GHC.Base

Copyright	(c) The University of Glasgow 1992-2002
License	see libraries/base/LICENSE
Maintainer	cvs-ghc@haskell.org
Stability	internal
Portability	non-portable (GHC extensions)
Safe Haskell	Unsafe
Language	Haskell2010

Description

Basic data types and classes.

data NonEmpty a Source

Non-empty (and non-strict) list type.

Since: base-4.9.0.0

Constructors

a :| [a] infixr 5

Instances

Instances details

MonadFix NonEmpty Source	Since: base-4.9.0.0
Instance details Defined in Control.Monad.Fix Methods mfix :: (a -> NonEmpty a) -> NonEmpty a Source
MonadZip NonEmpty Source	Since: base-4.9.0.0
Instance details Defined in Control.Monad.Zip Methods mzip :: NonEmpty a -> NonEmpty b -> NonEmpty (a, b) Source mzipWith :: (a -> b -> c) -> NonEmpty a -> NonEmpty b -> NonEmpty c Source munzip :: NonEmpty (a, b) -> (NonEmpty a, NonEmpty b) Source
Foldable NonEmpty Source	Since: base-4.9.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => NonEmpty m -> m Source foldMap :: Monoid m => (a -> m) -> NonEmpty a -> m Source foldMap' :: Monoid m => (a -> m) -> NonEmpty a -> m Source foldr :: (a -> b -> b) -> b -> NonEmpty a -> b Source foldr' :: (a -> b -> b) -> b -> NonEmpty a -> b Source foldl :: (b -> a -> b) -> b -> NonEmpty a -> b Source foldl' :: (b -> a -> b) -> b -> NonEmpty a -> b Source foldr1 :: (a -> a -> a) -> NonEmpty a -> a Source foldl1 :: (a -> a -> a) -> NonEmpty a -> a Source toList :: NonEmpty a -> [a] Source null :: NonEmpty a -> Bool Source length :: NonEmpty a -> Int Source elem :: Eq a => a -> NonEmpty a -> Bool Source maximum :: Ord a => NonEmpty a -> a Source minimum :: Ord a => NonEmpty a -> a Source sum :: Num a => NonEmpty a -> a Source product :: Num a => NonEmpty a -> a Source
Eq1 NonEmpty Source	Since: base-4.10.0.0
Instance details Defined in Data.Functor.Classes Methods liftEq :: (a -> b -> Bool) -> NonEmpty a -> NonEmpty b -> Bool Source
Ord1 NonEmpty Source	Since: base-4.10.0.0
Instance details Defined in Data.Functor.Classes Methods liftCompare :: (a -> b -> Ordering) -> NonEmpty a -> NonEmpty b -> Ordering Source
Read1 NonEmpty Source	Since: base-4.10.0.0
Instance details Defined in Data.Functor.Classes Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (NonEmpty a) Source liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [NonEmpty a] Source liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (NonEmpty a) Source liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [NonEmpty a] Source
Show1 NonEmpty Source	Since: base-4.10.0.0
Instance details Defined in Data.Functor.Classes Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> NonEmpty a -> ShowS Source liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [NonEmpty a] -> ShowS Source
Traversable NonEmpty Source	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> NonEmpty a -> f (NonEmpty b) Source sequenceA :: Applicative f => NonEmpty (f a) -> f (NonEmpty a) Source mapM :: Monad m => (a -> m b) -> NonEmpty a -> m (NonEmpty b) Source sequence :: Monad m => NonEmpty (m a) -> m (NonEmpty a) Source
Applicative NonEmpty Source	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
Functor NonEmpty Source	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods fmap :: (a -> b) -> NonEmpty a -> NonEmpty b Source (<$) :: a -> NonEmpty b -> NonEmpty a Source
Monad NonEmpty Source	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (>>=) :: NonEmpty a -> (a -> NonEmpty b) -> NonEmpty b Source (>>) :: NonEmpty a -> NonEmpty b -> NonEmpty b Source return :: a -> NonEmpty a Source
Generic1 NonEmpty Source
Instance details Defined in GHC.Generics Associated Types type Rep1 NonEmpty :: k -> Type Source Methods from1 :: forall (a :: k). NonEmpty a -> Rep1 NonEmpty a Source to1 :: forall (a :: k). Rep1 NonEmpty a -> NonEmpty a Source
Data a => Data (NonEmpty a) Source	Since: base-4.9.0.0
Instance details Defined in Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> NonEmpty a -> c (NonEmpty a) Source gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (NonEmpty a) Source toConstr :: NonEmpty a -> Constr Source dataTypeOf :: NonEmpty a -> DataType Source dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (NonEmpty a)) Source dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (NonEmpty a)) Source gmapT :: (forall b. Data b => b -> b) -> NonEmpty a -> NonEmpty a Source gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> NonEmpty a -> r Source gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> NonEmpty a -> r Source gmapQ :: (forall d. Data d => d -> u) -> NonEmpty a -> [u] Source gmapQi :: Int -> (forall d. Data d => d -> u) -> NonEmpty a -> u Source gmapM :: Monad m => (forall d. Data d => d -> m d) -> NonEmpty a -> m (NonEmpty a) Source gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> NonEmpty a -> m (NonEmpty a) Source gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> NonEmpty a -> m (NonEmpty a) Source
Semigroup (NonEmpty a) Source	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: NonEmpty a -> NonEmpty a -> NonEmpty a Source sconcat :: NonEmpty (NonEmpty a) -> NonEmpty a Source stimes :: Integral b => b -> NonEmpty a -> NonEmpty a Source
Generic (NonEmpty a) Source
Instance details Defined in GHC.Generics Associated Types type Rep (NonEmpty a) :: Type -> Type Source Methods from :: NonEmpty a -> Rep (NonEmpty a) x Source to :: Rep (NonEmpty a) x -> NonEmpty a Source
IsList (NonEmpty a) Source	Since: base-4.9.0.0
Instance details Defined in GHC.IsList Associated Types type Item (NonEmpty a) Source Methods fromList :: [Item (NonEmpty a)] -> NonEmpty a Source fromListN :: Int -> [Item (NonEmpty a)] -> NonEmpty a Source toList :: NonEmpty a -> [Item (NonEmpty a)] Source
Read a => Read (NonEmpty a) Source	Since: base-4.11.0.0
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS (NonEmpty a) Source readList :: ReadS [NonEmpty a] Source readPrec :: ReadPrec (NonEmpty a) Source readListPrec :: ReadPrec [NonEmpty a] Source
Show a => Show (NonEmpty a) Source	Since: base-4.11.0.0
Instance details Defined in GHC.Show Methods showsPrec :: Int -> NonEmpty a -> ShowS Source show :: NonEmpty a -> String Source showList :: [NonEmpty a] -> ShowS Source
Eq a => Eq (NonEmpty a) Source	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (==) :: NonEmpty a -> NonEmpty a -> Bool Source (/=) :: NonEmpty a -> NonEmpty a -> Bool Source
Ord a => Ord (NonEmpty a) Source	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods compare :: NonEmpty a -> NonEmpty a -> Ordering Source (<) :: NonEmpty a -> NonEmpty a -> Bool Source (<=) :: NonEmpty a -> NonEmpty a -> Bool Source (>) :: NonEmpty a -> NonEmpty a -> Bool Source (>=) :: NonEmpty a -> NonEmpty a -> Bool Source max :: NonEmpty a -> NonEmpty a -> NonEmpty a Source min :: NonEmpty a -> NonEmpty a -> NonEmpty a Source
type Rep1 NonEmpty Source	Since: base-4.6.0.0
Instance details Defined in GHC.Generics type Rep1 NonEmpty = D1 ('MetaData "NonEmpty" "GHC.Base" "base" 'False) (C1 ('MetaCons ":\|" ('InfixI 'RightAssociative 5) 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1 :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 [])))
type Rep (NonEmpty a) Source	Since: base-4.6.0.0
Instance details Defined in GHC.Generics type Rep (NonEmpty a) = D1 ('MetaData "NonEmpty" "GHC.Base" "base" 'False) (C1 ('MetaCons ":\|" ('InfixI 'RightAssociative 5) 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 [a])))
type Item (NonEmpty a) Source
Instance details Defined in GHC.IsList type Item (NonEmpty a) = a

class Applicative m => Monad m where Source

The Monad class defines the basic operations over a monad, a concept from a branch of mathematics known as category theory. From the perspective of a Haskell programmer, however, it is best to think of a monad as an abstract datatype of actions. Haskell's do expressions provide a convenient syntax for writing monadic expressions.

Instances of Monad should satisfy the following:

Left identity: return a >>= k = k a
Right identity: m >>= return = m
Associativity: m >>= (\x -> k x >>= h) = (m >>= k) >>= h

Furthermore, the Monad and Applicative operations should relate as follows:

```
pure = return
```

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

The above laws imply:

```
fmap f xs  =  xs >>= return . f
```
```
(>>) = (*>)
```

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

The instances of Monad for lists, Maybe and IO defined in the Prelude satisfy these laws.

Minimal complete definition

(>>=)

Methods

(>>=) :: forall a b. m a -> (a -> m b) -> m b infixl 1 Source

Sequentially compose two actions, passing any value produced by the first as an argument to the second.

'as >>= bs' can be understood as the do expression

do a <- as
   bs a

(>>) :: forall a b. m a -> m b -> m b infixl 1 Source

Sequentially compose two actions, discarding any value produced by the first, like sequencing operators (such as the semicolon) in imperative languages.

'as >> bs' can be understood as the do expression

do as
   bs

return :: a -> m a Source

Inject a value into the monadic type.

Instances

Instances details

Monad Complex Source	Since: base-4.9.0.0
Instance details Defined in Data.Complex Methods (>>=) :: Complex a -> (a -> Complex b) -> Complex b Source (>>) :: Complex a -> Complex b -> Complex b Source return :: a -> Complex a Source
Monad Identity Source	Since: base-4.8.0.0
Instance details Defined in Data.Functor.Identity Methods (>>=) :: Identity a -> (a -> Identity b) -> Identity b Source (>>) :: Identity a -> Identity b -> Identity b Source return :: a -> Identity a Source
Monad First Source	Since: base-4.8.0.0
Instance details Defined in Data.Monoid Methods (>>=) :: First a -> (a -> First b) -> First b Source (>>) :: First a -> First b -> First b Source return :: a -> First a Source
Monad Last Source	Since: base-4.8.0.0
Instance details Defined in Data.Monoid Methods (>>=) :: Last a -> (a -> Last b) -> Last b Source (>>) :: Last a -> Last b -> Last b Source return :: a -> Last a Source
Monad Down Source	Since: base-4.11.0.0
Instance details Defined in Data.Ord Methods (>>=) :: Down a -> (a -> Down b) -> Down b Source (>>) :: Down a -> Down b -> Down b Source return :: a -> Down a Source
Monad First Source	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (>>=) :: First a -> (a -> First b) -> First b Source (>>) :: First a -> First b -> First b Source return :: a -> First a Source
Monad Last Source	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (>>=) :: Last a -> (a -> Last b) -> Last b Source (>>) :: Last a -> Last b -> Last b Source return :: a -> Last a Source
Monad Max Source	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (>>=) :: Max a -> (a -> Max b) -> Max b Source (>>) :: Max a -> Max b -> Max b Source return :: a -> Max a Source
Monad Min Source	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (>>=) :: Min a -> (a -> Min b) -> Min b Source (>>) :: Min a -> Min b -> Min b Source return :: a -> Min a Source
Monad Dual Source	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods (>>=) :: Dual a -> (a -> Dual b) -> Dual b Source (>>) :: Dual a -> Dual b -> Dual b Source return :: a -> Dual a Source
Monad Product Source	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods (>>=) :: Product a -> (a -> Product b) -> Product b Source (>>) :: Product a -> Product b -> Product b Source return :: a -> Product a Source
Monad Sum Source	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods (>>=) :: Sum a -> (a -> Sum b) -> Sum b Source (>>) :: Sum a -> Sum b -> Sum b Source return :: a -> Sum a Source
Monad STM Source	Since: base-4.3.0.0
Instance details Defined in GHC.Conc.Sync Methods (>>=) :: STM a -> (a -> STM b) -> STM b Source (>>) :: STM a -> STM b -> STM b Source return :: a -> STM a Source
Monad NoIO Source	Since: base-4.4.0.0
Instance details Defined in GHC.GHCi Methods (>>=) :: NoIO a -> (a -> NoIO b) -> NoIO b Source (>>) :: NoIO a -> NoIO b -> NoIO b Source return :: a -> NoIO a Source
Monad Par1 Source	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods (>>=) :: Par1 a -> (a -> Par1 b) -> Par1 b Source (>>) :: Par1 a -> Par1 b -> Par1 b Source return :: a -> Par1 a Source
Monad ReadP Source	Since: base-2.1
Instance details Defined in Text.ParserCombinators.ReadP Methods (>>=) :: ReadP a -> (a -> ReadP b) -> ReadP b Source (>>) :: ReadP a -> ReadP b -> ReadP b Source return :: a -> ReadP a Source
Monad ReadPrec Source	Since: base-2.1
Instance details Defined in Text.ParserCombinators.ReadPrec Methods (>>=) :: ReadPrec a -> (a -> ReadPrec b) -> ReadPrec b Source (>>) :: ReadPrec a -> ReadPrec b -> ReadPrec b Source return :: a -> ReadPrec a Source
Monad IO Source	Since: base-2.1
Instance details Defined in GHC.Base Methods (>>=) :: IO a -> (a -> IO b) -> IO b Source (>>) :: IO a -> IO b -> IO b Source return :: a -> IO a Source
Monad NonEmpty Source	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (>>=) :: NonEmpty a -> (a -> NonEmpty b) -> NonEmpty b Source (>>) :: NonEmpty a -> NonEmpty b -> NonEmpty b Source return :: a -> NonEmpty a Source
Monad Maybe Source	Since: base-2.1
Instance details Defined in GHC.Base Methods (>>=) :: Maybe a -> (a -> Maybe b) -> Maybe b Source (>>) :: Maybe a -> Maybe b -> Maybe b Source return :: a -> Maybe a Source
Monad Solo Source	Since: base-4.15
Instance details Defined in GHC.Base Methods (>>=) :: Solo a -> (a -> Solo b) -> Solo b Source (>>) :: Solo a -> Solo b -> Solo b Source return :: a -> Solo a Source
Monad [] Source	Since: base-2.1
Instance details Defined in GHC.Base Methods (>>=) :: [a] -> (a -> [b]) -> [b] Source (>>) :: [a] -> [b] -> [b] Source return :: a -> [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
ArrowApply a => Monad (ArrowMonad a) Source	Since: base-2.1
Instance details Defined in Control.Arrow Methods (>>=) :: ArrowMonad a a0 -> (a0 -> ArrowMonad a b) -> ArrowMonad a b Source (>>) :: ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a b Source return :: a0 -> ArrowMonad a a0 Source
Monad (ST s) Source	Since: base-2.1
Instance details Defined in Control.Monad.ST.Lazy.Imp Methods (>>=) :: ST s a -> (a -> ST s b) -> ST s b Source (>>) :: ST s a -> ST s b -> ST s b Source return :: a -> ST s a Source
Monad (Either e) Source	Since: base-4.4.0.0
Instance details Defined in Data.Either Methods (>>=) :: Either e a -> (a -> Either e b) -> Either e b Source (>>) :: Either e a -> Either e b -> Either e b Source return :: a -> Either e a Source
Monad (Proxy :: Type -> Type) Source	Since: base-4.7.0.0
Instance details Defined in Data.Proxy Methods (>>=) :: Proxy a -> (a -> Proxy b) -> Proxy b Source (>>) :: Proxy a -> Proxy b -> Proxy b Source return :: a -> Proxy a Source
Monad (U1 :: Type -> Type) Source	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods (>>=) :: U1 a -> (a -> U1 b) -> U1 b Source (>>) :: U1 a -> U1 b -> U1 b Source return :: a -> U1 a Source
Monad (ST s) Source	Since: base-2.1
Instance details Defined in GHC.ST Methods (>>=) :: ST s a -> (a -> ST s b) -> ST s b Source (>>) :: ST s a -> ST s b -> ST s b Source return :: a -> ST s a Source
Monoid a => Monad ((,) a) Source	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (>>=) :: (a, a0) -> (a0 -> (a, b)) -> (a, b) Source (>>) :: (a, a0) -> (a, b) -> (a, b) Source return :: a0 -> (a, a0) Source
Monad m => Monad (Kleisli m a) Source	Since: base-4.14.0.0
Instance details Defined in Control.Arrow Methods (>>=) :: Kleisli m a a0 -> (a0 -> Kleisli m a b) -> Kleisli m a b Source (>>) :: Kleisli m a a0 -> Kleisli m a b -> Kleisli m a b Source return :: a0 -> Kleisli m a a0 Source
Monad f => Monad (Ap f) Source	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods (>>=) :: Ap f a -> (a -> Ap f b) -> Ap f b Source (>>) :: Ap f a -> Ap f b -> Ap f b Source return :: a -> Ap f a Source
Monad f => Monad (Alt f) Source	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods (>>=) :: Alt f a -> (a -> Alt f b) -> Alt f b Source (>>) :: Alt f a -> Alt f b -> Alt f b Source return :: a -> Alt f a Source
Monad f => Monad (Rec1 f) Source	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods (>>=) :: Rec1 f a -> (a -> Rec1 f b) -> Rec1 f b Source (>>) :: Rec1 f a -> Rec1 f b -> Rec1 f b Source return :: a -> Rec1 f a Source
(Monoid a, Monoid b) => Monad ((,,) a b) Source	Since: base-4.14.0.0
Instance details Defined in GHC.Base Methods (>>=) :: (a, b, a0) -> (a0 -> (a, b, b0)) -> (a, b, b0) Source (>>) :: (a, b, a0) -> (a, b, b0) -> (a, b, b0) Source return :: a0 -> (a, b, a0) Source
(Monad f, Monad g) => Monad (Product f g) Source	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods (>>=) :: Product f g a -> (a -> Product f g b) -> Product f g b Source (>>) :: Product f g a -> Product f g b -> Product f g b Source return :: a -> Product f g a Source
(Monad f, Monad g) => Monad (f :*: g) Source	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods (>>=) :: (f :: g) a -> (a -> (f :: g) b) -> (f :: g) b Source (>>) :: (f :: g) a -> (f :: g) b -> (f :: g) b Source return :: a -> (f :*: g) a Source
(Monoid a, Monoid b, Monoid c) => Monad ((,,,) a b c) Source	Since: base-4.14.0.0
Instance details Defined in GHC.Base Methods (>>=) :: (a, b, c, a0) -> (a0 -> (a, b, c, b0)) -> (a, b, c, b0) Source (>>) :: (a, b, c, a0) -> (a, b, c, b0) -> (a, b, c, b0) Source return :: a0 -> (a, b, c, a0) Source
Monad ((->) r) Source	Since: base-2.1
Instance details Defined in GHC.Base Methods (>>=) :: (r -> a) -> (a -> r -> b) -> r -> b Source (>>) :: (r -> a) -> (r -> b) -> r -> b Source return :: a -> r -> a Source
Monad f => Monad (M1 i c f) Source	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods (>>=) :: M1 i c f a -> (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 b Source return :: a -> M1 i c f a Source

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
```

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

```
(*>) = (>>)
```

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

Minimal complete definition

pure, ((<*>) | liftA2)

Methods

pure :: a -> f a Source

Lift a value.

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

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

Sequence actions, discarding the value of the second argument.

Instances

Instances details

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

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

Instances details

Alternative ZipList Source	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 STM Source	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 ReadP Source	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 Source	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 IO Source	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 Maybe Source	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 [] Source	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
MonadPlus m => Alternative (WrappedMonad m) Source	Since: base-2.1
Instance details Defined in Control.Applicative Methods empty :: WrappedMonad m a Source (<\|>) :: WrappedMonad m a -> WrappedMonad m a -> WrappedMonad m a Source some :: WrappedMonad m a -> WrappedMonad m [a] Source many :: WrappedMonad m a -> WrappedMonad m [a] Source
ArrowPlus a => Alternative (ArrowMonad a) Source	Since: base-4.6.0.0
Instance details Defined in Control.Arrow Methods empty :: ArrowMonad a a0 Source (<\|>) :: ArrowMonad a a0 -> ArrowMonad a a0 -> ArrowMonad a a0 Source some :: ArrowMonad a a0 -> ArrowMonad a [a0] Source many :: ArrowMonad a a0 -> ArrowMonad a [a0] Source
Alternative (Proxy :: Type -> Type) Source	Since: base-4.9.0.0
Instance details Defined in Data.Proxy Methods empty :: Proxy a Source (<\|>) :: Proxy a -> Proxy a -> Proxy a Source some :: Proxy a -> Proxy [a] Source many :: Proxy a -> Proxy [a] Source
Alternative (U1 :: Type -> Type) Source	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods empty :: U1 a Source (<\|>) :: U1 a -> U1 a -> U1 a Source some :: U1 a -> U1 [a] Source many :: U1 a -> U1 [a] Source
(ArrowZero a, ArrowPlus a) => Alternative (WrappedArrow a b) Source	Since: base-2.1
Instance details Defined in Control.Applicative Methods empty :: WrappedArrow a b a0 Source (<\|>) :: WrappedArrow a b a0 -> WrappedArrow a b a0 -> WrappedArrow a b a0 Source some :: WrappedArrow a b a0 -> WrappedArrow a b [a0] Source many :: WrappedArrow a b a0 -> WrappedArrow a b [a0] Source
Alternative m => Alternative (Kleisli m a) Source	Since: base-4.14.0.0
Instance details Defined in Control.Arrow Methods empty :: Kleisli m a a0 Source (<\|>) :: Kleisli m a a0 -> Kleisli m a a0 -> Kleisli m a a0 Source some :: Kleisli m a a0 -> Kleisli m a [a0] Source many :: Kleisli m a a0 -> Kleisli m a [a0] Source
Alternative f => Alternative (Ap f) Source	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods empty :: Ap f a Source (<\|>) :: Ap f a -> Ap f a -> Ap f a Source some :: Ap f a -> Ap f [a] Source many :: Ap f a -> Ap f [a] Source
Alternative f => Alternative (Alt f) Source	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods empty :: Alt f a Source (<\|>) :: Alt f a -> Alt f a -> Alt f a Source some :: Alt f a -> Alt f [a] Source many :: Alt f a -> Alt f [a] Source
(Generic1 f, Alternative (Rep1 f)) => Alternative (Generically1 f) Source	Since: base-4.17.0.0
Instance details Defined in GHC.Generics Methods empty :: Generically1 f a Source (<\|>) :: Generically1 f a -> Generically1 f a -> Generically1 f a Source some :: Generically1 f a -> Generically1 f [a] Source many :: Generically1 f a -> Generically1 f [a] Source
Alternative f => Alternative (Rec1 f) Source	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods empty :: Rec1 f a Source (<\|>) :: Rec1 f a -> Rec1 f a -> Rec1 f a Source some :: Rec1 f a -> Rec1 f [a] Source many :: Rec1 f a -> Rec1 f [a] Source
(Alternative f, Alternative g) => Alternative (Product f g) Source	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods empty :: Product f g a Source (<\|>) :: Product f g a -> Product f g a -> Product f g a Source some :: Product f g a -> Product f g [a] Source many :: Product f g a -> Product f g [a] Source
(Alternative f, Alternative g) => Alternative (f :*: g) Source	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods empty :: (f :: g) a Source (<\|>) :: (f :: g) a -> (f :: g) a -> (f :: g) a Source some :: (f :: g) a -> (f :: g) [a] Source many :: (f :: g) a -> (f :: g) [a] Source
(Alternative f, Applicative g) => Alternative (Compose f g) Source	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Compose Methods empty :: Compose f g a Source (<\|>) :: Compose f g a -> Compose f g a -> Compose f g a Source some :: Compose f g a -> Compose f g [a] Source many :: Compose f g a -> Compose f g [a] Source
(Alternative f, Applicative g) => Alternative (f :.: g) Source	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods empty :: (f :.: g) a Source (<\|>) :: (f :.: g) a -> (f :.: g) a -> (f :.: g) a Source some :: (f :.: g) a -> (f :.: g) [a] Source many :: (f :.: g) a -> (f :.: g) [a] Source
Alternative f => Alternative (M1 i c f) Source	Since: base-4.9.0.0
Instance details Defined in GHC.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

class Functor f where Source

A type f is a Functor if it provides a function fmap which, given any types a and b lets you apply any function from (a -> b) to turn an f a into an f b, preserving the structure of f. Furthermore f needs to adhere to the following:

Identity: fmap id == id
Composition: fmap (f . g) == fmap f . fmap g

Note, that the second law follows from the free theorem of the type fmap and the first law, so you need only check that the former condition holds. See https://www.schoolofhaskell.com/user/edwardk/snippets/fmap or https://github.com/quchen/articles/blob/master/second_functor_law.md for an explanation.

Minimal complete definition

fmap

Methods

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

fmap is used to apply a function of type (a -> b) to a value of type f a, where f is a functor, to produce a value of type f b. Note that for any type constructor with more than one parameter (e.g., Either), only the last type parameter can be modified with fmap (e.g., b in `Either a b`).

Some type constructors with two parameters or more have a Bifunctor instance that allows both the last and the penultimate parameters to be mapped over.

Examples

Expand

Convert from a Maybe Int to a Maybe String using show:

>>> fmap show Nothing
Nothing
>>> fmap show (Just 3)
Just "3"

Convert from an Either Int Int to an Either Int String using show:

>>> fmap show (Left 17)
Left 17
>>> fmap show (Right 17)
Right "17"

Double each element of a list:

>>> fmap (*2) [1,2,3]
[2,4,6]

Apply even to the second element of a pair:

>>> fmap even (2,2)
(2,True)

It may seem surprising that the function is only applied to the last element of the tuple compared to the list example above which applies it to every element in the list. To understand, remember that tuples are type constructors with multiple type parameters: a tuple of 3 elements (a,b,c) can also be written (,,) a b c and its Functor instance is defined for Functor ((,,) a b) (i.e., only the third parameter is free to be mapped over with fmap).

It explains why fmap can be used with tuples containing values of different types as in the following example:

>>> fmap even ("hello", 1.0, 4)
("hello",1.0,True)

(<$) :: 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.

Instances

Instances details

Functor ZipList Source	Since: base-2.1
Instance details Defined in Control.Applicative Methods fmap :: (a -> b) -> ZipList a -> ZipList b Source (<$) :: a -> ZipList b -> ZipList a Source
Functor Handler Source	Since: base-4.6.0.0
Instance details Defined in Control.Exception Methods fmap :: (a -> b) -> Handler a -> Handler b Source (<$) :: a -> Handler b -> Handler a Source
Functor Complex Source	Since: base-4.9.0.0
Instance details Defined in Data.Complex Methods fmap :: (a -> b) -> Complex a -> Complex b Source (<$) :: a -> Complex b -> Complex a Source
Functor Identity Source	Since: base-4.8.0.0
Instance details Defined in Data.Functor.Identity Methods fmap :: (a -> b) -> Identity a -> Identity b Source (<$) :: a -> Identity b -> Identity a Source
Functor First Source	Since: base-4.8.0.0
Instance details Defined in Data.Monoid Methods fmap :: (a -> b) -> First a -> First b Source (<$) :: a -> First b -> First a Source
Functor Last Source	Since: base-4.8.0.0
Instance details Defined in Data.Monoid Methods fmap :: (a -> b) -> Last a -> Last b Source (<$) :: a -> Last b -> Last a Source
Functor Down Source	Since: base-4.11.0.0
Instance details Defined in Data.Ord Methods fmap :: (a -> b) -> Down a -> Down b Source (<$) :: a -> Down b -> Down a Source
Functor First Source	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fmap :: (a -> b) -> First a -> First b Source (<$) :: a -> First b -> First a Source
Functor Last Source	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fmap :: (a -> b) -> Last a -> Last b Source (<$) :: a -> Last b -> Last a Source
Functor Max Source	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fmap :: (a -> b) -> Max a -> Max b Source (<$) :: a -> Max b -> Max a Source
Functor Min Source	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fmap :: (a -> b) -> Min a -> Min b Source (<$) :: a -> Min b -> Min a Source
Functor Dual Source	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods fmap :: (a -> b) -> Dual a -> Dual b Source (<$) :: a -> Dual b -> Dual a Source
Functor Product Source	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods fmap :: (a -> b) -> Product a -> Product b Source (<$) :: a -> Product b -> Product a Source
Functor Sum Source	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods fmap :: (a -> b) -> Sum a -> Sum b Source (<$) :: a -> Sum b -> Sum a Source
Functor STM Source	Since: base-4.3.0.0
Instance details Defined in GHC.Conc.Sync Methods fmap :: (a -> b) -> STM a -> STM b Source (<$) :: a -> STM b -> STM a Source
Functor NoIO Source	Since: base-4.8.0.0
Instance details Defined in GHC.GHCi Methods fmap :: (a -> b) -> NoIO a -> NoIO b Source (<$) :: a -> NoIO b -> NoIO a Source
Functor Par1 Source	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> Par1 a -> Par1 b Source (<$) :: a -> Par1 b -> Par1 a Source
Functor ArgDescr Source	Since: base-4.7.0.0
Instance details Defined in System.Console.GetOpt Methods fmap :: (a -> b) -> ArgDescr a -> ArgDescr b Source (<$) :: a -> ArgDescr b -> ArgDescr a Source
Functor ArgOrder Source	Since: base-4.7.0.0
Instance details Defined in System.Console.GetOpt Methods fmap :: (a -> b) -> ArgOrder a -> ArgOrder b Source (<$) :: a -> ArgOrder b -> ArgOrder a Source
Functor OptDescr Source	Since: base-4.7.0.0
Instance details Defined in System.Console.GetOpt Methods fmap :: (a -> b) -> OptDescr a -> OptDescr b Source (<$) :: a -> OptDescr b -> OptDescr a Source
Functor ReadP Source	Since: base-2.1
Instance details Defined in Text.ParserCombinators.ReadP Methods fmap :: (a -> b) -> ReadP a -> ReadP b Source (<$) :: a -> ReadP b -> ReadP a Source
Functor ReadPrec Source	Since: base-2.1
Instance details Defined in Text.ParserCombinators.ReadPrec Methods fmap :: (a -> b) -> ReadPrec a -> ReadPrec b Source (<$) :: a -> ReadPrec b -> ReadPrec a Source
Functor IO Source	Since: base-2.1
Instance details Defined in GHC.Base Methods fmap :: (a -> b) -> IO a -> IO b Source (<$) :: a -> IO b -> IO a Source
Functor NonEmpty Source	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods fmap :: (a -> b) -> NonEmpty a -> NonEmpty b Source (<$) :: a -> NonEmpty b -> NonEmpty a Source
Functor Maybe Source	Since: base-2.1
Instance details Defined in GHC.Base Methods fmap :: (a -> b) -> Maybe a -> Maybe b Source (<$) :: a -> Maybe b -> Maybe a Source
Functor Solo Source	Since: base-4.15
Instance details Defined in GHC.Base Methods fmap :: (a -> b) -> Solo a -> Solo b Source (<$) :: a -> Solo b -> Solo a Source
Functor [] Source	Since: base-2.1
Instance details Defined in GHC.Base Methods fmap :: (a -> b) -> [a] -> [b] Source (<$) :: a -> [b] -> [a] Source
Monad m => Functor (WrappedMonad m) Source	Since: base-2.1
Instance details Defined in Control.Applicative Methods fmap :: (a -> b) -> WrappedMonad m a -> WrappedMonad m b Source (<$) :: a -> WrappedMonad m b -> WrappedMonad m a Source
Arrow a => Functor (ArrowMonad a) Source	Since: base-4.6.0.0
Instance details Defined in Control.Arrow Methods fmap :: (a0 -> b) -> ArrowMonad a a0 -> ArrowMonad a b Source (<$) :: a0 -> ArrowMonad a b -> ArrowMonad a a0 Source
Functor (ST s) Source	Since: base-2.1
Instance details Defined in Control.Monad.ST.Lazy.Imp Methods fmap :: (a -> b) -> ST s a -> ST s b Source (<$) :: a -> ST s b -> ST s a Source
Functor (Either a) Source	Since: base-3.0
Instance details Defined in Data.Either Methods fmap :: (a0 -> b) -> Either a a0 -> Either a b Source (<$) :: a0 -> Either a b -> Either a a0 Source
Functor (Proxy :: Type -> Type) Source	Since: base-4.7.0.0
Instance details Defined in Data.Proxy Methods fmap :: (a -> b) -> Proxy a -> Proxy b Source (<$) :: a -> Proxy b -> Proxy a Source
Functor (Arg a) Source	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fmap :: (a0 -> b) -> Arg a a0 -> Arg a b Source (<$) :: a0 -> Arg a b -> Arg a a0 Source
Functor (Array i) Source	Since: base-2.1
Instance details Defined in GHC.Arr Methods fmap :: (a -> b) -> Array i a -> Array i b Source (<$) :: a -> Array i b -> Array i a Source
Functor (U1 :: Type -> Type) Source	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> U1 a -> U1 b Source (<$) :: a -> U1 b -> U1 a Source
Functor (V1 :: Type -> Type) Source	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> V1 a -> V1 b Source (<$) :: a -> V1 b -> V1 a Source
Functor (ST s) Source	Since: base-2.1
Instance details Defined in GHC.ST Methods fmap :: (a -> b) -> ST s a -> ST s b Source (<$) :: a -> ST s b -> ST s a Source
Functor ((,) a) Source	Since: base-2.1
Instance details Defined in GHC.Base Methods fmap :: (a0 -> b) -> (a, a0) -> (a, b) Source (<$) :: a0 -> (a, b) -> (a, 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 (<$) :: a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0 Source
Functor m => Functor (Kleisli m a) Source	Since: base-4.14.0.0
Instance details Defined in Control.Arrow Methods fmap :: (a0 -> b) -> Kleisli m a a0 -> Kleisli m a b Source (<$) :: a0 -> Kleisli m a b -> Kleisli m a a0 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 (<$) :: a -> Const m b -> Const m a Source
Functor f => Functor (Ap f) Source	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods fmap :: (a -> b) -> Ap f a -> Ap f b Source (<$) :: a -> Ap f b -> Ap f a Source
Functor f => Functor (Alt f) Source	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods fmap :: (a -> b) -> Alt f a -> Alt f b Source (<$) :: a -> Alt f b -> Alt f a Source
(Generic1 f, Functor (Rep1 f)) => Functor (Generically1 f) Source	Since: base-4.17.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> Generically1 f a -> Generically1 f b Source (<$) :: a -> Generically1 f b -> Generically1 f a Source
Functor f => Functor (Rec1 f) Source	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> Rec1 f a -> Rec1 f b Source (<$) :: a -> Rec1 f b -> Rec1 f a Source
Functor (URec (Ptr ()) :: Type -> Type) Source	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> URec (Ptr ()) a -> URec (Ptr ()) b Source (<$) :: a -> URec (Ptr ()) b -> URec (Ptr ()) a Source
Functor (URec Char :: Type -> Type) Source	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> URec Char a -> URec Char b Source (<$) :: a -> URec Char b -> URec Char a Source
Functor (URec Double :: Type -> Type) Source	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> URec Double a -> URec Double b Source (<$) :: a -> URec Double b -> URec Double a Source
Functor (URec Float :: Type -> Type) Source	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> URec Float a -> URec Float b Source (<$) :: a -> URec Float b -> URec Float a Source
Functor (URec Int :: Type -> Type) Source	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> URec Int a -> URec Int b Source (<$) :: a -> URec Int b -> URec Int a Source
Functor (URec Word :: Type -> Type) Source	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> URec Word a -> URec Word b Source (<$) :: a -> URec Word b -> URec Word a Source
Functor ((,,) a b) Source	Since: base-4.14.0.0
Instance details Defined in GHC.Base Methods fmap :: (a0 -> b0) -> (a, b, a0) -> (a, b, b0) Source (<$) :: a0 -> (a, b, b0) -> (a, b, a0) Source
(Functor f, Functor g) => Functor (Product f g) Source	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods fmap :: (a -> b) -> Product f g a -> Product f g b Source (<$) :: a -> Product f g b -> Product f g a Source
(Functor f, Functor g) => Functor (Sum f g) Source	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Sum Methods fmap :: (a -> b) -> Sum f g a -> Sum f g b Source (<$) :: a -> Sum f g b -> Sum f g a Source
(Functor f, Functor g) => Functor (f :*: g) Source	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> (f :: g) a -> (f :: g) b Source (<$) :: a -> (f :: g) b -> (f :: g) a Source
(Functor f, Functor g) => Functor (f :+: g) Source	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> (f :+: g) a -> (f :+: g) b Source (<$) :: a -> (f :+: g) b -> (f :+: g) a Source
Functor (K1 i c :: Type -> Type) Source	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> K1 i c a -> K1 i c b Source (<$) :: a -> K1 i c b -> K1 i c a Source
Functor ((,,,) a b c) Source	Since: base-4.14.0.0
Instance details Defined in GHC.Base Methods fmap :: (a0 -> b0) -> (a, b, c, a0) -> (a, b, c, b0) Source (<$) :: a0 -> (a, b, c, b0) -> (a, b, c, a0) Source
Functor ((->) r) Source	Since: base-2.1
Instance details Defined in GHC.Base Methods fmap :: (a -> b) -> (r -> a) -> r -> b Source (<$) :: a -> (r -> b) -> r -> a Source
(Functor f, Functor g) => Functor (Compose f g) Source	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Compose Methods fmap :: (a -> b) -> Compose f g a -> Compose f g b Source (<$) :: a -> Compose f g b -> Compose f g a Source
(Functor f, Functor g) => Functor (f :.: g) Source	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> (f :.: g) a -> (f :.: g) b Source (<$) :: a -> (f :.: g) b -> (f :.: g) a Source
Functor f => Functor (M1 i c f) Source	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> M1 i c f a -> M1 i c f b Source (<$) :: a -> M1 i c f b -> M1 i c f a Source

class (Alternative m, Monad m) => MonadPlus m where Source

Monads that also support choice and failure.

Minimal complete definition

Nothing

Methods

mzero :: m a Source

The identity of mplus. It should also satisfy the equations

mzero >>= f  =  mzero
v >> mzero   =  mzero

The default definition is

mzero = empty

mplus :: m a -> m a -> m a Source

An associative operation. The default definition is

mplus = (<|>)

Instances

Instances details

MonadPlus STM Source	Since: base-4.3.0.0
Instance details Defined in GHC.Conc.Sync Methods mzero :: STM a Source mplus :: STM a -> STM a -> STM a Source
MonadPlus ReadP Source	Since: base-2.1
Instance details Defined in Text.ParserCombinators.ReadP Methods mzero :: ReadP a Source mplus :: ReadP a -> ReadP a -> ReadP a Source
MonadPlus ReadPrec Source	Since: base-2.1
Instance details Defined in Text.ParserCombinators.ReadPrec Methods mzero :: ReadPrec a Source mplus :: ReadPrec a -> ReadPrec a -> ReadPrec a Source
MonadPlus IO Source	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods mzero :: IO a Source mplus :: IO a -> IO a -> IO a Source
MonadPlus Maybe Source	Since: base-2.1
Instance details Defined in GHC.Base Methods mzero :: Maybe a Source mplus :: Maybe a -> Maybe a -> Maybe a Source
MonadPlus [] Source	Since: base-2.1
Instance details Defined in GHC.Base Methods mzero :: [a] Source mplus :: [a] -> [a] -> [a] Source
(ArrowApply a, ArrowPlus a) => MonadPlus (ArrowMonad a) Source	Since: base-4.6.0.0
Instance details Defined in Control.Arrow Methods mzero :: ArrowMonad a a0 Source mplus :: ArrowMonad a a0 -> ArrowMonad a a0 -> ArrowMonad a a0 Source
MonadPlus (Proxy :: Type -> Type) Source	Since: base-4.9.0.0
Instance details Defined in Data.Proxy Methods mzero :: Proxy a Source mplus :: Proxy a -> Proxy a -> Proxy a Source
MonadPlus (U1 :: Type -> Type) Source	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods mzero :: U1 a Source mplus :: U1 a -> U1 a -> U1 a Source
MonadPlus m => MonadPlus (Kleisli m a) Source	Since: base-4.14.0.0
Instance details Defined in Control.Arrow Methods mzero :: Kleisli m a a0 Source mplus :: Kleisli m a a0 -> Kleisli m a a0 -> Kleisli m a a0 Source
MonadPlus f => MonadPlus (Ap f) Source	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods mzero :: Ap f a Source mplus :: Ap f a -> Ap f a -> Ap f a Source
MonadPlus f => MonadPlus (Alt f) Source	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods mzero :: Alt f a Source mplus :: Alt f a -> Alt f a -> Alt f a Source
MonadPlus f => MonadPlus (Rec1 f) Source	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods mzero :: Rec1 f a Source mplus :: Rec1 f a -> Rec1 f a -> Rec1 f a Source
(MonadPlus f, MonadPlus g) => MonadPlus (Product f g) Source	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods mzero :: Product f g a Source mplus :: Product f g a -> Product f g a -> Product f g a Source
(MonadPlus f, MonadPlus g) => MonadPlus (f :*: g) Source	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods mzero :: (f :: g) a Source mplus :: (f :: g) a -> (f :: g) a -> (f :: g) a Source
MonadPlus f => MonadPlus (M1 i c f) Source	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods mzero :: M1 i c f a Source mplus :: M1 i c f a -> M1 i c f a -> M1 i c f a Source

type String = [Char] Source

A String is a list of characters. String constants in Haskell are values of type String.

See Data.List for operations on lists.

class Semigroup a => Monoid a where Source

The class of monoids (types with an associative binary operation that has an identity). Instances should satisfy the following:

Right identity: x <> mempty = x
Left identity: mempty <> x = x
Associativity: x <> (y <> z) = (x <> y) <> z (Semigroup law)
Concatenation: mconcat = foldr (<>) mempty

The method names refer to the monoid of lists under concatenation, but there are many other instances.

Some types can be viewed as a monoid in more than one way, e.g. both addition and multiplication on numbers. In such cases we often define newtypes and make those instances of Monoid, e.g. Sum and Product.

NOTE: Semigroup is a superclass of Monoid since base-4.11.0.0.

Minimal complete definition

mempty

Methods

mempty :: a Source

Identity of mappend

>>> "Hello world" <> mempty
"Hello world"

mappend :: a -> a -> a Source

An associative operation

NOTE: This method is redundant and has the default implementation mappend = (<>) since base-4.11.0.0. Should it be implemented manually, since mappend is a synonym for (<>), it is expected that the two functions are defined the same way. In a future GHC release mappend will be removed from Monoid.

mconcat :: [a] -> a Source

Fold a list using the monoid.

For most types, the default definition for mconcat will be used, but the function is included in the class definition so that an optimized version can be provided for specific types.

>>> mconcat ["Hello", " ", "Haskell", "!"]
"Hello Haskell!"

Instances

Instances details

Monoid ByteArray Source	Since: base-4.17.0.0
Instance details Defined in Data.Array.Byte Methods mempty :: ByteArray Source mappend :: ByteArray -> ByteArray -> ByteArray Source mconcat :: [ByteArray] -> ByteArray Source
Monoid All Source	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: All Source mappend :: All -> All -> All Source mconcat :: [All] -> All Source
Monoid Any Source	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Any Source mappend :: Any -> Any -> Any Source mconcat :: [Any] -> Any Source
Monoid Event Source	Since: base-4.4.0.0
Instance details Defined in GHC.Event.Internal.Types Methods mempty :: Event Source mappend :: Event -> Event -> Event Source mconcat :: [Event] -> Event Source
Monoid Lifetime Source	`mappend` takes the longer of two lifetimes. Since: base-4.8.0.0
Instance details Defined in GHC.Event.Internal.Types Methods mempty :: Lifetime Source mappend :: Lifetime -> Lifetime -> Lifetime Source mconcat :: [Lifetime] -> Lifetime Source
Monoid Ordering Source	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: Ordering Source mappend :: Ordering -> Ordering -> Ordering Source mconcat :: [Ordering] -> Ordering Source
Monoid () Source	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: () Source mappend :: () -> () -> () Source mconcat :: [()] -> () Source
FiniteBits a => Monoid (And a) Source	This constraint is arguably too strong. However, as some types (such as `Natural`) have undefined `complement`, this is the only safe choice. Since: base-4.16
Instance details Defined in Data.Bits Methods mempty :: And a Source mappend :: And a -> And a -> And a Source mconcat :: [And a] -> And a Source
FiniteBits a => Monoid (Iff a) Source	This constraint is arguably too strong. However, as some types (such as `Natural`) have undefined `complement`, this is the only safe choice. Since: base-4.16
Instance details Defined in Data.Bits Methods mempty :: Iff a Source mappend :: Iff a -> Iff a -> Iff a Source mconcat :: [Iff a] -> Iff a Source
Bits a => Monoid (Ior a) Source	Since: base-4.16
Instance details Defined in Data.Bits Methods mempty :: Ior a Source mappend :: Ior a -> Ior a -> Ior a Source mconcat :: [Ior a] -> Ior a Source
Bits a => Monoid (Xor a) Source	Since: base-4.16
Instance details Defined in Data.Bits Methods mempty :: Xor a Source mappend :: Xor a -> Xor a -> Xor a Source mconcat :: [Xor a] -> Xor a Source
Monoid (Comparison a) Source	`mempty` on comparisons always returns `EQ`. Without newtypes this equals `pure (pure EQ)`. `mempty :: Comparison a mempty = Comparison _ _ -> EQ`
Instance details Defined in Data.Functor.Contravariant Methods mempty :: Comparison a Source mappend :: Comparison a -> Comparison a -> Comparison a Source mconcat :: [Comparison a] -> Comparison a Source
Monoid (Equivalence a) Source	`mempty` on equivalences always returns `True`. Without newtypes this equals `pure (pure True)`. `mempty :: Equivalence a mempty = Equivalence _ _ -> True`
Instance details Defined in Data.Functor.Contravariant Methods mempty :: Equivalence a Source mappend :: Equivalence a -> Equivalence a -> Equivalence a Source mconcat :: [Equivalence a] -> Equivalence a Source
Monoid (Predicate a) Source	`mempty` on predicates always returns `True`. Without newtypes this equals `pure True`. `mempty :: Predicate a mempty = _ -> True`
Instance details Defined in Data.Functor.Contravariant Methods mempty :: Predicate a Source mappend :: Predicate a -> Predicate a -> Predicate a Source mconcat :: [Predicate a] -> Predicate a Source
Monoid a => Monoid (Identity a) Source	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods mempty :: Identity a Source mappend :: Identity a -> Identity a -> Identity a Source mconcat :: [Identity a] -> Identity a Source
Monoid (First a) Source	Since: base-2.1
Instance details Defined in Data.Monoid Methods mempty :: First a Source mappend :: First a -> First a -> First a Source mconcat :: [First a] -> First a Source
Monoid (Last a) Source	Since: base-2.1
Instance details Defined in Data.Monoid Methods mempty :: Last a Source mappend :: Last a -> Last a -> Last a Source mconcat :: [Last a] -> Last a Source
Monoid a => Monoid (Down a) Source	Since: base-4.11.0.0
Instance details Defined in Data.Ord Methods mempty :: Down a Source mappend :: Down a -> Down a -> Down a Source mconcat :: [Down a] -> Down a Source
(Ord a, Bounded a) => Monoid (Max a) Source	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods mempty :: Max a Source mappend :: Max a -> Max a -> Max a Source mconcat :: [Max a] -> Max a Source
(Ord a, Bounded a) => Monoid (Min a) Source	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods mempty :: Min a Source mappend :: Min a -> Min a -> Min a Source mconcat :: [Min a] -> Min a Source
Monoid m => Monoid (WrappedMonoid m) Source	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods mempty :: WrappedMonoid m Source mappend :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m Source mconcat :: [WrappedMonoid m] -> WrappedMonoid m Source
Monoid a => Monoid (Dual a) Source	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Dual a Source mappend :: Dual a -> Dual a -> Dual a Source mconcat :: [Dual a] -> Dual a Source
Monoid (Endo a) Source	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Endo a Source mappend :: Endo a -> Endo a -> Endo a Source mconcat :: [Endo a] -> Endo a Source
Num a => Monoid (Product a) Source	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Product a Source mappend :: Product a -> Product a -> Product a Source mconcat :: [Product a] -> Product a Source
Num a => Monoid (Sum a) Source	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Sum a Source mappend :: Sum a -> Sum a -> Sum a Source mconcat :: [Sum a] -> Sum a Source
Monoid a => Monoid (STM a) Source	Since: base-4.17.0.0
Instance details Defined in GHC.Conc.Sync Methods mempty :: STM a Source mappend :: STM a -> STM a -> STM a Source mconcat :: [STM a] -> STM a Source
(Generic a, Monoid (Rep a ())) => Monoid (Generically a) Source	Since: base-4.17.0.0
Instance details Defined in GHC.Generics Methods mempty :: Generically a Source mappend :: Generically a -> Generically a -> Generically a Source mconcat :: [Generically a] -> Generically a Source
Monoid p => Monoid (Par1 p) Source	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods mempty :: Par1 p Source mappend :: Par1 p -> Par1 p -> Par1 p Source mconcat :: [Par1 p] -> Par1 p Source
Monoid a => Monoid (IO a) Source	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods mempty :: IO a Source mappend :: IO a -> IO a -> IO a Source mconcat :: [IO a] -> IO a Source
Semigroup a => Monoid (Maybe a) Source	Lift a semigroup into `Maybe` forming a `Monoid` according to http://en.wikipedia.org/wiki/Monoid: "Any semigroup `S` may be turned into a monoid simply by adjoining an element `e` not in `S` and defining `ee = e` and `es = s = s*e` for all `s ∈ S`." Since 4.11.0: constraint on inner `a` value generalised from `Monoid` to `Semigroup`. Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: Maybe a Source mappend :: Maybe a -> Maybe a -> Maybe a Source mconcat :: [Maybe a] -> Maybe a Source
Monoid a => Monoid (a) Source	Since: base-4.15
Instance details Defined in GHC.Base Methods mempty :: (a) Source mappend :: (a) -> (a) -> (a) Source mconcat :: [(a)] -> (a) Source
Monoid [a] Source	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: [a] Source mappend :: [a] -> [a] -> [a] Source mconcat :: [[a]] -> [a] Source
Monoid a => Monoid (Op a b) Source	`mempty @(Op a b)` without newtypes is `mempty @(b->a)` = `_ -> mempty`. `mempty :: Op a b mempty = Op _ -> mempty`
Instance details Defined in Data.Functor.Contravariant Methods mempty :: Op a b Source mappend :: Op a b -> Op a b -> Op a b Source mconcat :: [Op a b] -> Op a b Source
Monoid (Proxy s) Source	Since: base-4.7.0.0
Instance details Defined in Data.Proxy Methods mempty :: Proxy s Source mappend :: Proxy s -> Proxy s -> Proxy s Source mconcat :: [Proxy s] -> Proxy s Source
Monoid (U1 p) Source	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods mempty :: U1 p Source mappend :: U1 p -> U1 p -> U1 p Source mconcat :: [U1 p] -> U1 p Source
Monoid a => Monoid (ST s a) Source	Since: base-4.11.0.0
Instance details Defined in GHC.ST Methods mempty :: ST s a Source mappend :: ST s a -> ST s a -> ST s a Source mconcat :: [ST s a] -> ST s a Source
Monoid b => Monoid (a -> b) Source	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: a -> b Source mappend :: (a -> b) -> (a -> b) -> a -> b Source mconcat :: [a -> b] -> a -> b Source
(Monoid a, Monoid b) => Monoid (a, b) Source	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: (a, b) Source mappend :: (a, b) -> (a, b) -> (a, b) Source mconcat :: [(a, b)] -> (a, b) 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
(Applicative f, Monoid a) => Monoid (Ap f a) Source	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods mempty :: Ap f a Source mappend :: Ap f a -> Ap f a -> Ap f a Source mconcat :: [Ap f a] -> Ap f a Source
Alternative f => Monoid (Alt f a) Source	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Alt f a Source mappend :: Alt f a -> Alt f a -> Alt f a Source mconcat :: [Alt f a] -> Alt f a Source
Monoid (f p) => Monoid (Rec1 f p) Source	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods mempty :: Rec1 f p Source mappend :: Rec1 f p -> Rec1 f p -> Rec1 f p Source mconcat :: [Rec1 f p] ->

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