GHC.Base

Basic data types and classes.

Documentation

data NonEmpty a

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

Since: base-4.9.0.0

Constructors

a :| [a] infixr 5

Instances

MonadFix NonEmpty

Since: base-4.9.0.0

Defined in Control.Monad.Fix

Methods

mfix :: (a -> NonEmpty a) -> NonEmpty a

MonadZip NonEmpty

Since: base-4.9.0.0

Defined in Control.Monad.Zip

Methods

mzip :: NonEmpty a -> NonEmpty b -> NonEmpty (a, b)

mzipWith :: (a -> b -> c) -> NonEmpty a -> NonEmpty b -> NonEmpty c

munzip :: NonEmpty (a, b) -> (NonEmpty a, NonEmpty b)

Foldable NonEmpty

Since: base-4.9.0.0

Defined in Data.Foldable

Methods

fold :: Monoid m => NonEmpty m -> m

foldMap :: Monoid m => (a -> m) -> NonEmpty a -> m

foldMap' :: Monoid m => (a -> m) -> NonEmpty a -> m

foldr :: (a -> b -> b) -> b -> NonEmpty a -> b

foldr' :: (a -> b -> b) -> b -> NonEmpty a -> b

foldl :: (b -> a -> b) -> b -> NonEmpty a -> b

foldl' :: (b -> a -> b) -> b -> NonEmpty a -> b

foldr1 :: (a -> a -> a) -> NonEmpty a -> a

foldl1 :: (a -> a -> a) -> NonEmpty a -> a

toList :: NonEmpty a -> [a]

null :: NonEmpty a -> Bool

length :: NonEmpty a -> Int

elem :: Eq a => a -> NonEmpty a -> Bool

maximum :: Ord a => NonEmpty a -> a

minimum :: Ord a => NonEmpty a -> a

sum :: Num a => NonEmpty a -> a

product :: Num a => NonEmpty a -> a

Eq1 NonEmpty

Since: base-4.10.0.0

Defined in Data.Functor.Classes

Methods

liftEq :: (a -> b -> Bool) -> NonEmpty a -> NonEmpty b -> Bool

Ord1 NonEmpty

Since: base-4.10.0.0

Defined in Data.Functor.Classes

Methods

liftCompare :: (a -> b -> Ordering) -> NonEmpty a -> NonEmpty b -> Ordering

Read1 NonEmpty

Since: base-4.10.0.0

Defined in Data.Functor.Classes

Methods

liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (NonEmpty a)

liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [NonEmpty a]

liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (NonEmpty a)

liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [NonEmpty a]

Show1 NonEmpty

Since: base-4.10.0.0

Defined in Data.Functor.Classes

Methods

liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> NonEmpty a -> ShowS

liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [NonEmpty a] -> ShowS

Traversable NonEmpty

Since: base-4.9.0.0

Defined in Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> NonEmpty a -> f (NonEmpty b)

sequenceA :: Applicative f => NonEmpty (f a) -> f (NonEmpty a)

mapM :: Monad m => (a -> m b) -> NonEmpty a -> m (NonEmpty b)

sequence :: Monad m => NonEmpty (m a) -> m (NonEmpty a)

Applicative NonEmpty

Since: base-4.9.0.0

Defined in GHC.Base

Methods

pure :: a -> NonEmpty a

(<*>) :: NonEmpty (a -> b) -> NonEmpty a -> NonEmpty b

liftA2 :: (a -> b -> c) -> NonEmpty a -> NonEmpty b -> NonEmpty c

(*>) :: NonEmpty a -> NonEmpty b -> NonEmpty b

(<*) :: NonEmpty a -> NonEmpty b -> NonEmpty a

Functor NonEmpty

Since: base-4.9.0.0

Defined in GHC.Base

Methods

fmap :: (a -> b) -> NonEmpty a -> NonEmpty b

(<$) :: a -> NonEmpty b -> NonEmpty a

Monad NonEmpty

Since: base-4.9.0.0

Defined in GHC.Base

Methods

(>>=) :: NonEmpty a -> (a -> NonEmpty b) -> NonEmpty b

(>>) :: NonEmpty a -> NonEmpty b -> NonEmpty b

return :: a -> NonEmpty a

Generic1 NonEmpty

Defined in GHC.Generics

Associated Types

type Rep1 NonEmpty :: k -> Type

Methods

from1 :: forall (a :: k). NonEmpty a -> Rep1 NonEmpty a

to1 :: forall (a :: k). Rep1 NonEmpty a -> NonEmpty a

Data a => Data (NonEmpty a)

Since: base-4.9.0.0

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)

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

toConstr :: NonEmpty a -> Constr

dataTypeOf :: NonEmpty a -> DataType

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

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

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

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

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

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

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

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

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

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

Semigroup (NonEmpty a)

Since: base-4.9.0.0

Defined in GHC.Base

Methods

(<>) :: NonEmpty a -> NonEmpty a -> NonEmpty a

sconcat :: NonEmpty (NonEmpty a) -> NonEmpty a

stimes :: Integral b => b -> NonEmpty a -> NonEmpty a

Generic (NonEmpty a)

Defined in GHC.Generics

Associated Types

type Rep (NonEmpty a) :: Type -> Type

Methods

from :: NonEmpty a -> Rep (NonEmpty a) x

to :: Rep (NonEmpty a) x -> NonEmpty a

IsList (NonEmpty a)

Since: base-4.9.0.0

Defined in GHC.IsList

Associated Types

type Item (NonEmpty a)

Methods

fromList :: [Item (NonEmpty a)] -> NonEmpty a

fromListN :: Int -> [Item (NonEmpty a)] -> NonEmpty a

toList :: NonEmpty a -> [Item (NonEmpty a)]

Read a => Read (NonEmpty a)

Since: base-4.11.0.0

Defined in GHC.Read

Methods

readsPrec :: Int -> ReadS (NonEmpty a)

readList :: ReadS [NonEmpty a]

readPrec :: ReadPrec (NonEmpty a)

readListPrec :: ReadPrec [NonEmpty a]

Show a => Show (NonEmpty a)

Since: base-4.11.0.0

Defined in GHC.Show

Methods

showsPrec :: Int -> NonEmpty a -> ShowS

show :: NonEmpty a -> String

showList :: [NonEmpty a] -> ShowS

Eq a => Eq (NonEmpty a)

Since: base-4.9.0.0

Defined in GHC.Base

Methods

(==) :: NonEmpty a -> NonEmpty a -> Bool

(/=) :: NonEmpty a -> NonEmpty a -> Bool

Ord a => Ord (NonEmpty a)

Since: base-4.9.0.0

Defined in GHC.Base

Methods

compare :: NonEmpty a -> NonEmpty a -> Ordering

(<) :: NonEmpty a -> NonEmpty a -> Bool

(<=) :: NonEmpty a -> NonEmpty a -> Bool

(>) :: NonEmpty a -> NonEmpty a -> Bool

(>=) :: NonEmpty a -> NonEmpty a -> Bool

max :: NonEmpty a -> NonEmpty a -> NonEmpty a

min :: NonEmpty a -> NonEmpty a -> NonEmpty a

type Rep1 NonEmpty

Since: base-4.6.0.0

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)

Since: base-4.6.0.0

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)

Defined in GHC.IsList

type Item (NonEmpty a) = a

class Applicative m => Monad m where

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

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

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

Inject a value into the monadic type.

Instances

Monad Complex

Since: base-4.9.0.0

Defined in Data.Complex

Methods

(>>=) :: Complex a -> (a -> Complex b) -> Complex b

(>>) :: Complex a -> Complex b -> Complex b

return :: a -> Complex a

Monad Identity

Since: base-4.8.0.0

Defined in Data.Functor.Identity

Methods

(>>=) :: Identity a -> (a -> Identity b) -> Identity b

(>>) :: Identity a -> Identity b -> Identity b

return :: a -> Identity a

Monad First

Since: base-4.8.0.0

Defined in Data.Monoid

Methods

(>>=) :: First a -> (a -> First b) -> First b

(>>) :: First a -> First b -> First b

return :: a -> First a

Monad Last

Since: base-4.8.0.0

Defined in Data.Monoid

Methods

(>>=) :: Last a -> (a -> Last b) -> Last b

(>>) :: Last a -> Last b -> Last b

return :: a -> Last a

Monad Down

Since: base-4.11.0.0

Defined in Data.Ord

Methods

(>>=) :: Down a -> (a -> Down b) -> Down b

(>>) :: Down a -> Down b -> Down b

return :: a -> Down a

Monad First

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

(>>=) :: First a -> (a -> First b) -> First b

(>>) :: First a -> First b -> First b

return :: a -> First a

Monad Last

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

(>>=) :: Last a -> (a -> Last b) -> Last b

(>>) :: Last a -> Last b -> Last b

return :: a -> Last a

Monad Max

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

(>>=) :: Max a -> (a -> Max b) -> Max b

(>>) :: Max a -> Max b -> Max b

return :: a -> Max a

Monad Min

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

(>>=) :: Min a -> (a -> Min b) -> Min b

(>>) :: Min a -> Min b -> Min b

return :: a -> Min a

Monad Dual

Since: base-4.8.0.0

Defined in Data.Semigroup.Internal

Methods

(>>=) :: Dual a -> (a -> Dual b) -> Dual b

(>>) :: Dual a -> Dual b -> Dual b

return :: a -> Dual a

Monad Product

Since: base-4.8.0.0

Defined in Data.Semigroup.Internal

Methods

(>>=) :: Product a -> (a -> Product b) -> Product b

(>>) :: Product a -> Product b -> Product b

return :: a -> Product a

Monad Sum

Since: base-4.8.0.0

Defined in Data.Semigroup.Internal

Methods

(>>=) :: Sum a -> (a -> Sum b) -> Sum b

(>>) :: Sum a -> Sum b -> Sum b

return :: a -> Sum a

Monad STM

Since: base-4.3.0.0

Defined in GHC.Conc.Sync

Methods

(>>=) :: STM a -> (a -> STM b) -> STM b

(>>) :: STM a -> STM b -> STM b

return :: a -> STM a

Monad NoIO

Since: base-4.4.0.0

Defined in GHC.GHCi

Methods

(>>=) :: NoIO a -> (a -> NoIO b) -> NoIO b

(>>) :: NoIO a -> NoIO b -> NoIO b

return :: a -> NoIO a

Monad Par1

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

(>>=) :: Par1 a -> (a -> Par1 b) -> Par1 b

(>>) :: Par1 a -> Par1 b -> Par1 b

return :: a -> Par1 a

Monad ReadP

Since: base-2.1

Defined in Text.ParserCombinators.ReadP

Methods

(>>=) :: ReadP a -> (a -> ReadP b) -> ReadP b

(>>) :: ReadP a -> ReadP b -> ReadP b

return :: a -> ReadP a

Monad ReadPrec

Since: base-2.1

Defined in Text.ParserCombinators.ReadPrec

Methods

(>>=) :: ReadPrec a -> (a -> ReadPrec b) -> ReadPrec b

(>>) :: ReadPrec a -> ReadPrec b -> ReadPrec b

return :: a -> ReadPrec a

Monad IO

Since: base-2.1

Defined in GHC.Base

Methods

(>>=) :: IO a -> (a -> IO b) -> IO b

(>>) :: IO a -> IO b -> IO b

return :: a -> IO a

Monad NonEmpty

Since: base-4.9.0.0

Defined in GHC.Base

Methods

(>>=) :: NonEmpty a -> (a -> NonEmpty b) -> NonEmpty b

(>>) :: NonEmpty a -> NonEmpty b -> NonEmpty b

return :: a -> NonEmpty a

Monad Maybe

Since: base-2.1

Defined in GHC.Base

Methods

(>>=) :: Maybe a -> (a -> Maybe b) -> Maybe b

(>>) :: Maybe a -> Maybe b -> Maybe b

return :: a -> Maybe a

Monad Solo

Since: base-4.15

Defined in GHC.Base

Methods

(>>=) :: Solo a -> (a -> Solo b) -> Solo b

(>>) :: Solo a -> Solo b -> Solo b

return :: a -> Solo a

Monad []

Since: base-2.1

Defined in GHC.Base

Methods

(>>=) :: [a] -> (a -> [b]) -> [b]

(>>) :: [a] -> [b] -> [b]

return :: a -> [a]

Monad m => Monad (WrappedMonad m)

Since: base-4.7.0.0

Defined in Control.Applicative

Methods

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

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

return :: a -> WrappedMonad m a

ArrowApply a => Monad (ArrowMonad a)

Since: base-2.1

Defined in Control.Arrow

Methods

(>>=) :: ArrowMonad a a0 -> (a0 -> ArrowMonad a b) -> ArrowMonad a b

(>>) :: ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a b

return :: a0 -> ArrowMonad a a0

Monad (ST s)

Since: base-2.1

Defined in Control.Monad.ST.Lazy.Imp

Methods

(>>=) :: ST s a -> (a -> ST s b) -> ST s b

(>>) :: ST s a -> ST s b -> ST s b

return :: a -> ST s a

Monad (Either e)

Since: base-4.4.0.0

Defined in Data.Either

Methods

(>>=) :: Either e a -> (a -> Either e b) -> Either e b

(>>) :: Either e a -> Either e b -> Either e b

return :: a -> Either e a

Monad (Proxy :: Type -> Type)

Since: base-4.7.0.0

Defined in Data.Proxy

Methods

(>>=) :: Proxy a -> (a -> Proxy b) -> Proxy b

(>>) :: Proxy a -> Proxy b -> Proxy b

return :: a -> Proxy a

Monad (U1 :: Type -> Type)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

(>>=) :: U1 a -> (a -> U1 b) -> U1 b

(>>) :: U1 a -> U1 b -> U1 b

return :: a -> U1 a

Monad (ST s)

Since: base-2.1

Defined in GHC.ST

Methods

(>>=) :: ST s a -> (a -> ST s b) -> ST s b

(>>) :: ST s a -> ST s b -> ST s b

return :: a -> ST s a

Monoid a => Monad ((,) a)

Since: base-4.9.0.0

Defined in GHC.Base

Methods

(>>=) :: (a, a0) -> (a0 -> (a, b)) -> (a, b)

(>>) :: (a, a0) -> (a, b) -> (a, b)

return :: a0 -> (a, a0)

Monad m => Monad (Kleisli m a)

Since: base-4.14.0.0

Defined in Control.Arrow

Methods

(>>=) :: Kleisli m a a0 -> (a0 -> Kleisli m a b) -> Kleisli m a b

(>>) :: Kleisli m a a0 -> Kleisli m a b -> Kleisli m a b

return :: a0 -> Kleisli m a a0

Monad f => Monad (Ap f)

Since: base-4.12.0.0

Defined in Data.Monoid

Methods

(>>=) :: Ap f a -> (a -> Ap f b) -> Ap f b

(>>) :: Ap f a -> Ap f b -> Ap f b

return :: a -> Ap f a

Monad f => Monad (Alt f)

Since: base-4.8.0.0

Defined in Data.Semigroup.Internal

Methods

(>>=) :: Alt f a -> (a -> Alt f b) -> Alt f b

(>>) :: Alt f a -> Alt f b -> Alt f b

return :: a -> Alt f a

Monad f => Monad (Rec1 f)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

(>>=) :: Rec1 f a -> (a -> Rec1 f b) -> Rec1 f b

(>>) :: Rec1 f a -> Rec1 f b -> Rec1 f b

return :: a -> Rec1 f a

(Monoid a, Monoid b) => Monad ((,,) a b)

Since: base-4.14.0.0

Defined in GHC.Base

Methods

(>>=) :: (a, b, a0) -> (a0 -> (a, b, b0)) -> (a, b, b0)

(>>) :: (a, b, a0) -> (a, b, b0) -> (a, b, b0)

return :: a0 -> (a, b, a0)

(Monad f, Monad g) => Monad (Product f g)

Since: base-4.9.0.0

Defined in Data.Functor.Product

Methods

(>>=) :: Product f g a -> (a -> Product f g b) -> Product f g b

(>>) :: Product f g a -> Product f g b -> Product f g b

return :: a -> Product f g a

(Monad f, Monad g) => Monad (f :*: g)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

(>>=) :: (f :*: g) a -> (a -> (f :*: g) b) -> (f :*: g) b

(>>) :: (f :*: g) a -> (f :*: g) b -> (f :*: g) b

return :: a -> (f :*: g) a

(Monoid a, Monoid b, Monoid c) => Monad ((,,,) a b c)

Since: base-4.14.0.0

Defined in GHC.Base

Methods

(>>=) :: (a, b, c, a0) -> (a0 -> (a, b, c, b0)) -> (a, b, c, b0)

(>>) :: (a, b, c, a0) -> (a, b, c, b0) -> (a, b, c, b0)

return :: a0 -> (a, b, c, a0)

Monad ((->) r)

Since: base-2.1

Defined in GHC.Base

Methods

(>>=) :: (r -> a) -> (a -> r -> b) -> r -> b

(>>) :: (r -> a) -> (r -> b) -> r -> b

return :: a -> r -> a

Monad f => Monad (M1 i c f)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

(>>=) :: M1 i c f a -> (a -> M1 i c f b) -> M1 i c f b

(>>) :: M1 i c f a -> M1 i c f b -> M1 i c f b

return :: a -> M1 i c f a

class Functor f => Applicative f where

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

Lift a value.

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

Sequential application.

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

Example

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

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

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

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

Sequence actions, discarding the value of the first argument.

Examples

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

Sequence actions, discarding the value of the second argument.

Instances

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

Defined in Control.Applicative

Methods

pure :: a -> ZipList a

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

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

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

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

Applicative Complex

Since: base-4.9.0.0

Defined in Data.Complex

Methods

pure :: a -> Complex a

(<*>) :: Complex (a -> b) -> Complex a -> Complex b

liftA2 :: (a -> b -> c) -> Complex a -> Complex b -> Complex c

(*>) :: Complex a -> Complex b -> Complex b

(<*) :: Complex a -> Complex b -> Complex a

Applicative Identity

Since: base-4.8.0.0

Defined in Data.Functor.Identity

Methods

pure :: a -> Identity a

(<*>) :: Identity (a -> b) -> Identity a -> Identity b

liftA2 :: (a -> b -> c) -> Identity a -> Identity b -> Identity c

(*>) :: Identity a -> Identity b -> Identity b

(<*) :: Identity a -> Identity b -> Identity a

Applicative First

Since: base-4.8.0.0

Defined in Data.Monoid

Methods

pure :: a -> First a

(<*>) :: First (a -> b) -> First a -> First b

liftA2 :: (a -> b -> c) -> First a -> First b -> First c

(*>) :: First a -> First b -> First b

(<*) :: First a -> First b -> First a

Applicative Last

Since: base-4.8.0.0

Defined in Data.Monoid

Methods

pure :: a -> Last a

(<*>) :: Last (a -> b) -> Last a -> Last b

liftA2 :: (a -> b -> c) -> Last a -> Last b -> Last c

(*>) :: Last a -> Last b -> Last b

(<*) :: Last a -> Last b -> Last a

Applicative Down

Since: base-4.11.0.0

Defined in Data.Ord

Methods

pure :: a -> Down a

(<*>) :: Down (a -> b) -> Down a -> Down b

liftA2 :: (a -> b -> c) -> Down a -> Down b -> Down c

(*>) :: Down a -> Down b -> Down b

(<*) :: Down a -> Down b -> Down a

Applicative First

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

pure :: a -> First a

(<*>) :: First (a -> b) -> First a -> First b

liftA2 :: (a -> b -> c) -> First a -> First b -> First c

(*>) :: First a -> First b -> First b

(<*) :: First a -> First b -> First a

Applicative Last

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

pure :: a -> Last a

(<*>) :: Last (a -> b) -> Last a -> Last b

liftA2 :: (a -> b -> c) -> Last a -> Last b -> Last c

(*>) :: Last a -> Last b -> Last b

(<*) :: Last a -> Last b -> Last a

Applicative Max

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

pure :: a -> Max a

(<*>) :: Max (a -> b) -> Max a -> Max b

liftA2 :: (a -> b -> c) -> Max a -> Max b -> Max c

(*>) :: Max a -> Max b -> Max b

(<*) :: Max a -> Max b -> Max a

Applicative Min

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

pure :: a -> Min a

(<*>) :: Min (a -> b) -> Min a -> Min b

liftA2 :: (a -> b -> c) -> Min a -> Min b -> Min c

(*>) :: Min a -> Min b -> Min b

(<*) :: Min a -> Min b -> Min a

Applicative Dual

Since: base-4.8.0.0

Defined in Data.Semigroup.Internal

Methods

pure :: a -> Dual a

(<*>) :: Dual (a -> b) -> Dual a -> Dual b

liftA2 :: (a -> b -> c) -> Dual a -> Dual b -> Dual c

(*>) :: Dual a -> Dual b -> Dual b

(<*) :: Dual a -> Dual b -> Dual a

Applicative Product

Since: base-4.8.0.0

Defined in Data.Semigroup.Internal

Methods

pure :: a -> Product a

(<*>) :: Product (a -> b) -> Product a -> Product b

liftA2 :: (a -> b -> c) -> Product a -> Product b -> Product c

(*>) :: Product a -> Product b -> Product b

(<*) :: Product a -> Product b -> Product a

Applicative Sum

Since: base-4.8.0.0

Defined in Data.Semigroup.Internal

Methods

pure :: a -> Sum a

(<*>) :: Sum (a -> b) -> Sum a -> Sum b

liftA2 :: (a -> b -> c) -> Sum a -> Sum b -> Sum c

(*>) :: Sum a -> Sum b -> Sum b

(<*) :: Sum a -> Sum b -> Sum a

Applicative STM

Since: base-4.8.0.0

Defined in GHC.Conc.Sync

Methods

pure :: a -> STM a

(<*>) :: STM (a -> b) -> STM a -> STM b

liftA2 :: (a -> b -> c) -> STM a -> STM b -> STM c

(*>) :: STM a -> STM b -> STM b

(<*) :: STM a -> STM b -> STM a

Applicative NoIO

Since: base-4.8.0.0

Defined in GHC.GHCi

Methods

pure :: a -> NoIO a

(<*>) :: NoIO (a -> b) -> NoIO a -> NoIO b

liftA2 :: (a -> b -> c) -> NoIO a -> NoIO b -> NoIO c

(*>) :: NoIO a -> NoIO b -> NoIO b

(<*) :: NoIO a -> NoIO b -> NoIO a

Applicative Par1

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

pure :: a -> Par1 a

(<*>) :: Par1 (a -> b) -> Par1 a -> Par1 b

liftA2 :: (a -> b -> c) -> Par1 a -> Par1 b -> Par1 c

(*>) :: Par1 a -> Par1 b -> Par1 b

(<*) :: Par1 a -> Par1 b -> Par1 a

Applicative ReadP

Since: base-4.6.0.0

Defined in Text.ParserCombinators.ReadP

Methods

pure :: a -> ReadP a

(<*>) :: ReadP (a -> b) -> ReadP a -> ReadP b

liftA2 :: (a -> b -> c) -> ReadP a -> ReadP b -> ReadP c

(*>) :: ReadP a -> ReadP b -> ReadP b

(<*) :: ReadP a -> ReadP b -> ReadP a

Applicative ReadPrec

Since: base-4.6.0.0

Defined in Text.ParserCombinators.ReadPrec

Methods

pure :: a -> ReadPrec a

(<*>) :: ReadPrec (a -> b) -> ReadPrec a -> ReadPrec b

liftA2 :: (a -> b -> c) -> ReadPrec a -> ReadPrec b -> ReadPrec c

(*>) :: ReadPrec a -> ReadPrec b -> ReadPrec b

(<*) :: ReadPrec a -> ReadPrec b -> ReadPrec a

Applicative IO

Since: base-2.1

Defined in GHC.Base

Methods

pure :: a -> IO a

(<*>) :: IO (a -> b) -> IO a -> IO b

liftA2 :: (a -> b -> c) -> IO a -> IO b -> IO c

(*>) :: IO a -> IO b -> IO b

(<*) :: IO a -> IO b -> IO a

Applicative NonEmpty

Since: base-4.9.0.0

Defined in GHC.Base

Methods

pure :: a -> NonEmpty a

(<*>) :: NonEmpty (a -> b) -> NonEmpty a -> NonEmpty b

liftA2 :: (a -> b -> c) -> NonEmpty a -> NonEmpty b -> NonEmpty c

(*>) :: NonEmpty a -> NonEmpty b -> NonEmpty b

(<*) :: NonEmpty a -> NonEmpty b -> NonEmpty a

Applicative Maybe

Since: base-2.1

Defined in GHC.Base

Methods

pure :: a -> Maybe a

(<*>) :: Maybe (a -> b) -> Maybe a -> Maybe b

liftA2 :: (a -> b -> c) -> Maybe a -> Maybe b -> Maybe c

(*>) :: Maybe a -> Maybe b -> Maybe b

(<*) :: Maybe a -> Maybe b -> Maybe a

Applicative Solo

Since: base-4.15

Defined in GHC.Base

Methods

pure :: a -> Solo a

(<*>) :: Solo (a -> b) -> Solo a -> Solo b

liftA2 :: (a -> b -> c) -> Solo a -> Solo b -> Solo c

(*>) :: Solo a -> Solo b -> Solo b

(<*) :: Solo a -> Solo b -> Solo a

Applicative []

Since: base-2.1

Defined in GHC.Base

Methods

pure :: a -> [a]

(<*>) :: [a -> b] -> [a] -> [b]

liftA2 :: (a -> b -> c) -> [a] -> [b] -> [c]

(*>) :: [a] -> [b] -> [b]

(<*) :: [a] -> [b] -> [a]

Monad m => Applicative (WrappedMonad m)

Since: base-2.1

Defined in Control.Applicative

Methods

pure :: a -> WrappedMonad m a

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

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

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

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

Arrow a => Applicative (ArrowMonad a)

Since: base-4.6.0.0

Defined in Control.Arrow

Methods

pure :: a0 -> ArrowMonad a a0

(<*>) :: ArrowMonad a (a0 -> b) -> ArrowMonad a a0 -> ArrowMonad a b

liftA2 :: (a0 -> b -> c) -> ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a c

(*>) :: ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a b

(<*) :: ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a a0

Applicative (ST s)

Since: base-2.1

Defined in Control.Monad.ST.Lazy.Imp

Methods

pure :: a -> ST s a

(<*>) :: ST s (a -> b) -> ST s a -> ST s b

liftA2 :: (a -> b -> c) -> ST s a -> ST s b -> ST s c

(*>) :: ST s a -> ST s b -> ST s b

(<*) :: ST s a -> ST s b -> ST s a

Applicative (Either e)

Since: base-3.0

Defined in Data.Either

Methods

pure :: a -> Either e a

(<*>) :: Either e (a -> b) -> Either e a -> Either e b

liftA2 :: (a -> b -> c) -> Either e a -> Either e b -> Either e c

(*>) :: Either e a -> Either e b -> Either e b

(<*) :: Either e a -> Either e b -> Either e a

Applicative (Proxy :: Type -> Type)

Since: base-4.7.0.0

Defined in Data.Proxy

Methods

pure :: a -> Proxy a

(<*>) :: Proxy (a -> b) -> Proxy a -> Proxy b

liftA2 :: (a -> b -> c) -> Proxy a -> Proxy b -> Proxy c

(*>) :: Proxy a -> Proxy b -> Proxy b

(<*) :: Proxy a -> Proxy b -> Proxy a

Applicative (U1 :: Type -> Type)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

pure :: a -> U1 a

(<*>) :: U1 (a -> b) -> U1 a -> U1 b

liftA2 :: (a -> b -> c) -> U1 a -> U1 b -> U1 c

(*>) :: U1 a -> U1 b -> U1 b

(<*) :: U1 a -> U1 b -> U1 a

Applicative (ST s)

Since: base-4.4.0.0

Defined in GHC.ST

Methods

pure :: a -> ST s a

(<*>) :: ST s (a -> b) -> ST s a -> ST s b

liftA2 :: (a -> b -> c) -> ST s a -> ST s b -> ST s c

(*>) :: ST s a -> ST s b -> ST s b

(<*) :: ST s a -> ST s b -> ST s a

Monoid a => Applicative ((,) a)

For tuples, the Monoid constraint on a determines how the first values merge. For example, Strings concatenate:

("hello ", (+15)) <*> ("world!", 2002)
("hello world!",2017)

Since: base-2.1

Defined in GHC.Base

Methods

pure :: a0 -> (a, a0)

(<*>) :: (a, a0 -> b) -> (a, a0) -> (a, b)

liftA2 :: (a0 -> b -> c) -> (a, a0) -> (a, b) -> (a, c)

(*>) :: (a, a0) -> (a, b) -> (a, b)

(<*) :: (a, a0) -> (a, b) -> (a, a0)

Arrow a => Applicative (WrappedArrow a b)

Since: base-2.1

Defined in Control.Applicative

Methods

pure :: a0 -> WrappedArrow a b a0

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

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

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

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

Applicative m => Applicative (Kleisli m a)

Since: base-4.14.0.0

Defined in Control.Arrow

Methods

pure :: a0 -> Kleisli m a a0

(<*>) :: Kleisli m a (a0 -> b) -> Kleisli m a a0 -> Kleisli m a b

liftA2 :: (a0 -> b -> c) -> Kleisli m a a0 -> Kleisli m a b -> Kleisli m a c

(*>) :: Kleisli m a a0 -> Kleisli m a b -> Kleisli m a b

(<*) :: Kleisli m a a0 -> Kleisli m a b -> Kleisli m a a0

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

Since: base-2.0.1

Defined in Data.Functor.Const

Methods

pure :: a -> Const m a

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

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

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

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

Applicative f => Applicative (Ap f)

Since: base-4.12.0.0

Defined in Data.Monoid

Methods

pure :: a -> Ap f a

(<*>) :: Ap f (a -> b) -> Ap f a -> Ap f b

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

(*>) :: Ap f a -> Ap f b -> Ap f b

(<*) :: Ap f a -> Ap f b -> Ap f a

Applicative f => Applicative (Alt f)

Since: base-4.8.0.0

Defined in Data.Semigroup.Internal

Methods

pure :: a -> Alt f a

(<*>) :: Alt f (a -> b) -> Alt f a -> Alt f b

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

(*>) :: Alt f a -> Alt f b -> Alt f b

(<*) :: Alt f a -> Alt f b -> Alt f a

(Generic1 f, Applicative (Rep1 f)) => Applicative (Generically1 f)

Since: base-4.17.0.0

Defined in GHC.Generics

Methods

pure :: a -> Generically1 f a

(<*>) :: Generically1 f (a -> b) -> Generically1 f a -> Generically1 f b

liftA2 :: (a -> b -> c) -> Generically1 f a -> Generically1 f b -> Generically1 f c

(*>) :: Generically1 f a -> Generically1 f b -> Generically1 f b

(<*) :: Generically1 f a -> Generically1 f b -> Generically1 f a

Applicative f => Applicative (Rec1 f)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

pure :: a -> Rec1 f a

(<*>) :: Rec1 f (a -> b) -> Rec1 f a -> Rec1 f b

liftA2 :: (a -> b -> c) -> Rec1 f a -> Rec1 f b -> Rec1 f c

(*>) :: Rec1 f a -> Rec1 f b -> Rec1 f b

(<*) :: Rec1 f a -> Rec1 f b -> Rec1 f a

(Monoid a, Monoid b) => Applicative ((,,) a b)

Since: base-4.14.0.0

Defined in GHC.Base

Methods

pure :: a0 -> (a, b, a0)

(<*>) :: (a, b, a0 -> b0) -> (a, b, a0) -> (a, b, b0)

liftA2 :: (a0 -> b0 -> c) -> (a, b, a0) -> (a, b, b0) -> (a, b, c)

(*>) :: (a, b, a0) -> (a, b, b0) -> (a, b, b0)

(<*) :: (a, b, a0) -> (a, b, b0) -> (a, b, a0)

(Applicative f, Applicative g) => Applicative (Product f g)

Since: base-4.9.0.0

Defined in Data.Functor.Product

Methods

pure :: a -> Product f g a

(<*>) :: Product f g (a -> b) -> Product f g a -> Product f g b

liftA2 :: (a -> b -> c) -> Product f g a -> Product f g b -> Product f g c

(*>) :: Product f g a -> Product f g b -> Product f g b

(<*) :: Product f g a -> Product f g b -> Product f g a

(Applicative f, Applicative g) => Applicative (f :*: g)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

pure :: a -> (f :*: g) a

(<*>) :: (f :*: g) (a -> b) -> (f :*: g) a -> (f :*: g) b

liftA2 :: (a -> b -> c) -> (f :*: g) a -> (f :*: g) b -> (f :*: g) c

(*>) :: (f :*: g) a -> (f :*: g) b -> (f :*: g) b

(<*) :: (f :*: g) a -> (f :*: g) b -> (f :*: g) a

Monoid c => Applicative (K1 i c :: Type -> Type)

Since: base-4.12.0.0

Defined in GHC.Generics

Methods

pure :: a -> K1 i c a

(<*>) :: K1 i c (a -> b) -> K1 i c a -> K1 i c b

liftA2 :: (a -> b -> c0) -> K1 i c a -> K1 i c b -> K1 i c c0

(*>) :: K1 i c a -> K1 i c b -> K1 i c b

(<*) :: K1 i c a -> K1 i c b -> K1 i c a

(Monoid a, Monoid b, Monoid c) => Applicative ((,,,) a b c)

Since: base-4.14.0.0

Defined in GHC.Base

Methods

pure :: a0 -> (a, b, c, a0)

(<*>) :: (a, b, c, a0 -> b0) -> (a, b, c, a0) -> (a, b, c, b0)

liftA2 :: (a0 -> b0 -> c0) -> (a, b, c, a0) -> (a, b, c, b0) -> (a, b, c, c0)

(*>) :: (a, b, c, a0) -> (a, b, c, b0) -> (a, b, c, b0)

(<*) :: (a, b, c, a0) -> (a, b, c, b0) -> (a, b, c, a0)

Applicative ((->) r)

Since: base-2.1

Defined in GHC.Base

Methods

pure :: a -> r -> a

(<*>) :: (r -> (a -> b)) -> (r -> a) -> r -> b

liftA2 :: (a -> b -> c) -> (r -> a) -> (r -> b) -> r -> c

(*>) :: (r -> a) -> (r -> b) -> r -> b

(<*) :: (r -> a) -> (r -> b) -> r -> a

(Applicative f, Applicative g) => Applicative (Compose f g)

Since: base-4.9.0.0

Defined in Data.Functor.Compose

Methods

pure :: a -> Compose f g a

(<*>) :: Compose f g (a -> b) -> Compose f g a -> Compose f g b

liftA2 :: (a -> b -> c) -> Compose f g a -> Compose f g b -> Compose f g c

(*>) :: Compose f g a -> Compose f g b -> Compose f g b

(<*) :: Compose f g a -> Compose f g b -> Compose f g a

(Applicative f, Applicative g) => Applicative (f :.: g)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

pure :: a -> (f :.: g) a

(<*>) :: (f :.: g) (a -> b) -> (f :.: g) a -> (f :.: g) b

liftA2 :: (a -> b -> c) -> (f :.: g) a -> (f :.: g) b -> (f :.: g) c

(*>) :: (f :.: g) a -> (f :.: g) b -> (f :.: g) b

(<*) :: (f :.: g) a -> (f :.: g) b -> (f :.: g) a

Applicative f => Applicative (M1 i c f)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

pure :: a -> M1 i c f a

(<*>) :: M1 i c f (a -> b) -> M1 i c f a -> M1 i c f b

liftA2 :: (a -> b -> c0) -> M1 i c f a -> M1 i c f b -> M1 i c f c0

(*>) :: M1 i c f a -> M1 i c f b -> M1 i c f b

(<*) :: M1 i c f a -> M1 i c f b -> M1 i c f a

class Applicative f => Alternative f where

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

The identity of <|>

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

An associative binary operation

some :: f a -> f [a]

One or more.

many :: f a -> f [a]

Zero or more.

Instances

Alternative ZipList

Since: base-4.11.0.0

Defined in Control.Applicative

Methods

empty :: ZipList a

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

some :: ZipList a -> ZipList [a]

many :: ZipList a -> ZipList [a]

Alternative STM

Since: base-4.8.0.0

Defined in GHC.Conc.Sync

Methods

empty :: STM a

(<|>) :: STM a -> STM a -> STM a

some :: STM a -> STM [a]

many :: STM a -> STM [a]

Alternative ReadP

Since: base-4.6.0.0

Defined in Text.ParserCombinators.ReadP

Methods

empty :: ReadP a

(<|>) :: ReadP a -> ReadP a -> ReadP a

some :: ReadP a -> ReadP [a]

many :: ReadP a -> ReadP [a]

Alternative ReadPrec

Since: base-4.6.0.0

Defined in Text.ParserCombinators.ReadPrec

Methods

empty :: ReadPrec a

(<|>) :: ReadPrec a -> ReadPrec a -> ReadPrec a

some :: ReadPrec a -> ReadPrec [a]

many :: ReadPrec a -> ReadPrec [a]

Alternative IO

Since: base-4.9.0.0

Defined in GHC.Base

Methods

empty :: IO a

(<|>) :: IO a -> IO a -> IO a

some :: IO a -> IO [a]

many :: IO a -> IO [a]

Alternative Maybe

Since: base-2.1

Defined in GHC.Base

Methods

empty :: Maybe a

(<|>) :: Maybe a -> Maybe a -> Maybe a

some :: Maybe a -> Maybe [a]

many :: Maybe a -> Maybe [a]

Alternative []

Since: base-2.1

Defined in GHC.Base

Methods

empty :: [a]

(<|>) :: [a] -> [a] -> [a]

some :: [a] -> [[a]]

many :: [a] -> [[a]]

MonadPlus m => Alternative (WrappedMonad m)

Since: base-2.1

Defined in Control.Applicative

Methods

empty :: WrappedMonad m a

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

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

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

ArrowPlus a => Alternative (ArrowMonad a)

Since: base-4.6.0.0

Defined in Control.Arrow

Methods

empty :: ArrowMonad a a0

(<|>) :: ArrowMonad a a0 -> ArrowMonad a a0 -> ArrowMonad a a0

some :: ArrowMonad a a0 -> ArrowMonad a [a0]

many :: ArrowMonad a a0 -> ArrowMonad a [a0]

Alternative (Proxy :: Type -> Type)

Since: base-4.9.0.0

Defined in Data.Proxy

Methods

empty :: Proxy a

(<|>) :: Proxy a -> Proxy a -> Proxy a

some :: Proxy a -> Proxy [a]

many :: Proxy a -> Proxy [a]

Alternative (U1 :: Type -> Type)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

empty :: U1 a

(<|>) :: U1 a -> U1 a -> U1 a

some :: U1 a -> U1 [a]

many :: U1 a -> U1 [a]

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

Since: base-2.1

Defined in Control.Applicative

Methods

empty :: WrappedArrow a b a0

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

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

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

Alternative m => Alternative (Kleisli m a)

Since: base-4.14.0.0

Defined in Control.Arrow

Methods

empty :: Kleisli m a a0

(<|>) :: Kleisli m a a0 -> Kleisli m a a0 -> Kleisli m a a0

some :: Kleisli m a a0 -> Kleisli m a [a0]

many :: Kleisli m a a0 -> Kleisli m a [a0]

Alternative f => Alternative (Ap f)

Since: base-4.12.0.0

Defined in Data.Monoid

Methods

empty :: Ap f a

(<|>) :: Ap f a -> Ap f a -> Ap f a

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

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

Alternative f => Alternative (Alt f)

Since: base-4.8.0.0

Defined in Data.Semigroup.Internal

Methods

empty :: Alt f a

(<|>) :: Alt f a -> Alt f a -> Alt f a

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

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

(Generic1 f, Alternative (Rep1 f)) => Alternative (Generically1 f)

Since: base-4.17.0.0

Defined in GHC.Generics

Methods

empty :: Generically1 f a

(<|>) :: Generically1 f a -> Generically1 f a -> Generically1 f a

some :: Generically1 f a -> Generically1 f [a]

many :: Generically1 f a -> Generically1 f [a]

Alternative f => Alternative (Rec1 f)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

empty :: Rec1 f a

(<|>) :: Rec1 f a -> Rec1 f a -> Rec1 f a

some :: Rec1 f a -> Rec1 f [a]

many :: Rec1 f a -> Rec1 f [a]

(Alternative f, Alternative g) => Alternative (Product f g)

Since: base-4.9.0.0

Defined in Data.Functor.Product

Methods

empty :: Product f g a

(<|>) :: Product f g a -> Product f g a -> Product f g a

some :: Product f g a -> Product f g [a]

many :: Product f g a -> Product f g [a]

(Alternative f, Alternative g) => Alternative (f :*: g)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

empty :: (f :*: g) a

(<|>) :: (f :*: g) a -> (f :*: g) a -> (f :*: g) a

some :: (f :*: g) a -> (f :*: g) [a]

many :: (f :*: g) a -> (f :*: g) [a]

(Alternative f, Applicative g) => Alternative (Compose f g)

Since: base-4.9.0.0

Defined in Data.Functor.Compose

Methods

empty :: Compose f g a

(<|>) :: Compose f g a -> Compose f g a -> Compose f g a

some :: Compose f g a -> Compose f g [a]

many :: Compose f g a -> Compose f g [a]

(Alternative f, Applicative g) => Alternative (f :.: g)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

empty :: (f :.: g) a

(<|>) :: (f :.: g) a -> (f :.: g) a -> (f :.: g) a

some :: (f :.: g) a -> (f :.: g) [a]

many :: (f :.: g) a -> (f :.: g) [a]

Alternative f => Alternative (M1 i c f)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

empty :: M1 i c f a

(<|>) :: M1 i c f a -> M1 i c f a -> M1 i c f a

some :: M1 i c f a -> M1 i c f [a]

many :: M1 i c f a -> M1 i c f [a]

class Functor f where

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

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

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

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

Functor ZipList

Since: base-2.1

Defined in Control.Applicative

Methods

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

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

Functor Handler

Since: base-4.6.0.0

Defined in Control.Exception

Methods

fmap :: (a -> b) -> Handler a -> Handler b

(<$) :: a -> Handler b -> Handler a

Functor Complex

Since: base-4.9.0.0

Defined in Data.Complex

Methods

fmap :: (a -> b) -> Complex a -> Complex b

(<$) :: a -> Complex b -> Complex a

Functor Identity

Since: base-4.8.0.0

Defined in Data.Functor.Identity

Methods

fmap :: (a -> b) -> Identity a -> Identity b

(<$) :: a -> Identity b -> Identity a

Functor First

Since: base-4.8.0.0

Defined in Data.Monoid

Methods

fmap :: (a -> b) -> First a -> First b

(<$) :: a -> First b -> First a

Functor Last

Since: base-4.8.0.0

Defined in Data.Monoid

Methods

fmap :: (a -> b) -> Last a -> Last b

(<$) :: a -> Last b -> Last a

Functor Down

Since: base-4.11.0.0

Defined in Data.Ord

Methods

fmap :: (a -> b) -> Down a -> Down b

(<$) :: a -> Down b -> Down a

Functor First

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

fmap :: (a -> b) -> First a -> First b

(<$) :: a -> First b -> First a

Functor Last

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

fmap :: (a -> b) -> Last a -> Last b

(<$) :: a -> Last b -> Last a

Functor Max

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

fmap :: (a -> b) -> Max a -> Max b

(<$) :: a -> Max b -> Max a

Functor Min

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

fmap :: (a -> b) -> Min a -> Min b

(<$) :: a -> Min b -> Min a

Functor Dual

Since: base-4.8.0.0

Defined in Data.Semigroup.Internal

Methods

fmap :: (a -> b) -> Dual a -> Dual b

(<$) :: a -> Dual b -> Dual a

Functor Product

Since: base-4.8.0.0

Defined in Data.Semigroup.Internal

Methods

fmap :: (a -> b) -> Product a -> Product b

(<$) :: a -> Product b -> Product a

Functor Sum

Since: base-4.8.0.0

Defined in Data.Semigroup.Internal

Methods

fmap :: (a -> b) -> Sum a -> Sum b

(<$) :: a -> Sum b -> Sum a

Functor STM

Since: base-4.3.0.0

Defined in GHC.Conc.Sync

Methods

fmap :: (a -> b) -> STM a -> STM b

(<$) :: a -> STM b -> STM a

Functor NoIO

Since: base-4.8.0.0

Defined in GHC.GHCi

Methods

fmap :: (a -> b) -> NoIO a -> NoIO b

(<$) :: a -> NoIO b -> NoIO a

Functor Par1

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

fmap :: (a -> b) -> Par1 a -> Par1 b

(<$) :: a -> Par1 b -> Par1 a

Functor ArgDescr

Since: base-4.7.0.0

Defined in System.Console.GetOpt

Methods

fmap :: (a -> b) -> ArgDescr a -> ArgDescr b

(<$) :: a -> ArgDescr b -> ArgDescr a

Functor ArgOrder

Since: base-4.7.0.0

Defined in System.Console.GetOpt

Methods

fmap :: (a -> b) -> ArgOrder a -> ArgOrder b

(<$) :: a -> ArgOrder b -> ArgOrder a

Functor OptDescr

Since: base-4.7.0.0

Defined in System.Console.GetOpt

Methods

fmap :: (a -> b) -> OptDescr a -> OptDescr b

(<$) :: a -> OptDescr b -> OptDescr a

Functor ReadP

Since: base-2.1

Defined in Text.ParserCombinators.ReadP

Methods

fmap :: (a -> b) -> ReadP a -> ReadP b

(<$) :: a -> ReadP b -> ReadP a

Functor ReadPrec

Since: base-2.1

Defined in Text.ParserCombinators.ReadPrec

Methods

fmap :: (a -> b) -> ReadPrec a -> ReadPrec b

(<$) :: a -> ReadPrec b -> ReadPrec a

Functor IO

Since: base-2.1

Defined in GHC.Base

Methods

fmap :: (a -> b) -> IO a -> IO b

(<$) :: a -> IO b -> IO a

Functor NonEmpty

Since: base-4.9.0.0

Defined in GHC.Base

Methods

fmap :: (a -> b) -> NonEmpty a -> NonEmpty b

(<$) :: a -> NonEmpty b -> NonEmpty a

Functor Maybe

Since: base-2.1

Defined in GHC.Base

Methods

fmap :: (a -> b) -> Maybe a -> Maybe b

(<$) :: a -> Maybe b -> Maybe a

Functor Solo

Since: base-4.15

Defined in GHC.Base

Methods

fmap :: (a -> b) -> Solo a -> Solo b

(<$) :: a -> Solo b -> Solo a

Functor []

Since: base-2.1

Defined in GHC.Base

Methods

fmap :: (a -> b) -> [a] -> [b]

(<$) :: a -> [b] -> [a]

Monad m => Functor (WrappedMonad m)

Since: base-2.1

Defined in Control.Applicative

Methods

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

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

Arrow a => Functor (ArrowMonad a)

Since: base-4.6.0.0

Defined in Control.Arrow

Methods

fmap :: (a0 -> b) -> ArrowMonad a a0 -> ArrowMonad a b

(<$) :: a0 -> ArrowMonad a b -> ArrowMonad a a0

Functor (ST s)

Since: base-2.1

Defined in Control.Monad.ST.Lazy.Imp

Methods

fmap :: (a -> b) -> ST s a -> ST s b

(<$) :: a -> ST s b -> ST s a

Functor (Either a)

Since: base-3.0

Defined in Data.Either

Methods

fmap :: (a0 -> b) -> Either a a0 -> Either a b

(<$) :: a0 -> Either a b -> Either a a0

Functor (Proxy :: Type -> Type)

Since: base-4.7.0.0

Defined in Data.Proxy

Methods

fmap :: (a -> b) -> Proxy a -> Proxy b

(<$) :: a -> Proxy b -> Proxy a

Functor (Arg a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

fmap :: (a0 -> b) -> Arg a a0 -> Arg a b

(<$) :: a0 -> Arg a b -> Arg a a0

Functor (Array i)

Since: base-2.1

Defined in GHC.Arr

Methods

fmap :: (a -> b) -> Array i a -> Array i b

(<$) :: a -> Array i b -> Array i a

Functor (U1 :: Type -> Type)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

fmap :: (a -> b) -> U1 a -> U1 b

(<$) :: a -> U1 b -> U1 a

Functor (V1 :: Type -> Type)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

fmap :: (a -> b) -> V1 a -> V1 b

(<$) :: a -> V1 b -> V1 a

Functor (ST s)

Since: base-2.1

Defined in GHC.ST

Methods

fmap :: (a -> b) -> ST s a -> ST s b

(<$) :: a -> ST s b -> ST s a

Functor ((,) a)

Since: base-2.1

Defined in GHC.Base

Methods

fmap :: (a0 -> b) -> (a, a0) -> (a, b)

(<$) :: a0 -> (a, b) -> (a, a0)

Arrow a => Functor (WrappedArrow a b)

Since: base-2.1

Defined in Control.Applicative

Methods

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

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

Functor m => Functor (Kleisli m a)

Since: base-4.14.0.0

Defined in Control.Arrow

Methods

fmap :: (a0 -> b) -> Kleisli m a a0 -> Kleisli m a b

(<$) :: a0 -> Kleisli m a b -> Kleisli m a a0

Functor (Const m :: Type -> Type)

Since: base-2.1

Defined in Data.Functor.Const

Methods

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

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

Functor f => Functor (Ap f)

Since: base-4.12.0.0

Defined in Data.Monoid

Methods

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

(<$) :: a -> Ap f b -> Ap f a

Functor f => Functor (Alt f)

Since: base-4.8.0.0

Defined in Data.Semigroup.Internal

Methods

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

(<$) :: a -> Alt f b -> Alt f a

(Generic1 f, Functor (Rep1 f)) => Functor (Generically1 f)

Since: base-4.17.0.0

Defined in GHC.Generics

Methods

fmap :: (a -> b) -> Generically1 f a -> Generically1 f b

(<$) :: a -> Generically1 f b -> Generically1 f a

Functor f => Functor (Rec1 f)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

fmap :: (a -> b) -> Rec1 f a -> Rec1 f b

(<$) :: a -> Rec1 f b -> Rec1 f a

Functor (URec (Ptr ()) :: Type -> Type)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

fmap :: (a -> b) -> URec (Ptr ()) a -> URec (Ptr ()) b

(<$) :: a -> URec (Ptr ()) b -> URec (Ptr ()) a

Functor (URec Char :: Type -> Type)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

fmap :: (a -> b) -> URec Char a -> URec Char b

(<$) :: a -> URec Char b -> URec Char a

Functor (URec Double :: Type -> Type)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

fmap :: (a -> b) -> URec Double a -> URec Double b

(<$) :: a -> URec Double b -> URec Double a

Functor (URec Float :: Type -> Type)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

fmap :: (a -> b) -> URec Float a -> URec Float b

(<$) :: a -> URec Float b -> URec Float a

Functor (URec Int :: Type -> Type)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

fmap :: (a -> b) -> URec Int a -> URec Int b

(<$) :: a -> URec Int b -> URec Int a

Functor (URec Word :: Type -> Type)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

fmap :: (a -> b) -> URec Word a -> URec Word b

(<$) :: a -> URec Word b -> URec Word a

Functor ((,,) a b)

Since: base-4.14.0.0

Defined in GHC.Base

Methods

fmap :: (a0 -> b0) -> (a, b, a0) -> (a, b, b0)

(<$) :: a0 -> (a, b, b0) -> (a, b, a0)

(Functor f, Functor g) => Functor (Product f g)

Since: base-4.9.0.0

Defined in Data.Functor.Product

Methods

fmap :: (a -> b) -> Product f g a -> Product f g b

(<$) :: a -> Product f g b -> Product f g a

(Functor f, Functor g) => Functor (Sum f g)

Since: base-4.9.0.0

Defined in Data.Functor.Sum

Methods

fmap :: (a -> b) -> Sum f g a -> Sum f g b

(<$) :: a -> Sum f g b -> Sum f g a

(Functor f, Functor g) => Functor (f :*: g)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

fmap :: (a -> b) -> (f :*: g) a -> (f :*: g) b

(<$) :: a -> (f :*: g) b -> (f :*: g) a

(Functor f, Functor g) => Functor (f :+: g)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

fmap :: (a -> b) -> (f :+: g) a -> (f :+: g) b

(<$) :: a -> (f :+: g) b -> (f :+: g) a

Functor (K1 i c :: Type -> Type)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

fmap :: (a -> b) -> K1 i c a -> K1 i c b

(<$) :: a -> K1 i c b -> K1 i c a

Functor ((,,,) a b c)

Since: base-4.14.0.0

Defined in GHC.Base

Methods

fmap :: (a0 -> b0) -> (a, b, c, a0) -> (a, b, c, b0)

(<$) :: a0 -> (a, b, c, b0) -> (a, b, c, a0)

Functor ((->) r)

Since: base-2.1

Defined in GHC.Base

Methods

fmap :: (a -> b) -> (r -> a) -> r -> b

(<$) :: a -> (r -> b) -> r -> a

(Functor f, Functor g) => Functor (Compose f g)

Since: base-4.9.0.0

Defined in Data.Functor.Compose

Methods

fmap :: (a -> b) -> Compose f g a -> Compose f g b

(<$) :: a -> Compose f g b -> Compose f g a

(Functor f, Functor g) => Functor (f :.: g)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

fmap :: (a -> b) -> (f :.: g) a -> (f :.: g) b

(<$) :: a -> (f :.: g) b -> (f :.: g) a

Functor f => Functor (M1 i c f)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

fmap :: (a -> b) -> M1 i c f a -> M1 i c f b

(<$) :: a -> M1 i c f b -> M1 i c f a

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

Monads that also support choice and failure.

Minimal complete definition

Nothing

Methods

mzero :: m a

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

An associative operation. The default definition is

mplus = (<|>)

Instances

MonadPlus STM

Since: base-4.3.0.0

Defined in GHC.Conc.Sync

Methods

mzero :: STM a

mplus :: STM a -> STM a -> STM a

MonadPlus ReadP

Since: base-2.1

Defined in Text.ParserCombinators.ReadP

Methods

mzero :: ReadP a

mplus :: ReadP a -> ReadP a -> ReadP a

MonadPlus ReadPrec

Since: base-2.1

Defined in Text.ParserCombinators.ReadPrec

Methods

mzero :: ReadPrec a

mplus :: ReadPrec a -> ReadPrec a -> ReadPrec a

MonadPlus IO

Since: base-4.9.0.0

Defined in GHC.Base

Methods

mzero :: IO a

mplus :: IO a -> IO a -> IO a

MonadPlus Maybe

Since: base-2.1

Defined in GHC.Base

Methods

mzero :: Maybe a

mplus :: Maybe a -> Maybe a -> Maybe a

MonadPlus []

Since: base-2.1

Defined in GHC.Base

Methods

mzero :: [a]

mplus :: [a] -> [a] -> [a]

(ArrowApply a, ArrowPlus a) => MonadPlus (ArrowMonad a)

Since: base-4.6.0.0

Defined in Control.Arrow

Methods

mzero :: ArrowMonad a a0

mplus :: ArrowMonad a a0 -> ArrowMonad a a0 -> ArrowMonad a a0

MonadPlus (Proxy :: Type -> Type)

Since: base-4.9.0.0

Defined in Data.Proxy

Methods

mzero :: Proxy a

mplus :: Proxy a -> Proxy a -> Proxy a

MonadPlus (U1 :: Type -> Type)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

mzero :: U1 a

mplus :: U1 a -> U1 a -> U1 a

MonadPlus m => MonadPlus (Kleisli m a)

Since: base-4.14.0.0

Defined in Control.Arrow

Methods

mzero :: Kleisli m a a0

mplus :: Kleisli m a a0 -> Kleisli m a a0 -> Kleisli m a a0

MonadPlus f => MonadPlus (Ap f)

Since: base-4.12.0.0

Defined in Data.Monoid

Methods

mzero :: Ap f a

mplus :: Ap f a -> Ap f a -> Ap f a

MonadPlus f => MonadPlus (Alt f)

Since: base-4.8.0.0

Defined in Data.Semigroup.Internal

Methods

mzero :: Alt f a

mplus :: Alt f a -> Alt f a -> Alt f a

MonadPlus f => MonadPlus (Rec1 f)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

mzero :: Rec1 f a

mplus :: Rec1 f a -> Rec1 f a -> Rec1 f a

(MonadPlus f, MonadPlus g) => MonadPlus (Product f g)

Since: base-4.9.0.0

Defined in Data.Functor.Product

Methods

mzero :: Product f g a

mplus :: Product f g a -> Product f g a -> Product f g a

(MonadPlus f, MonadPlus g) => MonadPlus (f :*: g)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

mzero :: (f :*: g) a

mplus :: (f :*: g) a -> (f :*: g) a -> (f :*: g) a

MonadPlus f => MonadPlus (M1 i c f)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

mzero :: M1 i c f a

mplus :: M1 i c f a -> M1 i c f a -> M1 i c f a

type String = [Char]

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

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

Identity of mappend

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

mappend :: a -> a -> a

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

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

Monoid ByteArray

Since: base-4.17.0.0

Defined in Data.Array.Byte

Methods

mempty :: ByteArray

mappend :: ByteArray -> ByteArray -> ByteArray

mconcat :: [ByteArray] -> ByteArray

Monoid All

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

mempty :: All

mappend :: All -> All -> All

mconcat :: [All] -> All

Monoid Any

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

mempty :: Any

mappend :: Any -> Any -> Any

mconcat :: [Any] -> Any

Monoid Event

Since: base-4.4.0.0

Defined in GHC.Event.Internal.Types

Methods

mempty :: Event

mappend :: Event -> Event -> Event

mconcat :: [Event] -> Event

Monoid Lifetime

mappend takes the longer of two lifetimes.

Since: base-4.8.0.0

Defined in GHC.Event.Internal.Types

Methods

mempty :: Lifetime

mappend :: Lifetime -> Lifetime -> Lifetime

mconcat :: [Lifetime] -> Lifetime

Monoid Ordering

Since: base-2.1

Defined in GHC.Base

Methods

mempty :: Ordering

mappend :: Ordering -> Ordering -> Ordering

mconcat :: [Ordering] -> Ordering

Monoid ()

Since: base-2.1

Defined in GHC.Base

Methods

mempty :: ()

mappend :: () -> () -> ()

mconcat :: [()] -> ()

FiniteBits a => Monoid (And a)

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

Defined in Data.Bits

Methods

mempty :: And a

mappend :: And a -> And a -> And a

mconcat :: [And a] -> And a

FiniteBits a => Monoid (Iff a)

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

Defined in Data.Bits

Methods

mempty :: Iff a

mappend :: Iff a -> Iff a -> Iff a

mconcat :: [Iff a] -> Iff a

Bits a => Monoid (Ior a)

Since: base-4.16

Defined in Data.Bits

Methods

mempty :: Ior a

mappend :: Ior a -> Ior a -> Ior a

mconcat :: [Ior a] -> Ior a

Bits a => Monoid (Xor a)

Since: base-4.16

Defined in Data.Bits

Methods

mempty :: Xor a

mappend :: Xor a -> Xor a -> Xor a

mconcat :: [Xor a] -> Xor a

Monoid (Comparison a)

mempty on comparisons always returns EQ. Without newtypes this equals pure (pure EQ).

mempty :: Comparison a
mempty = Comparison _ _ -> EQ

Defined in Data.Functor.Contravariant

Methods

mempty :: Comparison a

mappend :: Comparison a -> Comparison a -> Comparison a

mconcat :: [Comparison a] -> Comparison a

Monoid (Equivalence a)

mempty on equivalences always returns True. Without newtypes this equals pure (pure True).

mempty :: Equivalence a
mempty = Equivalence _ _ -> True

Defined in Data.Functor.Contravariant

Methods

mempty :: Equivalence a

mappend :: Equivalence a -> Equivalence a -> Equivalence a

mconcat :: [Equivalence a] -> Equivalence a

Monoid (Predicate a)

mempty on predicates always returns True. Without newtypes this equals pure True.

mempty :: Predicate a
mempty = _ -> True

Defined in Data.Functor.Contravariant

Methods

mempty :: Predicate a

mappend :: Predicate a -> Predicate a -> Predicate a

mconcat :: [Predicate a] -> Predicate a

Monoid a => Monoid (Identity a)

Since: base-4.9.0.0

Defined in Data.Functor.Identity

Methods

mempty :: Identity a

mappend :: Identity a -> Identity a -> Identity a

mconcat :: [Identity a] -> Identity a

Monoid (First a)

Since: base-2.1

Defined in Data.Monoid

Methods

mempty :: First a

mappend :: First a -> First a -> First a

mconcat :: [First a] -> First a

Monoid (Last a)

Since: base-2.1

Defined in Data.Monoid

Methods

mempty :: Last a

mappend :: Last a -> Last a -> Last a

mconcat :: [Last a] -> Last a

Monoid a => Monoid (Down a)

Since: base-4.11.0.0

Defined in Data.Ord

Methods

mempty :: Down a

mappend :: Down a -> Down a -> Down a

mconcat :: [Down a] -> Down a

(Ord a, Bounded a) => Monoid (Max a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

mempty :: Max a

mappend :: Max a -> Max a -> Max a

mconcat :: [Max a] -> Max a

(Ord a, Bounded a) => Monoid (Min a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

mempty :: Min a

mappend :: Min a -> Min a -> Min a

mconcat :: [Min a] -> Min a

Monoid m => Monoid (WrappedMonoid m)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

mempty :: WrappedMonoid m

mappend :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m

mconcat :: [WrappedMonoid m] -> WrappedMonoid m

Monoid a => Monoid (Dual a)

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

mempty :: Dual a

mappend :: Dual a -> Dual a -> Dual a

mconcat :: [Dual a] -> Dual a

Monoid (Endo a)

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

mempty :: Endo a

mappend :: Endo a -> Endo a -> Endo a

mconcat :: [Endo a] -> Endo a

Num a => Monoid (Product a)

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

mempty :: Product a

mappend :: Product a -> Product a -> Product a

mconcat :: [Product a] -> Product a

Num a => Monoid (Sum a)

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

mempty :: Sum a

mappend :: Sum a -> Sum a -> Sum a

mconcat :: [Sum a] -> Sum a

Monoid a => Monoid (STM a)

Since: base-4.17.0.0

Defined in GHC.Conc.Sync

Methods

mempty :: STM a

mappend :: STM a -> STM a -> STM a

mconcat :: [STM a] -> STM a

(Generic a, Monoid (Rep a ())) => Monoid (Generically a)

Since: base-4.17.0.0

Defined in GHC.Generics

Methods

mempty :: Generically a

mappend :: Generically a -> Generically a -> Generically a

mconcat :: [Generically a] -> Generically a

Monoid p => Monoid (Par1 p)

Since: base-4.12.0.0

Defined in GHC.Generics

Methods

mempty :: Par1 p

mappend :: Par1 p -> Par1 p -> Par1 p

mconcat :: [Par1 p] -> Par1 p

Monoid a => Monoid (IO a)

Since: base-4.9.0.0

Defined in GHC.Base

Methods

mempty :: IO a

mappend :: IO a -> IO a -> IO a

mconcat :: [IO a] -> IO a

Semigroup a => Monoid (Maybe a)

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 e*e = e and e*s = 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

Defined in GHC.Base

Methods

mempty :: Maybe a

mappend :: Maybe a -> Maybe a -> Maybe a

mconcat :: [Maybe a] -> Maybe a

Monoid a => Monoid (a)

Since: base-4.15

Defined in GHC.Base

Methods

mempty :: (a)

mappend :: (a) -> (a) -> (a)

mconcat :: [(a)] -> (a)

Monoid [a]

Since: base-2.1

Defined in GHC.Base

Methods

mempty :: [a]

mappend :: [a] -> [a] -> [a]

mconcat :: [[a]] -> [a]

Monoid a => Monoid (Op a b)

mempty @(Op a b) without newtypes is mempty @(b->a) = _ -> mempty.

mempty :: Op a b
mempty = Op _ -> mempty

Defined in Data.Functor.Contravariant

Methods

mempty :: Op a b

mappend :: Op a b -> Op a b -> Op a b

mconcat :: [Op a b] -> Op a b

Monoid (Proxy s)

Since: base-4.7.0.0

Defined in Data.Proxy

Methods

mempty :: Proxy s

mappend :: Proxy s -> Proxy s -> Proxy s

mconcat :: [Proxy s] -> Proxy s

Monoid (U1 p)

Since: base-4.12.0.0

Defined in GHC.Generics

Methods

mempty :: U1 p

mappend :: U1 p -> U1 p -> U1 p

mconcat :: [U1 p] -> U1 p

Monoid a => Monoid (ST s a)

Since: base-4.11.0.0

Defined in GHC.ST

Methods

mempty :: ST s a

mappend :: ST s a -> ST s a -> ST s a

mconcat :: [ST s a] -> ST s a

Monoid b => Monoid (a -> b)

Since: base-2.1

Defined in GHC.Base

Methods

mempty :: a -> b

mappend :: (a -> b) -> (a -> b) -> a -> b

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

(Monoid a, Monoid b) => Monoid (a, b)

Since: base-2.1

Defined in GHC.Base

Methods

mempty :: (a, b)

mappend :: (a, b) -> (a, b) -> (a, b)

mconcat :: [(a, b)] -> (a, b)

Monoid a => Monoid (Const a b)

Since: base-4.9.0.0

Defined in Data.Functor.Const

Methods

mempty :: Const a b

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

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

(Applicative f, Monoid a) => Monoid (Ap f a)

Since: base-4.12.0.0

Defined in Data.Monoid

Methods

mempty :: Ap f a

mappend :: Ap f a -> Ap f a -> Ap f a

mconcat :: [Ap f a] -> Ap f a

Alternative f => Monoid (Alt f a)

Since: base-4.8.0.0

Defined in Data.Semigroup.Internal

Methods

mempty :: Alt f a

mappend :: Alt f a -> Alt f a -> Alt f a

mconcat :: [Alt f a] -> Alt f a

Monoid (f p) => Monoid (Rec1 f p)

Since: base-4.12.0.0

Defined in GHC.Generics

Methods

mempty :: Rec1 f p

mappend :: Rec1 f p -> Rec1 f p -> Rec1 f p

mconcat :: [Rec1 f p] -> Rec1 f p

(Monoid a, Monoid b, Monoid c) => Monoid (a, b, c)

Since: base-2.1

Defined in GHC.Base

Methods

mempty :: (a, b, c)

mappend :: (a, b, c) -> (a, b, c) -> (a, b, c)

mconcat :: [(a, b, c)] -> (a, b, c)

(Monoid (f a), Monoid (g a)) => Monoid (Product f g a)

Since: base-4.16.0.0

Defined in Data.Functor.Product

Methods

mempty :: Product f g a

mappend :: Product f g a -> Product f g a -> Product f g a

mconcat :: [Product f g a] -> Product f g a

(Monoid (f p), Monoid (g p)) => Monoid ((f :*: g) p)

Since: base-4.12.0.0

Defined in GHC.Generics

Methods

mempty :: (f :*: g) p

mappend :: (f :*: g) p -> (f :*: g) p -> (f :*: g) p

mconcat :: [(f :*: g) p] -> (f :*: g) p

Monoid c => Monoid (K1 i c p)

Since: base-4.12.0.0

Defined in GHC.Generics

Methods

mempty :: K1 i c p

mappend :: K1 i c p -> K1 i c p -> K1 i c p

mconcat :: [K1 i c p] -> K1 i c p

(Monoid a, Monoid b, Monoid c, Monoid d) => Monoid (a, b, c, d)

Since: base-2.1

Defined in GHC.Base

Methods

mempty :: (a, b, c, d)

mappend :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d)

mconcat :: [(a, b, c, d)] -> (a, b, c, d)

Monoid (f (g a)) => Monoid (Compose f g a)

Since: base-4.16.0.0

Defined in Data.Functor.Compose

Methods

mempty :: Compose f g a

mappend :: Compose f g a -> Compose f g a -> Compose f g a

mconcat :: [Compose f g a] -> Compose f g a

Monoid (f (g p)) => Monoid ((f :.: g) p)

Since: base-4.12.0.0

Defined in GHC.Generics

Methods

mempty :: (f :.: g) p

mappend :: (f :.: g) p -> (f :.: g) p -> (f :.: g) p

mconcat :: [(f :.: g) p] -> (f :.: g) p

Monoid (f p) => Monoid (M1 i c f p)

Since: base-4.12.0.0

Defined in GHC.Generics

Methods

mempty :: M1 i c f p

mappend :: M1 i c f p -> M1 i c f p -> M1 i c f p

mconcat :: [M1 i c f p] -> M1 i c f p

(Monoid a, Monoid b, Monoid c, Monoid d, Monoid e) => Monoid (a, b, c, d, e)

Since: base-2.1

Defined in GHC.Base

Methods

mempty :: (a, b, c, d, e)

mappend :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e)

mconcat :: [(a, b, c, d, e)] -> (a, b, c, d, e)

class Semigroup a where

The class of semigroups (types with an associative binary operation).

Instances should satisfy the following:

Associativity

x <> (y <> z) = (x <> y) <> z

Since: base-4.9.0.0

Minimal complete definition

(<>)

Methods

(<>) :: a -> a -> a infixr 6

An associative operation.

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

sconcat :: NonEmpty a -> a

Reduce a non-empty list with <>

The default definition should be sufficient, but this can be overridden for efficiency.

>>> import Data.List.NonEmpty (NonEmpty (..))
>>> sconcat $ "Hello" :| [" ", "Haskell", "!"]
"Hello Haskell!"

stimes :: Integral b => b -> a -> a

Repeat a value n times.

Given that this works on a Semigroup it is allowed to fail if you request 0 or fewer repetitions, and the default definition will do so.

By making this a member of the class, idempotent semigroups and monoids can upgrade this to execute in \(\mathcal{O}(1)\) by picking stimes = stimesIdempotent or stimes = stimesIdempotentMonoid respectively.

>>> stimes 4 [1]
[1,1,1,1]

Instances

Semigroup ByteArray

Since: base-4.17.0.0

Defined in Data.Array.Byte

Methods

(<>) :: ByteArray -> ByteArray -> ByteArray

sconcat :: NonEmpty ByteArray -> ByteArray

stimes :: Integral b => b -> ByteArray -> ByteArray

Semigroup All

Since: base-4.9.0.0

Defined in Data.Semigroup.Internal

Methods

(<>) :: All -> All -> All

sconcat :: NonEmpty All -> All

stimes :: Integral b => b -> All -> All

Semigroup Any

Since: base-4.9.0.0

Defined in Data.Semigroup.Internal

Methods

(<>) :: Any -> Any -> Any

sconcat :: NonEmpty Any -> Any

stimes :: Integral b => b -> Any -> Any

Semigroup Void

Since: base-4.9.0.0

Defined in Data.Void

Methods

(<>) :: Void -> Void -> Void

sconcat :: NonEmpty Void -> Void

stimes :: Integral b => b -> Void -> Void

Semigroup Event

Since: base-4.10.0.0

Defined in GHC.Event.Internal.Types

Methods

(<>) :: Event -> Event -> Event

sconcat :: NonEmpty Event -> Event

stimes :: Integral b => b -> Event -> Event

Semigroup Lifetime

Since: base-4.10.0.0

Defined in GHC.Event.Internal.Types

Methods

(<>) :: Lifetime -> Lifetime -> Lifetime

sconcat :: NonEmpty Lifetime -> Lifetime

stimes :: Integral b => b -> Lifetime -> Lifetime

Semigroup Ordering

Since: base-4.9.0.0

Defined in GHC.Base

Methods

(<>) :: Ordering -> Ordering -> Ordering

sconcat :: NonEmpty Ordering -> Ordering

stimes :: Integral b => b -> Ordering -> Ordering

Semigroup ()

Since: base-4.9.0.0

Defined in GHC.Base

Methods

(<>) :: () -> () -> ()

sconcat :: NonEmpty () -> ()

stimes :: Integral b => b -> () -> ()

Bits a => Semigroup (And a)

Since: base-4.16

Defined in Data.Bits

Methods

(<>) :: And a -> And a -> And a

sconcat :: NonEmpty (And a) -> And a

stimes :: Integral b => b -> And a -> And a

FiniteBits a => Semigroup (Iff a)

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

Defined in Data.Bits

Methods

(<>) :: Iff a -> Iff a -> Iff a

sconcat :: NonEmpty (Iff a) -> Iff a

stimes :: Integral b => b -> Iff a -> Iff a

Bits a => Semigroup (Ior a)

Since: base-4.16

Defined in Data.Bits

Methods

(<>) :: Ior a -> Ior a -> Ior a

sconcat :: NonEmpty (Ior a) -> Ior a

stimes :: Integral b => b -> Ior a -> Ior a

Bits a => Semigroup (Xor a)

Since: base-4.16

Defined in Data.Bits

Methods

(<>) :: Xor a -> Xor a -> Xor a

sconcat :: NonEmpty (Xor a) -> Xor a

stimes :: Integral b => b -> Xor a -> Xor a

Semigroup (Comparison a)

(<>) on comparisons combines results with (<>) @Ordering. Without newtypes this equals liftA2 (liftA2 (<>)).

(<>) :: Comparison a -> Comparison a -> Comparison a
Comparison cmp <> Comparison cmp' = Comparison a a' ->
  cmp a a' <> cmp a a'

Defined in Data.Functor.Contravariant

Methods

(<>) :: Comparison a -> Comparison a -> Comparison a

sconcat :: NonEmpty (Comparison a) -> Comparison a

stimes :: Integral b => b -> Comparison a -> Comparison a

Semigroup (Equivalence a)

(<>) on equivalences uses logical conjunction (&&) on the results. Without newtypes this equals liftA2 (liftA2 (&&)).

(<>) :: Equivalence a -> Equivalence a -> Equivalence a
Equivalence equiv <> Equivalence equiv' = Equivalence a b ->
  equiv a b && equiv' a b

Defined in Data.Functor.Contravariant

Methods

(<>) :: Equivalence a -> Equivalence a -> Equivalence a

sconcat :: NonEmpty (Equivalence a) -> Equivalence a

stimes :: Integral b => b -> Equivalence a -> Equivalence a

Semigroup (Predicate a)

(<>) on predicates uses logical conjunction (&&) on the results. Without newtypes this equals liftA2 (&&).

(<>) :: Predicate a -> Predicate a -> Predicate a
Predicate pred <> Predicate pred' = Predicate a ->
  pred a && pred' a

Defined in Data.Functor.Contravariant

Methods

(<>) :: Predicate a -> Predicate a -> Predicate a

sconcat :: NonEmpty (Predicate a) -> Predicate a

stimes :: Integral b => b -> Predicate a -> Predicate a

Semigroup a => Semigroup (Identity a)

Since: base-4.9.0.0

Defined in Data.Functor.Identity

Methods

(<>) :: Identity a -> Identity a -> Identity a

sconcat :: NonEmpty (Identity a) -> Identity a

stimes :: Integral b => b -> Identity a -> Identity a

Semigroup (First a)

Since: base-4.9.0.0

Defined in Data.Monoid

Methods

(<>) :: First a -> First a -> First a

sconcat :: NonEmpty (First a) -> First a

stimes :: Integral b => b -> First a -> First a

Semigroup (Last a)

Since: base-4.9.0.0

Defined in Data.Monoid

Methods

(<>) :: Last a -> Last a -> Last a

sconcat :: NonEmpty (Last a) -> Last a

stimes :: Integral b => b -> Last a -> Last a

Semigroup a => Semigroup (Down a)

Since: base-4.11.0.0

Defined in Data.Ord

Methods

(<>) :: Down a -> Down a -> Down a

sconcat :: NonEmpty (Down a) -> Down a

stimes :: Integral b => b -> Down a -> Down a

Semigroup (First a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

(<>) :: First a -> First a -> First a

sconcat :: NonEmpty (First a) -> First a

stimes :: Integral b => b -> First a -> First a

Semigroup (Last a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

(<>) :: Last a -> Last a -> Last a

sconcat :: NonEmpty (Last a) -> Last a

stimes :: Integral b => b -> Last a -> Last a

Ord a => Semigroup (Max a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

(<>) :: Max a -> Max a -> Max a

sconcat :: NonEmpty (Max a) -> Max a

stimes :: Integral b => b -> Max a -> Max a

Ord a => Semigroup (Min a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

(<>) :: Min a -> Min a -> Min a

sconcat :: NonEmpty (Min a) -> Min a

stimes :: Integral b => b -> Min a -> Min a

Monoid m => Semigroup (WrappedMonoid m)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

(<>) :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m

sconcat :: NonEmpty (WrappedMonoid m) -> WrappedMonoid m

stimes :: Integral b => b -> WrappedMonoid m -> WrappedMonoid m

Semigroup a => Semigroup (Dual a)

Since: base-4.9.0.0

Defined in Data.Semigroup.Internal

Methods

(<>) :: Dual a -> Dual a -> Dual a

sconcat :: NonEmpty (Dual a) -> Dual a

stimes :: Integral b => b -> Dual a -> Dual a

Semigroup (Endo a)

Since: base-4.9.0.0

Defined in Data.Semigroup.Internal

Methods

(<>) :: Endo a -> Endo a -> Endo a

sconcat :: NonEmpty (Endo a) -> Endo a

stimes :: Integral b => b -> Endo a -> Endo a

Num a => Semigroup (Product a)

Since: base-4.9.0.0

Defined in Data.Semigroup.Internal

Methods

(<>) :: Product a -> Product a -> Product a

sconcat :: NonEmpty (Product a) -> Product a

stimes :: Integral b => b -> Product a -> Product a

Num a => Semigroup (Sum a)

Since: base-4.9.0.0

Defined in Data.Semigroup.Internal

Methods

(<>) :: Sum a -> Sum a -> Sum a

sconcat :: NonEmpty (Sum a) -> Sum a

stimes :: Integral b => b -> Sum a -> Sum a

Semigroup a => Semigroup (STM a)

Since: base-4.17.0.0

Defined in GHC.Conc.Sync

Methods

(<>) :: STM a -> STM a -> STM a

sconcat :: NonEmpty (STM a) -> STM a

stimes :: Integral b => b -> STM a -> STM a

(Generic a, Semigroup (Rep a ())) => Semigroup (Generically a)

Since: base-4.17.0.0

Defined in GHC.Generics

Methods

(<>) :: Generically a -> Generically a -> Generically a

sconcat :: NonEmpty (Generically a) -> Generically a

stimes :: Integral b => b -> Generically a -> Generically a

Semigroup p => Semigroup (Par1 p)

Since: base-4.12.0.0

Defined in GHC.Generics

Methods

(<>) :: Par1 p -> Par1 p -> Par1 p

sconcat :: NonEmpty (Par1 p) -> Par1 p

stimes :: Integral b => b -> Par1 p -> Par1 p

Semigroup a => Semigroup (IO a)

Since: base-4.10.0.0

Defined in GHC.Base

Methods

(<>) :: IO a -> IO a -> IO a

sconcat :: NonEmpty (IO a) -> IO a

stimes :: Integral b => b -> IO a -> IO a

Semigroup (NonEmpty a)

Since: base-4.9.0.0

Defined in GHC.Base

Methods

(<>) :: NonEmpty a -> NonEmpty a -> NonEmpty a

sconcat :: NonEmpty (NonEmpty a) -> NonEmpty a

stimes :: Integral b => b -> NonEmpty a -> NonEmpty a

Semigroup a => Semigroup (Maybe a)

Since: base-4.9.0.0

Defined in GHC.Base

Methods

(<>) :: Maybe a -> Maybe a -> Maybe a

sconcat :: NonEmpty (Maybe a) -> Maybe a

stimes :: Integral b => b -> Maybe a -> Maybe a

Semigroup a => Semigroup (a)

Since: base-4.15

Defined in GHC.Base

Methods

(<>) :: (a) -> (a) -> (a)

sconcat :: NonEmpty (a) -> (a)

stimes :: Integral b => b -> (a) -> (a)

Semigroup [a]

Since: base-4.9.0.0

Defined in GHC.Base

Methods

(<>) :: [a] -> [a] -> [a]

sconcat :: NonEmpty [a] -> [a]

stimes :: Integral b => b -> [a] -> [a]

Semigroup (Either a b)

Since: base-4.9.0.0

Defined in Data.Either

Methods

(<>) :: Either a b -> Either a b -> Either a b

sconcat :: NonEmpty (Either a b) -> Either a b

stimes :: Integral b0 => b0 -> Either a b -> Either a b

Semigroup a => Semigroup (Op a b)

(<>) @(Op a b) without newtypes is (<>) @(b->a) = liftA2 (<>). This lifts the Semigroup operation (<>) over the output of a.

(<>) :: Op a b -> Op a b -> Op a b
Op f <> Op g = Op a -> f a <> g a

Defined in Data.Functor.Contravariant

Methods

(<>) :: Op a b -> Op a b -> Op a b

sconcat :: NonEmpty (Op a b) -> Op a b

stimes :: Integral b0 => b0 -> Op a b -> Op a b

Semigroup (Proxy s)

Since: base-4.9.0.0

Defined in Data.Proxy

Methods

(<>) :: Proxy s -> Proxy s -> Proxy s

sconcat :: NonEmpty (Proxy s) -> Proxy s

stimes :: Integral b => b -> Proxy s -> Proxy s

Semigroup (U1 p)

Since: base-4.12.0.0

Defined in GHC.Generics

Methods

(<>) :: U1 p -> U1 p -> U1 p

sconcat :: NonEmpty (U1 p) -> U1 p

stimes :: Integral b => b -> U1 p -> U1 p

Semigroup (V1 p)

Since: base-4.12.0.0

Defined in GHC.Generics

Methods

(<>) :: V1 p -> V1 p -> V1 p

sconcat :: NonEmpty (V1 p) -> V1 p

stimes :: Integral b => b -> V1 p -> V1 p

Semigroup a => Semigroup (ST s a)

Since: base-4.11.0.0

Defined in GHC.ST

Methods

(<>) :: ST s a -> ST s a -> ST s a

sconcat :: NonEmpty (ST s a) -> ST s a

stimes :: Integral b => b -> ST s a -> ST s a

Semigroup b => Semigroup (a -> b)

Since: base-4.9.0.0

Defined in GHC.Base

Methods

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

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

stimes :: Integral b0 => b0 -> (a -> b) -> a -> b

(Semigroup a, Semigroup b) => Semigroup (a, b)

Since: base-4.9.0.0

Defined in GHC.Base

Methods

(<>) :: (a, b) -> (a, b) -> (a, b)

sconcat :: NonEmpty (a, b) -> (a, b)

stimes :: Integral b0 => b0 -> (a, b) -> (a, b)

Semigroup a => Semigroup (Const a b)

Since: base-4.9.0.0

Defined in Data.Functor.Const

Methods

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

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

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

(Applicative f, Semigroup a) => Semigroup (Ap f a)

Since: base-4.12.0.0

Defined in Data.Monoid

Methods

(<>) :: Ap f a -> Ap f a -> Ap f a

sconcat :: NonEmpty (Ap f a) -> Ap f a

stimes :: Integral b => b -> Ap f a -> Ap f a

Alternative f => Semigroup (Alt f a)

Since: base-4.9.0.0

Defined in Data.Semigroup.Internal

Methods

(<>) :: Alt f a -> Alt f a -> Alt f a

sconcat :: NonEmpty (Alt f a) -> Alt f a

stimes :: Integral b => b -> Alt f a -> Alt f a

Semigroup (f p) => Semigroup (Rec1 f p)

Since: base-4.12.0.0

Defined in GHC.Generics

Methods

(<>) :: Rec1 f p -> Rec1 f p -> Rec1 f p

sconcat :: NonEmpty (Rec1 f p) -> Rec1 f p

stimes :: Integral b => b -> Rec1 f p -> Rec1 f p

(Semigroup a, Semigroup b, Semigroup c) => Semigroup (a, b, c)

Since: base-4.9.0.0

Defined in GHC.Base

Methods

(<>) :: (a, b, c) -> (a, b, c) -> (a, b, c)

sconcat :: NonEmpty (a, b, c) -> (a, b, c)

stimes :: Integral b0 => b0 -> (a, b, c) -> (a, b, c)

(Semigroup (f a), Semigroup (g a)) => Semigroup (Product f g a)

Since: base-4.16.0.0

Defined in Data.Functor.Product

Methods

(<>) :: Product f g a -> Product f g a -> Product f g a

sconcat :: NonEmpty (Product f g a) -> Product f g a

stimes :: Integral b => b -> Product f g a -> Product f g a

(Semigroup (f p), Semigroup (g p)) => Semigroup ((f :*: g) p)

Since: base-4.12.0.0

Defined in GHC.Generics

Methods

(<>) :: (f :*: g) p -> (f :*: g) p -> (f :*: g) p

sconcat :: NonEmpty ((f :*: g) p) -> (f :*: g) p

stimes :: Integral b => b -> (f :*: g) p -> (f :*: g) p

Semigroup c => Semigroup (K1 i c p)

Since: base-4.12.0.0

Defined in GHC.Generics

Methods

(<>) :: K1 i c p -> K1 i c p -> K1 i c p

sconcat :: NonEmpty (K1 i c p) -> K1 i c p

stimes :: Integral b => b -> K1 i c p -> K1 i c p

(Semigroup a, Semigroup b, Semigroup c, Semigroup d) => Semigroup (a, b, c, d)

Since: base-4.9.0.0

Defined in GHC.Base

Methods

(<>) :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d)

sconcat :: NonEmpty (a, b, c, d) -> (a, b, c, d)

stimes :: Integral b0 => b0 -> (a, b, c, d) -> (a, b, c, d)

Semigroup (f (g a)) => Semigroup (Compose f g a)

Since: base-4.16.0.0

Defined in Data.Functor.Compose

Methods

(<>) :: Compose f g a -> Compose f g a -> Compose f g a

sconcat :: NonEmpty (Compose f g a) -> Compose f g a

stimes :: Integral b => b -> Compose f g a -> Compose f g a

Semigroup (f (g p)) => Semigroup ((f :.: g) p)

Since: base-4.12.0.0

Defined in GHC.Generics

Methods

(<>) :: (f :.: g) p -> (f :.: g) p -> (f :.: g) p

sconcat :: NonEmpty ((f :.: g) p) -> (f :.: g) p

stimes :: Integral b => b -> (f :.: g) p -> (f :.: g) p

Semigroup (f p) => Semigroup (M1 i c f p)

Since: base-4.12.0.0

Defined in GHC.Generics

Methods

(<>) :: M1 i c f p -> M1 i c f p -> M1 i c f p

sconcat :: NonEmpty (M1 i c f p) -> M1 i c f p

stimes :: Integral b => b -> M1 i c f p -> M1 i c f p

(Semigroup a, Semigroup b, Semigroup c, Semigroup d, Semigroup e) => Semigroup (a, b, c, d, e)

Since: base-4.9.0.0

Defined in GHC.Base

Methods

(<>) :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e)

sconcat :: NonEmpty (a, b, c, d, e) -> (a, b, c, d, e)

stimes :: Integral b0 => b0 -> (a, b, c, d, e) -> (a, b, c, d, e)

data Opaque

Constructors

forall a. O a

ord :: Char -> Int

The fromEnum method restricted to the type Char.

(.) :: (b -> c) -> (a -> b) -> a -> c infixr 9

Function composition.

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

A variant of <*> with the arguments reversed.

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

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

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

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

Lift a ternary function to actions.

id :: a -> a

Identity function.

id x = x

when :: Applicative f => Bool -> f () -> f ()

Conditional execution of Applicative expressions. For example,

when debug (putStrLn "Debugging")

will output the string Debugging if the Boolean value debug is True, and otherwise do nothing.

assert :: Bool -> a -> a

If the first argument evaluates to True, then the result is the second argument. Otherwise an AssertionFailed exception is raised, containing a String with the source file and line number of the call to assert.

Assertions can normally be turned on or off with a compiler flag (for GHC, assertions are normally on unless optimisation is turned on with -O or the -fignore-asserts option is given). When assertions are turned off, the first argument to assert is ignored, and the second argument is returned as the result.

mapM :: Monad m => (a -> m b) -> [a] -> m [b]

mapM f is equivalent to sequence . map f.

sequence :: Monad m => [m a] -> m [a]

Evaluate each action in the sequence from left to right, and collect the results.

(=<<) :: Monad m => (a -> m b) -> m a -> m b infixr 1

Same as >>=, but with the arguments interchanged.

join :: Monad m => m (m a) -> m a

The join function is the conventional monad join operator. It is used to remove one level of monadic structure, projecting its bound argument into the outer level.

'join bss' can be understood as the do expression

do bs <- bss
   bs

Examples

A common use of join is to run an IO computation returned from an STM transaction, since STM transactions can't perform IO directly. Recall that

atomically :: STM a -> IO a

is used to run STM transactions atomically. So, by specializing the types of atomically and join to

atomically :: STM (IO b) -> IO (IO b)
join       :: IO (IO b)  -> IO b

we can compose them as

join . atomically :: STM (IO b) -> IO b

to run an STM transaction and the IO action it returns.

liftM :: Monad m => (a1 -> r) -> m a1 -> m r

Promote a function to a monad.

liftM2 :: Monad m => (a1 -> a2 -> r) -> m a1 -> m a2 -> m r

Promote a function to a monad, scanning the monadic arguments from left to right. For example,

liftM2 (+) [0,1] [0,2] = [0,2,1,3]
liftM2 (+) (Just 1) Nothing = Nothing

liftM3 :: Monad m => (a1 -> a2 -> a3 -> r) -> m a1 -> m a2 -> m a3 -> m r

Promote a function to a monad, scanning the monadic arguments from left to right (cf. liftM2).

liftM4 :: Monad m => (a1 -> a2 -> a3 -> a4 -> r) -> m a1 -> m a2 -> m a3 -> m a4 -> m r

Promote a function to a monad, scanning the monadic arguments from left to right (cf. liftM2).

liftM5 :: Monad m => (a1 -> a2 -> a3 -> a4 -> a5 -> r) -> m a1 -> m a2 -> m a3 -> m a4 -> m a5 -> m r

Promote a function to a monad, scanning the monadic arguments from left to right (cf. liftM2).

ap :: Monad m => m (a -> b) -> m a -> m b

In many situations, the liftM operations can be replaced by uses of ap, which promotes function application.

return f `ap` x1 `ap` ... `ap` xn

is equivalent to

liftMn f x1 x2 ... xn

failIO :: String -> IO a

($) :: forall r a (b :: TYPE r). (a -> b) -> a -> b infixr 0

Application operator. This operator is redundant, since ordinary application (f x) means the same as (f $ x). However, $ has low, right-associative binding precedence, so it sometimes allows parentheses to be omitted; for example:

f $ g $ h x  =  f (g (h x))

It is also useful in higher-order situations, such as map ($ 0) xs, or zipWith ($) fs xs.

Note that ($) is representation-polymorphic in its result type, so that foo $ True where foo :: Bool -> Int# is well-typed.

otherwise :: Bool

otherwise is defined as the value True. It helps to make guards more readable. eg.

 f x | x < 0     = ...
     | otherwise = ...

foldr :: (a -> b -> b) -> b -> [a] -> b

foldr, applied to a binary operator, a starting value (typically the right-identity of the operator), and a list, reduces the list using the binary operator, from right to left:

foldr f z [x1, x2, ..., xn] == x1 `f` (x2 `f` ... (xn `f` z)...)

const :: a -> b -> a

const x y always evaluates to x, ignoring its second argument.

>>> const 42 "hello"
42

>>> map (const 42) [0..3]
[42,42,42,42]

flip :: (a -> b -> c) -> b -> a -> c

flip f takes its (first) two arguments in the reverse order of f.

>>> flip (++) "hello" "world"
"worldhello"

(++) :: [a] -> [a] -> [a] infixr 5

Append two lists, i.e.,

[x1, ..., xm] ++ [y1, ..., yn] == [x1, ..., xm, y1, ..., yn]
[x1, ..., xm] ++ [y1, ...] == [x1, ..., xm, y1, ...]

If the first list is not finite, the result is the first list.

WARNING: This function takes linear time in the number of elements of the first list.

map :: (a -> b) -> [a] -> [b]

\(\mathcal{O}(n)\). map f xs is the list obtained by applying f to each element of xs, i.e.,

map f [x1, x2, ..., xn] == [f x1, f x2, ..., f xn]
map f [x1, x2, ...] == [f x1, f x2, ...]

>>> map (+1) [1, 2, 3]
[2,3,4]

($!) :: forall r a (b :: TYPE r). (a -> b) -> a -> b infixr 0

Strict (call-by-value) application operator. It takes a function and an argument, evaluates the argument to weak head normal form (WHNF), then calls the function with that value.

shiftL# :: Word# -> Int# -> Word#

Shift the argument left by the specified number of bits (which must be non-negative).

shiftRL# :: Word# -> Int# -> Word#

Shift the argument right by the specified number of bits (which must be non-negative). The RL means "right, logical" (as opposed to RA for arithmetic) (although an arithmetic right shift wouldn't make sense for Word#)

iShiftL# :: Int# -> Int# -> Int#

Shift the argument left by the specified number of bits (which must be non-negative).

iShiftRA# :: Int# -> Int# -> Int#

Shift the argument right (signed) by the specified number of bits (which must be non-negative). The RA means "right, arithmetic" (as opposed to RL for logical)

iShiftRL# :: Int# -> Int# -> Int#

Shift the argument right (unsigned) by the specified number of bits (which must be non-negative). The RL means "right, logical" (as opposed to RA for arithmetic)

build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]

A list producer that can be fused with foldr. This function is merely

   build g = g (:) []

but GHC's simplifier will transform an expression of the form foldr k z (build g), which may arise after inlining, to g k z, which avoids producing an intermediate list.

augment :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a] -> [a]

A list producer that can be fused with foldr. This function is merely

   augment g xs = g (:) xs

but GHC's simplifier will transform an expression of the form foldr k z (augment g xs), which may arise after inlining, to g k (foldr k z xs), which avoids producing an intermediate list.

breakpoint :: a -> a

breakpointCond :: Bool -> a -> a

unIO :: IO a -> State# RealWorld -> (# State# RealWorld, a #)

until :: (a -> Bool) -> (a -> a) -> a -> a

until p f yields the result of applying f until p holds.

asTypeOf :: a -> a -> a

asTypeOf is a type-restricted version of const. It is usually used as an infix operator, and its typing forces its first argument (which is usually overloaded) to have the same type as the second.

eqString :: String -> String -> Bool

This String equality predicate is used when desugaring pattern-matches against strings.

returnIO :: a -> IO a

bindIO :: IO a -> (a -> IO b) -> IO b

thenIO :: IO a -> IO b -> IO b

mapFB :: (elt -> lst -> lst) -> (a -> elt) -> a -> lst -> lst

unsafeChr :: Int -> Char

maxInt :: Int

minInt :: Int

getTag :: a -> Int#

Returns the tag of a constructor application; this function is used by the deriving code for Eq, Ord and Enum.

quotInt :: Int -> Int -> Int

Used to implement quot for the Integral typeclass. This performs integer division on its two parameters, truncated towards zero.

Example

>>> quotInt 10 2
5

>>> quot 10 2
5

remInt :: Int -> Int -> Int

Used to implement rem for the Integral typeclass. This gives the remainder after integer division of its two parameters, satisfying

((x `quot` y) * y) + (x `rem` y) == x

Example

>>> remInt 3 2
1

>>> rem 3 2
1

divInt :: Int -> Int -> Int

Used to implement div for the Integral typeclass. This performs integer division on its two parameters, truncated towards negative infinity.

Example

>>> 10 `divInt` 2
5

>>> 10 `div` 2
5

modInt :: Int -> Int -> Int

Used to implement mod for the Integral typeclass. This performs the modulo operation, satisfying

((x `div` y) * y) + (x `mod` y) == x

Example

>>> 7 `modInt` 3
1

>>> 7 `mod` 3
1

quotRemInt :: Int -> Int -> (Int, Int)

Used to implement quotRem for the Integral typeclass. This gives a tuple equivalent to

(quot x y, mod x y)

Example

>>> quotRemInt 10 2
(5,0)

>>> quotRem 10 2
(5,0)

divModInt :: Int -> Int -> (Int, Int)

Used to implement divMod for the Integral typeclass. This gives a tuple equivalent to

(div x y, mod x y)

Example

>>> divModInt 10 2
(5,0)

>>> divMod 10 2
(5,0)

shift_mask :: Int# -> Int# -> Int#

This function is used to implement branchless shifts. If the number of bits to shift is greater than or equal to the type size in bits, then the shift must return 0. Instead of doing a test, we use a mask obtained via this function which is branchless too.

shift_mask m b | b < m = 0xFF..FF | otherwise = 0

module GHC.Classes

module GHC.CString

module GHC.Magic

module GHC.Magic.Dict

module GHC.Types

module GHC.Prim

module GHC.Prim.Ext

module GHC.Prim.PtrEq

module GHC.Err

module GHC.Maybe