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/Haskell 8

GHC.Base

Copyright (c) The University of Glasgow 1992-2002
License see libraries/base/LICENSE
Maintainer [email protected]
Stability internal
Portability non-portable (GHC extensions)
Safe Haskell Unsafe
Language Haskell2010

Description

Basic data types and classes.

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

breakpointCond :: Bool -> a -> a Source

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

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]

($) :: 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.

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.

(>>) :: 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.

return :: a -> m a Source

Inject a value into the monadic type.

Instances
Instances details
Monad []

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 Maybe

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 IO

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 Par1

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 NonEmpty

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 NoIO

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 ReadP

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

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 Down

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 Product

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

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 Dual

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 Last

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 First

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 STM

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 Identity

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 Option

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

(>>=) :: Option a -> (a -> Option b) -> Option b Source

(>>) :: Option a -> Option b -> Option b Source

return :: a -> Option a Source

Monad Last

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 First

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 Max

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

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 Complex

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 (Either e)

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 (U1 :: Type -> Type)

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

Monoid a => Monad ((,) a)

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 (ST s)

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

Monad (Proxy :: Type -> Type)

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

ArrowApply a => Monad (ArrowMonad a)

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 m => Monad (WrappedMonad m)

Since: base-4.7.0.0

Instance details

Defined in Control.Applicative

Methods

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

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

return :: a -> WrappedMonad m a Source

Monad (ST s)

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 f => Monad (Rec1 f)

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

Monad f => Monad (Alt f)

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 (Ap f)

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 ((->) r :: Type -> Type)

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

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

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

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 (M1 i c f)

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

(<$) :: 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 []

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

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

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

Functor Maybe

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 IO

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 Par1

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 NonEmpty

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 NoIO

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 ReadP

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

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 Down

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 Product

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

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 Dual

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 Last

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 First

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 STM

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 Handler

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 Identity

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 ZipList

Since: base-2.1

Instance details

Defined in Control.Applicative

Methods

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

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

Functor ArgDescr

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 OptDescr

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 ArgOrder

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 Option

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

(<$) :: a -> Option b -> Option a Source

Functor Last

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 First

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 Max

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

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 Complex

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 (Either a)

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 (V1 :: Type -> Type)

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 (U1 :: Type -> Type)

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 ((,) a)

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

Functor (ST s)

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 (Array i)

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 (Proxy :: Type -> Type)

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

Arrow a => Functor (ArrowMonad a)

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

Monad m => Functor (WrappedMonad m)

Since: base-2.1

Instance details

Defined in Control.Applicative

Methods

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

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

Functor (ST s)

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 (Arg a)

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 f => Functor (Rec1 f)

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 Char :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

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

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

Functor (URec Double :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

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

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

Functor (URec Float :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

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

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

Functor (URec Int :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

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

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

Functor (URec Word :: Type -> Type)

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

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 f => Functor (Alt f)

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 (Ap f)

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 (Const m :: Type -> Type)

Since: base-2.1

Instance details

Defined in Data.Functor.Const

Methods

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

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

Arrow a => Functor (WrappedArrow a b)

Since: base-2.1

Instance details

Defined in Control.Applicative

Methods

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

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

Functor ((->) r :: Type -> Type)

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 (K1 i c :: Type -> Type)

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

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)

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 (Sum f g)

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 (Product f g)

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 (M1 i c f)

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

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

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 (Compose f g)

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

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.

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

Lift a binary function to actions.

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

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

Sequence actions, discarding the value of the first argument.

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

Sequence actions, discarding the value of the second argument.

Instances
Instances details
Applicative []

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

pure :: a -> [a] Source

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

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

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

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

Applicative Maybe

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

pure :: a -> Maybe a Source

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

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

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

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

Applicative IO

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

pure :: a -> IO a Source

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

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

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

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

Applicative Par1

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

pure :: a -> Par1 a Source

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

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

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

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

Applicative NonEmpty

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Methods

pure :: a -> NonEmpty a Source

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

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

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

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

Applicative NoIO

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 ReadP

Since: base-4.6.0.0

Instance details

Defined in Text.ParserCombinators.ReadP

Methods

pure :: a -> ReadP a Source

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

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

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

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

Applicative ReadPrec

Since: base-4.6.0.0

Instance details

Defined in Text.ParserCombinators.ReadPrec

Methods

pure :: a -> ReadPrec a Source

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

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

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

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

Applicative Down

Since: base-4.11.0.0

Instance details

Defined in Data.Ord

Methods

pure :: a -> Down a Source

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

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

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

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

Applicative Product

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

pure :: a -> Product a Source

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

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

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

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

Applicative Sum

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

pure :: a -> Sum a Source

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

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

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

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

Applicative Dual

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

pure :: a -> Dual a Source

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

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

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

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

Applicative Last

Since: base-4.8.0.0

Instance details

Defined in Data.Monoid

Methods

pure :: a -> Last a Source

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

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

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

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

Applicative First

Since: base-4.8.0.0

Instance details

Defined in Data.Monoid

Methods

pure :: a -> First a Source

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

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

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

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

Applicative STM

Since: base-4.8.0.0

Instance details

Defined in GHC.Conc.Sync

Methods

pure :: a -> STM a Source

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

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

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

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

Applicative Identity

Since: base-4.8.0.0

Instance details

Defined in Data.Functor.Identity

Methods

pure :: a -> Identity a Source

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

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

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

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

Applicative ZipList
f <$> ZipList xs1 <*> ... <*> ZipList xsN
    = ZipList (zipWithN f xs1 ... xsN)

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

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

Since: base-2.1

Instance details

Defined in Control.Applicative

Methods

pure :: a -> ZipList a Source

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

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

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

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

Applicative Option

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

pure :: a -> Option a Source

(<*>) :: Option (a -> b) -> Option a -> Option b Source

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

(*>) :: Option a -> Option b -> Option b Source

(<*) :: Option a -> Option b -> Option a Source

Applicative Last

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

pure :: a -> Last a Source

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

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

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

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

Applicative First

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

pure :: a -> First a Source

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

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

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

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

Applicative Max

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

pure :: a -> Max a Source

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

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

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

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

Applicative Min

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

pure :: a -> Min a Source

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

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

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

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

Applicative Complex

Since: base-4.9.0.0

Instance details

Defined in Data.Complex

Methods

pure :: a -> Complex a Source

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

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

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

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

Applicative (Either e)

Since: base-3.0

Instance details

Defined in Data.Either

Methods

pure :: a -> Either e a Source

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

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

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

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

Applicative (U1 :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

pure :: a -> U1 a Source

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

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

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

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

Monoid a => Applicative ((,) a)

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

Applicative (ST s)

Since: base-4.4.0.0

Instance details

Defined in GHC.ST

Methods

pure :: a -> ST s a Source

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

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

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

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

Applicative (Proxy :: Type -> Type)

Since: base-4.7.0.0

Instance details

Defined in Data.Proxy

Methods

pure :: a -> Proxy a Source

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

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

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

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

Arrow a => Applicative (ArrowMonad a)

Since: base-4.6.0.0

Instance details

Defined in Control.Arrow

Methods

pure :: a0 -> ArrowMonad a a0 Source

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

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

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

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

Monad m => Applicative (WrappedMonad m)

Since: base-2.1

Instance details

Defined in Control.Applicative

Methods

pure :: a -> WrappedMonad m a Source

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

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

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

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

Applicative (ST s)

Since: base-2.1

Instance details

Defined in Control.Monad.ST.Lazy.Imp

Methods

pure :: a -> ST s a Source

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

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

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

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

Applicative f => Applicative (Rec1 f)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

pure :: a -> Rec1 f a Source

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

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

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

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

Applicative f => Applicative (Alt f)

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

pure :: a -> Alt f a Source

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

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

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

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

Applicative f => Applicative (Ap f)

Since: base-4.12.0.0

Instance details

Defined in Data.Monoid

Methods

pure :: a -> Ap f a Source

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

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

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

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

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

Since: base-2.0.1

Instance details

Defined in Data.Functor.Const

Methods

pure :: a -> Const m a Source

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

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

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

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

Arrow a => Applicative (WrappedArrow a b)

Since: base-2.1

Instance details

Defined in Control.Applicative

Methods

pure :: a0 -> WrappedArrow a b a0 Source

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

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

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

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

Applicative ((->) a :: Type -> Type)

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

pure :: a0 -> a -> a0 Source

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

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

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

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

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

Since: base-4.12.0.0

Instance details

Defined in GHC.Generics

Methods

pure :: a -> K1 i c a Source

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

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

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

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

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

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

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

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

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

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

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

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

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Product

Methods

pure :: a -> Product f g a Source

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

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

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

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

Applicative f => Applicative (M1 i c f)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

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

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

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

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

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

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

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

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

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

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

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

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

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

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Compose

Methods

pure :: a -> Compose f g a Source

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

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

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

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

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.

sconcat :: NonEmpty a -> a Source

Reduce a non-empty list with <>

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

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 O(1) by picking stimes = stimesIdempotent or stimes = stimesIdempotentMonoid respectively.

Instances
Instances details
Semigroup Ordering

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Semigroup ()

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Methods

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

sconcat :: NonEmpty () -> () Source

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

Semigroup Any

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 All

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 Lifetime

Since: base-4.10.0.0

Instance details

Defined in GHC.Event.Internal

Semigroup Event

Since: base-4.10.0.0

Instance details

Defined in GHC.Event.Internal

Semigroup Void

Since: base-4.9.0.0

Instance details

Defined in Data.Void

Methods

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

sconcat :: NonEmpty Void -> Void Source

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

Semigroup [a]

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 a => Semigroup (Maybe a)

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 (IO a)

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 p => Semigroup (Par1 p)

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 (NonEmpty a)

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Semigroup a => Semigroup (Down a)

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

Num a => Semigroup (Product a)

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)

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 (Endo a)

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

Semigroup a => Semigroup (Dual a)

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 (Last a)

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 (First a)

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 a => Semigroup (Identity a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Identity

Semigroup a => Semigroup (Option a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

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

Monoid m => Semigroup (WrappedMonoid m)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Semigroup (Last a)

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

Semigroup (First a)

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

Ord a => Semigroup (Max a)

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)

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

Semigroup (Equivalence a)
Instance details

Defined in Data.Functor.Contravariant

Semigroup (Comparison a)
Instance details

Defined in Data.Functor.Contravariant

Semigroup (Predicate a)
Instance details

Defined in Data.Functor.Contravariant

Semigroup b => Semigroup (a -> b)

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 (Either a b)

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 (V1 p)

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 (U1 p)

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

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 (ST s a)

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 (Proxy s)

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 a => Semigroup (Op a b)
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 (f p) => Semigroup (Rec1 f p)

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)

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

Alternative f => Semigroup (Alt f a)

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

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

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

Semigroup a => Semigroup (Const a b)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Const

Methods

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

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

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

Semigroup c => Semigroup (K1 i c p)

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

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

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

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

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

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

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.

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.

Instances
Instances details
Monoid Ordering

Since: base-2.1

Instance details

Defined in GHC.Base

Monoid ()

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

mempty :: () Source

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

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

Monoid Any

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

mempty :: Any Source

mappend :: Any -> Any -> Any Source

mconcat :: [Any] -> Any Source

Monoid All

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

mempty :: All Source

mappend :: All -> All -> All Source

mconcat :: [All] -> All Source

Monoid Lifetime

mappend takes the longer of two lifetimes.

Since: base-4.8.0.0

Instance details

Defined in GHC.Event.Internal

Monoid Event

Since: base-4.4.0.0

Instance details

Defined in GHC.Event.Internal

Monoid [a]

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

mempty :: [a] Source

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

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

Semigroup a => Monoid (Maybe a)

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

Since 4.11.0: constraint on inner a value generalised from Monoid to Semigroup.

Since: base-2.1

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 (IO a)

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

Monoid p => Monoid (Par1 p)

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 (Down a)

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

Num a => Monoid (Product a)

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Num a => Monoid (Sum a)

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 (Endo a)

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

Monoid a => Monoid (Dual a)

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 (Last a)

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 (First a)

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 a => Monoid (Identity a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Identity

Semigroup a => Monoid (Option a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

mempty :: Option a Source

mappend :: Option a -> Option a -> Option a Source

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

Monoid m => Monoid (WrappedMonoid m)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

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

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)

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 (Equivalence a)
Instance details

Defined in Data.Functor.Contravariant

Monoid (Comparison a)
Instance details

Defined in Data.Functor.Contravariant

Monoid (Predicate a)
Instance details

Defined in Data.Functor.Contravariant

Monoid b => Monoid (a -> b)

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 (U1 p)

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 b) => Monoid (a, b)

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 (ST s a)

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 (Proxy s)

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 a => Monoid (Op a b)
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 (f p) => Monoid (Rec1 f p)

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)

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

Alternative f => Monoid (Alt f a)

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

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

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

Monoid a => Monoid (Const a b)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Const

Methods

mempty :: Const a b Source

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

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

Monoid c => Monoid (K1 i c p)

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

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

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

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

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

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

data Opaque Source

Constructors

forall a. O a

type String = [Char] Source

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

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
Monad NonEmpty

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

Functor NonEmpty

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

MonadFix NonEmpty

Since: base-4.9.0.0

Instance details

Defined in Control.Monad.Fix

Methods

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

Applicative NonEmpty

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Methods

pure :: a -> NonEmpty a Source

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

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

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

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

Foldable NonEmpty

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

Traversable NonEmpty

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

MonadZip NonEmpty

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

Show1 NonEmpty

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

Read1 NonEmpty

Since: base-4.10.0.0

Instance details

Defined in Data.Functor.Classes

Ord1 NonEmpty

Since: base-4.10.0.0

Instance details

Defined in Data.Functor.Classes

Methods

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

Eq1 NonEmpty

Since: base-4.10.0.0

Instance details

Defined in Data.Functor.Classes

Methods

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

IsList (NonEmpty a)

Since: base-4.9.0.0

Instance details

Defined in GHC.Exts

Associated Types

type Item (NonEmpty a) Source

Methods

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

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

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

Eq a => Eq (NonEmpty a)

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

Data a => Data (NonEmpty a)

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

Ord a => Ord (NonEmpty a)

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Read a => Read (NonEmpty a)

Since: base-4.11.0.0

Instance details

Defined in GHC.Read

Show a => Show (NonEmpty a)

Since: base-4.11.0.0

Instance details

Defined in GHC.Show

Generic (NonEmpty a)

Since: base-4.6.0.0

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

Semigroup (NonEmpty a)

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Generic1 NonEmpty

Since: base-4.6.0.0

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

type Rep (NonEmpty a)
Instance details

Defined in GHC.Generics

type Item (NonEmpty a)
Instance details

Defined in GHC.Exts

type Item (NonEmpty a) = a
type Rep1 NonEmpty
Instance details

Defined in GHC.Generics

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 []

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

mzero :: [a] Source

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

MonadPlus Maybe

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

mzero :: Maybe a Source

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

MonadPlus IO

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 ReadP

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

Since: base-2.1

Instance details

Defined in Text.ParserCombinators.ReadPrec

Methods

mzero :: ReadPrec a Source

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

MonadPlus STM

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 Option

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

mzero :: Option a Source

mplus :: Option a -> Option a -> Option a Source

MonadPlus (U1 :: Type -> Type)

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 (Proxy :: Type -> Type)

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

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

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 f => MonadPlus (Rec1 f)

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 (Alt f)

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 (Ap f)

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

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 g) => MonadPlus (Product f g)

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 (M1 i c f)

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

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 []

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

empty :: [a] Source

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

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

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

Alternative Maybe

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

empty :: Maybe a Source

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

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

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

Alternative IO

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Methods

empty :: IO a Source

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

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

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

Alternative ReadP

Since: base-4.6.0.0

Instance details

Defined in Text.ParserCombinators.ReadP

Methods

empty :: ReadP a Source

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

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

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

Alternative ReadPrec

Since: base-4.6.0.0

Instance details

Defined in Text.ParserCombinators.ReadPrec

Alternative STM

Since: base-4.8.0.0

Instance details

Defined in GHC.Conc.Sync

Methods

empty :: STM a Source

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

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

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

Alternative ZipList

Since: base-4.11.0.0

Instance details

Defined in Control.Applicative

Methods

empty :: ZipList a Source

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

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

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

Alternative Option

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

empty :: Option a Source

(<|>) :: Option a -> Option a -> Option a Source

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

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

Alternative (U1 :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

empty :: U1 a Source

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

some :: U1 a -> U1 [a] Source

many :: U1 a -> U1 [a] Source

Alternative (Proxy :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in Data.Proxy

Methods

empty :: Proxy a Source

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

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

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

ArrowPlus a => Alternative (ArrowMonad a)

Since: base-4.6.0.0

Instance details

Defined in Control.Arrow

Methods

empty :: ArrowMonad a a0 Source

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

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

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

MonadPlus m => Alternative (WrappedMonad m)

Since: base-2.1

Instance details

Defined in Control.Applicative

Alternative f => Alternative (Rec1 f)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

empty :: Rec1 f a Source

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

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

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

Alternative f => Alternative (Alt f)

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

empty :: Alt f a Source

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

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

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

Alternative f => Alternative (Ap f)

Since: base-4.12.0.0

Instance details

Defined in Data.Monoid

Methods

empty :: Ap f a Source

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

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

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

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

Since: base-2.1

Instance details

Defined in Control.Applicative

Methods

empty :: WrappedArrow a b a0 Source

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

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

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

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

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

empty :: (f :*: g) a Source

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

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

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

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

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Product

Methods

empty :: Product f g a Source

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

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

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

Alternative f => Alternative (M1 i c f)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

empty :: M1 i c f a Source

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

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

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

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

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

empty :: (f :.: g) a Source

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

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

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

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

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Compose

Methods

empty :: Compose f g a Source

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

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

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

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

A variant of <*> with the arguments reversed.

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

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

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

Lift a ternary function to actions.

(=<<) :: Monad m => (a -> m b) -> m a -> m b infixr 1 Source

Same as >>=, but with the arguments interchanged.

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.

sequence :: Monad m => [m a] -> m [a] Source

Evaluate each action in the sequence from left to right, and collect the results.

mapM :: Monad m => (a -> m b) -> [a] -> m [b] Source

mapM f is equivalent to sequence . map f.

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).

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

mapFB :: (elt -> lst -> lst) -> (a -> elt) -> a -> lst -> lst Source

unsafeChr :: Int -> Char Source

ord :: Char -> Int Source

The fromEnum method restricted to the type Char.

minInt :: Int Source

maxInt :: Int Source

id :: a -> a Source

Identity function.

id x = x

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]

(.) :: (b -> c) -> (a -> b) -> a -> c infixr 9 Source

Function composition.

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"

($!) :: 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.

until :: (a -> Bool) -> (a -> a) -> a -> a Source

until p f yields the result of applying f until p holds.

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.

unIO :: IO a -> State# RealWorld -> (# State# RealWorld, a #) Source

getTag :: a -> Int# Source

Returns the tag of a constructor application; this function is used by the deriving code for Eq, Ord and Enum.

quotInt :: Int -> Int -> Int Source

remInt :: Int -> Int -> Int Source

divInt :: Int -> Int -> Int Source

modInt :: Int -> Int -> Int Source

quotRemInt :: Int -> Int -> (Int, Int) Source

divModInt :: Int -> Int -> (Int, Int) Source

divModInt# :: Int# -> Int# -> (# Int#, Int# #) Source

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#)

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)

module GHC.Classes

module GHC.CString

module GHC.Magic

module GHC.Types

module GHC.Prim

module GHC.Err

module GHC.Maybe

© The University of Glasgow and others
Licensed under a BSD-style license (see top of the page).
https://downloads.haskell.org/~ghc/8.8.3/docs/html/libraries/base-4.13.0.0/GHC-Base.html