base-4.19.0.0: Basic libraries

Control.Applicative

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.

Synopsis

# 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:

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

It may be useful to note that supposing

forall x y. p (q x y) = f x . g y

it follows from the above that

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

If f is also a Monad, it should satisfy

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

Minimal complete definition

pure, ((<*>) | liftA2)

Methods

pure :: a -> f a Source #

Lift a value.

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

Sequential application.

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

#### 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)

(*>) :: 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
>>> 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
 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 detailsDefined in Control.Applicative Methodspure :: 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 # Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Complex Methodspure :: 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 # Source # Since: base-4.8.0.0 Instance detailsDefined in Data.Functor.Identity Methodspure :: 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 # Source # Since: base-4.8.0.0 Instance detailsDefined in Data.Monoid Methodspure :: 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 # Source # Since: base-4.8.0.0 Instance detailsDefined in Data.Monoid Methodspure :: 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 # Source # Since: base-4.11.0.0 Instance detailsDefined in Data.Ord Methodspure :: 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 # Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodspure :: 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 # Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodspure :: 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 # Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodspure :: 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 # Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodspure :: 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 # Source # Since: base-4.8.0.0 Instance detailsDefined in Data.Semigroup.Internal Methodspure :: 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 # Source # Since: base-4.8.0.0 Instance detailsDefined in Data.Semigroup.Internal Methodspure :: 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 # Source # Since: base-4.8.0.0 Instance detailsDefined in Data.Semigroup.Internal Methodspure :: 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 # Source # Since: base-4.9.0.0 Instance detailsDefined in GHC.Base Methodspure :: 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 # Source # Since: base-4.8.0.0 Instance detailsDefined in GHC.Conc.Sync Methodspure :: 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 # Source # Since: base-4.8.0.0 Instance detailsDefined in GHC.GHCi Methodspure :: 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 # Source # Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methodspure :: 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 # Source # Since: base-4.6.0.0 Instance detailsDefined in Text.ParserCombinators.ReadP Methodspure :: 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 # Source # Since: base-4.6.0.0 Instance detailsDefined in Text.ParserCombinators.ReadPrec Methodspure :: 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 # Source # Since: base-2.1 Instance detailsDefined in GHC.Base Methodspure :: 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 # Source # Since: base-2.1 Instance detailsDefined in GHC.Base Methodspure :: 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 # Source # Since: base-4.15 Instance detailsDefined in GHC.Base Methodspure :: 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 # Source # Since: base-2.1 Instance detailsDefined in GHC.Base Methodspure :: 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 detailsDefined in Control.Applicative Methodspure :: 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 detailsDefined in Control.Arrow Methodspure :: 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 # Source # Since: base-2.1 Instance detailsDefined in Control.Monad.ST.Lazy.Imp Methodspure :: 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 # Source # Since: base-3.0 Instance detailsDefined in Data.Either Methodspure :: 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 (Proxy :: Type -> Type) Source # Since: base-4.7.0.0 Instance detailsDefined in Data.Proxy Methodspure :: 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 detailsDefined in GHC.Generics Methodspure :: 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 # Source # Since: base-4.4.0.0 Instance detailsDefined in GHC.ST Methodspure :: 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, Strings concatenate:("hello ", (+15)) <*> ("world!", 2002) ("hello world!",2017)Since: base-2.1 Instance detailsDefined in GHC.Base Methodspure :: 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 detailsDefined in Control.Applicative Methodspure :: 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 detailsDefined in Control.Arrow Methodspure :: 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 detailsDefined in Data.Functor.Const Methodspure :: a -> Const m a Source #(<*>) :: Const m (a -> b) -> Const m a -> Const m b Source #liftA2 :: (a -> b -> c) -> Const m a -> Const m b -> Const m c Source #(*>) :: Const m a -> Const m b -> Const m b Source #(<*) :: Const m a -> Const m b -> Const m a Source # Applicative f => Applicative (Ap f) Source # Since: base-4.12.0.0 Instance detailsDefined in Data.Monoid Methodspure :: 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 detailsDefined in Data.Semigroup.Internal Methodspure :: 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 detailsDefined in GHC.Generics Methodspure :: 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 detailsDefined in GHC.Generics Methodspure :: 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 detailsDefined in GHC.Base Methodspure :: 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 detailsDefined in Data.Functor.Product Methodspure :: 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 detailsDefined in GHC.Generics Methodspure :: 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 detailsDefined in GHC.Generics Methodspure :: 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 detailsDefined in GHC.Base Methodspure :: 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 detailsDefined in GHC.Base Methodspure :: 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 detailsDefined in Data.Functor.Compose Methodspure :: 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 detailsDefined in GHC.Generics Methodspure :: 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 detailsDefined in GHC.Generics Methodspure :: 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:

Minimal complete definition

Methods

empty :: f a Source #

The identity of <|>

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

An associative binary operation

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

One or more.

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

Zero or more.

#### Instances

Instances details

# Instances

newtype Const a (b :: k) Source #

The Const functor.

Constructors

 Const FieldsgetConst :: a

#### Instances

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

Defined in Data.Functor.Const

Associated Types

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

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

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 #

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

Since: base-4.7.0.0

Instance details

Defined in Data.Functor.Const

Methods

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

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

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

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

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

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

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

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

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

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

null :: Const m a -> Bool Source #

length :: Const m a -> Int Source #

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

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

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

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

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

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

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 #

(>$) :: b -> Const a b -> Const a a0 Source # Traversable (Const m :: Type -> Type) Source # Since: base-4.7.0.0 Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Const m a -> f (Const m b) Source # sequenceA :: Applicative f => Const m (f a) -> f (Const m a) Source # mapM :: Monad m0 => (a -> m0 b) -> Const m a -> m0 (Const m b) Source # sequence :: Monad m0 => Const m (m0 a) -> m0 (Const m a) Source # Monoid m => Applicative (Const m :: Type -> Type) Source # Since: base-2.0.1 Instance details Defined in Data.Functor.Const Methods pure :: a -> Const m a Source # (<*>) :: Const m (a -> b) -> Const m a -> Const m b Source # liftA2 :: (a -> b -> c) -> Const m a -> Const m b -> Const m c Source # (*>) :: Const m a -> Const m b -> Const m b Source # (<*) :: Const m a -> Const m b -> Const m a Source # Functor (Const m :: Type -> Type) Source # Since: base-2.1 Instance details Defined in Data.Functor.Const Methods fmap :: (a -> b) -> Const m a -> Const m b Source # (<$) :: a -> Const m b -> Const m a Source #

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

Since: base-4.10.0.0

Instance details

Defined in Data.Data

Methods

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

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

toConstr :: Const a b -> Constr Source #

dataTypeOf :: Const a b -> DataType Source #

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

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

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

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

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

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

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

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

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

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

IsString a => IsString (Const a b) Source #

Since: base-4.9.0.0

Instance details

Defined in Data.String

Methods

fromString :: String -> Const a b Source #

Storable a => Storable (Const a b) Source #

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Const

Methods

sizeOf :: Const a b -> Int Source #

alignment :: Const a b -> Int Source #

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

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

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

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

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

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

Monoid a => Monoid (Const a b) Source #

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Const

Methods

mempty :: Const a b Source #

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

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

Semigroup a => Semigroup (Const a b) Source #

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Const

Methods

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

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

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

Bits a => Bits (Const a b) Source #

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Const

Methods

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

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

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

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

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

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

zeroBits :: Const a b Source #

bit :: Int -> Const a b Source #

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

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

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

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

bitSizeMaybe :: Const a b -> Maybe Int Source #

bitSize :: Const a b -> Int Source #

isSigned :: Const a b -> Bool Source #

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

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

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

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

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

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

popCount :: Const a b -> Int Source #

FiniteBits a => FiniteBits (Const a b) Source #

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Const

Bounded a => Bounded (Const a b) Source #

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Const

Methods

minBound :: Const a b Source #

maxBound :: Const a b Source #

Enum a => Enum (Const a b) Source #

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Const

Methods

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

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

toEnum :: Int -> Const a b Source #

fromEnum :: Const a b -> Int Source #

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

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

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

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

Floating a => Floating (Const a b) Source #

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Const

Methods

pi :: Const a b Source #

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

RealFloat a => RealFloat (Const a b) Source #

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Const

Generic (Const a b) Source #
Instance details

Defined in Data.Functor.Const

Associated Types

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

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 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 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 #

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

Since: base-4.8.0.0

Instance details

Defined in Data.Functor.Const

Fractional a => Fractional (Const a b) Source #

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Const

Methods

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

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

Integral a => Integral (Const a b) Source #

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Const

Methods

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

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

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

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

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

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

toInteger :: Const a b -> Integer Source #

Real a => Real (Const a b) Source #

Since: base-4.9.0.0

Instance details

Defined in 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 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 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 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 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 Data.Functor.Const

type Rep1 (Const a :: k -> Type) = D1 ('MetaData "Const" "Data.Functor.Const" "base" 'True) (C1 ('MetaCons "Const" 'PrefixI 'True) (S1 ('MetaSel ('Just "getConst") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))
type Rep (Const a b) Source #

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Const

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

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

Constructors

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

Since: base-2.1

Instance details

Defined in Control.Applicative

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 #

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 Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> WrappedMonad m a -> c (WrappedMonad m a) Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (WrappedMonad m a) Source # 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 detailsDefined in Control.Applicative type Rep (WrappedMonad m a) = D1 ('MetaData "WrappedMonad" "Control.Applicative" "base" 'True) (C1 ('MetaCons "WrapMonad" 'PrefixI 'True) (S1 ('MetaSel ('Just "unwrapMonad") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (m a)))) 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" '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" '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 FieldsunwrapArrow :: 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 detailsDefined in Control.Applicative type Rep1 (WrappedArrow a b :: Type -> Type) = D1 ('MetaData "WrappedArrow" "Control.Applicative" "base" 'True) (C1 ('MetaCons "WrapArrow" 'PrefixI 'True) (S1 ('MetaSel ('Just "unwrapArrow") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 (a b)))) 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 Data.Data

Methods

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

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

toConstr :: WrappedArrow a b c -> Constr Source #

dataTypeOf :: WrappedArrow a b c -> DataType Source #

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

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

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

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

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

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

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

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

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

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

Generic (WrappedArrow a b c) Source #
Instance details

Defined in Control.Applicative

Associated Types

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

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" '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" 'True) (C1 ('MetaCons "WrapArrow" 'PrefixI 'True) (S1 ('MetaSel ('Just "unwrapArrow") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (a b c))))

newtype ZipList a Source #

Lists, but with an Applicative functor based on zipping.

Constructors

 ZipList FieldsgetZipList :: [a]

#### Instances

Instances details
Source #

Since: base-4.9.0.0

Instance details

Defined in Control.Applicative

Methods

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

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

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

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

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

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

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

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

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

toList :: ZipList a -> [a] Source #

null :: ZipList a -> Bool Source #

length :: ZipList a -> Int Source #

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

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

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

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

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

Source #

Since: base-4.9.0.0

Instance details

Defined in Data.Traversable

Methods

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

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

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

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

Source #

Since: base-4.11.0.0

Instance details

Defined in Control.Applicative

Methods

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

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

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

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 Control.Applicative

Methods

pure :: a -> ZipList a Source #

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

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

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

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

Source #

Since: base-2.1

Instance details

Defined in Control.Applicative

Methods

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

(<$) :: a -> ZipList b -> ZipList a Source # Source # Instance details Defined in Control.Applicative Associated Types  type Rep1 ZipList Since: base-4.7.0.0 Instance detailsDefined in Control.Applicative type Rep1 ZipList = D1 ('MetaData "ZipList" "Control.Applicative" "base" 'True) (C1 ('MetaCons "ZipList" 'PrefixI 'True) (S1 ('MetaSel ('Just "getZipList") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 []))) Methods to1 :: Rep1 ZipList a -> ZipList a Source # Data a => Data (ZipList a) Source # Since: base-4.14.0.0 Instance details Defined in Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> ZipList a -> c (ZipList a) Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (ZipList a) Source # 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 # Source # Instance details Defined in Control.Applicative Associated Types  type Rep (ZipList a) Since: base-4.7.0.0 Instance detailsDefined in Control.Applicative type Rep (ZipList a) = D1 ('MetaData "ZipList" "Control.Applicative" "base" 'True) (C1 ('MetaCons "ZipList" 'PrefixI 'True) (S1 ('MetaSel ('Just "getZipList") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 [a]))) Methods from :: ZipList a -> Rep (ZipList a) x Source # to :: Rep (ZipList a) x -> ZipList a Source # Source # Since: base-4.15.0.0 Instance details Defined in GHC.IsList Associated Types  type Item (ZipList a) Instance detailsDefined in GHC.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 Control.Applicative Methods Show a => Show (ZipList a) Source # Since: base-4.7.0.0 Instance details Defined in Control.Applicative Eq a => Eq (ZipList a) Source # Since: base-4.7.0.0 Instance details Defined in Control.Applicative Methods (==) :: ZipList a -> ZipList a -> Bool Source # (/=) :: ZipList a -> ZipList a -> Bool Source # Ord a => Ord (ZipList a) Source # Since: base-4.7.0.0 Instance details Defined in Control.Applicative type Rep1 ZipList Source # Since: base-4.7.0.0 Instance details Defined in Control.Applicative type Rep1 ZipList = D1 ('MetaData "ZipList" "Control.Applicative" "base" 'True) (C1 ('MetaCons "ZipList" 'PrefixI 'True) (S1 ('MetaSel ('Just "getZipList") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 []))) type Rep (ZipList a) Source # Since: base-4.7.0.0 Instance details Defined in Control.Applicative type Rep (ZipList a) = D1 ('MetaData "ZipList" "Control.Applicative" "base" 'True) (C1 ('MetaCons "ZipList" 'PrefixI 'True) (S1 ('MetaSel ('Just "getZipList") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 [a]))) type Item (ZipList a) Source # Instance details Defined in GHC.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, <$> is function application lifted over a Functor. #### Examples Expand Convert from a Maybe Int to a Maybe String using show: >>> show <$> Nothing
Nothing
>>> show <$> Just 3 Just "3" Convert from an Either Int Int to an Either Int String using show: >>> show <$> Left 17
Left 17
>>> show <$> Right 17 Right "17" Double each element of a list: >>> (*2) <$> [1,2,3]
[2,4,6]

Apply even to the second element of a pair:

>>> even <$> (2,2) (2,True) (<$) :: Functor f => a -> f b -> f a infixl 4 Source #

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

#### Examples

Expand

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.

#### Examples

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

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.

#### Examples

Expand

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.

#### Examples

Expand

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

>>> 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

Expand

Basic usage:

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