| Copyright | (c) The University of Glasgow 1992-2002 |
|---|---|
| License | see libraries/base/LICENSE |
| Maintainer | cvs-ghc@haskell.org |
| Stability | internal |
| Portability | non-portable (GHC extensions) |
| Safe Haskell | Unsafe |
| Language | Haskell2010 |
GHC.Base
Description
Basic data types and classes.
Synopsis
- class Applicative m => Monad m where
- class Functor f => Applicative f where
- class Applicative f => Alternative f where
- class Functor f where
- class (Alternative m, Monad m) => MonadPlus m where
- type String = [Char]
- class Semigroup a => Monoid a where
- data NonEmpty a = a :| [a]
- class Semigroup a where
- data Opaque = forall a. O a
- ord :: Char -> Int
- (.) :: (b -> c) -> (a -> b) -> a -> c
- (<**>) :: Applicative f => f a -> f (a -> b) -> f b
- liftA :: Applicative f => (a -> b) -> f a -> f b
- liftA3 :: Applicative f => (a -> b -> c -> d) -> f a -> f b -> f c -> f d
- id :: a -> a
- when :: Applicative f => Bool -> f () -> f ()
- assert :: Bool -> a -> a
- mapM :: Monad m => (a -> m b) -> [a] -> m [b]
- sequence :: Monad m => [m a] -> m [a]
- (=<<) :: Monad m => (a -> m b) -> m a -> m b
- join :: Monad m => m (m a) -> m a
- liftM :: Monad m => (a1 -> r) -> m a1 -> m r
- liftM2 :: Monad m => (a1 -> a2 -> r) -> m a1 -> m a2 -> m r
- liftM3 :: Monad m => (a1 -> a2 -> a3 -> r) -> m a1 -> m a2 -> m a3 -> m r
- liftM4 :: Monad m => (a1 -> a2 -> a3 -> a4 -> r) -> m a1 -> m a2 -> m a3 -> m a4 -> m r
- liftM5 :: Monad m => (a1 -> a2 -> a3 -> a4 -> a5 -> r) -> m a1 -> m a2 -> m a3 -> m a4 -> m a5 -> m r
- ap :: Monad m => m (a -> b) -> m a -> m b
- failIO :: String -> IO a
- ($) :: forall r a (b :: TYPE r). (a -> b) -> a -> b
- otherwise :: Bool
- foldr :: (a -> b -> b) -> b -> [a] -> b
- const :: a -> b -> a
- flip :: (a -> b -> c) -> b -> a -> c
- (++) :: [a] -> [a] -> [a]
- map :: (a -> b) -> [a] -> [b]
- ($!) :: forall r a (b :: TYPE r). (a -> b) -> a -> b
- shiftL# :: Word# -> Int# -> Word#
- shiftRL# :: Word# -> Int# -> Word#
- iShiftL# :: Int# -> Int# -> Int#
- iShiftRA# :: Int# -> Int# -> Int#
- iShiftRL# :: Int# -> Int# -> Int#
- build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
- augment :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a] -> [a]
- breakpoint :: a -> a
- breakpointCond :: Bool -> a -> a
- unIO :: IO a -> State# RealWorld -> (# State# RealWorld, a #)
- until :: (a -> Bool) -> (a -> a) -> a -> a
- asTypeOf :: a -> a -> a
- eqString :: String -> String -> Bool
- returnIO :: a -> IO a
- bindIO :: IO a -> (a -> IO b) -> IO b
- thenIO :: IO a -> IO b -> IO b
- mapFB :: (elt -> lst -> lst) -> (a -> elt) -> a -> lst -> lst
- divInt :: Int -> Int -> Int
- divModInt :: Int -> Int -> (Int, Int)
- getTag :: a -> Int#
- maxInt :: Int
- minInt :: Int
- modInt :: Int -> Int -> Int
- quotInt :: Int -> Int -> Int
- quotRemInt :: Int -> Int -> (Int, Int)
- remInt :: Int -> Int -> Int
- unsafeChr :: Int -> Char
- module GHC.Classes
- module GHC.CString
- module GHC.Magic
- module GHC.Magic.Dict
- module GHC.Types
- module GHC.Prim
- module GHC.Prim.Ext
- module GHC.Prim.PtrEq
- module GHC.Err
- module GHC.Maybe
Documentation
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
returna>>=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 ' can be understood as the >>= bsdo 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 ' can be understood as the >> bsdo expression
do as bs
Inject a value into the monadic type.
Instances
| Monad Complex Source # | Since: base-4.9.0.0 |
| Monad Identity Source # | Since: base-4.8.0.0 |
| Monad First Source # | Since: base-4.8.0.0 |
| Monad Last Source # | Since: base-4.8.0.0 |
| Monad Down Source # | Since: base-4.11.0.0 |
| Monad First Source # | Since: base-4.9.0.0 |
| Monad Last Source # | Since: base-4.9.0.0 |
| Monad Max Source # | Since: base-4.9.0.0 |
| Monad Min Source # | Since: base-4.9.0.0 |
| Monad Dual Source # | Since: base-4.8.0.0 |
| Monad Product Source # | Since: base-4.8.0.0 |
| Monad Sum Source # | Since: base-4.8.0.0 |
| Monad NonEmpty Source # | Since: base-4.9.0.0 |
| Monad STM Source # | Since: base-4.3.0.0 |
| Monad NoIO Source # | Since: base-4.4.0.0 |
| Monad Par1 Source # | Since: base-4.9.0.0 |
| Monad ReadP Source # | Since: base-2.1 |
| Monad ReadPrec Source # | Since: base-2.1 |
| Monad IO Source # | Since: base-2.1 |
| Monad Maybe Source # | Since: base-2.1 |
| Monad Solo Source # | Since: base-4.15 |
| Monad [] Source # | Since: base-2.1 |
| Monad m => Monad (WrappedMonad m) Source # | Since: base-4.7.0.0 |
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 |
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 |
| Monad (Either e) Source # | Since: base-4.4.0.0 |
| Monad (Proxy :: Type -> Type) Source # | Since: base-4.7.0.0 |
| Monad (U1 :: Type -> Type) Source # | Since: base-4.9.0.0 |
| Monad (ST s) Source # | Since: base-2.1 |
| Monoid a => Monad ((,) a) Source # | Since: base-4.9.0.0 |
| Monad m => Monad (Kleisli m a) Source # | Since: base-4.14.0.0 |
| Monad f => Monad (Ap f) Source # | Since: base-4.12.0.0 |
| Monad f => Monad (Alt f) Source # | Since: base-4.8.0.0 |
| Monad f => Monad (Rec1 f) Source # | Since: base-4.9.0.0 |
| (Monoid a, Monoid b) => Monad ((,,) a b) Source # | Since: base-4.14.0.0 |
| (Monad f, Monad g) => Monad (Product f g) Source # | Since: base-4.9.0.0 |
| (Monad f, Monad g) => Monad (f :*: g) Source # | Since: base-4.9.0.0 |
| (Monoid a, Monoid b, Monoid c) => Monad ((,,,) a b c) Source # | Since: base-4.14.0.0 |
| Monad ((->) r) Source # | Since: base-2.1 |
| Monad f => Monad (M1 i c f) Source # | Since: base-4.9.0.0 |
class Functor f => Applicative f where Source #
A functor with application, providing operations to
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:
(<*>) =liftA2id
liftA2f x y = f<$>x<*>y
Further, any definition must satisfy the following:
- Identity
pureid<*>v = v- Composition
pure(.)<*>u<*>v<*>w = u<*>(v<*>w)- Homomorphism
puref<*>purex =pure(f x)- Interchange
u
<*>purey =pure($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
liftA2p (liftA2q u v) =liftA2f u .liftA2g v
If f is also a Monad, it should satisfy
(which implies that pure and <*> satisfy the applicative functor laws).
Methods
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
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
>>>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
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 3Just 3
>>>Nothing *> Just 3Nothing
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
| Applicative ZipList Source # | f <$> ZipList xs1 <*> ... <*> ZipList xsN
= ZipList (zipWithN f xs1 ... xsN)where (\a b c -> stimes c [a, b]) <$> ZipList "abcd" <*> ZipList "567" <*> ZipList [1..]
= ZipList (zipWith3 (\a b c -> stimes c [a, b]) "abcd" "567" [1..])
= ZipList {getZipList = ["a5","b6b6","c7c7c7"]}Since: base-2.1 |
Defined in Control.Applicative | |
| Applicative Complex Source # | Since: base-4.9.0.0 |
| Applicative Identity Source # | Since: base-4.8.0.0 |
Defined in Data.Functor.Identity | |
| Applicative First Source # | Since: base-4.8.0.0 |
| Applicative Last Source # | Since: base-4.8.0.0 |
| Applicative Down Source # | Since: base-4.11.0.0 |
| Applicative First Source # | Since: base-4.9.0.0 |
| Applicative Last Source # | Since: base-4.9.0.0 |
| Applicative Max Source # | Since: base-4.9.0.0 |
| Applicative Min Source # | Since: base-4.9.0.0 |
| Applicative Dual Source # | Since: base-4.8.0.0 |
| Applicative Product Source # | Since: base-4.8.0.0 |
Defined in Data.Semigroup.Internal | |
| Applicative Sum Source # | Since: base-4.8.0.0 |
| Applicative NonEmpty Source # | Since: base-4.9.0.0 |
Defined in GHC.Base | |
| Applicative STM Source # | Since: base-4.8.0.0 |
| Applicative NoIO Source # | Since: base-4.8.0.0 |
| Applicative Par1 Source # | Since: base-4.9.0.0 |
| Applicative ReadP Source # | Since: base-4.6.0.0 |
| Applicative ReadPrec Source # | Since: base-4.6.0.0 |
Defined in Text.ParserCombinators.ReadPrec | |
| Applicative IO Source # | Since: base-2.1 |
| Applicative Maybe Source # | Since: base-2.1 |
| Applicative Solo Source # | Since: base-4.15 |
| Applicative [] Source # | Since: base-2.1 |
| Monad m => Applicative (WrappedMonad m) Source # | Since: base-2.1 |
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 |
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 |
| Applicative (Either e) Source # | Since: base-3.0 |
Defined in Data.Either | |
| Applicative (Proxy :: Type -> Type) Source # | Since: base-4.7.0.0 |
| Applicative (U1 :: Type -> Type) Source # | Since: base-4.9.0.0 |
| Applicative (ST s) Source # | Since: base-4.4.0.0 |
| Monoid a => Applicative ((,) a) Source # | For tuples, the ("hello ", (+15)) <*> ("world!", 2002)
("hello world!",2017)Since: base-2.1 |
| Arrow a => Applicative (WrappedArrow a b) Source # | Since: base-2.1 |
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 |
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 |
Defined in Data.Functor.Const | |
| Applicative f => Applicative (Ap f) Source # | Since: base-4.12.0.0 |
| Applicative f => Applicative (Alt f) Source # | Since: base-4.8.0.0 |
| (Generic1 f, Applicative (Rep1 f)) => Applicative (Generically1 f) Source # | Since: base-4.17.0.0 |
Defined in GHC.Generics Methods pure :: a -> Generically1 f a Source # (<*>) :: Generically1 f (a -> b) -> Generically1 f a -> Generically1 f b Source # liftA2 :: (a -> b -> c) -> Generically1 f a -> Generically1 f b -> Generically1 f c Source # (*>) :: Generically1 f a -> Generically1 f b -> Generically1 f b Source # (<*) :: Generically1 f a -> Generically1 f b -> Generically1 f a Source # | |
| Applicative f => Applicative (Rec1 f) Source # | Since: base-4.9.0.0 |
| (Monoid a, Monoid b) => Applicative ((,,) a b) Source # | Since: base-4.14.0.0 |
Defined in GHC.Base | |
| (Applicative f, Applicative g) => Applicative (Product f g) Source # | Since: base-4.9.0.0 |
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 |
Defined in GHC.Generics | |
| Monoid c => Applicative (K1 i c :: Type -> Type) Source # | Since: base-4.12.0.0 |
| (Monoid a, Monoid b, Monoid c) => Applicative ((,,,) a b c) Source # | Since: base-4.14.0.0 |
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 |
| (Applicative f, Applicative g) => Applicative (Compose f g) Source # | Since: base-4.9.0.0 |
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 |
Defined in GHC.Generics | |
| Applicative f => Applicative (M1 i c f) Source # | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
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:
Methods
The identity of <|>
(<|>) :: f a -> f a -> f a infixl 3 Source #
An associative binary operation
One or more.
Zero or more.
Instances
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:
Note, that the second law follows from the free theorem of the type fmap and
the first law, so you need only check that the former condition holds.
See https://www.schoolofhaskell.com/user/edwardk/snippets/fmap or
https://github.com/quchen/articles/blob/master/second_functor_law.md
for an explanation.
Minimal complete definition
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
Examples
Convert from a Maybe IntMaybe String
using show:
>>>fmap show NothingNothing>>>fmap show (Just 3)Just "3"
Convert from an Either Int IntEither 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)
Instances
| Functor ZipList Source # | Since: base-2.1 |
| Functor Handler Source # | Since: base-4.6.0.0 |
| Functor Complex Source # | Since: base-4.9.0.0 |
| Functor Identity Source # | Since: base-4.8.0.0 |
| Functor First Source # | Since: base-4.8.0.0 |
| Functor Last Source # | Since: base-4.8.0.0 |
| Functor Down Source # | Since: base-4.11.0.0 |
| Functor First Source # | Since: base-4.9.0.0 |
| Functor Last Source # | Since: base-4.9.0.0 |
| Functor Max Source # | Since: base-4.9.0.0 |
| Functor Min Source # | Since: base-4.9.0.0 |
| Functor Dual Source # | Since: base-4.8.0.0 |
| Functor Product Source # | Since: base-4.8.0.0 |
| Functor Sum Source # | Since: base-4.8.0.0 |
| Functor NonEmpty Source # | Since: base-4.9.0.0 |
| Functor STM Source # | Since: base-4.3.0.0 |
| Functor NoIO Source # | Since: base-4.8.0.0 |
| Functor Par1 Source # | Since: base-4.9.0.0 |
| Functor ArgDescr Source # | Since: base-4.7.0.0 |
| Functor ArgOrder Source # | Since: base-4.7.0.0 |
| Functor OptDescr Source # | Since: base-4.7.0.0 |
| Functor ReadP Source # | Since: base-2.1 |
| Functor ReadPrec Source # | Since: base-2.1 |
| Functor IO Source # | Since: base-2.1 |
| Functor Maybe Source # | Since: base-2.1 |
| Functor Solo Source # | Since: base-4.15 |
| Functor [] Source # | Since: base-2.1 |
| Monad m => Functor (WrappedMonad m) Source # | Since: base-2.1 |
Defined in Control.Applicative Methods fmap :: (a -> b) -> WrappedMonad m a -> WrappedMonad m b Source # (<$) :: a -> WrappedMonad m b -> WrappedMonad m a Source # | |
| Arrow a => Functor (ArrowMonad a) Source # | Since: base-4.6.0.0 |
Defined in Control.Arrow Methods fmap :: (a0 -> b) -> ArrowMonad a a0 -> ArrowMonad a b Source # (<$) :: a0 -> ArrowMonad a b -> ArrowMonad a a0 Source # | |
| Functor (ST s) Source # | Since: base-2.1 |
| Functor (Either a) Source # | Since: base-3.0 |
| Functor (Proxy :: Type -> Type) Source # | Since: base-4.7.0.0 |
| Functor (Arg a) Source # | Since: base-4.9.0.0 |
| Functor (Array i) Source # | Since: base-2.1 |
| Functor (U1 :: Type -> Type) Source # | Since: base-4.9.0.0 |
| Functor (V1 :: TYPE LiftedRep -> Type) Source # | Since: base-4.9.0.0 |
| Functor (ST s) Source # | Since: base-2.1 |
| Functor ((,) a) Source # | Since: base-2.1 |
| Arrow a => Functor (WrappedArrow a b) Source # | Since: base-2.1 |
Defined in Control.Applicative Methods fmap :: (a0 -> b0) -> WrappedArrow a b a0 -> WrappedArrow a b b0 Source # (<$) :: a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0 Source # | |
| Functor m => Functor (Kleisli m a) Source # | Since: base-4.14.0.0 |
| Functor (Const m :: Type -> Type) Source # | Since: base-2.1 |
| Functor f => Functor (Ap f) Source # | Since: base-4.12.0.0 |
| Functor f => Functor (Alt f) Source # | Since: base-4.8.0.0 |
| (Generic1 f, Functor (Rep1 f)) => Functor (Generically1 f) Source # | Since: base-4.17.0.0 |
Defined in GHC.Generics Methods fmap :: (a -> b) -> Generically1 f a -> Generically1 f b Source # (<$) :: a -> Generically1 f b -> Generically1 f a Source # | |
| Functor f => Functor (Rec1 f) Source # | Since: base-4.9.0.0 |
| Functor (URec (Ptr ()) :: TYPE LiftedRep -> Type) Source # | Since: base-4.9.0.0 |
| Functor (URec Char :: TYPE LiftedRep -> Type) Source # | Since: base-4.9.0.0 |
| Functor (URec Double :: TYPE LiftedRep -> Type) Source # | Since: base-4.9.0.0 |
| Functor (URec Float :: TYPE LiftedRep -> Type) Source # | Since: base-4.9.0.0 |
| Functor (URec Int :: TYPE LiftedRep -> Type) Source # | Since: base-4.9.0.0 |
| Functor (URec Word :: TYPE LiftedRep -> Type) Source # | Since: base-4.9.0.0 |
| Functor ((,,) a b) Source # | Since: base-4.14.0.0 |
| (Functor f, Functor g) => Functor (Product f g) Source # | Since: base-4.9.0.0 |
| (Functor f, Functor g) => Functor (Sum f g) Source # | Since: base-4.9.0.0 |
| (Functor f, Functor g) => Functor (f :*: g) Source # | Since: base-4.9.0.0 |
| (Functor f, Functor g) => Functor (f :+: g) Source # | Since: base-4.9.0.0 |
| Functor (K1 i c :: TYPE LiftedRep -> Type) Source # | Since: base-4.9.0.0 |
| Functor ((,,,) a b c) Source # | Since: base-4.14.0.0 |
| Functor ((->) r) Source # | Since: base-2.1 |
| (Functor f, Functor g) => Functor (Compose f g) Source # | Since: base-4.9.0.0 |
| (Functor f, Functor g) => Functor (f :.: g) Source # | Since: base-4.9.0.0 |
| Functor f => Functor (M1 i c f) Source # | Since: base-4.9.0.0 |
class (Alternative m, Monad m) => MonadPlus m where Source #
Monads that also support choice and failure.
Minimal complete definition
Nothing
Methods
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
| MonadPlus STM Source # | Since: base-4.3.0.0 |
| MonadPlus ReadP Source # | Since: base-2.1 |
| MonadPlus ReadPrec Source # | Since: base-2.1 |
| MonadPlus IO Source # | Since: base-4.9.0.0 |
| MonadPlus Maybe Source # | Since: base-2.1 |
| MonadPlus [] Source # | Since: base-2.1 |
| (ArrowApply a, ArrowPlus a) => MonadPlus (ArrowMonad a) Source # | Since: base-4.6.0.0 |
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 |
| MonadPlus (U1 :: Type -> Type) Source # | Since: base-4.9.0.0 |
| MonadPlus m => MonadPlus (Kleisli m a) Source # | Since: base-4.14.0.0 |
| MonadPlus f => MonadPlus (Ap f) Source # | Since: base-4.12.0.0 |
| MonadPlus f => MonadPlus (Alt f) Source # | Since: base-4.8.0.0 |
| MonadPlus f => MonadPlus (Rec1 f) Source # | Since: base-4.9.0.0 |
| (MonadPlus f, MonadPlus g) => MonadPlus (Product f g) Source # | Since: base-4.9.0.0 |
| (MonadPlus f, MonadPlus g) => MonadPlus (f :*: g) Source # | Since: base-4.9.0.0 |
| MonadPlus f => MonadPlus (M1 i c f) Source # | Since: base-4.9.0.0 |
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)<>zSemigrouplaw)- 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
Methods
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 = (<>)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.
Fold a list using the monoid.
For most types, the default definition for mconcat will be
used, but the function is included in the class definition so
that an optimized version can be provided for specific types.
>>>mconcat ["Hello", " ", "Haskell", "!"]"Hello Haskell!"
Instances
| Monoid ByteArray Source # | |
| Monoid All Source # | Since: base-2.1 |
| Monoid Any Source # | Since: base-2.1 |
| Monoid Event Source # | Since: base-4.4.0.0 |
| Monoid Lifetime Source # |
Since: base-4.8.0.0 |
| Monoid Ordering Source # | Since: base-2.1 |
| Monoid () Source # | Since: base-2.1 |
| FiniteBits a => Monoid (And a) Source # | This constraint is arguably too strong. However,
as some types (such as Since: base-4.16 |
| FiniteBits a => Monoid (Iff a) Source # | This constraint is arguably
too strong. However, as some types (such as Since: base-4.16 |
| Bits a => Monoid (Ior a) Source # | Since: base-4.16 |
| Bits a => Monoid (Xor a) Source # | Since: base-4.16 |
| Monoid (Comparison a) Source # |
mempty :: Comparison a mempty = Comparison _ _ -> EQ |
Defined in Data.Functor.Contravariant Methods mempty :: Comparison a Source # mappend :: Comparison a -> Comparison a -> Comparison a Source # mconcat :: [Comparison a] -> Comparison a Source # | |
| Monoid (Equivalence a) Source # |
mempty :: Equivalence a mempty = Equivalence _ _ -> True |
Defined in Data.Functor.Contravariant Methods mempty :: Equivalence a Source # mappend :: Equivalence a -> Equivalence a -> Equivalence a Source # mconcat :: [Equivalence a] -> Equivalence a Source # | |
| Monoid (Predicate a) Source # |
mempty :: Predicate a mempty = _ -> True |
| Monoid a => Monoid (Identity a) Source # | Since: base-4.9.0.0 |
| Monoid (First a) Source # | Since: base-2.1 |
| Monoid (Last a) Source # | Since: base-2.1 |
| Monoid a => Monoid (Down a) Source # | Since: base-4.11.0.0 |
| (Ord a, Bounded a) => Monoid (Max a) Source # | Since: base-4.9.0.0 |
| (Ord a, Bounded a) => Monoid (Min a) Source # | Since: base-4.9.0.0 |
| Monoid m => Monoid (WrappedMonoid m) Source # | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods mempty :: WrappedMonoid m Source # mappend :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m Source # mconcat :: [WrappedMonoid m] -> WrappedMonoid m Source # | |
| Monoid a => Monoid (Dual a) Source # | Since: base-2.1 |
| Monoid (Endo a) Source # | Since: base-2.1 |
| Num a => Monoid (Product a) Source # | Since: base-2.1 |
| Num a => Monoid (Sum a) Source # | Since: base-2.1 |
| (Semigroup a, Generic a, Monoid (Rep a ())) => Monoid (Generically a) Source # | Since: base-4.17.0.0 |
Defined in GHC.Generics Methods mempty :: Generically a Source # mappend :: Generically a -> Generically a -> Generically a Source # mconcat :: [Generically a] -> Generically a Source # | |
| Monoid p => Monoid (Par1 p) Source # | Since: base-4.12.0.0 |
| Monoid a => Monoid (IO a) Source # | Since: base-4.9.0.0 |
| Semigroup a => Monoid (Maybe a) Source # | Lift a semigroup into Since 4.11.0: constraint on inner Since: base-2.1 |
| Monoid a => Monoid (a) Source # | Since: base-4.15 |
| Monoid [a] Source # | Since: base-2.1 |
| Monoid a => Monoid (Op a b) Source # |
mempty :: Op a b mempty = Op _ -> mempty |
| Monoid (Proxy s) Source # | Since: base-4.7.0.0 |
| Monoid (U1 p) Source # | Since: base-4.12.0.0 |
| Monoid a => Monoid (ST s a) Source # | Since: base-4.11.0.0 |
| Monoid b => Monoid (a -> b) Source # | Since: base-2.1 |
| (Monoid a, Monoid b) => Monoid (a, b) Source # | Since: base-2.1 |
| Monoid a => Monoid (Const a b) Source # | Since: base-4.9.0.0 |
| (Applicative f, Monoid a) => Monoid (Ap f a) Source # | Since: base-4.12.0.0 |
| Alternative f => Monoid (Alt f a) Source # | Since: base-4.8.0.0 |
| Monoid (f p) => Monoid (Rec1 f p) Source # | Since: base-4.12.0.0 |
| (Monoid a, Monoid b, Monoid c) => Monoid (a, b, c) Source # | Since: base-2.1 |
| (Monoid (f a), Monoid (g a)) => Monoid (Product f g a) Source # | Since: base-4.16.0.0 |
| (Monoid (f p), Monoid (g p)) => Monoid ((f :*: g) p) Source # | Since: base-4.12.0.0 |
| Monoid c => Monoid (K1 i c p) Source # | Since: base-4.12.0.0 |
| (Monoid a, Monoid b, Monoid c, Monoid d) => Monoid (a, b, c, d) Source # | Since: base-2.1 |
| Monoid (f (g a)) => Monoid (Compose f g a) Source # | Since: base-4.16.0.0 |
| Monoid (f (g p)) => Monoid ((f :.: g) p) Source # | Since: base-4.12.0.0 |
| Monoid (f p) => Monoid (M1 i c f p) Source # | Since: base-4.12.0.0 |
| (Monoid a, Monoid b, Monoid c, Monoid d, Monoid e) => Monoid (a, b, c, d, e) Source # | Since: base-2.1 |
Non-empty (and non-strict) list type.
Since: base-4.9.0.0
Constructors
| a :| [a] infixr 5 |
Instances
| MonadFix NonEmpty Source # | Since: base-4.9.0.0 |
| MonadZip NonEmpty Source # | Since: base-4.9.0.0 |
| Foldable NonEmpty Source # | Since: base-4.9.0.0 |
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 # | |
| Eq1 NonEmpty Source # | Since: base-4.10.0.0 |
| Ord1 NonEmpty Source # | Since: base-4.10.0.0 |
Defined in Data.Functor.Classes | |
| Read1 NonEmpty Source # | Since: base-4.10.0.0 |
Defined in Data.Functor.Classes Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (NonEmpty a) Source # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [NonEmpty a] Source # liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (NonEmpty a) Source # liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [NonEmpty a] Source # | |
| Show1 NonEmpty Source # | Since: base-4.10.0.0 |
| Traversable NonEmpty Source # | Since: base-4.9.0.0 |
Defined in Data.Traversable | |
| Applicative NonEmpty Source # | Since: base-4.9.0.0 |
Defined in GHC.Base | |
| Functor NonEmpty Source # | Since: base-4.9.0.0 |
| Monad NonEmpty Source # | Since: base-4.9.0.0 |
| Data a => Data (NonEmpty a) Source # | Since: base-4.9.0.0 |
Defined in Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> NonEmpty a -> c (NonEmpty a) 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 |
| IsList (NonEmpty a) Source # | Since: base-4.9.0.0 |
| Generic (NonEmpty a) Source # | |
| Read a => Read (NonEmpty a) Source # | Since: base-4.11.0.0 |
| Show a => Show (NonEmpty a) Source # | Since: base-4.11.0.0 |
| Eq a => Eq (NonEmpty a) Source # | Since: base-4.9.0.0 |
| Ord a => Ord (NonEmpty a) Source # | Since: base-4.9.0.0 |
Defined in GHC.Base Methods compare :: NonEmpty a -> NonEmpty a -> Ordering Source # (<) :: NonEmpty a -> NonEmpty a -> Bool Source # (<=) :: NonEmpty a -> NonEmpty a -> Bool Source # (>) :: NonEmpty a -> NonEmpty a -> Bool Source # (>=) :: NonEmpty a -> NonEmpty a -> Bool Source # | |
| Generic1 NonEmpty Source # | |
| type Item (NonEmpty a) Source # | |
| type Rep (NonEmpty a) Source # | Since: base-4.6.0.0 |
Defined in GHC.Generics type Rep (NonEmpty a) = D1 ('MetaData "NonEmpty" "GHC.Base" "base" 'False) (C1 ('MetaCons ":|" ('InfixI 'LeftAssociative 9) 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 [a]))) | |
| type Rep1 NonEmpty Source # | Since: base-4.6.0.0 |
Defined in GHC.Generics type Rep1 NonEmpty = D1 ('MetaData "NonEmpty" "GHC.Base" "base" 'False) (C1 ('MetaCons ":|" ('InfixI 'LeftAssociative 9) 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1 :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 []))) | |
class Semigroup a where Source #
The class of semigroups (types with an associative binary operation).
Instances should satisfy the following:
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 = or stimesIdempotentstimes =
respectively.stimesIdempotentMonoid
>>>stimes 4 [1][1,1,1,1]
Instances
| Semigroup ByteArray Source # | |
| Semigroup All Source # | Since: base-4.9.0.0 |
| Semigroup Any Source # | Since: base-4.9.0.0 |
| Semigroup Void Source # | Since: base-4.9.0.0 |
| Semigroup Event Source # | Since: base-4.10.0.0 |
| Semigroup Lifetime Source # | Since: base-4.10.0.0 |
| Semigroup Ordering Source # | Since: base-4.9.0.0 |
| Semigroup () Source # | Since: base-4.9.0.0 |
| Bits a => Semigroup (And a) Source # | Since: base-4.16 |
| FiniteBits a => Semigroup (Iff a) Source # | This constraint is arguably
too strong. However, as some types (such as Since: base-4.16 |
| Bits a => Semigroup (Ior a) Source # | Since: base-4.16 |
| Bits a => Semigroup (Xor a) Source # | Since: base-4.16 |
| Semigroup (Comparison a) Source # |
(<>) :: Comparison a -> Comparison a -> Comparison a Comparison cmp <> Comparison cmp' = Comparison a a' -> cmp a a' <> cmp a a' |
Defined in Data.Functor.Contravariant Methods (<>) :: Comparison a -> Comparison a -> Comparison a Source # sconcat :: NonEmpty (Comparison a) -> Comparison a Source # stimes :: Integral b => b -> Comparison a -> Comparison a Source # | |
| Semigroup (Equivalence a) Source # |
(<>) :: Equivalence a -> Equivalence a -> Equivalence a Equivalence equiv <> Equivalence equiv' = Equivalence a b -> equiv a b && equiv a b |
Defined in Data.Functor.Contravariant Methods (<>) :: Equivalence a -> Equivalence a -> Equivalence a Source # sconcat :: NonEmpty (Equivalence a) -> Equivalence a Source # stimes :: Integral b => b -> Equivalence a -> Equivalence a Source # | |
| Semigroup (Predicate a) Source # |
(<>) :: Predicate a -> Predicate a -> Predicate a Predicate pred <> Predicate pred' = Predicate a -> pred a && pred' a |
| Semigroup a => Semigroup (Identity a) Source # | Since: base-4.9.0.0 |
| Semigroup (First a) Source # | Since: base-4.9.0.0 |
| Semigroup (Last a) Source # | Since: base-4.9.0.0 |
| Semigroup a => Semigroup (Down a) Source # | Since: base-4.11.0.0 |
| Semigroup (First a) Source # | Since: base-4.9.0.0 |
| Semigroup (Last a) Source # | Since: base-4.9.0.0 |
| Ord a => Semigroup (Max a) Source # | Since: base-4.9.0.0 |
| Ord a => Semigroup (Min a) Source # | Since: base-4.9.0.0 |
| Monoid m => Semigroup (WrappedMonoid m) Source # | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods (<>) :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m Source # sconcat :: NonEmpty (WrappedMonoid m) -> WrappedMonoid m Source # stimes :: Integral b => b -> WrappedMonoid m -> WrappedMonoid m Source # | |
| Semigroup a => Semigroup (Dual a) Source # | Since: base-4.9.0.0 |
| Semigroup (Endo a) Source # | Since: base-4.9.0.0 |
| Num a => Semigroup (Product a) Source # | Since: base-4.9.0.0 |
| Num a => Semigroup (Sum a) Source # | Since: base-4.9.0.0 |
| Semigroup (NonEmpty a) Source # | Since: base-4.9.0.0 |
| (Generic a, Semigroup (Rep a ())) => Semigroup (Generically a) Source # | Since: base-4.17.0.0 |
Defined in GHC.Generics Methods (<>) :: Generically a -> Generically a -> Generically a Source # sconcat :: NonEmpty (Generically a) -> Generically a Source # stimes :: Integral b => b -> Generically a -> Generically a Source # | |
| Semigroup p => Semigroup (Par1 p) Source # | Since: base-4.12.0.0 |
| Semigroup a => Semigroup (IO a) Source # | Since: base-4.10.0.0 |
| Semigroup a => Semigroup (Maybe a) Source # | Since: base-4.9.0.0 |
| Semigroup a => Semigroup (a) Source # | Since: base-4.15 |
| Semigroup [a] Source # | Since: base-4.9.0.0 |
| Semigroup (Either a b) Source # | Since: base-4.9.0.0 |
| Semigroup a => Semigroup (Op a b) Source # |
(<>) :: Op a b -> Op a b -> Op a b Op f <> Op g = Op a -> f a <> g a |
| Semigroup (Proxy s) Source # | Since: base-4.9.0.0 |
| Semigroup (U1 p) Source # | Since: base-4.12.0.0 |
| Semigroup (V1 p) Source # | Since: base-4.12.0.0 |
| Semigroup a => Semigroup (ST s a) Source # | Since: base-4.11.0.0 |
| Semigroup b => Semigroup (a -> b) Source # | Since: base-4.9.0.0 |
| (Semigroup a, Semigroup b) => Semigroup (a, b) Source # | Since: base-4.9.0.0 |
| Semigroup a => Semigroup (Const a b) Source # | Since: base-4.9.0.0 |
| (Applicative f, Semigroup a) => Semigroup (Ap f a) Source # | Since: base-4.12.0.0 |
| Alternative f => Semigroup (Alt f a) Source # | Since: base-4.9.0.0 |
| Semigroup (f p) => Semigroup (Rec1 f p) Source # | Since: base-4.12.0.0 |
| (Semigroup a, Semigroup b, Semigroup c) => Semigroup (a, b, c) Source # | Since: base-4.9.0.0 |
| (Semigroup (f a), Semigroup (g a)) => Semigroup (Product f g a) Source # | Since: base-4.16.0.0 |
| (Semigroup (f p), Semigroup (g p)) => Semigroup ((f :*: g) p) Source # | Since: base-4.12.0.0 |
| Semigroup c => Semigroup (K1 i c p) Source # | Since: base-4.12.0.0 |
| (Semigroup a, Semigroup b, Semigroup c, Semigroup d) => Semigroup (a, b, c, d) Source # | Since: base-4.9.0.0 |
| Semigroup (f (g a)) => Semigroup (Compose f g a) Source # | Since: base-4.16.0.0 |
| Semigroup (f (g p)) => Semigroup ((f :.: g) p) Source # | Since: base-4.12.0.0 |
| Semigroup (f p) => Semigroup (M1 i c f p) Source # | Since: base-4.12.0.0 |
| (Semigroup a, Semigroup b, Semigroup c, Semigroup d, Semigroup e) => Semigroup (a, b, c, d, e) Source # | Since: base-4.9.0.0 |
(<**>) :: 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.
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.
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.
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.
sequence :: Monad m => [m a] -> m [a] Source #
Evaluate each action in the sequence from left to right, and collect the results.
(=<<) :: Monad m => (a -> m b) -> m a -> m b infixr 1 Source #
Same as >>=, but with the arguments interchanged.
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 bssdo expression
do bs <- bss bs
Examples
A common use of join is to run an IO computation returned from
an STM transaction, since STM transactions
can't perform IO directly. Recall that
atomically :: STM a -> IO a
is used to run STM transactions atomically. So, by
specializing the types of atomically and join to
atomically:: STM (IO b) -> IO (IO b)join:: IO (IO b) -> IO b
we can compose them as
join.atomically:: STM (IO b) -> IO b
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).
($) :: 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 . However, $ x)$ 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) xszipWith ($) fs xs
Note that ( is representation-polymorphic in its result type, so that
$)foo where $ Truefoo :: Bool -> Int# is well-typed.
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)...)
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]
flip :: (a -> b -> c) -> b -> a -> c Source #
flip ff.
>>>flip (++) "hello" "world""worldhello"
(++) :: [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.
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 #
Strict (call-by-value) application operator. It takes a function and an argument, evaluates the argument to weak head normal form (WHNF), then calls the function with that value.
shiftL# :: Word# -> Int# -> Word# 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)
breakpoint :: a -> a Source #
breakpointCond :: Bool -> a -> a Source #
until :: (a -> Bool) -> (a -> a) -> a -> a Source #
until p ff until p holds.
eqString :: String -> String -> Bool Source #
This String equality predicate is used when desugaring
pattern-matches against strings.
Returns the tag of a constructor application; this function is used by the deriving code for Eq, Ord and Enum.
module GHC.Classes
module GHC.CString
module GHC.Magic
module GHC.Magic.Dict
module GHC.Types
module GHC.Prim
module GHC.Prim.Ext
module GHC.Prim.PtrEq
module GHC.Err
module GHC.Maybe