Control.Applicative

Copyright	Conor McBride and Ross Paterson 2005
License	BSD-style (see the LICENSE file in the distribution)
Maintainer	libraries@haskell.org
Stability	stable
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 :: Type -> Type) 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
```

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 Source

Lift a value into the Structure.

Examples

Expand

>>> pure 1 :: Maybe Int
Just 1

>>> pure 'z' :: [Char]
"z"

>>> pure (pure ":D") :: Maybe [String]
Just [":D"]

(<*>) :: 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.

Example

Expand

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 Source

Lift a binary function to actions.

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

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

Example

Expand

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

>>> liftA2 (+) [1, 2, 3] [4, 5, 6]
[5,6,7,6,7,8,7,8,9]

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

Sequence actions, discarding the value of the first argument.

Examples

Expand

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 GHC.Internal.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 Source

Sequence actions, discarding the value of the second argument.

Instances

Instances details

Applicative Complex Source	Since: base-4.9.0.0
Instance details Defined in Data.Complex Methods pure :: a -> Complex a Source (<>) :: Complex (a -> b) -> Complex a -> Complex b Source liftA2 :: (a -> b -> c) -> Complex a -> Complex b -> Complex c Source (>) :: Complex a -> Complex b -> Complex b Source (<*) :: Complex a -> Complex b -> Complex a Source
Applicative First Source	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods pure :: a -> First a Source (<>) :: First (a -> b) -> First a -> First b Source liftA2 :: (a -> b -> c) -> First a -> First b -> First c Source (>) :: First a -> First b -> First b Source (<*) :: First a -> First b -> First a Source
Applicative Last Source	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods pure :: a -> Last a Source (<>) :: Last (a -> b) -> Last a -> Last b Source liftA2 :: (a -> b -> c) -> Last a -> Last b -> Last c Source (>) :: Last a -> Last b -> Last b Source (<*) :: Last a -> Last b -> Last a Source
Applicative Max Source	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods pure :: a -> Max a Source (<>) :: Max (a -> b) -> Max a -> Max b Source liftA2 :: (a -> b -> c) -> Max a -> Max b -> Max c Source (>) :: Max a -> Max b -> Max b Source (<*) :: Max a -> Max b -> Max a Source
Applicative Min Source	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods pure :: a -> Min a Source (<>) :: Min (a -> b) -> Min a -> Min b Source liftA2 :: (a -> b -> c) -> Min a -> Min b -> Min c Source (>) :: Min a -> Min b -> Min b Source (<*) :: Min a -> Min b -> Min a Source
Applicative NonEmpty Source	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Base Methods pure :: a -> NonEmpty a Source (<>) :: NonEmpty (a -> b) -> NonEmpty a -> NonEmpty b Source liftA2 :: (a -> b -> c) -> NonEmpty a -> NonEmpty b -> NonEmpty c Source (>) :: NonEmpty a -> NonEmpty b -> NonEmpty b Source (<*) :: NonEmpty a -> NonEmpty b -> NonEmpty a Source
Applicative STM Source	Since: base-4.8.0.0
Instance details Defined in GHC.Internal.Conc.Sync Methods pure :: a -> STM a Source (<>) :: STM (a -> b) -> STM a -> STM b Source liftA2 :: (a -> b -> c) -> STM a -> STM b -> STM c Source (>) :: STM a -> STM b -> STM b Source (<*) :: STM a -> STM b -> STM a Source
Applicative Identity Source	Since: base-4.8.0.0
Instance details Defined in GHC.Internal.Data.Functor.Identity Methods pure :: a -> Identity a Source (<>) :: Identity (a -> b) -> Identity a -> Identity b Source liftA2 :: (a -> b -> c) -> Identity a -> Identity b -> Identity c Source (>) :: Identity a -> Identity b -> Identity b Source (<*) :: Identity a -> Identity b -> Identity a Source
Applicative First Source	Since: base-4.8.0.0
Instance details Defined in GHC.Internal.Data.Monoid Methods pure :: a -> First a Source (<>) :: First (a -> b) -> First a -> First b Source liftA2 :: (a -> b -> c) -> First a -> First b -> First c Source (>) :: First a -> First b -> First b Source (<*) :: First a -> First b -> First a Source
Applicative Last Source	Since: base-4.8.0.0
Instance details Defined in GHC.Internal.Data.Monoid Methods pure :: a -> Last a Source (<>) :: Last (a -> b) -> Last a -> Last b Source liftA2 :: (a -> b -> c) -> Last a -> Last b -> Last c Source (>) :: Last a -> Last b -> Last b Source (<*) :: Last a -> Last b -> Last a Source
Applicative Down Source	Since: base-4.11.0.0
Instance details Defined in GHC.Internal.Data.Ord Methods pure :: a -> Down a Source (<>) :: Down (a -> b) -> Down a -> Down b Source liftA2 :: (a -> b -> c) -> Down a -> Down b -> Down c Source (>) :: Down a -> Down b -> Down b Source (<*) :: Down a -> Down b -> Down a Source
Applicative Dual Source	Since: base-4.8.0.0
Instance details Defined in GHC.Internal.Data.Semigroup.Internal Methods pure :: a -> Dual a Source (<>) :: Dual (a -> b) -> Dual a -> Dual b Source liftA2 :: (a -> b -> c) -> Dual a -> Dual b -> Dual c Source (>) :: Dual a -> Dual b -> Dual b Source (<*) :: Dual a -> Dual b -> Dual a Source
Applicative Product Source	Since: base-4.8.0.0
Instance details Defined in GHC.Internal.Data.Semigroup.Internal Methods pure :: a -> Product a Source (<>) :: Product (a -> b) -> Product a -> Product b Source liftA2 :: (a -> b -> c) -> Product a -> Product b -> Product c Source (>) :: Product a -> Product b -> Product b Source (<*) :: Product a -> Product b -> Product a Source
Applicative Sum Source	Since: base-4.8.0.0
Instance details Defined in GHC.Internal.Data.Semigroup.Internal Methods pure :: a -> Sum a Source (<>) :: Sum (a -> b) -> Sum a -> Sum b Source liftA2 :: (a -> b -> c) -> Sum a -> Sum b -> Sum c Source (>) :: Sum a -> Sum b -> Sum b Source (<*) :: Sum a -> Sum b -> Sum a Source
Applicative ZipList Source	f <$> ZipList xs1 <> ... <> ZipList xsN = ZipList (zipWithN f xs1 ... xsN) where `zipWithN` refers to the `zipWith` function of the appropriate arity (`zipWith`, `zipWith3`, `zipWith4`, ...). For example: (\a b c -> stimes c [a, b]) <$> ZipList "abcd" <> ZipList "567" <> ZipList [1..] = ZipList (zipWith3 (\a b c -> stimes c [a, b]) "abcd" "567" [1..]) = ZipList {getZipList = ["a5","b6b6","c7c7c7"]} Since: base-2.1
Instance details Defined in GHC.Internal.Functor.ZipList 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 NoIO Source	Since: base-4.8.0.0
Instance details Defined in GHC.Internal.GHCi Methods pure :: a -> NoIO a Source (<>) :: NoIO (a -> b) -> NoIO a -> NoIO b Source liftA2 :: (a -> b -> c) -> NoIO a -> NoIO b -> NoIO c Source (>) :: NoIO a -> NoIO b -> NoIO b Source (<*) :: NoIO a -> NoIO b -> NoIO a Source
Applicative Par1 Source	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Generics Methods pure :: a -> Par1 a Source (<>) :: Par1 (a -> b) -> Par1 a -> Par1 b Source liftA2 :: (a -> b -> c) -> Par1 a -> Par1 b -> Par1 c Source (>) :: Par1 a -> Par1 b -> Par1 b Source (<*) :: Par1 a -> Par1 b -> Par1 a Source
Applicative Q Source
Instance details Defined in GHC.Internal.TH.Syntax Methods pure :: a -> Q a Source (<>) :: Q (a -> b) -> Q a -> Q b Source liftA2 :: (a -> b -> c) -> Q a -> Q b -> Q c Source (>) :: Q a -> Q b -> Q b Source (<*) :: Q a -> Q b -> Q a Source
Applicative P Source	Since: base-4.5.0.0
Instance details Defined in GHC.Internal.Text.ParserCombinators.ReadP Methods pure :: a -> P a Source (<>) :: P (a -> b) -> P a -> P b Source liftA2 :: (a -> b -> c) -> P a -> P b -> P c Source (>) :: P a -> P b -> P b Source (<*) :: P a -> P b -> P a Source
Applicative ReadP Source	Since: base-4.6.0.0
Instance details Defined in GHC.Internal.Text.ParserCombinators.ReadP Methods pure :: a -> ReadP a Source (<>) :: ReadP (a -> b) -> ReadP a -> ReadP b Source liftA2 :: (a -> b -> c) -> ReadP a -> ReadP b -> ReadP c Source (>) :: ReadP a -> ReadP b -> ReadP b Source (<*) :: ReadP a -> ReadP b -> ReadP a Source
Applicative ReadPrec Source	Since: base-4.6.0.0
Instance details Defined in GHC.Internal.Text.ParserCombinators.ReadPrec Methods pure :: a -> ReadPrec a Source (<>) :: ReadPrec (a -> b) -> ReadPrec a -> ReadPrec b Source liftA2 :: (a -> b -> c) -> ReadPrec a -> ReadPrec b -> ReadPrec c Source (>) :: ReadPrec a -> ReadPrec b -> ReadPrec b Source (<*) :: ReadPrec a -> ReadPrec b -> ReadPrec a Source
Applicative IO Source	Since: base-2.1
Instance details Defined in GHC.Internal.Base Methods pure :: a -> IO a Source (<>) :: IO (a -> b) -> IO a -> IO b Source liftA2 :: (a -> b -> c) -> IO a -> IO b -> IO c Source (>) :: IO a -> IO b -> IO b Source (<*) :: IO a -> IO b -> IO a Source
Applicative Maybe Source	Since: base-2.1
Instance details Defined in GHC.Internal.Base Methods pure :: a -> Maybe a Source (<>) :: Maybe (a -> b) -> Maybe a -> Maybe b Source liftA2 :: (a -> b -> c) -> Maybe a -> Maybe b -> Maybe c Source (>) :: Maybe a -> Maybe b -> Maybe b Source (<*) :: Maybe a -> Maybe b -> Maybe a Source
Applicative Solo Source	Since: base-4.15
Instance details Defined in GHC.Internal.Base Methods pure :: a -> Solo a Source (<>) :: Solo (a -> b) -> Solo a -> Solo b Source liftA2 :: (a -> b -> c) -> Solo a -> Solo b -> Solo c Source (>) :: Solo a -> Solo b -> Solo b Source (<*) :: Solo a -> Solo b -> Solo a Source
Applicative [] Source	Since: base-2.1
Instance details Defined in GHC.Internal.Base Methods pure :: a -> [a] Source (<>) :: [a -> b] -> [a] -> [b] Source liftA2 :: (a -> b -> c) -> [a] -> [b] -> [c] Source (>) :: [a] -> [b] -> [b] Source (<*) :: [a] -> [b] -> [a] Source
Monad m => Applicative (WrappedMonad m) Source	Since: base-2.1
Instance details Defined in Control.Applicative Methods pure :: a -> WrappedMonad m a Source (<>) :: WrappedMonad m (a -> b) -> WrappedMonad m a -> WrappedMonad m b Source liftA2 :: (a -> b -> c) -> WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m c Source (>) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m b Source (<*) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m a Source
Arrow a => Applicative (ArrowMonad a) Source	Since: base-4.6.0.0
Instance details Defined in GHC.Internal.Control.Arrow Methods pure :: a0 -> ArrowMonad a a0 Source (<>) :: ArrowMonad a (a0 -> b) -> ArrowMonad a a0 -> ArrowMonad a b Source liftA2 :: (a0 -> b -> c) -> ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a c Source (>) :: ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a b Source (<*) :: ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a a0 Source
Applicative (ST s) Source	Since: base-2.1
Instance details Defined in GHC.Internal.Control.Monad.ST.Lazy.Imp Methods pure :: a -> ST s a Source (<>) :: ST s (a -> b) -> ST s a -> ST s b Source liftA2 :: (a -> b -> c) -> ST s a -> ST s b -> ST s c Source (>) :: ST s a -> ST s b -> ST s b Source (<*) :: ST s a -> ST s b -> ST s a Source
Applicative (Either e) Source	Since: base-3.0
Instance details Defined in GHC.Internal.Data.Either Methods pure :: a -> Either e a Source (<>) :: Either e (a -> b) -> Either e a -> Either e b Source liftA2 :: (a -> b -> c) -> Either e a -> Either e b -> Either e c Source (>) :: Either e a -> Either e b -> Either e b Source (<*) :: Either e a -> Either e b -> Either e a Source
Applicative (StateL s) Source	Since: base-4.0
Instance details Defined in GHC.Internal.Data.Functor.Utils Methods pure :: a -> StateL s a Source (<>) :: StateL s (a -> b) -> StateL s a -> StateL s b Source liftA2 :: (a -> b -> c) -> StateL s a -> StateL s b -> StateL s c Source (>) :: StateL s a -> StateL s b -> StateL s b Source (<*) :: StateL s a -> StateL s b -> StateL s a Source
Applicative (StateR s) Source	Since: base-4.0
Instance details Defined in GHC.Internal.Data.Functor.Utils Methods pure :: a -> StateR s a Source (<>) :: StateR s (a -> b) -> StateR s a -> StateR s b Source liftA2 :: (a -> b -> c) -> StateR s a -> StateR s b -> StateR s c Source (>) :: StateR s a -> StateR s b -> StateR s b Source (<*) :: StateR s a -> StateR s b -> StateR s a Source
Applicative (Proxy :: Type -> Type) Source	Since: base-4.7.0.0
Instance details Defined in GHC.Internal.Data.Proxy Methods pure :: a -> Proxy a Source (<>) :: Proxy (a -> b) -> Proxy a -> Proxy b Source liftA2 :: (a -> b -> c) -> Proxy a -> Proxy b -> Proxy c Source (>) :: Proxy a -> Proxy b -> Proxy b Source (<*) :: Proxy a -> Proxy b -> Proxy a Source
Applicative (U1 :: Type -> Type) Source	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Generics Methods pure :: a -> U1 a Source (<>) :: U1 (a -> b) -> U1 a -> U1 b Source liftA2 :: (a -> b -> c) -> U1 a -> U1 b -> U1 c Source (>) :: U1 a -> U1 b -> U1 b Source (<*) :: U1 a -> U1 b -> U1 a Source
Applicative (ST s) Source	Since: base-4.4.0.0
Instance details Defined in GHC.Internal.ST Methods pure :: a -> ST s a Source (<>) :: ST s (a -> b) -> ST s a -> ST s b Source liftA2 :: (a -> b -> c) -> ST s a -> ST s b -> ST s c Source (>) :: ST s a -> ST s b -> ST s b Source (<*) :: ST s a -> ST s b -> ST s a Source
Monoid a => Applicative ((,) a) Source	For tuples, the `Monoid` constraint on `a` determines how the first values merge. For example, `String`s concatenate: ("hello ", (+15)) <*> ("world!", 2002) ("hello world!",2017) Since: base-2.1
Instance details Defined in GHC.Internal.Base Methods pure :: a0 -> (a, a0) Source (<>) :: (a, a0 -> b) -> (a, a0) -> (a, b) Source liftA2 :: (a0 -> b -> c) -> (a, a0) -> (a, b) -> (a, c) Source (>) :: (a, a0) -> (a, b) -> (a, b) Source (<*) :: (a, a0) -> (a, b) -> (a, a0) Source
Arrow a => Applicative (WrappedArrow a b) Source	Since: base-2.1
Instance details Defined in Control.Applicative Methods pure :: a0 -> WrappedArrow a b a0 Source (<>) :: WrappedArrow a b (a0 -> b0) -> WrappedArrow a b a0 -> WrappedArrow a b b0 Source liftA2 :: (a0 -> b0 -> c) -> WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b c Source (>) :: WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b b0 Source (<*) :: WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0 Source
Applicative m => Applicative (Kleisli m a) Source	Since: base-4.14.0.0
Instance details Defined in GHC.Internal.Control.Arrow Methods pure :: a0 -> Kleisli m a a0 Source (<>) :: Kleisli m a (a0 -> b) -> Kleisli m a a0 -> Kleisli m a b Source liftA2 :: (a0 -> b -> c) -> Kleisli m a a0 -> Kleisli m a b -> Kleisli m a c Source (>) :: Kleisli m a a0 -> Kleisli m a b -> Kleisli m a b Source (<*) :: Kleisli m a a0 -> Kleisli m a b -> Kleisli m a a0 Source
Monoid m => Applicative (Const m :: Type -> Type) Source	Since: base-2.0.1
Instance details Defined in GHC.Internal.Data.Functor.Const Methods pure :: a -> Const m a Source (<>) :: Const m (a -> b) -> Const m a -> Const m b Source liftA2 :: (a -> b -> c) -> Const m a -> Const m b -> Const m c Source (>) :: Const m a -> Const m b -> Const m b Source (<*) :: Const m a -> Const m b -> Const m a Source
Monad m => Applicative (StateT s m) Source	Since: base-4.18.0.0
Instance details Defined in GHC.Internal.Data.Functor.Utils Methods pure :: a -> StateT s m a Source (<>) :: StateT s m (a -> b) -> StateT s m a -> StateT s m b Source liftA2 :: (a -> b -> c) -> StateT s m a -> StateT s m b -> StateT s m c Source (>) :: StateT s m a -> StateT s m b -> StateT s m b Source (<*) :: StateT s m a -> StateT s m b -> StateT s m a Source
Applicative f => Applicative (Ap f) Source	Since: base-4.12.0.0
Instance details Defined in GHC.Internal.Data.Monoid Methods pure :: a -> Ap f a Source (<>) :: Ap f (a -> b) -> Ap f a -> Ap f b Source liftA2 :: (a -> b -> c) -> Ap f a -> Ap f b -> Ap f c Source (>) :: Ap f a -> Ap f b -> Ap f b Source (<*) :: Ap f a -> Ap f b -> Ap f a Source
Applicative f => Applicative (Alt f) Source	Since: base-4.8.0.0
Instance details Defined in GHC.Internal.Data.Semigroup.Internal Methods pure :: a -> Alt f a Source (<>) :: Alt f (a -> b) -> Alt f a -> Alt f b Source liftA2 :: (a -> b -> c) -> Alt f a -> Alt f b -> Alt f c Source (>) :: Alt f a -> Alt f b -> Alt f b Source (<*) :: Alt f a -> Alt f b -> Alt f a Source
(Generic1 f, Applicative (Rep1 f)) => Applicative (Generically1 f) Source	Since: base-4.17.0.0
Instance details Defined in GHC.Internal.Generics Methods pure :: a -> Generically1 f a Source (<>) :: Generically1 f (a -> b) -> Generically1 f a -> Generically1 f b Source liftA2 :: (a -> b -> c) -> Generically1 f a -> Generically1 f b -> Generically1 f c Source (>) :: Generically1 f a -> Generically1 f b -> Generically1 f b Source (<*) :: Generically1 f a -> Generically1 f b -> Generically1 f a Source
Applicative f => Applicative (Rec1 f) Source	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Generics Methods pure :: a -> Rec1 f a Source (<>) :: Rec1 f (a -> b) -> Rec1 f a -> Rec1 f b Source liftA2 :: (a -> b -> c) -> Rec1 f a -> Rec1 f b -> Rec1 f c Source (>) :: Rec1 f a -> Rec1 f b -> Rec1 f b Source (<*) :: Rec1 f a -> Rec1 f b -> Rec1 f a Source
(Monoid a, Monoid b) => Applicative ((,,) a b) Source	Since: base-4.14.0.0
Instance details Defined in GHC.Internal.Base Methods pure :: a0 -> (a, b, a0) Source (<>) :: (a, b, a0 -> b0) -> (a, b, a0) -> (a, b, b0) Source liftA2 :: (a0 -> b0 -> c) -> (a, b, a0) -> (a, b, b0) -> (a, b, c) Source (>) :: (a, b, a0) -> (a, b, b0) -> (a, b, b0) Source (<*) :: (a, b, a0) -> (a, b, b0) -> (a, b, a0) Source
(Applicative f, Applicative g) => Applicative (Product f g) Source	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods pure :: a -> Product f g a Source (<>) :: Product f g (a -> b) -> Product f g a -> Product f g b Source liftA2 :: (a -> b -> c) -> Product f g a -> Product f g b -> Product f g c Source (>) :: Product f g a -> Product f g b -> Product f g b Source (<*) :: Product f g a -> Product f g b -> Product f g a Source
(Applicative f, Applicative g) => Applicative (f :*: g) Source	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Generics Methods pure :: a -> (f :: g) a Source (<>) :: (f :: g) (a -> b) -> (f :: g) a -> (f :: g) b Source liftA2 :: (a -> b -> c) -> (f :: g) a -> (f :: g) b -> (f :: g) c Source (>) :: (f :: g) a -> (f :: g) b -> (f :: g) b Source (<) :: (f :: g) a -> (f :: g) b -> (f :: g) a Source
Monoid c => Applicative (K1 i c :: Type -> Type) Source	Since: base-4.12.0.0
Instance details Defined in GHC.Internal.Generics Methods pure :: a -> K1 i c a Source (<>) :: K1 i c (a -> b) -> K1 i c a -> K1 i c b Source liftA2 :: (a -> b -> c0) -> K1 i c a -> K1 i c b -> K1 i c c0 Source (>) :: K1 i c a -> K1 i c b -> K1 i c b Source (<*) :: K1 i c a -> K1 i c b -> K1 i c a Source
(Monoid a, Monoid b, Monoid c) => Applicative ((,,,) a b c) Source	Since: base-4.14.0.0
Instance details Defined in GHC.Internal.Base Methods pure :: a0 -> (a, b, c, a0) Source (<>) :: (a, b, c, a0 -> b0) -> (a, b, c, a0) -> (a, b, c, b0) Source liftA2 :: (a0 -> b0 -> c0) -> (a, b, c, a0) -> (a, b, c, b0) -> (a, b, c, c0) Source (>) :: (a, b, c, a0) -> (a, b, c, b0) -> (a, b, c, b0) Source (<*) :: (a, b, c, a0) -> (a, b, c, b0) -> (a, b, c, a0) Source
Applicative ((->) r) Source	Since: base-2.1
Instance details Defined in GHC.Internal.Base Methods pure :: a -> r -> a Source (<>) :: (r -> (a -> b)) -> (r -> a) -> r -> b Source liftA2 :: (a -> b -> c) -> (r -> a) -> (r -> b) -> r -> c Source (>) :: (r -> a) -> (r -> b) -> r -> b Source (<*) :: (r -> a) -> (r -> b) -> r -> a Source
(Applicative f, Applicative g) => Applicative (Compose f g) Source	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Compose Methods pure :: a -> Compose f g a Source (<>) :: Compose f g (a -> b) -> Compose f g a -> Compose f g b Source liftA2 :: (a -> b -> c) -> Compose f g a -> Compose f g b -> Compose f g c Source (>) :: Compose f g a -> Compose f g b -> Compose f g b Source (<*) :: Compose f g a -> Compose f g b -> Compose f g a Source
(Applicative f, Applicative g) => Applicative (f :.: g) Source	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Generics Methods pure :: a -> (f :.: g) a Source (<>) :: (f :.: g) (a -> b) -> (f :.: g) a -> (f :.: g) b Source liftA2 :: (a -> b -> c) -> (f :.: g) a -> (f :.: g) b -> (f :.: g) c Source (>) :: (f :.: g) a -> (f :.: g) b -> (f :.: g) b Source (<*) :: (f :.: g) a -> (f :.: g) b -> (f :.: g) a Source
Applicative f => Applicative (M1 i c f) Source	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Generics Methods pure :: a -> M1 i c f a Source (<>) :: M1 i c f (a -> b) -> M1 i c f a -> M1 i c f b Source liftA2 :: (a -> b -> c0) -> M1 i c f a -> M1 i c f b -> M1 i c f c0 Source (>) :: M1 i c f a -> M1 i c f b -> M1 i c f b Source (<*) :: M1 i c f a -> M1 i c f b -> M1 i c f a Source

Alternatives

class Applicative f => Alternative (f :: Type -> Type) 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 []
```

Examples

Expand

>>> Nothing <|> Just 42
Just 42

>>> [1, 2] <|> [3, 4]
[1,2,3,4]

>>> empty <|> print (2^15)
32768

Minimal complete definition

empty, (<|>)

Methods

empty :: f a Source

The identity of <|>

empty <|> a     == a
a     <|> empty == a

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

An associative binary operation

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

One or more.

Examples

Expand

>>> some (putStr "la")
lalalalalalalalala... * goes on forever *

>>> some Nothing
nothing

>>> take 5 <$> some (Just 1)
* hangs forever *

Note that this function can be used with Parsers based on Applicatives. In that case some parser will attempt to parse parser one or more times until it fails.

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

Zero or more.

Examples

Expand

>>> many (putStr "la")
lalalalalalalalala... * goes on forever *

>>> many Nothing
Just []

>>> take 5 <$> many (Just 1)
* hangs forever *

Note that this function can be used with Parsers based on Applicatives. In that case many parser will attempt to parse parser zero or more times until it fails.

Instances

Instances details

Alternative STM Source	Takes the first non-`retry`ing `STM` action. Since: base-4.8.0.0
Instance details Defined in GHC.Internal.Conc.Sync Methods empty :: STM a Source (<\|>) :: STM a -> STM a -> STM a Source some :: STM a -> STM [a] Source many :: STM a -> STM [a] Source
Alternative ZipList Source	Since: base-4.11.0.0
Instance details Defined in GHC.Internal.Functor.ZipList Methods empty :: ZipList a Source (<\|>) :: ZipList a -> ZipList a -> ZipList a Source some :: ZipList a -> ZipList [a] Source many :: ZipList a -> ZipList [a] Source
Alternative P Source	Since: base-4.5.0.0
Instance details Defined in GHC.Internal.Text.ParserCombinators.ReadP Methods empty :: P a Source (<\|>) :: P a -> P a -> P a Source some :: P a -> P [a] Source many :: P a -> P [a] Source
Alternative ReadP Source	Since: base-4.6.0.0
Instance details Defined in GHC.Internal.Text.ParserCombinators.ReadP Methods empty :: ReadP a Source (<\|>) :: ReadP a -> ReadP a -> ReadP a Source some :: ReadP a -> ReadP [a] Source many :: ReadP a -> ReadP [a] Source
Alternative ReadPrec Source	Since: base-4.6.0.0
Instance details Defined in GHC.Internal.Text.ParserCombinators.ReadPrec Methods empty :: ReadPrec a Source (<\|>) :: ReadPrec a -> ReadPrec a -> ReadPrec a Source some :: ReadPrec a -> ReadPrec [a] Source many :: ReadPrec a -> ReadPrec [a] Source
Alternative IO Source	Takes the first non-throwing `IO` action's result. `empty` throws an exception. Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Base Methods empty :: IO a Source (<\|>) :: IO a -> IO a -> IO a Source some :: IO a -> IO [a] Source many :: IO a -> IO [a] Source
Alternative Maybe Source	Picks the leftmost `Just` value, or, alternatively, `Nothing`. Since: base-2.1
Instance details Defined in GHC.Internal.Base Methods empty :: Maybe a Source (<\|>) :: Maybe a -> Maybe a -> Maybe a Source some :: Maybe a -> Maybe [a] Source many :: Maybe a -> Maybe [a] Source
Alternative [] Source	Combines lists by concatenation, starting from the empty list. Since: base-2.1
Instance details Defined in GHC.Internal.Base Methods empty :: [a] Source (<\|>) :: [a] -> [a] -> [a] Source some :: [a] -> [[a]] Source many :: [a] -> [[a]] Source
MonadPlus m => Alternative (WrappedMonad m) Source	Since: base-2.1
Instance details Defined in Control.Applicative Methods empty :: WrappedMonad m a Source (<\|>) :: WrappedMonad m a -> WrappedMonad m a -> WrappedMonad m a Source some :: WrappedMonad m a -> WrappedMonad m [a] Source many :: WrappedMonad m a -> WrappedMonad m [a] Source
ArrowPlus a => Alternative (ArrowMonad a) Source	Since: base-4.6.0.0
Instance details Defined in GHC.Internal.Control.Arrow Methods empty :: ArrowMonad a a0 Source (<\|>) :: ArrowMonad a a0 -> ArrowMonad a a0 -> ArrowMonad a a0 Source some :: ArrowMonad a a0 -> ArrowMonad a [a0] Source many :: ArrowMonad a a0 -> ArrowMonad a [a0] Source
Alternative (Proxy :: Type -> Type) Source	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Data.Proxy Methods empty :: Proxy a Source (<\|>) :: Proxy a -> Proxy a -> Proxy a Source some :: Proxy a -> Proxy [a] Source many :: Proxy a -> Proxy [a] Source
Alternative (U1 :: Type -> Type) Source	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Generics Methods empty :: U1 a Source (<\|>) :: U1 a -> U1 a -> U1 a Source some :: U1 a -> U1 [a] Source many :: U1 a -> U1 [a] Source
(ArrowZero a, ArrowPlus a) => Alternative (WrappedArrow a b) Source	Since: base-2.1
Instance details Defined in Control.Applicative Methods empty :: WrappedArrow a b a0 Source (<\|>) :: WrappedArrow a b a0 -> WrappedArrow a b a0 -> WrappedArrow a b a0 Source some :: WrappedArrow a b a0 -> WrappedArrow a b [a0] Source many :: WrappedArrow a b a0 -> WrappedArrow a b [a0] Source
Alternative m => Alternative (Kleisli m a) Source	Since: base-4.14.0.0
Instance details Defined in GHC.Internal.Control.Arrow Methods empty :: Kleisli m a a0 Source (<\|>) :: Kleisli m a a0 -> Kleisli m a a0 -> Kleisli m a a0 Source some :: Kleisli m a a0 -> Kleisli m a [a0] Source many :: Kleisli m a a0 -> Kleisli m a [a0] Source
Alternative f => Alternative (Ap f) Source	Since: base-4.12.0.0
Instance details Defined in GHC.Internal.Data.Monoid Methods empty :: Ap f a Source (<\|>) :: Ap f a -> Ap f a -> Ap f a Source some :: Ap f a -> Ap f [a] Source many :: Ap f a -> Ap f [a] Source
Alternative f => Alternative (Alt f) Source	Since: base-4.8.0.0
Instance details Defined in GHC.Internal.Data.Semigroup.Internal Methods empty :: Alt f a Source (<\|>) :: Alt f a -> Alt f a -> Alt f a Source some :: Alt f a -> Alt f [a] Source many :: Alt f a -> Alt f [a] Source
(Generic1 f, Alternative (Rep1 f)) => Alternative (Generically1 f) Source	Since: base-4.17.0.0
Instance details Defined in GHC.Internal.Generics Methods empty :: Generically1 f a Source (<\|>) :: Generically1 f a -> Generically1 f a -> Generically1 f a Source some :: Generically1 f a -> Generically1 f [a] Source many :: Generically1 f a -> Generically1 f [a] Source
Alternative f => Alternative (Rec1 f) Source	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Generics Methods empty :: Rec1 f a Source (<\|>) :: Rec1 f a -> Rec1 f a -> Rec1 f a Source some :: Rec1 f a -> Rec1 f [a] Source many :: Rec1 f a -> Rec1 f [a] Source
(Alternative f, Alternative g) => Alternative (Product f g) Source	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods empty :: Product f g a Source (<\|>) :: Product f g a -> Product f g a -> Product f g a Source some :: Product f g a -> Product f g [a] Source many :: Product f g a -> Product f g [a] Source
(Alternative f, Alternative g) => Alternative (f :*: g) Source	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Generics Methods empty :: (f :: g) a Source (<\|>) :: (f :: g) a -> (f :: g) a -> (f :: g) a Source some :: (f :: g) a -> (f :: g) [a] Source many :: (f :: g) a -> (f :: g) [a] Source
(Alternative f, Applicative g) => Alternative (Compose f g) Source	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Compose Methods empty :: Compose f g a Source (<\|>) :: Compose f g a -> Compose f g a -> Compose f g a Source some :: Compose f g a -> Compose f g [a] Source many :: Compose f g a -> Compose f g [a] Source
(Alternative f, Applicative g) => Alternative (f :.: g) Source	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Generics Methods empty :: (f :.: g) a Source (<\|>) :: (f :.: g) a -> (f :.: g) a -> (f :.: g) a Source some :: (f :.: g) a -> (f :.: g) [a] Source many :: (f :.: g) a -> (f :.: g) [a] Source
Alternative f => Alternative (M1 i c f) Source	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Generics Methods empty :: M1 i c f a Source (<\|>) :: M1 i c f a -> M1 i c f a -> M1 i c f a Source some :: M1 i c f a -> M1 i c f [a] Source many :: M1 i c f a -> M1 i c f [a] Source

Instances

newtype Const a (b :: k) Source

The Const functor.

Examples

Expand

>>> fmap (++ "World") (Const "Hello")
Const "Hello"

Because we ignore the second type parameter to Const, the Applicative instance, which has (<*>) :: Monoid m => Const m (a -> b) -> Const m a -> Const m b essentially turns into Monoid m => m -> m -> m, which is (<>)

>>> Const [1, 2, 3] <*> Const [4, 5, 6]
Const [1,2,3,4,5,6]

Constructors

Const
Fields getConst :: a

Instances

Instances details

Generic1 (Const a :: k -> Type) Source

Instance details

Defined in GHC.Internal.Data.Functor.Const

Associated Types

type Rep1 (Const a :: k -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Data.Functor.Const type Rep1 (Const a :: k -> Type) = D1 ('MetaData "Const" "GHC.Internal.Data.Functor.Const" "ghc-internal" 'True) (C1 ('MetaCons "Const" 'PrefixI 'True) (S1 ('MetaSel ('Just "getConst") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))

Methods

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

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

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

Since: base-4.10.0.0

Instance details

Defined in Data.Bifoldable

Methods

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

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

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

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

Bifoldable1 (Const :: Type -> Type -> Type) Source

Instance details

Defined in Data.Bifoldable1

Methods

bifold1 :: Semigroup m => Const m m -> m Source

bifoldMap1 :: Semigroup m => (a -> m) -> (b -> m) -> Const a b -> m Source

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

Since: base-4.8.0.0

Instance details

Defined in Data.Bifunctor

Methods

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

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

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

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

Since: base-4.10.0.0

Instance details

Defined in Data.Bitraversable

Methods

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

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

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Classes

Methods

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

Ord2 (Const :: Type -> Type -> Type) Source

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Classes

Methods

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

Read2 (Const :: Type -> Type -> Type) Source

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Classes

Methods

liftReadsPrec2 :: (Int -> ReadS a) -> ReadS [a] -> (Int -> ReadS b) -> ReadS [b] -> Int -> ReadS (Const a b) Source

liftReadList2 :: (Int -> ReadS a) -> ReadS [a] -> (Int -> ReadS b) -> ReadS [b] -> ReadS [Const a b] Source

liftReadPrec2 :: ReadPrec a -> ReadPrec [a] -> ReadPrec b -> ReadPrec [b] -> ReadPrec (Const a b) Source

liftReadListPrec2 :: ReadPrec a -> ReadPrec [a] -> ReadPrec b -> ReadPrec [b] -> ReadPrec [Const a b] Source

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

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Classes

Methods

liftShowsPrec2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> Int -> Const a b -> ShowS Source

liftShowList2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> [Const a b] -> ShowS Source

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

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Classes

Methods

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

Ord a => Ord1 (Const a :: Type -> Type) Source

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Classes

Methods

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

Read a => Read1 (Const a :: Type -> Type) Source

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Classes

Methods

liftReadsPrec :: (Int -> ReadS a0) -> ReadS [a0] -> Int -> ReadS (Const a a0) Source

liftReadList :: (Int -> ReadS a0) -> ReadS [a0] -> ReadS [Const a a0] Source

liftReadPrec :: ReadPrec a0 -> ReadPrec [a0] -> ReadPrec (Const a a0) Source

liftReadListPrec :: ReadPrec a0 -> ReadPrec [a0] -> ReadPrec [Const a a0] Source

Show a => Show1 (Const a :: Type -> Type) Source

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Classes

Methods

liftShowsPrec :: (Int -> a0 -> ShowS) -> ([a0] -> ShowS) -> Int -> Const a a0 -> ShowS Source

liftShowList :: (Int -> a0 -> ShowS) -> ([a0] -> ShowS) -> [Const a a0] -> ShowS Source

Contravariant (Const a :: Type -> Type) Source

Instance details

Defined in Data.Functor.Contravariant

Methods

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

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

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

Since: base-2.0.1

Instance details

Defined in GHC.Internal.Data.Functor.Const

Methods

pure :: a -> Const m a Source

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

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

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

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

Functor (Const m :: Type -> Type) Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Functor.Const

Methods

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

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

Foldable (Const m :: Type -> Type) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Const

Methods

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

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

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

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

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

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

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

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

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

toList :: Const m a -> [a] Source

null :: Const m a -> Bool Source

length :: Const m a -> Int Source

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

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

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

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

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

Traversable (Const m :: Type -> Type) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Traversable

Methods

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

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

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

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

Monoid a => Monoid (Const a b) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Const

Methods

mempty :: Const a b Source

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

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

Semigroup a => Semigroup (Const a b) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Const

Methods

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

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

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

Bits a => Bits (Const a b) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Const

Methods

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

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

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

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

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

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

zeroBits :: Const a b Source

bit :: Int -> Const a b Source

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

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

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

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

bitSizeMaybe :: Const a b -> Maybe Int Source

bitSize :: Const a b -> Int Source

isSigned :: Const a b -> Bool Source

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

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

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

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

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

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

popCount :: Const a b -> Int Source

FiniteBits a => FiniteBits (Const a b) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Const

Methods

finiteBitSize :: Const a b -> Int Source

countLeadingZeros :: Const a b -> Int Source

countTrailingZeros :: Const a b -> Int Source

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

Since: base-4.10.0.0

Instance details

Defined in GHC.Internal.Data.Data

Methods

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

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

toConstr :: Const a b -> Constr Source

dataTypeOf :: Const a b -> DataType Source

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

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

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

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

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

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

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

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

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

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

IsString a => IsString (Const a b) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.String

Methods

fromString :: String -> Const a b Source

Bounded a => Bounded (Const a b) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Const

Methods

minBound :: Const a b Source

maxBound :: Const a b Source

Enum a => Enum (Const a b) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Const

Methods

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

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

toEnum :: Int -> Const a b Source

fromEnum :: Const a b -> Int Source

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

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

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

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

Floating a => Floating (Const a b) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Const

Methods

pi :: Const a b Source

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

RealFloat a => RealFloat (Const a b) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Const

Methods

floatRadix :: Const a b -> Integer Source

floatDigits :: Const a b -> Int Source

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

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

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

exponent :: Const a b -> Int Source

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

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

isNaN :: Const a b -> Bool Source

isInfinite :: Const a b -> Bool Source

isDenormalized :: Const a b -> Bool Source

isNegativeZero :: Const a b -> Bool Source

isIEEE :: Const a b -> Bool Source

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

Storable a => Storable (Const a b) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Const

Methods

sizeOf :: Const a b -> Int Source

alignment :: Const a b -> Int Source

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

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

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

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

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

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

Generic (Const a b) Source

Instance details

Defined in GHC.Internal.Data.Functor.Const

Associated Types

type Rep (Const a b)	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Data.Functor.Const type Rep (Const a b) = D1 ('MetaData "Const" "GHC.Internal.Data.Functor.Const" "ghc-internal" 'True) (C1 ('MetaCons "Const" 'PrefixI 'True) (S1 ('MetaSel ('Just "getConst") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))

Methods

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

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

Ix a => Ix (Const a b) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Const

Methods

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

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

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

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

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

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

Num a => Num (Const a b) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Const

Methods

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

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

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

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

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

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

fromInteger :: Integer -> Const a b Source

Read a => Read (Const a b) Source

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

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Const

Methods

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

readList :: ReadS [Const a b] Source

readPrec :: ReadPrec (Const a b) Source

readListPrec :: ReadPrec [Const a b] Source

Fractional a => Fractional (Const a b) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Const

Methods

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

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

fromRational :: Rational -> Const a b Source

Integral a => Integral (Const a b) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Const

Methods

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

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

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

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

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

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

toInteger :: Const a b -> Integer Source

Real a => Real (Const a b) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Const

Methods

toRational :: Const a b -> Rational Source

RealFrac a => RealFrac (Const a b) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Const

Methods

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

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

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

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

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

Show a => Show (Const a b) Source

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

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Const

Methods

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

show :: Const a b -> String Source

showList :: [Const a b] -> ShowS Source

Eq a => Eq (Const a b) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Const

Methods

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

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

Ord a => Ord (Const a b) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Const

Methods

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

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

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

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

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

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

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

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

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Const

type Rep1 (Const a :: k -> Type) = D1 ('MetaData "Const" "GHC.Internal.Data.Functor.Const" "ghc-internal" 'True) (C1 ('MetaCons "Const" 'PrefixI 'True) (S1 ('MetaSel ('Just "getConst") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))

type Rep (Const a b) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Const

type Rep (Const a b) = D1 ('MetaData "Const" "GHC.Internal.Data.Functor.Const" "ghc-internal" 'True) (C1 ('MetaCons "Const" 'PrefixI 'True) (S1 ('MetaSel ('Just "getConst") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))

newtype WrappedMonad (m :: Type -> Type) a Source

Constructors

WrapMonad
Fields unwrapMonad :: m a

Instances

Instances details

Generic1 (WrappedMonad m :: Type -> Type) Source

Instance details

Defined in Control.Applicative

Associated Types

type Rep1 (WrappedMonad m :: Type -> Type)	Since: base-4.7.0.0
Instance details Defined in Control.Applicative type Rep1 (WrappedMonad m :: Type -> Type) = D1 ('MetaData "WrappedMonad" "Control.Applicative" "base-4.21.0.0-8e62" 'True) (C1 ('MetaCons "WrapMonad" 'PrefixI 'True) (S1 ('MetaSel ('Just "unwrapMonad") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 m)))

Methods

from1 :: WrappedMonad m a -> Rep1 (WrappedMonad m) a Source

to1 :: Rep1 (WrappedMonad m) a -> WrappedMonad m a Source

MonadPlus m => Alternative (WrappedMonad m) Source

Since: base-2.1

Instance details

Defined in Control.Applicative

Methods

empty :: WrappedMonad m a Source

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

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

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

Monad m => Applicative (WrappedMonad m) Source

Since: base-2.1

Instance details

Defined in Control.Applicative

Methods

pure :: a -> WrappedMonad m a Source

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

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

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

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

Monad m => Functor (WrappedMonad m) Source

Since: base-2.1

Instance details

Defined in Control.Applicative

Methods

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

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

Monad m => Monad (WrappedMonad m) Source

Since: base-4.7.0.0

Instance details

Defined in Control.Applicative

Methods

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

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

return :: a -> WrappedMonad m a Source

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

Since: base-4.14.0.0

Instance details

Defined in Control.Applicative

Methods

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

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

toConstr :: WrappedMonad m a -> Constr Source

dataTypeOf :: WrappedMonad m a -> DataType Source

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

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

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

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

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

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

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

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

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

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

Generic (WrappedMonad m a) Source

Instance details

Defined in Control.Applicative

Associated Types

type Rep (WrappedMonad m a)	Since: base-4.7.0.0
Instance details Defined in Control.Applicative type Rep (WrappedMonad m a) = D1 ('MetaData "WrappedMonad" "Control.Applicative" "base-4.21.0.0-8e62" 'True) (C1 ('MetaCons "WrapMonad" 'PrefixI 'True) (S1 ('MetaSel ('Just "unwrapMonad") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (m a))))

Methods

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

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

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

Since: base-4.7.0.0

Instance details

Defined in Control.Applicative

type Rep1 (WrappedMonad m :: Type -> Type) = D1 ('MetaData "WrappedMonad" "Control.Applicative" "base-4.21.0.0-8e62" 'True) (C1 ('MetaCons "WrapMonad" 'PrefixI 'True) (S1 ('MetaSel ('Just "unwrapMonad") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 m)))

type Rep (WrappedMonad m a) Source

Since: base-4.7.0.0

Instance details

Defined in Control.Applicative

type Rep (WrappedMonad m a) = D1 ('MetaData "WrappedMonad" "Control.Applicative" "base-4.21.0.0-8e62" 'True) (C1 ('MetaCons "WrapMonad" 'PrefixI 'True) (S1 ('MetaSel ('Just "unwrapMonad") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (m a))))

newtype WrappedArrow (a :: Type -> Type -> Type) b c Source

Constructors

WrapArrow
Fields unwrapArrow :: a b c

Instances

Instances details

Generic1 (WrappedArrow a b :: Type -> Type) Source

Instance details

Defined in Control.Applicative

Associated Types

type Rep1 (WrappedArrow a b :: Type -> Type)	Since: base-4.7.0.0
Instance details Defined in Control.Applicative type Rep1 (WrappedArrow a b :: Type -> Type) = D1 ('MetaData "WrappedArrow" "Control.Applicative" "base-4.21.0.0-8e62" 'True) (C1 ('MetaCons "WrapArrow" 'PrefixI 'True) (S1 ('MetaSel ('Just "unwrapArrow") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 (a b))))

Methods

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

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

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

Since: base-2.1

Instance details

Defined in Control.Applicative

Methods

empty :: WrappedArrow a b a0 Source

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

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

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

Arrow a => Applicative (WrappedArrow a b) Source

Since: base-2.1

Instance details

Defined in Control.Applicative

Methods

pure :: a0 -> WrappedArrow a b a0 Source

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

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

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

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

Arrow a => Functor (WrappedArrow a b) Source

Since: base-2.1

Instance details

Defined in Control.Applicative

Methods

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

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

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

Since: base-4.14.0.0

Instance details

Defined in Control.Applicative

Methods

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

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

toConstr :: WrappedArrow a b c -> Constr Source

dataTypeOf :: WrappedArrow a b c -> DataType Source

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

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

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

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

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

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

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

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

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

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

Generic (WrappedArrow a b c) Source

Instance details

Defined in Control.Applicative

Associated Types

type Rep (WrappedArrow a b c)	Since: base-4.7.0.0
Instance details Defined in Control.Applicative type Rep (WrappedArrow a b c) = D1 ('MetaData "WrappedArrow" "Control.Applicative" "base-4.21.0.0-8e62" 'True) (C1 ('MetaCons "WrapArrow" 'PrefixI 'True) (S1 ('MetaSel ('Just "unwrapArrow") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (a b c))))

Methods

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

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

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

Since: base-4.7.0.0

Instance details

Defined in Control.Applicative

type Rep1 (WrappedArrow a b :: Type -> Type) = D1 ('MetaData "WrappedArrow" "Control.Applicative" "base-4.21.0.0-8e62" 'True) (C1 ('MetaCons "WrapArrow" 'PrefixI 'True) (S1 ('MetaSel ('Just "unwrapArrow") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 (a b))))

type Rep (WrappedArrow a b c) Source

Since: base-4.7.0.0

Instance details

Defined in Control.Applicative

type Rep (WrappedArrow a b c) = D1 ('MetaData "WrappedArrow" "Control.Applicative" "base-4.21.0.0-8e62" 'True) (C1 ('MetaCons "WrapArrow" 'PrefixI 'True) (S1 ('MetaSel ('Just "unwrapArrow") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (a b c))))

newtype ZipList a Source

Lists, but with an Applicative functor based on zipping.

Examples

Expand

In contrast to the Applicative for List:

>>> (+) <$> [1, 2, 3] <*> [4, 5, 6]
[5,6,7,6,7,8,7,8,9]

The Applicative instance of ZipList applies the operation by pairing up the elements, analogous to zipWithN

>>> (+) <$> ZipList [1, 2, 3] <*> ZipList [4, 5, 6]
ZipList {getZipList = [5,7,9]}

>>> (,,,) <$> ZipList [1, 2] <*> ZipList [3, 4] <*> ZipList [5, 6] <*> ZipList [7, 8]
ZipList {getZipList = [(1,3,5,7),(2,4,6,8)]}

>>> ZipList [(+1), (^2), (/ 2)] <*> ZipList [5, 5, 5]
ZipList {getZipList = [6.0,25.0,2.5]}

Constructors

ZipList
Fields getZipList :: [a]

Instances

Instances details

Alternative ZipList Source

Since: base-4.11.0.0

Instance details

Defined in GHC.Internal.Functor.ZipList

Methods

empty :: ZipList a Source

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

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

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

Applicative ZipList Source

f <$> ZipList xs1 <*> ... <*> ZipList xsN
    = ZipList (zipWithN f xs1 ... xsN)

where zipWithN refers to the zipWith function of the appropriate arity (zipWith, zipWith3, zipWith4, ...). For example:

(\a b c -> stimes c [a, b]) <$> ZipList "abcd" <*> ZipList "567" <*> ZipList [1..]
    = ZipList (zipWith3 (\a b c -> stimes c [a, b]) "abcd" "567" [1..])
    = ZipList {getZipList = ["a5","b6b6","c7c7c7"]}

Since: base-2.1

Instance details

Defined in GHC.Internal.Functor.ZipList

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

Functor ZipList Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Functor.ZipList

Methods

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

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

Foldable ZipList Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Functor.ZipList

Methods

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

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

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

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

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

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

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

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

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

toList :: ZipList a -> [a] Source

null :: ZipList a -> Bool Source

length :: ZipList a -> Int Source

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

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

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

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

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

Traversable ZipList Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Functor.ZipList

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

Generic1 ZipList Source

Instance details

Defined in GHC.Internal.Functor.ZipList

Associated Types

type Rep1 ZipList	Since: base-4.7.0.0
Instance details Defined in GHC.Internal.Functor.ZipList type Rep1 ZipList = D1 ('MetaData "ZipList" "GHC.Internal.Functor.ZipList" "ghc-internal" 'True) (C1 ('MetaCons "ZipList" 'PrefixI 'True) (S1 ('MetaSel ('Just "getZipList") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 [])))

Methods

from1 :: ZipList a -> Rep1 ZipList a Source

to1 :: Rep1 ZipList a -> ZipList a Source

Data a => Data (ZipList a) Source

Since: base-4.14.0.0

Instance details

Defined in GHC.Internal.Functor.ZipList

Methods

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

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

toConstr :: ZipList a -> Constr Source

dataTypeOf :: ZipList a -> DataType Source

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

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

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

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

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

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

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

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

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

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

Generic (ZipList a) Source

Instance details

Defined in GHC.Internal.Functor.ZipList

Associated Types

type Rep (ZipList a)	Since: base-4.7.0.0
Instance details Defined in GHC.Internal.Functor.ZipList type Rep (ZipList a) = D1 ('MetaData "ZipList" "GHC.Internal.Functor.ZipList" "ghc-internal" 'True) (C1 ('MetaCons "ZipList" 'PrefixI 'True) (S1 ('MetaSel ('Just "getZipList") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 [a])))

Methods

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

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

IsList (ZipList a) Source

Since: base-4.15.0.0

Instance details

Defined in GHC.Internal.IsList

Associated Types

type Item (ZipList a)
Instance details Defined in GHC.Internal.IsList type Item (ZipList a) = a

Methods

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

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

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

Read a => Read (ZipList a) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Functor.ZipList

Methods

readsPrec :: Int -> ReadS (ZipList a) Source

readList :: ReadS [ZipList a] Source

readPrec :: ReadPrec (ZipList a) Source

readListPrec :: ReadPrec [ZipList a] Source

Show a => Show (ZipList a) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Functor.ZipList

Methods

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

show :: ZipList a -> String Source

showList :: [ZipList a] -> ShowS Source

Eq a => Eq (ZipList a) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Functor.ZipList

Methods

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

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

Ord a => Ord (ZipList a) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Functor.ZipList

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

type Rep1 ZipList Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Functor.ZipList

type Rep1 ZipList = D1 ('MetaData "ZipList" "GHC.Internal.Functor.ZipList" "ghc-internal" 'True) (C1 ('MetaCons "ZipList" 'PrefixI 'True) (S1 ('MetaSel ('Just "getZipList") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 [])))

type Rep (ZipList a) Source

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Functor.ZipList

type Rep (ZipList a) = D1 ('MetaData "ZipList" "GHC.Internal.Functor.ZipList" "ghc-internal" 'True) (C1 ('MetaCons "ZipList" 'PrefixI 'True) (S1 ('MetaSel ('Just "getZipList") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 [a])))

type Item (ZipList a) Source

Instance details

Defined in GHC.Internal.IsList

type Item (ZipList a) = a

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.

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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.

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Perform a computation with Maybe and replace the result with a constant value if it is Just:

>>> 'a' <$ Just 2
Just 'a'
>>> 'a' <$ Nothing
Nothing

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

A variant of <*> with the types of the arguments reversed. It differs from flip (<*>) in that the effects are resolved in the order the arguments are presented.

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>>> (<**>) (print 1) (id <$ print 2)
1
2

>>> flip (<*>) (print 1) (id <$ print 2)
2
1

>>> ZipList [4, 5, 6] <**> ZipList [(+1), (*2), (/3)]
ZipList {getZipList = [5.0,10.0,2.0]}

liftA :: Applicative f => (a -> b) -> f a -> f b Source

Lift a function to actions. Equivalent to Functor's fmap but implemented using only Applicative's methods: liftA f a = pure f <*> a

As such this function may be used to implement a Functor instance from an Applicative one.

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Using the Applicative instance for Lists:

>>> liftA (+1) [1, 2]
[2,3]

Or the Applicative instance for Maybe

>>> liftA (+1) (Just 3)
Just 4

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.

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

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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

asum :: (Foldable t, Alternative f) => t (f a) -> f a Source

The sum of a collection of actions using (<|>), generalizing concat.

asum is just like msum, but generalised to Alternative.

Examples

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Basic usage:

>>> asum [Just "Hello", Nothing, Just "World"]
Just "Hello"

© The University of Glasgow and others
Licensed under a BSD-style license (see top of the page).
https://downloads.haskell.org/~ghc/9.12.1/docs/libraries/base-4.21.0.0-8e62/Control-Applicative.html

Control.Applicative

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Applicative functors

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