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/Haskell 8

Control.Applicative

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

Applicative functors
Alternatives
Instances
Utility functions

Description

This module describes a structure intermediate between a functor and a monad (technically, a strong lax monoidal functor). Compared with monads, this interface lacks the full power of the binding operation >>=, but

it has more instances.
it is sufficient for many uses, e.g. context-free parsing, or the Traversable class.
instances can perform analysis of computations before they are executed, and thus produce shared optimizations.

This interface was introduced for parsers by Niklas Röjemo, because it admits more sharing than the monadic interface. The names here are mostly based on parsing work by Doaitse Swierstra.

For more details, see Applicative Programming with Effects, by Conor McBride and Ross Paterson.

Applicative functors

class Functor f => Applicative f where Source

A functor with application, providing operations to

embed pure expressions (pure), and
sequence computations and combine their results (<*> and liftA2).

A minimal complete definition must include implementations of pure and of either <*> or liftA2. If it defines both, then they must behave the same as their default definitions:

(<*>) = liftA2 id

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

Further, any definition must satisfy the following:

identity

pure id <*> v = v

composition

pure (.) <*> u <*> v <*> w = u <*> (v <*> w)

homomorphism

pure f <*> pure x = pure (f x)

interchange

u <*> pure y = pure ($ y) <*> u

The other methods have the following default definitions, which may be overridden with equivalent specialized implementations:

```
u *> v = (id <$ u) <*> v
```
```
u <* v = liftA2 const u v
```

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

```
fmap f x = pure f <*> x
```

It may be useful to note that supposing

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

it follows from the above that

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

If f is also a Monad, it should satisfy

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

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

Minimal complete definition

pure, ((<*>) | liftA2)

Methods

pure :: a -> f a Source

Lift a value.

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

Sequential application.

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

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

Lift a binary function to actions.

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

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

Sequence actions, discarding the value of the first argument.

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

Sequence actions, discarding the value of the second argument.

Instances

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

Alternatives

class Applicative f => Alternative f where Source

A monoid on applicative functors.

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

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

Minimal complete definition

empty, (<|>)

Methods

empty :: f a Source

The identity of <|>

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

An associative binary operation

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

One or more.

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

Zero or more.

Instances

Alternative []	Since: base-2.1
Instance details Defined in GHC.Base Methods empty :: [a] Source (<\|>) :: [a] -> [a] -> [a] Source some :: [a] -> [[a]] Source many :: [a] -> [[a]] Source
Alternative Maybe	Since: base-2.1
Instance details Defined in GHC.Base Methods empty :: Maybe a Source (<\|>) :: Maybe a -> Maybe a -> Maybe a Source some :: Maybe a -> Maybe [a] Source many :: Maybe a -> Maybe [a] Source
Alternative IO	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods empty :: IO a Source (<\|>) :: IO a -> IO a -> IO a Source some :: IO a -> IO [a] Source many :: IO a -> IO [a] Source
Alternative ReadP	Since: base-4.6.0.0
Instance details Defined in Text.ParserCombinators.ReadP Methods empty :: ReadP a Source (<\|>) :: ReadP a -> ReadP a -> ReadP a Source some :: ReadP a -> ReadP [a] Source many :: ReadP a -> ReadP [a] Source
Alternative ReadPrec	Since: base-4.6.0.0
Instance details Defined in Text.ParserCombinators.ReadPrec Methods empty :: ReadPrec a Source (<\|>) :: ReadPrec a -> ReadPrec a -> ReadPrec a Source some :: ReadPrec a -> ReadPrec [a] Source many :: ReadPrec a -> ReadPrec [a] Source
Alternative STM	Since: base-4.8.0.0
Instance details Defined in GHC.Conc.Sync Methods empty :: STM a Source (<\|>) :: STM a -> STM a -> STM a Source some :: STM a -> STM [a] Source many :: STM a -> STM [a] Source
Alternative ZipList	Since: base-4.11.0.0
Instance details Defined in Control.Applicative Methods empty :: ZipList a Source (<\|>) :: ZipList a -> ZipList a -> ZipList a Source some :: ZipList a -> ZipList [a] Source many :: ZipList a -> ZipList [a] Source
Alternative Option	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods empty :: Option a Source (<\|>) :: Option a -> Option a -> Option a Source some :: Option a -> Option [a] Source many :: Option a -> Option [a] Source
Alternative (U1 :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods empty :: U1 a Source (<\|>) :: U1 a -> U1 a -> U1 a Source some :: U1 a -> U1 [a] Source many :: U1 a -> U1 [a] Source
Alternative (Proxy :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Proxy Methods empty :: Proxy a Source (<\|>) :: Proxy a -> Proxy a -> Proxy a Source some :: Proxy a -> Proxy [a] Source many :: Proxy a -> Proxy [a] Source
ArrowPlus a => Alternative (ArrowMonad a)	Since: base-4.6.0.0
Instance details Defined in Control.Arrow Methods empty :: ArrowMonad a a0 Source (<\|>) :: ArrowMonad a a0 -> ArrowMonad a a0 -> ArrowMonad a a0 Source some :: ArrowMonad a a0 -> ArrowMonad a [a0] Source many :: ArrowMonad a a0 -> ArrowMonad a [a0] Source
MonadPlus m => Alternative (WrappedMonad m)	Since: base-2.1
Instance details Defined in Control.Applicative Methods empty :: WrappedMonad m a Source (<\|>) :: WrappedMonad m a -> WrappedMonad m a -> WrappedMonad m a Source some :: WrappedMonad m a -> WrappedMonad m [a] Source many :: WrappedMonad m a -> WrappedMonad m [a] Source
Alternative f => Alternative (Rec1 f)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods empty :: Rec1 f a Source (<\|>) :: Rec1 f a -> Rec1 f a -> Rec1 f a Source some :: Rec1 f a -> Rec1 f [a] Source many :: Rec1 f a -> Rec1 f [a] Source
Alternative f => Alternative (Alt f)	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods empty :: Alt f a Source (<\|>) :: Alt f a -> Alt f a -> Alt f a Source some :: Alt f a -> Alt f [a] Source many :: Alt f a -> Alt f [a] Source
Alternative f => Alternative (Ap f)	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods empty :: Ap f a Source (<\|>) :: Ap f a -> Ap f a -> Ap f a Source some :: Ap f a -> Ap f [a] Source many :: Ap f a -> Ap f [a] Source
(ArrowZero a, ArrowPlus a) => Alternative (WrappedArrow a b)	Since: base-2.1
Instance details Defined in Control.Applicative Methods empty :: WrappedArrow a b a0 Source (<\|>) :: WrappedArrow a b a0 -> WrappedArrow a b a0 -> WrappedArrow a b a0 Source some :: WrappedArrow a b a0 -> WrappedArrow a b [a0] Source many :: WrappedArrow a b a0 -> WrappedArrow a b [a0] Source
(Alternative f, Alternative g) => Alternative (f :*: g)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods empty :: (f :: g) a Source (<\|>) :: (f :: g) a -> (f :: g) a -> (f :: g) a Source some :: (f :: g) a -> (f :: g) [a] Source many :: (f :: g) a -> (f :: g) [a] Source
(Alternative f, Alternative g) => Alternative (Product f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods empty :: Product f g a Source (<\|>) :: Product f g a -> Product f g a -> Product f g a Source some :: Product f g a -> Product f g [a] Source many :: Product f g a -> Product f g [a] Source
Alternative f => Alternative (M1 i c f)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods empty :: M1 i c f a Source (<\|>) :: M1 i c f a -> M1 i c f a -> M1 i c f a Source some :: M1 i c f a -> M1 i c f [a] Source many :: M1 i c f a -> M1 i c f [a] Source
(Alternative f, Applicative g) => Alternative (f :.: g)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods empty :: (f :.: g) a Source (<\|>) :: (f :.: g) a -> (f :.: g) a -> (f :.: g) a Source some :: (f :.: g) a -> (f :.: g) [a] Source many :: (f :.: g) a -> (f :.: g) [a] Source
(Alternative f, Applicative g) => Alternative (Compose f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Compose Methods empty :: Compose f g a Source (<\|>) :: Compose f g a -> Compose f g a -> Compose f g a Source some :: Compose f g a -> Compose f g [a] Source many :: Compose f g a -> Compose f g [a] Source

Instances

newtype Const a b Source

The Const functor.

Constructors

Const
Fields getConst :: a

Instances

Generic1 (Const a :: k -> Type)
Instance details Defined in Data.Functor.Const Associated Types type Rep1 (Const a) :: k -> Type Source Methods from1 :: Const a a0 -> Rep1 (Const a) a0 Source to1 :: Rep1 (Const a) a0 -> Const a a0 Source
Show2 (Const :: Type -> Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Classes Methods liftShowsPrec2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> Int -> Const a b -> ShowS Source liftShowList2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> [Const a b] -> ShowS Source
Read2 (Const :: Type -> Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Classes Methods liftReadsPrec2 :: (Int -> ReadS a) -> ReadS [a] -> (Int -> ReadS b) -> ReadS [b] -> Int -> ReadS (Const a b) Source liftReadList2 :: (Int -> ReadS a) -> ReadS [a] -> (Int -> ReadS b) -> ReadS [b] -> ReadS [Const a b] Source liftReadPrec2 :: ReadPrec a -> ReadPrec [a] -> ReadPrec b -> ReadPrec [b] -> ReadPrec (Const a b) Source liftReadListPrec2 :: ReadPrec a -> ReadPrec [a] -> ReadPrec b -> ReadPrec [b] -> ReadPrec [Const a b] Source
Ord2 (Const :: Type -> Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Classes Methods liftCompare2 :: (a -> b -> Ordering) -> (c -> d -> Ordering) -> Const a c -> Const b d -> Ordering Source
Eq2 (Const :: Type -> Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Classes Methods liftEq2 :: (a -> b -> Bool) -> (c -> d -> Bool) -> Const a c -> Const b d -> Bool Source
Bifunctor (Const :: Type -> Type -> Type)	Since: base-4.8.0.0
Instance details Defined in Data.Bifunctor Methods bimap :: (a -> b) -> (c -> d) -> Const a c -> Const b d Source first :: (a -> b) -> Const a c -> Const b c Source second :: (b -> c) -> Const a b -> Const a c Source
Bifoldable (Const :: Type -> Type -> Type)	Since: base-4.10.0.0
Instance details Defined in Data.Bifoldable Methods bifold :: Monoid m => Const m m -> m Source bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> Const a b -> m Source bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> Const a b -> c Source bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> Const a b -> c Source
Bitraversable (Const :: Type -> Type -> Type)	Since: base-4.10.0.0
Instance details Defined in Data.Bitraversable Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> Const a b -> f (Const c d) Source
Functor (Const m :: Type -> Type)	Since: base-2.1
Instance details Defined in Data.Functor.Const Methods fmap :: (a -> b) -> Const m a -> Const m b Source (<$) :: a -> Const m b -> Const m a Source
Monoid m => Applicative (Const m :: Type -> Type)	Since: base-2.0.1
Instance details Defined in Data.Functor.Const Methods pure :: a -> Const m a Source (<>) :: Const m (a -> b) -> Const m a -> Const m b Source liftA2 :: (a -> b -> c) -> Const m a -> Const m b -> Const m c Source (>) :: Const m a -> Const m b -> Const m b Source (<*) :: Const m a -> Const m b -> Const m a Source
Foldable (Const m :: Type -> Type)	Since: base-4.7.0.0
Instance details Defined in Data.Functor.Const Methods fold :: Monoid m0 => Const m m0 -> m0 Source foldMap :: Monoid m0 => (a -> m0) -> Const m a -> m0 Source foldr :: (a -> b -> b) -> b -> Const m a -> b Source foldr' :: (a -> b -> b) -> b -> Const m a -> b Source foldl :: (b -> a -> b) -> b -> Const m a -> b Source foldl' :: (b -> a -> b) -> b -> Const m a -> b Source foldr1 :: (a -> a -> a) -> Const m a -> a Source foldl1 :: (a -> a -> a) -> Const m a -> a Source toList :: Const m a -> [a] Source null :: Const m a -> Bool Source length :: Const m a -> Int Source elem :: Eq a => a -> Const m a -> Bool Source maximum :: Ord a => Const m a -> a Source minimum :: Ord a => Const m a -> a Source sum :: Num a => Const m a -> a Source product :: Num a => Const m a -> a Source
Traversable (Const m :: Type -> Type)	Since: base-4.7.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Const m a -> f (Const m b) Source sequenceA :: Applicative f => Const m (f a) -> f (Const m a) Source mapM :: Monad m0 => (a -> m0 b) -> Const m a -> m0 (Const m b) Source sequence :: Monad m0 => Const m (m0 a) -> m0 (Const m a) Source
Show a => Show1 (Const a :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Classes Methods liftShowsPrec :: (Int -> a0 -> ShowS) -> ([a0] -> ShowS) -> Int -> Const a a0 -> ShowS Source liftShowList :: (Int -> a0 -> ShowS) -> ([a0] -> ShowS) -> [Const a a0] -> ShowS Source
Read a => Read1 (Const a :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Classes Methods liftReadsPrec :: (Int -> ReadS a0) -> ReadS [a0] -> Int -> ReadS (Const a a0) Source liftReadList :: (Int -> ReadS a0) -> ReadS [a0] -> ReadS [Const a a0] Source liftReadPrec :: ReadPrec a0 -> ReadPrec [a0] -> ReadPrec (Const a a0) Source liftReadListPrec :: ReadPrec a0 -> ReadPrec [a0] -> ReadPrec [Const a a0] Source
Ord a => Ord1 (Const a :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Classes Methods liftCompare :: (a0 -> b -> Ordering) -> Const a a0 -> Const a b -> Ordering Source
Eq a => Eq1 (Const a :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Classes Methods liftEq :: (a0 -> b -> Bool) -> Const a a0 -> Const a b -> Bool Source
Contravariant (Const a :: Type -> Type)
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a0 -> b) -> Const a b -> Const a a0 Source (>$) :: b -> Const a b -> Const a a0 Source
Bounded a => Bounded (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods minBound :: Const a b Source maxBound :: Const a b Source
Enum a => Enum (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods succ :: Const a b -> Const a b Source pred :: Const a b -> Const a b Source toEnum :: Int -> Const a b Source fromEnum :: Const a b -> Int Source enumFrom :: Const a b -> [Const a b] Source enumFromThen :: Const a b -> Const a b -> [Const a b] Source enumFromTo :: Const a b -> Const a b -> [Const a b] Source enumFromThenTo :: Const a b -> Const a b -> Const a b -> [Const a b] Source
Eq a => Eq (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods (==) :: Const a b -> Const a b -> Bool Source (/=) :: Const a b -> Const a b -> Bool Source
Floating a => Floating (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods pi :: Const a b Source exp :: Const a b -> Const a b Source log :: Const a b -> Const a b Source sqrt :: Const a b -> Const a b Source (**) :: Const a b -> Const a b -> Const a b Source logBase :: Const a b -> Const a b -> Const a b Source sin :: Const a b -> Const a b Source cos :: Const a b -> Const a b Source tan :: Const a b -> Const a b Source asin :: Const a b -> Const a b Source acos :: Const a b -> Const a b Source atan :: Const a b -> Const a b Source sinh :: Const a b -> Const a b Source cosh :: Const a b -> Const a b Source tanh :: Const a b -> Const a b Source asinh :: Const a b -> Const a b Source acosh :: Const a b -> Const a b Source atanh :: Const a b -> Const a b Source log1p :: Const a b -> Const a b Source expm1 :: Const a b -> Const a b Source log1pexp :: Const a b -> Const a b Source log1mexp :: Const a b -> Const a b Source
Fractional a => Fractional (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods (/) :: Const a b -> Const a b -> Const a b Source recip :: Const a b -> Const a b Source fromRational :: Rational -> Const a b Source
Integral a => Integral (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods quot :: Const a b -> Const a b -> Const a b Source rem :: Const a b -> Const a b -> Const a b Source div :: Const a b -> Const a b -> Const a b Source mod :: Const a b -> Const a b -> Const a b Source quotRem :: Const a b -> Const a b -> (Const a b, Const a b) Source divMod :: Const a b -> Const a b -> (Const a b, Const a b) Source toInteger :: Const a b -> Integer Source
(Typeable k, Data a, Typeable b) => Data (Const a b)	Since: base-4.10.0.0
Instance details Defined in Data.Data Methods gfoldl :: (forall d b0. Data d => c (d -> b0) -> d -> c b0) -> (forall g. g -> c g) -> Const a b -> c (Const a b) Source gunfold :: (forall b0 r. Data b0 => c (b0 -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Const a b) Source toConstr :: Const a b -> Constr Source dataTypeOf :: Const a b -> DataType Source dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Const a b)) Source dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Const a b)) Source gmapT :: (forall b0. Data b0 => b0 -> b0) -> Const a b -> Const a b Source gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Const a b -> r Source gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Const a b -> r Source gmapQ :: (forall d. Data d => d -> u) -> Const a b -> [u] Source gmapQi :: Int -> (forall d. Data d => d -> u) -> Const a b -> u Source gmapM :: Monad m => (forall d. Data d => d -> m d) -> Const a b -> m (Const a b) Source gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Const a b -> m (Const a b) Source gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Const a b -> m (Const a b) Source
Num a => Num (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods (+) :: Const a b -> Const a b -> Const a b Source (-) :: Const a b -> Const a b -> Const a b Source (*) :: Const a b -> Const a b -> Const a b Source negate :: Const a b -> Const a b Source abs :: Const a b -> Const a b Source signum :: Const a b -> Const a b Source fromInteger :: Integer -> Const a b Source
Ord a => Ord (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods compare :: Const a b -> Const a b -> Ordering Source (<) :: Const a b -> Const a b -> Bool Source (<=) :: Const a b -> Const a b -> Bool Source (>) :: Const a b -> Const a b -> Bool Source (>=) :: Const a b -> Const a b -> Bool Source max :: Const a b -> Const a b -> Const a b Source min :: Const a b -> Const a b -> Const a b Source
Read a => Read (Const a b)	This instance would be equivalent to the derived instances of the `Const` newtype if the `runConst` field were removed Since: base-4.8.0.0
Instance details Defined in Data.Functor.Const Methods readsPrec :: Int -> ReadS (Const a b) Source readList :: ReadS [Const a b] Source readPrec :: ReadPrec (Const a b) Source readListPrec :: ReadPrec [Const a b] Source
Real a => Real (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods toRational :: Const a b -> Rational Source
RealFloat a => RealFloat (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods floatRadix :: Const a b -> Integer Source floatDigits :: Const a b -> Int Source floatRange :: Const a b -> (Int, Int) Source decodeFloat :: Const a b -> (Integer, Int) Source encodeFloat :: Integer -> Int -> Const a b Source exponent :: Const a b -> Int Source significand :: Const a b -> Const a b Source scaleFloat :: Int -> Const a b -> Const a b Source isNaN :: Const a b -> Bool Source isInfinite :: Const a b -> Bool Source isDenormalized :: Const a b -> Bool Source isNegativeZero :: Const a b -> Bool Source isIEEE :: Const a b -> Bool Source atan2 :: Const a b -> Const a b -> Const a b Source
RealFrac a => RealFrac (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods properFraction :: Integral b0 => Const a b -> (b0, Const a b) Source truncate :: Integral b0 => Const a b -> b0 Source round :: Integral b0 => Const a b -> b0 Source ceiling :: Integral b0 => Const a b -> b0 Source floor :: Integral b0 => Const a b -> b0 Source
Show a => Show (Const a b)	This instance would be equivalent to the derived instances of the `Const` newtype if the `runConst` field were removed Since: base-4.8.0.0
Instance details Defined in Data.Functor.Const Methods showsPrec :: Int -> Const a b -> ShowS Source show :: Const a b -> String Source showList :: [Const a b] -> ShowS Source
Ix a => Ix (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods range :: (Const a b, Const a b) -> [Const a b] Source index :: (Const a b, Const a b) -> Const a b -> Int Source unsafeIndex :: (Const a b, Const a b) -> Const a b -> Int 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
IsString a => IsString (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.String Methods fromString :: String -> Const a b Source
Generic (Const a b)
Instance details Defined in Data.Functor.Const Associated Types type Rep (Const a b) :: Type -> Type Source Methods from :: Const a b -> Rep (Const a b) x Source to :: Rep (Const a b) x -> Const a b Source
Semigroup a => Semigroup (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods (<>) :: Const a b -> Const a b -> Const a b Source sconcat :: NonEmpty (Const a b) -> Const a b Source stimes :: Integral b0 => b0 -> Const a b -> Const a b Source
Monoid a => Monoid (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods mempty :: Const a b Source mappend :: Const a b -> Const a b -> Const a b Source mconcat :: [Const a b] -> Const a b Source
FiniteBits a => FiniteBits (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods finiteBitSize :: Const a b -> Int Source countLeadingZeros :: Const a b -> Int Source countTrailingZeros :: Const a b -> Int Source
Bits a => Bits (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods (.&.) :: Const a b -> Const a b -> Const a b Source (.\|.) :: Const a b -> Const a b -> Const a b Source xor :: Const a b -> Const a b -> Const a b Source complement :: Const a b -> Const a b Source shift :: Const a b -> Int -> Const a b Source rotate :: Const a b -> Int -> Const a b Source zeroBits :: Const a b Source bit :: Int -> Const a b Source setBit :: Const a b -> Int -> Const a b Source clearBit :: Const a b -> Int -> Const a b Source complementBit :: Const a b -> Int -> Const a b Source testBit :: Const a b -> Int -> Bool Source bitSizeMaybe :: Const a b -> Maybe Int Source bitSize :: Const a b -> Int Source isSigned :: Const a b -> Bool Source shiftL :: Const a b -> Int -> Const a b Source unsafeShiftL :: Const a b -> Int -> Const a b Source shiftR :: Const a b -> Int -> Const a b Source unsafeShiftR :: Const a b -> Int -> Const a b Source rotateL :: Const a b -> Int -> Const a b Source rotateR :: Const a b -> Int -> Const a b Source popCount :: Const a b -> Int Source
Storable a => Storable (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods sizeOf :: Const a b -> Int Source alignment :: Const a b -> Int Source peekElemOff :: Ptr (Const a b) -> Int -> IO (Const a b) Source pokeElemOff :: Ptr (Const a b) -> Int -> Const a b -> IO () Source peekByteOff :: Ptr b0 -> Int -> IO (Const a b) Source pokeByteOff :: Ptr b0 -> Int -> Const a b -> IO () Source peek :: Ptr (Const a b) -> IO (Const a b) Source poke :: Ptr (Const a b) -> Const a b -> IO () Source
type Rep1 (Const a :: k -> Type)	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)	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 a Source

Constructors

WrapMonad
Fields unwrapMonad :: m a

Instances

Monad m => Monad (WrappedMonad m)	Since: base-4.7.0.0
Instance details Defined in Control.Applicative Methods (>>=) :: WrappedMonad m a -> (a -> WrappedMonad m b) -> WrappedMonad m b Source (>>) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m b Source return :: a -> WrappedMonad m a Source fail :: String -> WrappedMonad m a Source
Monad m => Functor (WrappedMonad m)	Since: base-2.1
Instance details Defined in Control.Applicative Methods fmap :: (a -> b) -> WrappedMonad m a -> WrappedMonad m b Source (<$) :: a -> WrappedMonad m b -> WrappedMonad m a Source
Monad m => Applicative (WrappedMonad m)	Since: base-2.1
Instance details Defined in Control.Applicative Methods pure :: a -> WrappedMonad m a Source (<>) :: WrappedMonad m (a -> b) -> WrappedMonad m a -> WrappedMonad m b Source liftA2 :: (a -> b -> c) -> WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m c Source (>) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m b Source (<*) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m a Source
MonadPlus m => Alternative (WrappedMonad m)	Since: base-2.1
Instance details Defined in Control.Applicative Methods empty :: WrappedMonad m a Source (<\|>) :: WrappedMonad m a -> WrappedMonad m a -> WrappedMonad m a Source some :: WrappedMonad m a -> WrappedMonad m [a] Source many :: WrappedMonad m a -> WrappedMonad m [a] Source
Generic1 (WrappedMonad m :: Type -> Type)
Instance details Defined in Control.Applicative Associated Types type Rep1 (WrappedMonad m) :: k -> Type Source Methods from1 :: WrappedMonad m a -> Rep1 (WrappedMonad m) a Source to1 :: Rep1 (WrappedMonad m) a -> WrappedMonad m a Source
Generic (WrappedMonad m a)
Instance details Defined in Control.Applicative Associated Types type Rep (WrappedMonad m a) :: Type -> Type Source Methods from :: WrappedMonad m a -> Rep (WrappedMonad m a) x Source to :: Rep (WrappedMonad m a) x -> WrappedMonad m a Source
type Rep1 (WrappedMonad m :: Type -> Type)	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)	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 b c Source

Constructors

WrapArrow
Fields unwrapArrow :: a b c

Instances

Generic1 (WrappedArrow a b :: Type -> Type)
Instance details Defined in Control.Applicative Associated Types type Rep1 (WrappedArrow a b) :: k -> Type Source Methods from1 :: WrappedArrow a b a0 -> Rep1 (WrappedArrow a b) a0 Source to1 :: Rep1 (WrappedArrow a b) a0 -> WrappedArrow a b a0 Source
Arrow a => Functor (WrappedArrow a b)	Since: base-2.1
Instance details Defined in Control.Applicative Methods fmap :: (a0 -> b0) -> WrappedArrow a b a0 -> WrappedArrow a b b0 Source (<$) :: a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0 Source
Arrow a => Applicative (WrappedArrow a b)	Since: base-2.1
Instance details Defined in Control.Applicative Methods pure :: a0 -> WrappedArrow a b a0 Source (<>) :: WrappedArrow a b (a0 -> b0) -> WrappedArrow a b a0 -> WrappedArrow a b b0 Source liftA2 :: (a0 -> b0 -> c) -> WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b c Source (>) :: WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b b0 Source (<*) :: WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0 Source
(ArrowZero a, ArrowPlus a) => Alternative (WrappedArrow a b)	Since: base-2.1
Instance details Defined in Control.Applicative Methods empty :: WrappedArrow a b a0 Source (<\|>) :: WrappedArrow a b a0 -> WrappedArrow a b a0 -> WrappedArrow a b a0 Source some :: WrappedArrow a b a0 -> WrappedArrow a b [a0] Source many :: WrappedArrow a b a0 -> WrappedArrow a b [a0] Source
Generic (WrappedArrow a b c)
Instance details Defined in Control.Applicative Associated Types type Rep (WrappedArrow a b c) :: Type -> Type Source Methods from :: WrappedArrow a b c -> Rep (WrappedArrow a b c) x Source to :: Rep (WrappedArrow a b c) x -> WrappedArrow a b c Source
type Rep1 (WrappedArrow a b :: Type -> Type)	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)	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
Fields getZipList :: [a]

Instances

Functor ZipList	Since: base-2.1
Instance details Defined in Control.Applicative Methods fmap :: (a -> b) -> ZipList a -> ZipList b Source (<$) :: a -> ZipList b -> ZipList a Source
Applicative ZipList	f '<$>' 'ZipList' xs1 '<>' ... '<>' 'ZipList' xsN = 'ZipList' (zipWithN f xs1 ... xsN) where `zipWithN` refers to the `zipWith` function of the appropriate arity (`zipWith`, `zipWith3`, `zipWith4`, ...). For example: (\a b c -> stimes c [a, b]) <$> ZipList "abcd" <> ZipList "567" <> ZipList [1..] = ZipList (zipWith3 (\a b c -> stimes c [a, b]) "abcd" "567" [1..]) = ZipList {getZipList = ["a5","b6b6","c7c7c7"]} Since: base-2.1
Instance details Defined in Control.Applicative Methods pure :: a -> ZipList a Source (<>) :: ZipList (a -> b) -> ZipList a -> ZipList b Source liftA2 :: (a -> b -> c) -> ZipList a -> ZipList b -> ZipList c Source (>) :: ZipList a -> ZipList b -> ZipList b Source (<*) :: ZipList a -> ZipList b -> ZipList a Source
Foldable ZipList	Since: base-4.9.0.0
Instance details Defined in Control.Applicative Methods fold :: Monoid m => ZipList m -> m Source foldMap :: Monoid m => (a -> m) -> ZipList a -> m Source foldr :: (a -> b -> b) -> b -> ZipList a -> b Source foldr' :: (a -> b -> b) -> b -> ZipList a -> b Source foldl :: (b -> a -> b) -> b -> ZipList a -> b Source foldl' :: (b -> a -> b) -> b -> ZipList a -> b Source foldr1 :: (a -> a -> a) -> ZipList a -> a Source foldl1 :: (a -> a -> a) -> ZipList a -> a Source toList :: ZipList a -> [a] Source null :: ZipList a -> Bool Source length :: ZipList a -> Int Source elem :: Eq a => a -> ZipList a -> Bool Source maximum :: Ord a => ZipList a -> a Source minimum :: Ord a => ZipList a -> a Source sum :: Num a => ZipList a -> a Source product :: Num a => ZipList a -> a Source
Traversable ZipList	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> ZipList a -> f (ZipList b) Source sequenceA :: Applicative f => ZipList (f a) -> f (ZipList a) Source mapM :: Monad m => (a -> m b) -> ZipList a -> m (ZipList b) Source sequence :: Monad m => ZipList (m a) -> m (ZipList a) Source
Alternative ZipList	Since: base-4.11.0.0
Instance details Defined in Control.Applicative Methods empty :: ZipList a Source (<\|>) :: ZipList a -> ZipList a -> ZipList a Source some :: ZipList a -> ZipList [a] Source many :: ZipList a -> ZipList [a] Source
Eq a => Eq (ZipList a)	Since: base-4.7.0.0
Instance details Defined in Control.Applicative Methods (==) :: ZipList a -> ZipList a -> Bool Source (/=) :: ZipList a -> ZipList a -> Bool Source
Ord a => Ord (ZipList a)	Since: base-4.7.0.0
Instance details Defined in Control.Applicative Methods compare :: ZipList a -> ZipList a -> Ordering Source (<) :: ZipList a -> ZipList a -> Bool Source (<=) :: ZipList a -> ZipList a -> Bool Source (>) :: ZipList a -> ZipList a -> Bool Source (>=) :: ZipList a -> ZipList a -> Bool Source max :: ZipList a -> ZipList a -> ZipList a Source min :: ZipList a -> ZipList a -> ZipList a Source
Read a => Read (ZipList a)	Since: base-4.7.0.0
Instance details Defined in Control.Applicative Methods readsPrec :: Int -> ReadS (ZipList a) Source readList :: ReadS [ZipList a] Source readPrec :: ReadPrec (ZipList a) Source readListPrec :: ReadPrec [ZipList a] Source
Show a => Show (ZipList a)	Since: base-4.7.0.0
Instance details Defined in Control.Applicative Methods showsPrec :: Int -> ZipList a -> ShowS Source show :: ZipList a -> String Source showList :: [ZipList a] -> ShowS Source
Generic (ZipList a)
Instance details Defined in Control.Applicative Associated Types type Rep (ZipList a) :: Type -> Type Source Methods from :: ZipList a -> Rep (ZipList a) x Source to :: Rep (ZipList a) x -> ZipList a Source
Generic1 ZipList
Instance details Defined in Control.Applicative Associated Types type Rep1 ZipList :: k -> Type Source Methods from1 :: ZipList a -> Rep1 ZipList a Source to1 :: Rep1 ZipList a -> ZipList a Source
type Rep (ZipList a)	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 Rep1 ZipList	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 [])))

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.

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

A variant of <*> with the arguments reversed.

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

Lift a function to actions. This function may be used as a value for fmap in a Functor instance.

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

Lift a ternary function to actions.

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

One or none.

© The University of Glasgow and others
Licensed under a BSD-style license (see top of the page).
https://downloads.haskell.org/~ghc/8.6.1/docs/html/libraries/base-4.12.0.0/Control-Applicative.html

Control.Applicative

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Applicative functors

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