base-4.16.4.0: Basic libraries
Copyright(c) The University of Glasgow 1992-2002
Licensesee libraries/base/LICENSE
Maintainercvs-ghc@haskell.org
Stabilityinternal
Portabilitynon-portable (GHC extensions)
Safe HaskellUnsafe
LanguageHaskell2010

GHC.Base

Description

Basic data types and classes.

Synopsis

Documentation

augment :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a] -> [a] Source #

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.

(++) :: [a] -> [a] -> [a] infixr 5 Source #

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.

build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a] Source #

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.

foldr :: (a -> b -> b) -> b -> [a] -> b Source #

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)...)

eqString :: String -> String -> Bool Source #

This String equality predicate is used when desugaring pattern-matches against strings.

bindIO :: IO a -> (a -> IO b) -> IO b Source #

returnIO :: a -> IO a Source #

otherwise :: Bool Source #

otherwise is defined as the value True. It helps to make guards more readable. eg.

 f x | x < 0     = ...
     | otherwise = ...

assert :: Bool -> a -> a Source #

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.

thenIO :: IO a -> IO b -> IO b Source #

breakpoint :: a -> a Source #

map :: (a -> b) -> [a] -> [b] Source #

\(\mathcal{O}(n)\). 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 Source #

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 levity-polymorphic in its result type, so that foo $ True where foo :: Bool -> Int# is well-typed.

join :: Monad m => m (m a) -> m a Source #

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

Expand

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.

class Applicative m => Monad m where Source #

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

Instances of Monad should satisfy the following:

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

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

The above laws imply:

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

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

Minimal complete definition

(>>=)

Methods

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

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

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

do a <- as
   bs a

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

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

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

do as
   bs

return :: a -> m a Source #

Inject a value into the monadic type.

Instances

Instances details
Monad Complex Source #

Since: base-4.9.0.0

Instance details

Defined in Data.Complex

Methods

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

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

return :: a -> Complex a Source #

Monad Identity Source #

Since: base-4.8.0.0

Instance details

Defined in Data.Functor.Identity

Methods

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

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

return :: a -> Identity a Source #

Monad First Source #

Since: base-4.8.0.0

Instance details

Defined in Data.Monoid

Methods

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

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

return :: a -> First a Source #

Monad Last Source #

Since: base-4.8.0.0

Instance details

Defined in Data.Monoid

Methods

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

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

return :: a -> Last a Source #

Monad Down Source #

Since: base-4.11.0.0

Instance details

Defined in Data.Ord

Methods

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

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

return :: a -> Down a Source #

Monad First Source #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

return :: a -> First a Source #

Monad Last Source #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

return :: a -> Last a Source #

Monad Max Source #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

return :: a -> Max a Source #

Monad Min Source #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

return :: a -> Min a Source #

Monad Dual Source #

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

return :: a -> Dual a Source #

Monad Product Source #

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

return :: a -> Product a Source #

Monad Sum Source #

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

return :: a -> Sum a Source #

Monad STM Source #

Since: base-4.3.0.0

Instance details

Defined in GHC.Conc.Sync

Methods

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

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

return :: a -> STM a Source #

Monad NoIO Source #

Since: base-4.4.0.0

Instance details

Defined in GHC.GHCi

Methods

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

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

return :: a -> NoIO a Source #

Monad Par1 Source #

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

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

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

return :: a -> Par1 a Source #

Monad ReadP Source #

Since: base-2.1

Instance details

Defined in Text.ParserCombinators.ReadP

Methods

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

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

return :: a -> ReadP a Source #

Monad ReadPrec Source #

Since: base-2.1

Instance details

Defined in Text.ParserCombinators.ReadPrec

Methods

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

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

return :: a -> ReadPrec a Source #

Monad IO Source #

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

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

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

return :: a -> IO a Source #

Monad NonEmpty Source #

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Methods

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

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

return :: a -> NonEmpty a Source #

Monad Maybe Source #

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

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

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

return :: a -> Maybe a Source #

Monad Solo Source #

Since: base-4.15

Instance details

Defined in GHC.Base

Methods

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

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

return :: a -> Solo a Source #

Monad [] Source #

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

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

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

return :: a -> [a] Source #

Monad m => Monad (WrappedMonad m) Source #

Since: base-4.7.0.0

Instance details

Defined in Control.Applicative

Methods

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

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

return :: a -> WrappedMonad m a Source #

ArrowApply a => Monad (ArrowMonad a) Source #

Since: base-2.1

Instance details

Defined in Control.Arrow

Methods

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

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

return :: a0 -> ArrowMonad a a0 Source #

Monad (ST s) Source #

Since: base-2.1

Instance details

Defined in Control.Monad.ST.Lazy.Imp

Methods

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

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

return :: a -> ST s a Source #

Monad (Either e) Source #

Since: base-4.4.0.0

Instance details

Defined in Data.Either

Methods

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

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

return :: a -> Either e a Source #

Monad (Proxy :: Type -> Type) Source #

Since: base-4.7.0.0

Instance details

Defined in Data.Proxy

Methods

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

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

return :: a -> Proxy a Source #

Monad (U1 :: Type -> Type) Source #

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

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

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

return :: a -> U1 a Source #

Monad (ST s) Source #

Since: base-2.1

Instance details

Defined in GHC.ST

Methods

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

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

return :: a -> ST s a Source #

Monoid a => Monad ((,) a) Source #

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Methods

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

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

return :: a0 -> (a, a0) Source #

Monad m => Monad (Kleisli m a) Source #

Since: base-4.14.0.0

Instance details

Defined in Control.Arrow

Methods

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

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

return :: a0 -> Kleisli m a a0 Source #

Monad f => Monad (Ap f) Source #

Since: base-4.12.0.0

Instance details

Defined in Data.Monoid

Methods

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

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

return :: a -> Ap f a Source #

Monad f => Monad (Alt f) Source #

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

return :: a -> Alt f a Source #

Monad f => Monad (Rec1 f) Source #

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

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

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

return :: a -> Rec1 f a Source #

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

Since: base-4.14.0.0

Instance details

Defined in GHC.Base

Methods

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

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

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

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

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Product

Methods

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

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

return :: a -> Product f g a Source #

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

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

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

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

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

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

Since: base-4.14.0.0

Instance details

Defined in GHC.Base

Methods

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

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

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

Monad ((->) r) Source #

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

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

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

return :: a -> r -> a Source #

Monad f => Monad (M1 i c f) Source #

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

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

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

return :: a -> M1 i c f a Source #

class Functor f where Source #

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

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

Note, that the second law follows from the free theorem of the type fmap and the first law, so you need only check that the former condition holds.

Minimal complete definition

fmap

Methods

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

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

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

Examples

Expand

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

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

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

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

Double each element of a list:

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

Apply even to the second element of a pair:

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

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

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

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

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

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

Instances

Instances details
Functor ZipList Source #

Since: base-2.1

Instance details

Defined in Control.Applicative

Methods

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

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

Functor Handler Source #

Since: base-4.6.0.0

Instance details

Defined in Control.Exception

Methods

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

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

Functor Complex Source #

Since: base-4.9.0.0

Instance details

Defined in Data.Complex

Methods

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

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

Functor Identity Source #

Since: base-4.8.0.0

Instance details

Defined in Data.Functor.Identity

Methods

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

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

Functor First Source #

Since: base-4.8.0.0

Instance details

Defined in Data.Monoid

Methods

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

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

Functor Last Source #

Since: base-4.8.0.0

Instance details

Defined in Data.Monoid

Methods

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

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

Functor Down Source #

Since: base-4.11.0.0

Instance details

Defined in Data.Ord

Methods

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

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

Functor First Source #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

Functor Last Source #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

Functor Max Source #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

Functor Min Source #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

Functor Dual Source #

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

Functor Product Source #

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

Functor Sum Source #

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

Functor STM Source #

Since: base-4.3.0.0

Instance details

Defined in GHC.Conc.Sync

Methods

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

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

Functor NoIO Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.GHCi

Methods

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

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

Functor Par1 Source #

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

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

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

Functor ArgDescr Source #

Since: base-4.6.0.0

Instance details

Defined in System.Console.GetOpt

Methods

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

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

Functor ArgOrder Source #

Since: base-4.6.0.0

Instance details

Defined in System.Console.GetOpt

Methods

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

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

Functor OptDescr Source #

Since: base-4.6.0.0

Instance details

Defined in System.Console.GetOpt

Methods

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

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

Functor ReadP Source #

Since: base-2.1

Instance details

Defined in Text.ParserCombinators.ReadP

Methods

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

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

Functor ReadPrec Source #

Since: base-2.1

Instance details

Defined in Text.ParserCombinators.ReadPrec

Methods

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

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

Functor IO Source #

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

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

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

Functor NonEmpty Source #

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Methods

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

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

Functor Maybe Source #

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

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

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

Functor Solo Source #

Since: base-4.15

Instance details

Defined in GHC.Base

Methods

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

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

Functor [] Source #

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

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

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

Monad m => Functor (WrappedMonad m) Source #

Since: base-2.1

Instance details

Defined in Control.Applicative

Methods

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

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

Arrow a => Functor (ArrowMonad a) Source #

Since: base-4.6.0.0

Instance details

Defined in Control.Arrow

Methods

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

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

Functor (ST s) Source #

Since: base-2.1

Instance details

Defined in Control.Monad.ST.Lazy.Imp

Methods

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

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

Functor (Either a) Source #

Since: base-3.0

Instance details

Defined in Data.Either

Methods

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

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

Functor (Proxy :: Type -> Type) Source #

Since: base-4.7.0.0

Instance details

Defined in Data.Proxy

Methods

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

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

Functor (Arg a) Source #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

Functor (Array i) Source #

Since: base-2.1

Instance details

Defined in GHC.Arr

Methods

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

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

Functor (U1 :: Type -> Type) Source #

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

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

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

Functor (V1 :: TYPE LiftedRep -> Type) Source #

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

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

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

Functor (ST s) Source #

Since: base-2.1

Instance details

Defined in GHC.ST

Methods

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

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

Functor ((,) a) Source #

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

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

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

Arrow a => Functor (WrappedArrow a b) Source #

Since: base-2.1

Instance details

Defined in Control.Applicative

Methods

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

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

Functor m => Functor (Kleisli m a) Source #

Since: base-4.14.0.0

Instance details

Defined in Control.Arrow

Methods

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

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

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

Since: base-2.1

Instance details

Defined in Data.Functor.Const

Methods

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

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

Functor f => Functor (Ap f) Source #

Since: base-4.12.0.0

Instance details

Defined in Data.Monoid

Methods

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

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

Functor f => Functor (Alt f) Source #

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

Functor f => Functor (Rec1 f) Source #

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

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

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

Functor (URec (Ptr ()) :: TYPE LiftedRep -> Type) Source #

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

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

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

Functor (URec Char :: TYPE LiftedRep -> Type) Source #

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

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

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

Functor (URec Double :: TYPE LiftedRep -> Type) Source #

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

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

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

Functor (URec Float :: TYPE LiftedRep -> Type) Source #

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

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

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

Functor (URec Int :: TYPE LiftedRep -> Type) Source #

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

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

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

Functor (URec Word :: TYPE LiftedRep -> Type) Source #

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

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

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

Functor ((,,) a b) Source #

Since: base-4.14.0.0

Instance details

Defined in GHC.Base

Methods

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

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

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

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Product

Methods

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

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

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

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Sum

Methods

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

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

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

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

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

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

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

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

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

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

Functor (K1 i c :: TYPE LiftedRep -> Type) Source #

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

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

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

Functor ((,,,) a b c) Source #

Since: base-4.14.0.0

Instance details

Defined in GHC.Base

Methods

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

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

Functor ((->) r) Source #

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

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

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

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

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Compose

Methods

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

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

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

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

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

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

Functor f => Functor (M1 i c f) Source #

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

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

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

class Functor f => Applicative f where Source #

A functor with application, providing operations to

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

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

(<*>) = liftA2 id
liftA2 f x y = f <$> x <*> y

Further, any definition must satisfy the following:

Identity
pure id <*> v = v
Composition
pure (.) <*> u <*> v <*> w = u <*> (v <*> w)
Homomorphism
pure f <*> pure x = pure (f x)
Interchange
u <*> pure y = pure ($ y) <*> u

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

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

It may be useful to note that supposing

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

it follows from the above that

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

If f is also a Monad, it should satisfy

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

Minimal complete definition

pure, ((<*>) | liftA2)

Methods

pure :: a -> f a Source #

Lift a value.

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

Sequential application.

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

Example

Expand

Used in combination with (<$>), (<*>) can be used to build a record.

>>> data MyState = MyState {arg1 :: Foo, arg2 :: Bar, arg3 :: Baz}
>>> produceFoo :: Applicative f => f Foo
>>> produceBar :: Applicative f => f Bar
>>> produceBaz :: Applicative f => f Baz
>>> mkState :: Applicative f => f MyState
>>> mkState = MyState <$> produceFoo <*> produceBar <*> produceBaz

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

Lift a binary function to actions.

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

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

Example

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

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

Sequence actions, discarding the value of the first argument.

Examples

Expand

If used in conjunction with the Applicative instance for Maybe, you can chain Maybe computations, with a possible "early return" in case of Nothing.

>>> Just 2 *> Just 3
Just 3
>>> Nothing *> Just 3
Nothing

Of course a more interesting use case would be to have effectful computations instead of just returning pure values.

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

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

Sequence actions, discarding the value of the second argument.

Instances

Instances details
Applicative ZipList Source #
f <$> ZipList xs1 <*> ... <*> ZipList xsN
    = ZipList (zipWithN f xs1 ... xsN)

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

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

Since: base-2.1

Instance details

Defined in Control.Applicative

Methods

pure :: a -> ZipList a Source #

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

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

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

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

Applicative Complex Source #

Since: base-4.9.0.0

Instance details

Defined in Data.Complex

Methods

pure :: a -> Complex a Source #

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

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

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

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

Applicative Identity Source #

Since: base-4.8.0.0

Instance details

Defined in Data.Functor.Identity

Methods

pure :: a -> Identity a Source #

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

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

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

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

Applicative First Source #

Since: base-4.8.0.0

Instance details

Defined in Data.Monoid

Methods

pure :: a -> First a Source #

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

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

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

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

Applicative Last Source #

Since: base-4.8.0.0

Instance details

Defined in Data.Monoid

Methods

pure :: a -> Last a Source #

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

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

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

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

Applicative Down Source #

Since: base-4.11.0.0

Instance details

Defined in Data.Ord

Methods

pure :: a -> Down a Source #

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

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

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

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

Applicative First Source #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

pure :: a -> First a Source #

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

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

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

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

Applicative Last Source #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

pure :: a -> Last a Source #

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

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

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

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

Applicative Max Source #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

pure :: a -> Max a Source #

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

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

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

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

Applicative Min Source #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

pure :: a -> Min a Source #

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

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

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

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

Applicative Dual Source #

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

pure :: a -> Dual a Source #

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

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

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

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

Applicative Product Source #

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

pure :: a -> Product a Source #

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

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

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

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

Applicative Sum Source #

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

pure :: a -> Sum a Source #

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

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

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

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

Applicative STM Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Conc.Sync

Methods

pure :: a -> STM a Source #

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

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

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

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

Applicative NoIO Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.GHCi

Methods

pure :: a -> NoIO a Source #

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

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

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

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

Applicative Par1 Source #

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

pure :: a -> Par1 a Source #

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

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

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

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

Applicative ReadP Source #

Since: base-4.6.0.0

Instance details

Defined in Text.ParserCombinators.ReadP

Methods

pure :: a -> ReadP a Source #

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

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

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

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

Applicative ReadPrec Source #

Since: base-4.6.0.0

Instance details

Defined in Text.ParserCombinators.ReadPrec

Methods

pure :: a -> ReadPrec a Source #

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

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

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

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

Applicative IO Source #

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

pure :: a -> IO a Source #

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

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

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

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

Applicative NonEmpty Source #

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Methods

pure :: a -> NonEmpty a Source #

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

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

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

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

Applicative Maybe Source #

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

pure :: a -> Maybe a Source #

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

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

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

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

Applicative Solo Source #

Since: base-4.15

Instance details

Defined in GHC.Base

Methods

pure :: a -> Solo a Source #

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

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

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

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

Applicative [] Source #

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

pure :: a -> [a] Source #

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

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

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

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

Monad m => Applicative (WrappedMonad m) Source #

Since: base-2.1

Instance details

Defined in Control.Applicative

Methods

pure :: a -> WrappedMonad m a Source #

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

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

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

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

Arrow a => Applicative (ArrowMonad a) Source #

Since: base-4.6.0.0

Instance details

Defined in Control.Arrow

Methods

pure :: a0 -> ArrowMonad a a0 Source #

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

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

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

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

Applicative (ST s) Source #

Since: base-2.1

Instance details

Defined in Control.Monad.ST.Lazy.Imp

Methods

pure :: a -> ST s a Source #

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

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

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

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

Applicative (Either e) Source #

Since: base-3.0

Instance details

Defined in Data.Either

Methods

pure :: a -> Either e a Source #

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

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

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

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

Applicative (Proxy :: Type -> Type) Source #

Since: base-4.7.0.0

Instance details

Defined in Data.Proxy

Methods

pure :: a -> Proxy a Source #

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

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

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

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

Applicative (U1 :: Type -> Type) Source #

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

pure :: a -> U1 a Source #

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

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

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

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

Applicative (ST s) Source #

Since: base-4.4.0.0

Instance details

Defined in GHC.ST

Methods

pure :: a -> ST s a Source #

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

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

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

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

Monoid a => Applicative ((,) a) Source #

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

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

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

pure :: a0 -> (a, a0) Source #

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

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

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

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

Arrow a => Applicative (WrappedArrow a b) Source #

Since: base-2.1

Instance details

Defined in Control.Applicative

Methods

pure :: a0 -> WrappedArrow a b a0 Source #

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

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

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

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

Applicative m => Applicative (Kleisli m a) Source #

Since: base-4.14.0.0

Instance details

Defined in Control.Arrow

Methods

pure :: a0 -> Kleisli m a a0 Source #

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

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

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

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

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

Since: base-2.0.1

Instance details

Defined in Data.Functor.Const

Methods

pure :: a -> Const m a Source #

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

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

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

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

Applicative f => Applicative (Ap f) Source #

Since: base-4.12.0.0

Instance details

Defined in Data.Monoid

Methods

pure :: a -> Ap f a Source #

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

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

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

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

Applicative f => Applicative (Alt f) Source #

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

pure :: a -> Alt f a Source #

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

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

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

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

Applicative f => Applicative (Rec1 f) Source #

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

pure :: a -> Rec1 f a Source #

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

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

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

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

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

Since: base-4.14.0.0

Instance details

Defined in GHC.Base

Methods

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

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

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

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

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

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

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Product

Methods

pure :: a -> Product f g a Source #

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

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

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

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

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

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

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

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

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

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

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

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

Since: base-4.12.0.0

Instance details

Defined in GHC.Generics

Methods

pure :: a -> K1 i c a Source #

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

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

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

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

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

Since: base-4.14.0.0

Instance details

Defined in GHC.Base

Methods

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

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

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

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

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

Applicative ((->) r) Source #

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

pure :: a -> r -> a Source #

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

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

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

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

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

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Compose

Methods

pure :: a -> Compose f g a Source #

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

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

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

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

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

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

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

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

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

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

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

Applicative f => Applicative (M1 i c f) Source #

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

pure :: a -> M1 i c f a Source #

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

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

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

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

class Semigroup a where Source #

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 Source #

An associative operation.

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

sconcat :: NonEmpty a -> a Source #

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 Source #

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

Instances details
Semigroup All Source #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

(<>) :: All -> All -> All Source #

sconcat :: NonEmpty All -> All Source #

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

Semigroup Any Source #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

(<>) :: Any -> Any -> Any Source #

sconcat :: NonEmpty Any -> Any Source #

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

Semigroup Void Source #

Since: base-4.9.0.0

Instance details

Defined in Data.Void

Semigroup Event Source #

Since: base-4.10.0.0

Instance details

Defined in GHC.Event.Internal.Types

Semigroup Lifetime Source #

Since: base-4.10.0.0

Instance details

Defined in GHC.Event.Internal.Types

Semigroup Ordering Source #

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Semigroup () Source #

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Methods

(<>) :: () -> () -> () Source #

sconcat :: NonEmpty () -> () Source #

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

Bits a => Semigroup (And a) Source #

Since: base-4.16

Instance details

Defined in Data.Bits

Methods

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

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

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

FiniteBits a => Semigroup (Iff a) Source #

This constraint is arguably too strong. However, as some types (such as Natural) have undefined complement, this is the only safe choice.

Since: base-4.16

Instance details

Defined in Data.Bits

Methods

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

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

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

Bits a => Semigroup (Ior a) Source #

Since: base-4.16

Instance details

Defined in Data.Bits

Methods

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

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

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

Bits a => Semigroup (Xor a) Source #

Since: base-4.16

Instance details

Defined in Data.Bits

Methods

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

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

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

Semigroup (Comparison a) Source #

(<>) 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'
Instance details

Defined in Data.Functor.Contravariant

Semigroup (Equivalence a) Source #

(<>) 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
Instance details

Defined in Data.Functor.Contravariant

Semigroup (Predicate a) Source #

(<>) 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
Instance details

Defined in Data.Functor.Contravariant

Semigroup a => Semigroup (Identity a) Source #

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Identity

Semigroup (First a) Source #

Since: base-4.9.0.0

Instance details

Defined in Data.Monoid

Methods

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

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

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

Semigroup (Last a) Source #

Since: base-4.9.0.0

Instance details

Defined in Data.Monoid

Methods

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

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

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

Semigroup a => Semigroup (Down a) Source #

Since: base-4.11.0.0

Instance details

Defined in Data.Ord

Methods

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

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

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

Semigroup (First a) Source #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

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

Semigroup (Last a) Source #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

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

Ord a => Semigroup (Max a) Source #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

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

Ord a => Semigroup (Min a) Source #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

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

Monoid m => Semigroup (WrappedMonoid m) Source #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Semigroup a => Semigroup (Dual a) Source #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

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

Semigroup (Endo a) Source #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

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

Num a => Semigroup (Product a) Source #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

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

Num a => Semigroup (Sum a) Source #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

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

Semigroup p => Semigroup (Par1 p) Source #

Since: base-4.12.0.0

Instance details

Defined in GHC.Generics

Methods

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

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

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

Semigroup a => Semigroup (IO a) Source #

Since: base-4.10.0.0

Instance details

Defined in GHC.Base

Methods

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

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

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

Semigroup (NonEmpty a) Source #

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Semigroup a => Semigroup (Maybe a) Source #

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Methods

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

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

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

Semigroup a => Semigroup (a) Source #

Since: base-4.15

Instance details

Defined in GHC.Base

Methods

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

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

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

Semigroup [a] Source #

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Methods

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

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

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

Semigroup (Either a b) Source #

Since: base-4.9.0.0

Instance details

Defined in Data.Either

Methods

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

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

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

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

(<>) @(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
Instance details

Defined in Data.Functor.Contravariant

Methods

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

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

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

Semigroup (Proxy s) Source #

Since: base-4.9.0.0

Instance details

Defined in Data.Proxy

Methods

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

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

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

Semigroup (U1 p) Source #

Since: base-4.12.0.0

Instance details

Defined in GHC.Generics

Methods

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

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

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

Semigroup (V1 p) Source #

Since: base-4.12.0.0

Instance details

Defined in GHC.Generics

Methods

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

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

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

Semigroup a => Semigroup (ST s a) Source #

Since: base-4.11.0.0

Instance details

Defined in GHC.ST

Methods

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

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

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

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

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Methods

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

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

stimes :: Integral b0 => b0 -> (a -> b) -> a -> b Source #

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

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Methods

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

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

stimes :: Integral b0 => b0 -> (a, b) -> (a, b) Source #

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

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Const

Methods

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

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

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

(Applicative f, Semigroup a) => Semigroup (Ap f a) Source #

Since: base-4.12.0.0

Instance details

Defined in Data.Monoid

Methods

(<>) :: Ap f a -> Ap f a -> Ap f a Source #

sconcat :: NonEmpty (Ap f a) -> Ap f a Source #

stimes :: Integral b => b -> Ap f a -> Ap f a Source #

Alternative f => Semigroup (Alt f a) Source #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

(<>) :: Alt f a -> Alt f a -> Alt f a Source #

sconcat :: NonEmpty (Alt f a) -> Alt f a Source #

stimes :: Integral b => b -> Alt f a -> Alt f a Source #

Semigroup (f p) => Semigroup (Rec1 f p) Source #

Since: base-4.12.0.0

Instance details

Defined in GHC.Generics

Methods

(<>) :: Rec1 f p -> Rec1 f p -> Rec1 f p Source #

sconcat :: NonEmpty (Rec1 f p) -> Rec1 f p Source #

stimes :: Integral b => b -> Rec1 f p -> Rec1 f p Source #

(Semigroup a, Semigroup b, Semigroup c) => Semigroup (a, b, c) Source #

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Methods

(<>) :: (a, b, c) -> (a, b, c) -> (a, b, c) Source #

sconcat :: NonEmpty (a, b, c) -> (a, b, c) Source #

stimes :: Integral b0 => b0 -> (a, b, c) -> (a, b, c) Source #

(Semigroup (f a), Semigroup (g a)) => Semigroup (Product f g a) Source #

Since: base-4.16.0.0

Instance details

Defined in Data.Functor.Product

Methods

(<>) :: Product f g a -> Product f g a -> Product f g a Source #

sconcat :: NonEmpty (Product f g a) -> Product f g a Source #

stimes :: Integral b => b -> Product f g a -> Product f g a Source #

(Semigroup (f p), Semigroup (g p)) => Semigroup ((f :*: g) p) Source #

Since: base-4.12.0.0

Instance details

Defined in GHC.Generics

Methods

(<>) :: (f :*: g) p -> (f :*: g) p -> (f :*: g) p Source #

sconcat :: NonEmpty ((f :*: g) p) -> (f :*: g) p Source #

stimes :: Integral b => b -> (f :*: g) p -> (f :*: g) p Source #

Semigroup c => Semigroup (K1 i c p) Source #

Since: base-4.12.0.0

Instance details

Defined in GHC.Generics

Methods

(<>) :: K1 i c p -> K1 i c p -> K1 i c p Source #

sconcat :: NonEmpty (K1 i c p) -> K1 i c p Source #

stimes :: Integral b => b -> K1 i c p -> K1 i c p Source #

(Semigroup a, Semigroup b, Semigroup c, Semigroup d) => Semigroup (a, b, c, d) Source #

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Methods

(<>) :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) Source #

sconcat :: NonEmpty (a, b, c, d) -> (a, b, c, d) Source #

stimes :: Integral b0 => b0 -> (a, b, c, d) -> (a, b, c, d) Source #

Semigroup (f (g a)) => Semigroup (Compose f g a) Source #

Since: base-4.16.0.0

Instance details

Defined in Data.Functor.Compose

Methods

(<>) :: Compose f g a -> Compose f g a -> Compose f g a Source #

sconcat :: NonEmpty (Compose f g a) -> Compose f g a Source #

stimes :: Integral b => b -> Compose f g a -> Compose f g a Source #

Semigroup (f (g p)) => Semigroup ((f :.: g) p) Source #

Since: base-4.12.0.0

Instance details

Defined in GHC.Generics

Methods

(<>) :: (f :.: g) p -> (f :.: g) p -> (f :.: g) p Source #

sconcat :: NonEmpty ((f :.: g) p) -> (f :.: g) p Source #

stimes :: Integral b => b -> (f :.: g) p -> (f :.: g) p Source #

Semigroup (f p) => Semigroup (M1 i c f p) Source #

Since: base-4.12.0.0

Instance details

Defined in GHC.Generics

Methods

(<>) :: M1 i c f p -> M1 i c f p -> M1 i c f p Source #

sconcat :: NonEmpty (M1 i c f p) -> M1 i c f p Source #

stimes :: Integral b => b -> M1 i c f p -> M1 i c f p Source #

(Semigroup a, Semigroup b, Semigroup c, Semigroup d, Semigroup e) => Semigroup (a, b, c, d, e) Source #

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Methods

(<>) :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) Source #

sconcat :: NonEmpty (a, b, c, d, e) -> (a, b, c, d, e) Source #

stimes :: Integral b0 => b0 -> (a, b, c, d, e) -> (a, b, c, d, e) Source #

class Semigroup a => Monoid a where Source #

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

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

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

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

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

Minimal complete definition

mempty

Methods

mempty :: a Source #

Identity of mappend

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

mappend :: a -> a -> a Source #

An associative operation

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

mconcat :: [a] -> a Source #

Fold a list using the monoid.

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

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

Instances

Instances details
Monoid All Source #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Monoid Any Source #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Monoid Event Source #

Since: base-4.4.0.0

Instance details

Defined in GHC.Event.Internal.Types

Monoid Lifetime Source #

mappend takes the longer of two lifetimes.

Since: base-4.8.0.0

Instance details

Defined in GHC.Event.Internal.Types

Monoid Ordering Source #

Since: base-2.1

Instance details

Defined in GHC.Base

Monoid () Source #

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

mempty :: () Source #

mappend :: () -> () -> () Source #

mconcat :: [()] -> () Source #

FiniteBits a => Monoid (And a) Source #

This constraint is arguably too strong. However, as some types (such as Natural) have undefined complement, this is the only safe choice.

Since: base-4.16

Instance details

Defined in Data.Bits

Methods

mempty :: And a Source #

mappend :: And a -> And a -> And a Source #

mconcat :: [And a] -> And a Source #

FiniteBits a => Monoid (Iff a) Source #

This constraint is arguably too strong. However, as some types (such as Natural) have undefined complement, this is the only safe choice.

Since: base-4.16

Instance details

Defined in Data.Bits

Methods

mempty :: Iff a Source #

mappend :: Iff a -> Iff a -> Iff a Source #

mconcat :: [Iff a] -> Iff a Source #

Bits a => Monoid (Ior a) Source #

Since: base-4.16

Instance details

Defined in Data.Bits

Methods

mempty :: Ior a Source #

mappend :: Ior a -> Ior a -> Ior a Source #

mconcat :: [Ior a] -> Ior a Source #

Bits a => Monoid (Xor a) Source #

Since: base-4.16

Instance details

Defined in Data.Bits

Methods

mempty :: Xor a Source #

mappend :: Xor a -> Xor a -> Xor a Source #

mconcat :: [Xor a] -> Xor a Source #

Monoid (Comparison a) Source #

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

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

Defined in Data.Functor.Contravariant

Monoid (Equivalence a) Source #

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

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

Defined in Data.Functor.Contravariant

Monoid (Predicate a) Source #

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

mempty :: Predicate a
mempty = _ -> True
Instance details

Defined in Data.Functor.Contravariant

Monoid a => Monoid (Identity a) Source #

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Identity

Monoid (First a) Source #

Since: base-2.1

Instance details

Defined in Data.Monoid

Methods

mempty :: First a Source #

mappend :: First a -> First a -> First a Source #

mconcat :: [First a] -> First a Source #

Monoid (Last a) Source #

Since: base-2.1

Instance details

Defined in Data.Monoid

Methods

mempty :: Last a Source #

mappend :: Last a -> Last a -> Last a Source #

mconcat :: [Last a] -> Last a Source #

Monoid a => Monoid (Down a) Source #

Since: base-4.11.0.0

Instance details

Defined in Data.Ord

Methods

mempty :: Down a Source #

mappend :: Down a -> Down a -> Down a Source #

mconcat :: [Down a] -> Down a Source #

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

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

mempty :: Max a Source #

mappend :: Max a -> Max a -> Max a Source #

mconcat :: [Max a] -> Max a Source #

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

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

mempty :: Min a Source #

mappend :: Min a -> Min a -> Min a Source #

mconcat :: [Min a] -> Min a Source #

Monoid m => Monoid (WrappedMonoid m) Source #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Monoid a => Monoid (Dual a) Source #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

mempty :: Dual a Source #

mappend :: Dual a -> Dual a -> Dual a Source #

mconcat :: [Dual a] -> Dual a Source #

Monoid (Endo a) Source #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

mempty :: Endo a Source #

mappend :: Endo a -> Endo a -> Endo a Source #

mconcat :: [Endo a] -> Endo a Source #

Num a => Monoid (Product a) Source #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Num a => Monoid (Sum a) Source #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

mempty :: Sum a Source #

mappend :: Sum a -> Sum a -> Sum a Source #

mconcat :: [Sum a] -> Sum a Source #

Monoid p => Monoid (Par1 p) Source #

Since: base-4.12.0.0

Instance details

Defined in GHC.Generics

Methods

mempty :: Par1 p Source #

mappend :: Par1 p -> Par1 p -> Par1 p Source #

mconcat :: [Par1 p] -> Par1 p Source #

Monoid a => Monoid (IO a) Source #

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Methods

mempty :: IO a Source #

mappend :: IO a -> IO a -> IO a Source #

mconcat :: [IO a] -> IO a Source #

Semigroup a => Monoid (Maybe a) Source #

Lift a semigroup into Maybe forming a Monoid according to http://en.wikipedia.org/wiki/Monoid: "Any semigroup S may be turned into a monoid simply by adjoining an element e not in S and defining 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

Instance details

Defined in GHC.Base

Methods

mempty :: Maybe a Source #

mappend :: Maybe a -> Maybe a -> Maybe a Source #

mconcat :: [Maybe a] -> Maybe a Source #

Monoid a => Monoid (a) Source #

Since: base-4.15

Instance details

Defined in GHC.Base

Methods

mempty :: (a) Source #

mappend :: (a) -> (a) -> (a) Source #

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

Monoid [a] Source #

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

mempty :: [a] Source #

mappend :: [a] -> [a] -> [a] Source #

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

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

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

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

Defined in Data.Functor.Contravariant

Methods

mempty :: Op a b Source #

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

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

Monoid (Proxy s) Source #

Since: base-4.7.0.0

Instance details

Defined in Data.Proxy

Methods

mempty :: Proxy s Source #

mappend :: Proxy s -> Proxy s -> Proxy s Source #

mconcat :: [Proxy s] -> Proxy s Source #

Monoid (U1 p) Source #

Since: base-4.12.0.0

Instance details

Defined in GHC.Generics

Methods

mempty :: U1 p Source #

mappend :: U1 p -> U1 p -> U1 p Source #

mconcat :: [U1 p] -> U1 p Source #

Monoid a => Monoid (ST s a) Source #

Since: base-4.11.0.0

Instance details

Defined in GHC.ST

Methods

mempty :: ST s a Source #

mappend :: ST s a -> ST s a -> ST s a Source #

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

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

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

mempty :: a -> b Source #

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

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

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

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

mempty :: (a, b) Source #

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

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

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

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Const

Methods

mempty :: Const a b Source #

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

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

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

Since: base-4.12.0.0

Instance details

Defined in Data.Monoid

Methods

mempty :: Ap f a Source #

mappend :: Ap f a -> Ap f a -> Ap f a Source #

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

Alternative f => Monoid (Alt f a) Source #

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

mempty :: Alt f a Source #

mappend :: Alt f a -> Alt f a -> Alt f a Source #

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

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

Since: base-4.12.0.0

Instance details

Defined in GHC.Generics

Methods

mempty :: Rec1 f p Source #

mappend :: Rec1 f p -> Rec1 f p -> Rec1 f p Source #

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

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

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

mempty :: (a, b, c) Source #

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

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

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

Since: base-4.16.0.0

Instance details

Defined in Data.Functor.Product

Methods

mempty :: Product f g a Source #

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

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

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

Since: base-4.12.0.0

Instance details

Defined in GHC.Generics

Methods

mempty :: (f :*: g) p Source #

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

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

Monoid c => Monoid (K1 i c p) Source #

Since: base-4.12.0.0

Instance details

Defined in GHC.Generics

Methods

mempty :: K1 i c p Source #

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

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

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

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

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

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

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

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

Since: base-4.16.0.0

Instance details

Defined in Data.Functor.Compose

Methods

mempty :: Compose f g a Source #

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

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

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

Since: base-4.12.0.0

Instance details

Defined in GHC.Generics

Methods

mempty :: (f :.: g) p Source #

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

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

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

Since: base-4.12.0.0

Instance details

Defined in GHC.Generics

Methods

mempty :: M1 i c f p Source #

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

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

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

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

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

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

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

type String = [Char] Source #

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

See Data.List for operations on lists.

data NonEmpty a Source #

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

Since: base-4.9.0.0

Constructors

a :| [a] infixr 5 

Instances

Instances details
MonadFix NonEmpty Source #

Since: base-4.9.0.0

Instance details

Defined in Control.Monad.Fix

Methods

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

MonadZip NonEmpty Source #

Since: base-4.9.0.0

Instance details

Defined in Control.Monad.Zip

Methods

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

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

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

Foldable NonEmpty Source #

Since: base-4.9.0.0

Instance details

Defined in Data.Foldable

Methods

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

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

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

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

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

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

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

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

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

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

null :: NonEmpty a -> Bool Source #

length :: NonEmpty a -> Int Source #

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

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

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

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

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

Eq1 NonEmpty Source #

Since: base-4.10.0.0

Instance details

Defined in Data.Functor.Classes

Methods

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

Ord1 NonEmpty Source #

Since: base-4.10.0.0

Instance details

Defined in Data.Functor.Classes

Methods

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

Read1 NonEmpty Source #

Since: base-4.10.0.0

Instance details

Defined in Data.Functor.Classes

Show1 NonEmpty Source #

Since: base-4.10.0.0

Instance details

Defined in Data.Functor.Classes

Methods

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

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

Traversable NonEmpty Source #

Since: base-4.9.0.0

Instance details

Defined in Data.Traversable

Methods

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

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

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

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

Applicative NonEmpty Source #

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Methods

pure :: a -> NonEmpty a Source #

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

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

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

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

Functor NonEmpty Source #

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Methods

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

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

Monad NonEmpty Source #

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Methods

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

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

return :: a -> NonEmpty a Source #

Generic1 NonEmpty Source # 
Instance details

Defined in GHC.Generics

Associated Types

type Rep1 NonEmpty :: k -> Type Source #

Methods

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

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

Data a => Data (NonEmpty a) Source #

Since: base-4.9.0.0

Instance details

Defined in Data.Data

Methods

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

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

toConstr :: NonEmpty a -> Constr Source #

dataTypeOf :: NonEmpty a -> DataType Source #

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

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

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

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

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

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

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

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

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

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

Semigroup (NonEmpty a) Source #

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

IsList (NonEmpty a) Source #

Since: base-4.9.0.0

Instance details

Defined in GHC.Exts

Associated Types

type Item (NonEmpty a) Source #

Generic (NonEmpty a) Source # 
Instance details

Defined in GHC.Generics

Associated Types

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

Methods

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

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

Read a => Read (NonEmpty a) Source #

Since: base-4.11.0.0

Instance details

Defined in GHC.Read

Show a => Show (NonEmpty a) Source #

Since: base-4.11.0.0

Instance details

Defined in GHC.Show

Eq a => Eq (NonEmpty a) Source #

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Methods

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

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

Ord a => Ord (NonEmpty a) Source #

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

type Rep1 NonEmpty Source #

Since: base-4.6.0.0

Instance details

Defined in GHC.Generics

type Item (NonEmpty a) Source # 
Instance details

Defined in GHC.Exts

type Item (NonEmpty a) = a
type Rep (NonEmpty a) Source #

Since: base-4.6.0.0

Instance details

Defined in GHC.Generics

data Opaque Source #

Constructors

forall a. O a 

($!) :: forall r a (b :: TYPE r). (a -> b) -> a -> b infixr 0 Source #

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.

(.) :: (b -> c) -> (a -> b) -> a -> c infixr 9 Source #

Function composition.

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

A variant of <*> with the arguments reversed.

(=<<) :: Monad m => (a -> m b) -> m a -> m b infixr 1 Source #

Same as >>=, but with the arguments interchanged.

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

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

asTypeOf :: a -> a -> a Source #

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.

const :: a -> b -> a Source #

const x is a unary function which evaluates to x for all inputs.

>>> const 42 "hello"
42
>>> map (const 42) [0..3]
[42,42,42,42]

divModInt# :: Int# -> Int# -> (# Int#, Int# #) Source #

flip :: (a -> b -> c) -> b -> a -> c Source #

flip f takes its (first) two arguments in the reverse order of f.

>>> flip (++) "hello" "world"
"worldhello"

getTag :: a -> Int# Source #

Returns the tag of a constructor application; this function is used by the deriving code for Eq, Ord and Enum.

iShiftL# :: Int# -> Int# -> Int# Source #

Shift the argument left by the specified number of bits (which must be non-negative).

iShiftRA# :: Int# -> Int# -> Int# Source #

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# Source #

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)

id :: a -> a Source #

Identity function.

id x = x

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

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

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

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

Lift a ternary function to actions.

liftM :: Monad m => (a1 -> r) -> m a1 -> m r Source #

Promote a function to a monad.

liftM2 :: Monad m => (a1 -> a2 -> r) -> m a1 -> m a2 -> m r Source #

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 Source #

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 Source #

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 Source #

Promote a function to a monad, scanning the monadic arguments from left to right (cf. liftM2).

mapFB :: (elt -> lst -> lst) -> (a -> elt) -> a -> lst -> lst Source #

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

mapM f is equivalent to sequence . map f.

ord :: Char -> Int Source #

The fromEnum method restricted to the type Char.

sequence :: Monad m => [m a] -> m [a] Source #

Evaluate each action in the sequence from left to right, and collect the results.

shiftL# :: Word# -> Int# -> Word# Source #

Shift the argument left by the specified number of bits (which must be non-negative).

shiftRL# :: Word# -> Int# -> Word# Source #

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#)

until :: (a -> Bool) -> (a -> a) -> a -> a Source #

until p f yields the result of applying f until p holds.

when :: Applicative f => Bool -> f () -> f () Source #

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.

class Applicative f => Alternative f where Source #

A monoid on applicative functors.

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

Minimal complete definition

empty, (<|>)

Methods

empty :: f a Source #

The identity of <|>

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

An associative binary operation

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

One or more.

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

Zero or more.

Instances

Instances details
Alternative ZipList Source #

Since: base-4.11.0.0

Instance details

Defined in Control.Applicative

Alternative STM Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Conc.Sync

Methods

empty :: STM a Source #

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

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

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

Alternative ReadP Source #

Since: base-4.6.0.0

Instance details

Defined in Text.ParserCombinators.ReadP

Methods

empty :: ReadP a Source #

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

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

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

Alternative ReadPrec Source #

Since: base-4.6.0.0

Instance details

Defined in Text.ParserCombinators.ReadPrec

Alternative IO Source #

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Methods

empty :: IO a Source #

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

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

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

Alternative Maybe Source #

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

empty :: Maybe a Source #

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

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

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

Alternative [] Source #

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

empty :: [a] Source #

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

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

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

MonadPlus m => Alternative (WrappedMonad m) Source #

Since: base-2.1

Instance details

Defined in Control.Applicative

ArrowPlus a => Alternative (ArrowMonad a) Source #

Since: base-4.6.0.0

Instance details

Defined in Control.Arrow

Methods

empty :: ArrowMonad a a0 Source #

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

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

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

Alternative (Proxy :: Type -> Type) Source #

Since: base-4.9.0.0

Instance details

Defined in Data.Proxy

Methods

empty :: Proxy a Source #

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

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

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

Alternative (U1 :: Type -> Type) Source #

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

empty :: U1 a Source #

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

some :: U1 a -> U1 [a] Source #

many :: U1 a -> U1 [a] Source #

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

Since: base-2.1

Instance details

Defined in Control.Applicative

Methods

empty :: WrappedArrow a b a0 Source #

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

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

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

Alternative m => Alternative (Kleisli m a) Source #

Since: base-4.14.0.0

Instance details

Defined in Control.Arrow

Methods

empty :: Kleisli m a a0 Source #

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

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

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

Alternative f => Alternative (Ap f) Source #

Since: base-4.12.0.0

Instance details

Defined in Data.Monoid

Methods

empty :: Ap f a Source #

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

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

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

Alternative f => Alternative (Alt f) Source #

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

empty :: Alt f a Source #

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

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

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

Alternative f => Alternative (Rec1 f) Source #

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

empty :: Rec1 f a Source #

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

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

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

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

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Product

Methods

empty :: Product f g a Source #

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

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

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

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

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

empty :: (f :*: g) a Source #

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

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

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

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

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Compose

Methods

empty :: Compose f g a Source #

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

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

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

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

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

empty :: (f :.: g) a Source #

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

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

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

Alternative f => Alternative (M1 i c f) Source #

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

empty :: M1 i c f a Source #

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

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

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

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

Monads that also support choice and failure.

Minimal complete definition

Nothing

Methods

mzero :: m a Source #

The identity of mplus. It should also satisfy the equations

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

The default definition is

mzero = empty

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

An associative operation. The default definition is

mplus = (<|>)

Instances

Instances details
MonadPlus STM Source #

Since: base-4.3.0.0

Instance details

Defined in GHC.Conc.Sync

Methods

mzero :: STM a Source #

mplus :: STM a -> STM a -> STM a Source #

MonadPlus ReadP Source #

Since: base-2.1

Instance details

Defined in Text.ParserCombinators.ReadP

Methods

mzero :: ReadP a Source #

mplus :: ReadP a -> ReadP a -> ReadP a Source #

MonadPlus ReadPrec Source #

Since: base-2.1

Instance details

Defined in Text.ParserCombinators.ReadPrec

MonadPlus IO Source #

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Methods

mzero :: IO a Source #

mplus :: IO a -> IO a -> IO a Source #

MonadPlus Maybe Source #

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

mzero :: Maybe a Source #

mplus :: Maybe a -> Maybe a -> Maybe a Source #

MonadPlus [] Source #

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

mzero :: [a] Source #

mplus :: [a] -> [a] -> [a] Source #

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

Since: base-4.6.0.0

Instance details

Defined in Control.Arrow

Methods

mzero :: ArrowMonad a a0 Source #

mplus :: ArrowMonad a a0 -> ArrowMonad a a0 -> ArrowMonad a a0 Source #

MonadPlus (Proxy :: Type -> Type) Source #

Since: base-4.9.0.0

Instance details

Defined in Data.Proxy

Methods

mzero :: Proxy a Source #

mplus :: Proxy a -> Proxy a -> Proxy a Source #

MonadPlus (U1 :: Type -> Type) Source #

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

mzero :: U1 a Source #

mplus :: U1 a -> U1 a -> U1 a Source #

MonadPlus m => MonadPlus (Kleisli m a) Source #

Since: base-4.14.0.0

Instance details

Defined in Control.Arrow

Methods

mzero :: Kleisli m a a0 Source #

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

MonadPlus f => MonadPlus (Ap f) Source #

Since: base-4.12.0.0

Instance details

Defined in Data.Monoid

Methods

mzero :: Ap f a Source #

mplus :: Ap f a -> Ap f a -> Ap f a Source #

MonadPlus f => MonadPlus (Alt f) Source #

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

mzero :: Alt f a Source #

mplus :: Alt f a -> Alt f a -> Alt f a Source #

MonadPlus f => MonadPlus (Rec1 f) Source #

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

mzero :: Rec1 f a Source #

mplus :: Rec1 f a -> Rec1 f a -> Rec1 f a Source #

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

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Product

Methods

mzero :: Product f g a Source #

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

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

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

mzero :: (f :*: g) a Source #

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

MonadPlus f => MonadPlus (M1 i c f) Source #

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

mzero :: M1 i c f a Source #

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

module GHC.Magic

module GHC.Types

module GHC.Prim

module GHC.Err

module GHC.Maybe