftedRep) a b -> (LiftedRep -> LiftedRep) a c Source (>) :: (LiftedRep -> LiftedRep) a a -> (LiftedRep -> LiftedRep) a b -> (LiftedRep -> LiftedRep) a b Source (<*) :: (LiftedRep -> LiftedRep) a a -> (LiftedRep -> LiftedRep) a b -> (LiftedRep -> LiftedRep) a a Source
(Applicative f, Applicative g) => Applicative ((::) f g)	Since: 4.9.0.0
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 (Product * f g)	Since: 4.9.0.0
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: 4.9.0.0
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 -> c) -> M1 * i c f a -> M1 * i c f b -> M1 * i c f c 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: 4.9.0.0
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: 4.9.0.0
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:

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

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

Alternative []	Since: 2.1
Methods empty :: [a] Source (<\|>) :: [a] -> [a] -> [a] Source some :: [a] -> [[a]] Source many :: [a] -> [[a]] Source
Alternative Maybe	Since: 2.1
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: 4.9.0.0
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: 4.6.0.0
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: 4.6.0.0
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: 4.8.0.0
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 Option	Since: 4.9.0.0
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 *)	Since: 4.9.0.0
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 *)	Since: 4.9.0.0
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: 4.6.0.0
Methods empty :: ArrowMonad a a Source (<\|>) :: ArrowMonad a a -> ArrowMonad a a -> ArrowMonad a a Source some :: ArrowMonad a a -> ArrowMonad a [a] Source many :: ArrowMonad a a -> ArrowMonad a [a] Source
MonadPlus m => Alternative (WrappedMonad m)	Since: 2.1
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: 4.9.0.0
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)
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
(ArrowZero a, ArrowPlus a) => Alternative (WrappedArrow a b)	Since: 2.1
Methods empty :: WrappedArrow a b a Source (<\|>) :: WrappedArrow a b a -> WrappedArrow a b a -> WrappedArrow a b a Source some :: WrappedArrow a b a -> WrappedArrow a b [a] Source many :: WrappedArrow a b a -> WrappedArrow a b [a] Source
(Alternative f, Alternative g) => Alternative ((::) f g)	Since: 4.9.0.0
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: 4.9.0.0
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: 4.9.0.0
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: 4.9.0.0
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: 4.9.0.0
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 getConst :: a

Instances

Generic1 k (Const k a)
Associated Types type Rep1 (Const k a) (f :: Const k a -> ) :: k -> Source Methods from1 :: f a -> Rep1 (Const k a) f a Source to1 :: Rep1 (Const k a) f a -> f a Source
Show2 (Const *)	Since: 4.9.0.0
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 *)	Since: 4.9.0.0
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 *)	Since: 4.9.0.0
Methods liftCompare2 :: (a -> b -> Ordering) -> (c -> d -> Ordering) -> Const * a c -> Const * b d -> Ordering Source
Eq2 (Const *)	Since: 4.9.0.0
Methods liftEq2 :: (a -> b -> Bool) -> (c -> d -> Bool) -> Const * a c -> Const * b d -> Bool Source
Bifunctor (Const *)	Since: 4.8.0.0
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 *)	Since: 4.10.0.0
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 *)	Since: 4.10.0.0
Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> Const * a b -> f (Const * c d) Source
Functor (Const * m)	Since: 2.1
Methods fmap :: (a -> b) -> Const * m a -> Const * m b Source (<$) :: a -> Const * m b -> Const * m a Source
Monoid m => Applicative (Const * m)	Since: 2.0.1
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)	Since: 4.7.0.0
Methods fold :: Monoid m => Const * m m -> m Source foldMap :: Monoid m => (a -> m) -> Const * m a -> m 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)	Since: 4.7.0.0
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 m => (a -> m b) -> Const * m a -> m (Const * m b) Source sequence :: Monad m => Const * m (m a) -> m (Const * m a) Source
Show a => Show1 (Const * a)	Since: 4.9.0.0
Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Const * a a -> ShowS Source liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Const * a a] -> ShowS Source
Read a => Read1 (Const * a)	Since: 4.9.0.0
Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Const * a a) Source liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Const * a a] Source liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (Const * a a) Source liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [Const * a a] Source
Ord a => Ord1 (Const * a)	Since: 4.9.0.0
Methods liftCompare :: (a -> b -> Ordering) -> Const * a a -> Const * a b -> Ordering Source
Eq a => Eq1 (Const * a)	Since: 4.9.0.0
Methods liftEq :: (a -> b -> Bool) -> Const * a a -> Const * a b -> Bool Source
Bounded a => Bounded (Const k a b)
Methods minBound :: Const k a b Source maxBound :: Const k a b Source
Enum a => Enum (Const k a b)
Methods succ :: Const k a b -> Const k a b Source pred :: Const k a b -> Const k a b Source toEnum :: Int -> Const k a b Source fromEnum :: Const k a b -> Int Source enumFrom :: Const k a b -> [Const k a b] Source enumFromThen :: Const k a b -> Const k a b -> [Const k a b] Source enumFromTo :: Const k a b -> Const k a b -> [Const k a b] Source enumFromThenTo :: Const k a b -> Const k a b -> Const k a b -> [Const k a b] Source
Eq a => Eq (Const k a b)
Methods (==) :: Const k a b -> Const k a b -> Bool Source (/=) :: Const k a b -> Const k a b -> Bool Source
Floating a => Floating (Const k a b)
Methods pi :: Const k a b Source exp :: Const k a b -> Const k a b Source log :: Const k a b -> Const k a b Source sqrt :: Const k a b -> Const k a b Source (**) :: Const k a b -> Const k a b -> Const k a b Source logBase :: Const k a b -> Const k a b -> Const k a b Source sin :: Const k a b -> Const k a b Source cos :: Const k a b -> Const k a b Source tan :: Const k a b -> Const k a b Source asin :: Const k a b -> Const k a b Source acos :: Const k a b -> Const k a b Source atan :: Const k a b -> Const k a b Source sinh :: Const k a b -> Const k a b Source cosh :: Const k a b -> Const k a b Source tanh :: Const k a b -> Const k a b Source asinh :: Const k a b -> Const k a b Source acosh :: Const k a b -> Const k a b Source atanh :: Const k a b -> Const k a b Source log1p :: Const k a b -> Const k a b Source expm1 :: Const k a b -> Const k a b Source log1pexp :: Const k a b -> Const k a b Source log1mexp :: Const k a b -> Const k a b Source
Fractional a => Fractional (Const k a b)
Methods (/) :: Const k a b -> Const k a b -> Const k a b Source recip :: Const k a b -> Const k a b Source fromRational :: Rational -> Const k a b Source
Integral a => Integral (Const k a b)
Methods quot :: Const k a b -> Const k a b -> Const k a b Source rem :: Const k a b -> Const k a b -> Const k a b Source div :: Const k a b -> Const k a b -> Const k a b Source mod :: Const k a b -> Const k a b -> Const k a b Source quotRem :: Const k a b -> Const k a b -> (Const k a b, Const k a b) Source divMod :: Const k a b -> Const k a b -> (Const k a b, Const k a b) Source toInteger :: Const k a b -> Integer Source
(Typeable * k3, Data a, Typeable k3 b) => Data (Const k3 a b)	Since: 4.10.0.0
Methods gfoldl :: (forall d c. Data d => c (d -> c) -> d -> c c) -> (forall g. g -> c g) -> Const k3 a b -> c (Const k3 a b) Source gunfold :: (forall c r. Data c => c (c -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Const k3 a b) Source toConstr :: Const k3 a b -> Constr Source dataTypeOf :: Const k3 a b -> DataType Source dataCast1 :: Typeable (* -> ) t => (forall d. Data d => c (t d)) -> Maybe (c (Const k3 a b)) Source dataCast2 :: Typeable ( -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Const k3 a b)) Source gmapT :: (forall c. Data c => c -> c) -> Const k3 a b -> Const k3 a b Source gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Const k3 a b -> r Source gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Const k3 a b -> r Source gmapQ :: (forall d. Data d => d -> u) -> Const k3 a b -> [u] Source gmapQi :: Int -> (forall d. Data d => d -> u) -> Const k3 a b -> u Source gmapM :: Monad m => (forall d. Data d => d -> m d) -> Const k3 a b -> m (Const k3 a b) Source gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Const k3 a b -> m (Const k3 a b) Source gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Const k3 a b -> m (Const k3 a b) Source
Num a => Num (Const k a b)
Methods (+) :: Const k a b -> Const k a b -> Const k a b Source (-) :: Const k a b -> Const k a b -> Const k a b Source (*) :: Const k a b -> Const k a b -> Const k a b Source negate :: Const k a b -> Const k a b Source abs :: Const k a b -> Const k a b Source signum :: Const k a b -> Const k a b Source fromInteger :: Integer -> Const k a b Source
Ord a => Ord (Const k a b)
Methods compare :: Const k a b -> Const k a b -> Ordering Source (<) :: Const k a b -> Const k a b -> Bool Source (<=) :: Const k a b -> Const k a b -> Bool Source (>) :: Const k a b -> Const k a b -> Bool Source (>=) :: Const k a b -> Const k a b -> Bool Source max :: Const k a b -> Const k a b -> Const k a b Source min :: Const k a b -> Const k a b -> Const k a b Source
Read a => Read (Const k a b)	This instance would be equivalent to the derived instances of the `Const` newtype if the `runConst` field were removed Since: 4.8.0.0
Methods readsPrec :: Int -> ReadS (Const k a b) Source readList :: ReadS [Const k a b] Source readPrec :: ReadPrec (Const k a b) Source readListPrec :: ReadPrec [Const k a b] Source
Real a => Real (Const k a b)
Methods toRational :: Const k a b -> Rational Source
RealFloat a => RealFloat (Const k a b)
Methods floatRadix :: Const k a b -> Integer Source floatDigits :: Const k a b -> Int Source floatRange :: Const k a b -> (Int, Int) Source decodeFloat :: Const k a b -> (Integer, Int) Source encodeFloat :: Integer -> Int -> Const k a b Source exponent :: Const k a b -> Int Source significand :: Const k a b -> Const k a b Source scaleFloat :: Int -> Const k a b -> Const k a b Source isNaN :: Const k a b -> Bool Source isInfinite :: Const k a b -> Bool Source isDenormalized :: Const k a b -> Bool Source isNegativeZero :: Const k a b -> Bool Source isIEEE :: Const k a b -> Bool Source atan2 :: Const k a b -> Const k a b -> Const k a b Source
RealFrac a => RealFrac (Const k a b)
Methods properFraction :: Integral b => Const k a b -> (b, Const k a b) Source truncate :: Integral b => Const k a b -> b Source round :: Integral b => Const k a b -> b Source ceiling :: Integral b => Const k a b -> b Source floor :: Integral b => Const k a b -> b Source
Show a => Show (Const k a b)	This instance would be equivalent to the derived instances of the `Const` newtype if the `runConst` field were removed Since: 4.8.0.0
Methods showsPrec :: Int -> Const k a b -> ShowS Source show :: Const k a b -> String Source showList :: [Const k a b] -> ShowS Source
Ix a => Ix (Const k a b)
Methods range :: (Const k a b, Const k a b) -> [Const k a b] Source index :: (Const k a b, Const k a b) -> Const k a b -> Int Source unsafeIndex :: (Const k a b, Const k a b) -> Const k a b -> Int inRange :: (Const k a b, Const k a b) -> Const k a b -> Bool Source rangeSize :: (Const k a b, Const k a b) -> Int Source unsafeRangeSize :: (Const k a b, Const k a b) -> Int
IsString a => IsString (Const * a b)	Since: 4.9.0.0
Methods fromString :: String -> Const * a b Source
Generic (Const k a b)
Associated Types type Rep (Const k a b) :: * -> * Source Methods from :: Const k a b -> Rep (Const k a b) x Source to :: Rep (Const k a b) x -> Const k a b Source
Semigroup a => Semigroup (Const k a b)	Since: 4.9.0.0
Methods (<>) :: Const k a b -> Const k a b -> Const k a b Source sconcat :: NonEmpty (Const k a b) -> Const k a b Source stimes :: Integral b => b -> Const k a b -> Const k a b Source
Monoid a => Monoid (Const k a b)
Methods mempty :: Const k a b Source mappend :: Const k a b -> Const k a b -> Const k a b Source mconcat :: [Const k a b] -> Const k a b Source
FiniteBits a => FiniteBits (Const k a b)
Methods finiteBitSize :: Const k a b -> Int Source countLeadingZeros :: Const k a b -> Int Source countTrailingZeros :: Const k a b -> Int Source
Bits a => Bits (Const k a b)
Methods (.&.) :: Const k a b -> Const k a b -> Const k a b Source (.\|.) :: Const k a b -> Const k a b -> Const k a b Source xor :: Const k a b -> Const k a b -> Const k a b Source complement :: Const k a b -> Const k a b Source shift :: Const k a b -> Int -> Const k a b Source rotate :: Const k a b -> Int -> Const k a b Source zeroBits :: Const k a b Source bit :: Int -> Const k a b Source setBit :: Const k a b -> Int -> Const k a b Source clearBit :: Const k a b -> Int -> Const k a b Source complementBit :: Const k a b -> Int -> Const k a b Source testBit :: Const k a b -> Int -> Bool Source bitSizeMaybe :: Const k a b -> Maybe Int Source bitSize :: Const k a b -> Int Source isSigned :: Const k a b -> Bool Source shiftL :: Const k a b -> Int -> Const k a b Source unsafeShiftL :: Const k a b -> Int -> Const k a b Source shiftR :: Const k a b -> Int -> Const k a b Source unsafeShiftR :: Const k a b -> Int -> Const k a b Source rotateL :: Const k a b -> Int -> Const k a b Source rotateR :: Const k a b -> Int -> Const k a b Source popCount :: Const k a b -> Int Source
Storable a => Storable (Const k a b)
Methods sizeOf :: Const k a b -> Int Source alignment :: Const k a b -> Int Source peekElemOff :: Ptr (Const k a b) -> Int -> IO (Const k a b) Source pokeElemOff :: Ptr (Const k a b) -> Int -> Const k a b -> IO () Source peekByteOff :: Ptr b -> Int -> IO (Const k a b) Source pokeByteOff :: Ptr b -> Int -> Const k a b -> IO () Source peek :: Ptr (Const k a b) -> IO (Const k a b) Source poke :: Ptr (Const k a b) -> Const k a b -> IO () Source
type Rep1 k (Const k a)
type Rep1 k (Const k a) = D1 k (MetaData "Const" "Data.Functor.Const" "base" True) (C1 k (MetaCons "Const" PrefixI True) (S1 k (MetaSel (Just Symbol "getConst") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 k a)))
type Rep (Const k a b)
type Rep (Const k a b) = D1 * (MetaData "Const" "Data.Functor.Const" "base" True) (C1 * (MetaCons "Const" PrefixI True) (S1 * (MetaSel (Just Symbol "getConst") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * a)))

newtype WrappedMonad m a Source

Constructors

WrapMonad
Fields unwrapMonad :: m a

Instances

Monad m => Monad (WrappedMonad m)
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 fail :: String -> WrappedMonad m a Source
Monad m => Functor (WrappedMonad m)	Since: 2.1
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: 2.1
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: 2.1
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)
Associated Types type Rep1 (WrappedMonad m) (f :: WrappedMonad m -> ) :: k -> Source Methods from1 :: f a -> Rep1 (WrappedMonad m) f a Source to1 :: Rep1 (WrappedMonad m) f a -> f a Source
Generic (WrappedMonad m a)
Associated Types type Rep (WrappedMonad m a) :: * -> * 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 Rep1 * (WrappedMonad m) = D1 * (MetaData "WrappedMonad" "Control.Applicative" "base" True) (C1 * (MetaCons "WrapMonad" PrefixI True) (S1 * (MetaSel (Just Symbol "unwrapMonad") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec1 * m)))
type Rep (WrappedMonad m a)
type Rep (WrappedMonad m a) = D1 * (MetaData "WrappedMonad" "Control.Applicative" "base" True) (C1 * (MetaCons "WrapMonad" PrefixI True) (S1 * (MetaSel (Just Symbol "unwrapMonad") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * (m a))))

newtype WrappedArrow a b c Source

Constructors

WrapArrow
Fields unwrapArrow :: a b c

Instances

Generic1 * (WrappedArrow a b)
Associated Types type Rep1 (WrappedArrow a b) (f :: WrappedArrow a b -> ) :: k -> Source Methods from1 :: f a -> Rep1 (WrappedArrow a b) f a Source to1 :: Rep1 (WrappedArrow a b) f a -> f a Source
Arrow a => Functor (WrappedArrow a b)	Since: 2.1
Methods fmap :: (a -> b) -> WrappedArrow a b a -> WrappedArrow a b b Source (<$) :: a -> WrappedArrow a b b -> WrappedArrow a b a Source
Arrow a => Applicative (WrappedArrow a b)	Since: 2.1
Methods pure :: a -> WrappedArrow a b a Source (<>) :: WrappedArrow a b (a -> b) -> WrappedArrow a b a -> WrappedArrow a b b Source liftA2 :: (a -> b -> c) -> WrappedArrow a b a -> WrappedArrow a b b -> WrappedArrow a b c Source (>) :: WrappedArrow a b a -> WrappedArrow a b b -> WrappedArrow a b b Source (<*) :: WrappedArrow a b a -> WrappedArrow a b b -> WrappedArrow a b a Source
(ArrowZero a, ArrowPlus a) => Alternative (WrappedArrow a b)	Since: 2.1
Methods empty :: WrappedArrow a b a Source (<\|>) :: WrappedArrow a b a -> WrappedArrow a b a -> WrappedArrow a b a Source some :: WrappedArrow a b a -> WrappedArrow a b [a] Source many :: WrappedArrow a b a -> WrappedArrow a b [a] Source
Generic (WrappedArrow a b c)
Associated Types type Rep (WrappedArrow a b c) :: * -> * 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 Rep1 * (WrappedArrow a b) = D1 * (MetaData "WrappedArrow" "Control.Applicative" "base" True) (C1 * (MetaCons "WrapArrow" PrefixI True) (S1 * (MetaSel (Just Symbol "unwrapArrow") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec1 * (a b))))
type Rep (WrappedArrow a b c)
type Rep (WrappedArrow a b c) = D1 * (MetaData "WrappedArrow" "Control.Applicative" "base" True) (C1 * (MetaCons "WrapArrow" PrefixI True) (S1 * (MetaSel (Just Symbol "unwrapArrow") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * (a b c))))

newtype ZipList a Source

Lists, but with an Applicative functor based on zipping.

Constructors

ZipList
Fields getZipList :: [a]

Instances

Functor ZipList
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: 2.1
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
Methods fold :: Monoid m => ZipList m -> 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: 4.9.0.0
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
Eq a => Eq (ZipList a)
Methods (==) :: ZipList a -> ZipList a -> Bool Source (/=) :: ZipList a -> ZipList a -> Bool Source
Ord a => Ord (ZipList a)
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)
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)
Methods showsPrec :: Int -> ZipList a -> ShowS Source show :: ZipList a -> String Source showList :: [ZipList a] -> ShowS Source
Generic (ZipList a)
Associated Types type Rep (ZipList a) :: * -> * Source Methods from :: ZipList a -> Rep (ZipList a) x Source to :: Rep (ZipList a) x -> ZipList a Source
Generic1 * ZipList
Associated Types type Rep1 ZipList (f :: ZipList -> ) :: k -> Source Methods from1 :: f a -> Rep1 ZipList f a Source to1 :: Rep1 ZipList f a -> f a Source
type Rep (ZipList a)
type Rep (ZipList a) = D1 * (MetaData "ZipList" "Control.Applicative" "base" True) (C1 * (MetaCons "ZipList" PrefixI True) (S1 * (MetaSel (Just Symbol "getZipList") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * [a])))
type Rep1 * ZipList
type Rep1 * ZipList = D1 * (MetaData "ZipList" "Control.Applicative" "base" True) (C1 * (MetaCons "ZipList" PrefixI True) (S1 * (MetaSel (Just Symbol "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

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.

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

A variant of <*> with the arguments reversed.

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.

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

Lift a ternary function to actions.

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/8.2.1/docs/html/libraries/base-4.10.0.0/Control-Applicative.html

Control.Applicative

Contents

Description

Applicative functors

Minimal complete definition

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ZipList (zipWithN f xs1 ... xsN)

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Alternatives

Minimal complete definition

Methods

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