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
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
\(\mathcal{O}(n)\). 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]
($) :: forall r a (b :: TYPE r). (a -> b) -> a -> b infixr 0 Source
Application operator. This operator is redundant, since ordinary application (f x) means the same as (f $ x). However, $ has low, right-associative binding precedence, so it sometimes allows parentheses to be omitted; for example:
f $ g $ h x = f (g (h x))
It is also useful in higher-order situations, such as map ($ 0) xs, or zipWith ($) fs xs.
Note that ($) is levity-polymorphic in its result type, so that foo $ True where foo :: Bool -> Int# is well-typed.
join :: Monad m => m (m a) -> m a Source
The join function is the conventional monad join operator. It is used to remove one level of monadic structure, projecting its bound argument into the outer level.
'join bss' can be understood as the do expression
do bs <- bss bs
Examples
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
class Applicative m => Monad m where Source
The Monad class defines the basic operations over a monad, a concept from a branch of mathematics known as category theory. From the perspective of a Haskell programmer, however, it is best to think of a monad as an abstract datatype of actions. Haskell's do expressions provide a convenient syntax for writing monadic expressions.
Instances of Monad should satisfy the following:
- Left identity
return a >>= k = k a- Right identity
m >>= return = m- Associativity
m >>= (\x -> k x >>= h) = (m >>= k) >>= h
Furthermore, the Monad and Applicative operations should relate as follows:
The above laws imply:
and that pure and (<*>) satisfy the applicative functor laws.
The instances of Monad for lists, Maybe and IO defined in the Prelude satisfy these laws.
Minimal complete definition
Methods
(>>=) :: forall a b. m a -> (a -> m b) -> m b infixl 1 Source
Sequentially compose two actions, passing any value produced by the first as an argument to the second.
'as >>= bs' can be understood as the do expression
do a <- as bs a
(>>) :: forall a b. m a -> m b -> m b infixl 1 Source
Sequentially compose two actions, discarding any value produced by the first, like sequencing operators (such as the semicolon) in imperative languages.
'as >> bs' can be understood as the do expression
do as bs
Inject a value into the monadic type.
Instances
| Monad [] | Since: base-2.1 |
| Monad Maybe | Since: base-2.1 |
| Monad IO | Since: base-2.1 |
| Monad Par1 | Since: base-4.9.0.0 |
| Monad NonEmpty | Since: base-4.9.0.0 |
| Monad NoIO | Since: base-4.4.0.0 |
| Monad ReadP | Since: base-2.1 |
| Monad ReadPrec | Since: base-2.1 |
| Monad Down | Since: base-4.11.0.0 |
| Monad Product | Since: base-4.8.0.0 |
| Monad Sum | Since: base-4.8.0.0 |
| Monad Dual | Since: base-4.8.0.0 |
| Monad Last | Since: base-4.8.0.0 |
| Monad First | Since: base-4.8.0.0 |
| Monad STM | Since: base-4.3.0.0 |
| Monad Identity | Since: base-4.8.0.0 |
| Monad Option | Since: base-4.9.0.0 |
| Monad Last | Since: base-4.9.0.0 |
| Monad First | Since: base-4.9.0.0 |
| Monad Max | Since: base-4.9.0.0 |
| Monad Min | Since: base-4.9.0.0 |
| Monad Complex | Since: base-4.9.0.0 |
| Monad (Either e) | Since: base-4.4.0.0 |
| Monad (U1 :: Type -> Type) | Since: base-4.9.0.0 |
| Monoid a => Monad ((,) a) | Since: base-4.9.0.0 |
| Monad (ST s) | Since: base-2.1 |
| Monad (Proxy :: Type -> Type) | Since: base-4.7.0.0 |
| ArrowApply a => Monad (ArrowMonad a) | 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 m => Monad (WrappedMonad m) | Since: base-4.7.0.0 |
Defined in Control.Applicative Methods(>>=) :: WrappedMonad m a -> (a -> WrappedMonad m b) -> WrappedMonad m b Source (>>) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m b Source return :: a -> WrappedMonad m a Source | |
| Monad (ST s) | Since: base-2.1 |
| Monad f => Monad (Rec1 f) | Since: base-4.9.0.0 |
| (Monoid a, Monoid b) => Monad ((,,) a b) | Since: base-4.14.0.0 |
| Monad f => Monad (Alt f) | Since: base-4.8.0.0 |
| Monad f => Monad (Ap f) | Since: base-4.12.0.0 |
| Monad m => Monad (Kleisli m a) | Since: base-4.14.0.0 |
| Monad ((->) r :: Type -> Type) | Since: base-2.1 |
| (Monad f, Monad g) => Monad (f :*: g) | Since: base-4.9.0.0 |
| (Monoid a, Monoid b, Monoid c) => Monad ((,,,) a b c) | Since: base-4.14.0.0 |
| (Monad f, Monad g) => Monad (Product f g) | Since: base-4.9.0.0 |
| Monad f => Monad (M1 i c f) | Since: base-4.9.0.0 |
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.
Minimal complete definition
Methods
fmap :: (a -> b) -> f a -> f b Source
Using ApplicativeDo: 'fmap f as' can be understood as the do expression
do a <- as pure (f a)
with an inferred Functor constraint.
(<$) :: a -> f b -> f a infixl 4 Source
Replace all locations in the input with the same value. The default definition is fmap . const, but this may be overridden with a more efficient version.
Using ApplicativeDo: 'a <$ bs' can be understood as the do expression
do bs pure a
with an inferred Functor constraint.
Instances
| Functor [] | Since: base-2.1 |
| Functor Maybe | Since: base-2.1 |
| Functor IO | Since: base-2.1 |
| Functor Par1 | Since: base-4.9.0.0 |
| Functor NonEmpty | Since: base-4.9.0.0 |
| Functor NoIO | Since: base-4.8.0.0 |
| Functor ReadP | Since: base-2.1 |
| Functor ReadPrec | Since: base-2.1 |
| Functor Down | Since: base-4.11.0.0 |
| Functor Product | Since: base-4.8.0.0 |
| Functor Sum | Since: base-4.8.0.0 |
| Functor Dual | Since: base-4.8.0.0 |
| Functor Last | Since: base-4.8.0.0 |
| Functor First | Since: base-4.8.0.0 |
| Functor STM | Since: base-4.3.0.0 |
| Functor Handler | Since: base-4.6.0.0 |
| Functor Identity | Since: base-4.8.0.0 |
| Functor ZipList | Since: base-2.1 |
| Functor ArgDescr | Since: base-4.6.0.0 |
| Functor OptDescr | Since: base-4.6.0.0 |
| Functor ArgOrder | Since: base-4.6.0.0 |
| Functor Option | Since: base-4.9.0.0 |
| Functor Last | Since: base-4.9.0.0 |
| Functor First | Since: base-4.9.0.0 |
| Functor Max | Since: base-4.9.0.0 |
| Functor Min | Since: base-4.9.0.0 |
| Functor Complex | Since: base-4.9.0.0 |
| Functor (Either a) | Since: base-3.0 |
| Functor (V1 :: Type -> Type) | Since: base-4.9.0.0 |
| Functor (U1 :: Type -> Type) | Since: base-4.9.0.0 |
| Functor ((,) a) | Since: base-2.1 |
| Functor (ST s) | Since: base-2.1 |
| Functor (Array i) | Since: base-2.1 |
| Functor (Proxy :: Type -> Type) | Since: base-4.7.0.0 |
| Arrow a => Functor (ArrowMonad a) | Since: base-4.6.0.0 |
Defined in Control.Arrow Methodsfmap :: (a0 -> b) -> ArrowMonad a a0 -> ArrowMonad a b Source (<$) :: a0 -> ArrowMonad a b -> ArrowMonad a a0 Source | |
| Monad m => Functor (WrappedMonad m) | Since: base-2.1 |
Defined in Control.Applicative Methodsfmap :: (a -> b) -> WrappedMonad m a -> WrappedMonad m b Source (<$) :: a -> WrappedMonad m b -> WrappedMonad m a Source | |
| Functor (ST s) | Since: base-2.1 |
| Functor (Arg a) | Since: base-4.9.0.0 |
| Functor f => Functor (Rec1 f) | Since: base-4.9.0.0 |
| Functor (URec Char :: Type -> Type) | Since: base-4.9.0.0 |
| Functor (URec Double :: Type -> Type) | Since: base-4.9.0.0 |
| Functor (URec Float :: Type -> Type) | Since: base-4.9.0.0 |
| Functor (URec Int :: Type -> Type) | Since: base-4.9.0.0 |
| Functor (URec Word :: Type -> Type) | Since: base-4.9.0.0 |
| Functor (URec (Ptr ()) :: Type -> Type) | Since: base-4.9.0.0 |
| Functor ((,,) a b) | Since: base-4.14.0.0 |
| Functor f => Functor (Alt f) | Since: base-4.8.0.0 |
| Functor f => Functor (Ap f) | Since: base-4.12.0.0 |
| Functor (Const m :: Type -> Type) | Since: base-2.1 |
| Functor m => Functor (Kleisli m a) | Since: base-4.14.0.0 |
| Arrow a => Functor (WrappedArrow a b) | Since: base-2.1 |
Defined in Control.Applicative Methodsfmap :: (a0 -> b0) -> WrappedArrow a b a0 -> WrappedArrow a b b0 Source (<$) :: a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0 Source | |
| Functor ((->) r :: Type -> Type) | Since: base-2.1 |
| Functor (K1 i c :: Type -> Type) | Since: base-4.9.0.0 |
| (Functor f, Functor g) => Functor (f :+: g) | Since: base-4.9.0.0 |
| (Functor f, Functor g) => Functor (f :*: g) | Since: base-4.9.0.0 |
| Functor ((,,,) a b c) | Since: base-4.14.0.0 |
| (Functor f, Functor g) => Functor (Sum f g) | Since: base-4.9.0.0 |
| (Functor f, Functor g) => Functor (Product f g) | Since: base-4.9.0.0 |
| Functor f => Functor (M1 i c f) | Since: base-4.9.0.0 |
| (Functor f, Functor g) => Functor (f :.: g) | Since: base-4.9.0.0 |
| (Functor f, Functor g) => Functor (Compose f g) | Since: base-4.9.0.0 |
class Functor f => Applicative f where Source
A functor with application, providing operations to
- embed pure expressions (
pure), and - sequence computations and combine their results (
<*>andliftA2).
A minimal complete definition must include implementations of pure and of either <*> or liftA2. If it defines both, then they must behave the same as their default definitions:
(<*>) = liftA2 id
liftA2 f x y = f <$> 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).
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.
Using ApplicativeDo: 'fs <*> as' can be understood as the do expression
do f <- fs a <- as pure (f a)
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.
Using ApplicativeDo: 'liftA2 f as bs' can be understood as the do expression
do a <- as b <- bs pure (f a b)
(*>) :: f a -> f b -> f b infixl 4 Source
Sequence actions, discarding the value of the first argument.
'as *> bs' can be understood as the do expression
do as bs
This is a tad complicated for our ApplicativeDo extension which will give it a Monad constraint. For an Applicative constraint we write it of the form
do _ <- as b <- bs pure b
(<*) :: f a -> f b -> f a infixl 4 Source
Sequence actions, discarding the value of the second argument.
Using ApplicativeDo: 'as <* bs' can be understood as the do expression
do a <- as bs pure a
Instances
| Applicative [] | Since: base-2.1 |
| Applicative Maybe | Since: base-2.1 |
| Applicative IO | Since: base-2.1 |
| Applicative Par1 | Since: base-4.9.0.0 |
| Applicative NonEmpty | Since: base-4.9.0.0 |
Defined in GHC.Base | |
| Applicative NoIO | Since: base-4.8.0.0 |
| Applicative ReadP | Since: base-4.6.0.0 |
| Applicative ReadPrec | Since: base-4.6.0.0 |
Defined in Text.ParserCombinators.ReadPrec | |
| Applicative Down | Since: base-4.11.0.0 |
| Applicative Product | Since: base-4.8.0.0 |
Defined in Data.Semigroup.Internal | |
| Applicative Sum | Since: base-4.8.0.0 |
| Applicative Dual | Since: base-4.8.0.0 |
| Applicative Last | Since: base-4.8.0.0 |
| Applicative First | Since: base-4.8.0.0 |
| Applicative STM | Since: base-4.8.0.0 |
| Applicative Identity | Since: base-4.8.0.0 |
Defined in Data.Functor.Identity | |
| Applicative ZipList |
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 |
| Applicative Option | Since: base-4.9.0.0 |
| Applicative Last | Since: base-4.9.0.0 |
| Applicative First | Since: base-4.9.0.0 |
| Applicative Max | Since: base-4.9.0.0 |
| Applicative Min | Since: base-4.9.0.0 |
| Applicative Complex | Since: base-4.9.0.0 |
| Applicative (Either e) | Since: base-3.0 |
Defined in Data.Either | |
| Applicative (U1 :: Type -> Type) | Since: base-4.9.0.0 |
| Monoid a => Applicative ((,) a) |
For tuples, the ("hello ", (+15)) <*> ("world!", 2002)
("hello world!",2017)
Since: base-2.1 |
| Applicative (ST s) | Since: base-4.4.0.0 |
| Applicative (Proxy :: Type -> Type) | Since: base-4.7.0.0 |
| Arrow a => Applicative (ArrowMonad a) | Since: base-4.6.0.0 |
Defined in Control.Arrow Methodspure :: 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 |
Defined in Control.Applicative Methodspure :: 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 |
| Applicative f => Applicative (Rec1 f) | Since: base-4.9.0.0 |
| (Monoid a, Monoid b) => Applicative ((,,) a b) | Since: base-4.14.0.0 |
Defined in GHC.Base | |
| Applicative f => Applicative (Alt f) | Since: base-4.8.0.0 |
| Applicative f => Applicative (Ap f) | Since: base-4.12.0.0 |
| Monoid m => Applicative (Const m :: Type -> Type) | Since: base-2.0.1 |
| Applicative m => Applicative (Kleisli m a) | Since: base-4.14.0.0 |
Defined in Control.Arrow Methodspure :: 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 | |
| Arrow a => Applicative (WrappedArrow a b) | Since: base-2.1 |
Defined in Control.Applicative Methodspure :: 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 ((->) r :: Type -> Type) | Since: base-2.1 |
| Monoid c => Applicative (K1 i c :: Type -> Type) | Since: base-4.12.0.0 |
| (Applicative f, Applicative g) => Applicative (f :*: g) | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
| (Monoid a, Monoid b, Monoid c) => Applicative ((,,,) a b c) | Since: base-4.14.0.0 |
Defined in GHC.Base Methodspure :: 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 f, Applicative g) => Applicative (Product f g) | Since: base-4.9.0.0 |
Defined in Data.Functor.Product Methodspure :: 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 |
Defined in GHC.Generics | |
| (Applicative f, Applicative g) => Applicative (f :.: g) | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
| (Applicative f, Applicative g) => Applicative (Compose f g) | Since: base-4.9.0.0 |
Defined in Data.Functor.Compose Methodspure :: 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:
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 >>> sconcat $ "Hello" :| [" ", "Haskell", "!"] "Hello Haskell!"
stimes :: Integral b => b -> a -> a Source
Repeat a value n times.
Given that this works on a Semigroup it is allowed to fail if you request 0 or fewer repetitions, and the default definition will do so.
By making this a member of the class, idempotent semigroups and monoids can upgrade this to execute in \(\mathcal{O}(1)\) by picking stimes = stimesIdempotent or stimes =
stimesIdempotentMonoid respectively.
>>> stimes 4 [1] [1,1,1,1]
Instances
| Semigroup Ordering | Since: base-4.9.0.0 |
| Semigroup () | Since: base-4.9.0.0 |
| Semigroup Any | Since: base-4.9.0.0 |
| Semigroup All | Since: base-4.9.0.0 |
| Semigroup Lifetime | Since: base-4.10.0.0 |
| Semigroup Event | Since: base-4.10.0.0 |
| Semigroup Void | Since: base-4.9.0.0 |
| Semigroup [a] | Since: base-4.9.0.0 |
| Semigroup a => Semigroup (Maybe a) | Since: base-4.9.0.0 |
| Semigroup a => Semigroup (IO a) | Since: base-4.10.0.0 |
| Semigroup p => Semigroup (Par1 p) | Since: base-4.12.0.0 |
| Semigroup (NonEmpty a) | Since: base-4.9.0.0 |
| Semigroup a => Semigroup (Down a) | Since: base-4.11.0.0 |
| Num a => Semigroup (Product a) | Since: base-4.9.0.0 |
| Num a => Semigroup (Sum a) | Since: base-4.9.0.0 |
| Semigroup (Endo a) | Since: base-4.9.0.0 |
| Semigroup a => Semigroup (Dual a) | Since: base-4.9.0.0 |
| Semigroup (Last a) | Since: base-4.9.0.0 |
| Semigroup (First a) | Since: base-4.9.0.0 |
| Semigroup a => Semigroup (Identity a) | Since: base-4.9.0.0 |
| Semigroup a => Semigroup (Option a) | Since: base-4.9.0.0 |
| Monoid m => Semigroup (WrappedMonoid m) | 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 (Last a) | Since: base-4.9.0.0 |
| Semigroup (First a) | Since: base-4.9.0.0 |
| Ord a => Semigroup (Max a) | Since: base-4.9.0.0 |
| Ord a => Semigroup (Min a) | Since: base-4.9.0.0 |
| Semigroup (Equivalence a) | |
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 (Comparison 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 (Predicate a) | |
| Semigroup b => Semigroup (a -> b) | Since: base-4.9.0.0 |
| Semigroup (Either a b) | Since: base-4.9.0.0 |
| Semigroup (V1 p) | Since: base-4.12.0.0 |
| Semigroup (U1 p) | Since: base-4.12.0.0 |
| (Semigroup a, Semigroup b) => Semigroup (a, b) | Since: base-4.9.0.0 |
| Semigroup a => Semigroup (ST s a) | Since: base-4.11.0.0 |
| Semigroup (Proxy s) | Since: base-4.9.0.0 |
| Semigroup a => Semigroup (Op a b) | |
| Semigroup (f p) => Semigroup (Rec1 f p) | Since: base-4.12.0.0 |
| (Semigroup a, Semigroup b, Semigroup c) => Semigroup (a, b, c) | Since: base-4.9.0.0 |
| Alternative f => Semigroup (Alt f a) | Since: base-4.9.0.0 |
| (Applicative f, Semigroup a) => Semigroup (Ap f a) | Since: base-4.12.0.0 |
| Semigroup a => Semigroup (Const a b) | Since: base-4.9.0.0 |
| Semigroup c => Semigroup (K1 i c p) | Since: base-4.12.0.0 |
| (Semigroup (f p), Semigroup (g p)) => Semigroup ((f :*: g) p) | Since: base-4.12.0.0 |
| (Semigroup a, Semigroup b, Semigroup c, Semigroup d) => Semigroup (a, b, c, d) | Since: base-4.9.0.0 |
| Semigroup (f p) => Semigroup (M1 i c f p) | Since: base-4.12.0.0 |
| Semigroup (f (g p)) => Semigroup ((f :.: g) p) | Since: base-4.12.0.0 |
| (Semigroup a, Semigroup b, Semigroup c, Semigroup d, Semigroup e) => Semigroup (a, b, c, d, e) | 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) <> z(Semigrouplaw) - 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"
An associative operation
NOTE: This method is redundant and has the default implementation mappend = (<>) since base-4.11.0.0. Should it be implemented manually, since mappend is a synonym for (<>), it is expected that the two functions are defined the same way. In a future GHC release mappend will be removed from Monoid.
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 Ordering | Since: base-2.1 |
| Monoid () | Since: base-2.1 |
| Monoid Any | Since: base-2.1 |
| Monoid All | Since: base-2.1 |
| Monoid Lifetime |
Since: base-4.8.0.0 |
| Monoid Event | Since: base-4.4.0.0 |
| Monoid [a] | Since: base-2.1 |
| Semigroup a => Monoid (Maybe a) |
Lift a semigroup into Since 4.11.0: constraint on inner Since: base-2.1 |
| Monoid a => Monoid (IO a) | Since: base-4.9.0.0 |
| Monoid p => Monoid (Par1 p) | Since: base-4.12.0.0 |
| Monoid a => Monoid (Down a) | Since: base-4.11.0.0 |
| Num a => Monoid (Product a) | Since: base-2.1 |
| Num a => Monoid (Sum a) | Since: base-2.1 |
| Monoid (Endo a) | Since: base-2.1 |
| Monoid a => Monoid (Dual a) | Since: base-2.1 |
| Monoid (Last a) | Since: base-2.1 |
| Monoid (First a) | Since: base-2.1 |
| Monoid a => Monoid (Identity a) | Since: base-4.9.0.0 |
| Semigroup a => Monoid (Option a) | Since: base-4.9.0.0 |
| Monoid m => Monoid (WrappedMonoid m) | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methodsmempty :: WrappedMonoid m Source mappend :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m Source mconcat :: [WrappedMonoid m] -> WrappedMonoid m Source | |
| (Ord a, Bounded a) => Monoid (Max a) | Since: base-4.9.0.0 |
| (Ord a, Bounded a) => Monoid (Min a) | Since: base-4.9.0.0 |
| Monoid (Equivalence a) | |
Defined in Data.Functor.Contravariant Methodsmempty :: Equivalence a Source mappend :: Equivalence a -> Equivalence a -> Equivalence a Source mconcat :: [Equivalence a] -> Equivalence a Source | |
| Monoid (Comparison a) | |
Defined in Data.Functor.Contravariant Methodsmempty :: Comparison a Source mappend :: Comparison a -> Comparison a -> Comparison a Source mconcat :: [Comparison a] -> Comparison a Source | |
| Monoid (Predicate a) | |
| Monoid b => Monoid (a -> b) | Since: base-2.1 |
| Monoid (U1 p) | Since: base-4.12.0.0 |
| (Monoid a, Monoid b) => Monoid (a, b) | Since: base-2.1 |
| Monoid a => Monoid (ST s a) | Since: base-4.11.0.0 |
| Monoid (Proxy s) | Since: base-4.7.0.0 |
| Monoid a => Monoid (Op a b) | |
| Monoid (f p) => Monoid (Rec1 f p) | Since: base-4.12.0.0 |
| (Monoid a, Monoid b, Monoid c) => Monoid (a, b, c) | Since: base-2.1 |
| Alternative f => Monoid (Alt f a) | Since: base-4.8.0.0 |
| (Applicative f, Monoid a) => Monoid (Ap f a) | Since: base-4.12.0.0 |
| Monoid a => Monoid (Const a b) | Since: base-4.9.0.0 |
| Monoid c => Monoid (K1 i c p) | Since: base-4.12.0.0 |
| (Monoid (f p), Monoid (g p)) => Monoid ((f :*: g) p) | Since: base-4.12.0.0 |
| (Monoid a, Monoid b, Monoid c, Monoid d) => Monoid (a, b, c, d) | Since: base-2.1 |
| Monoid (f p) => Monoid (M1 i c f p) | Since: base-4.12.0.0 |
| Monoid (f (g p)) => Monoid ((f :.: g) p) | Since: base-4.12.0.0 |
| (Monoid a, Monoid b, Monoid c, Monoid d, Monoid e) => Monoid (a, b, c, d, e) | Since: base-2.1 |
Constructors
| forall a. O a |
A String is a list of characters. String constants in Haskell are values of type String.
See Data.List for operations on lists.
Non-empty (and non-strict) list type.
Since: base-4.9.0.0
Constructors
| a :| [a] infixr 5 |
Instances
| Monad NonEmpty | Since: base-4.9.0.0 |
| Functor NonEmpty | Since: base-4.9.0.0 |
| MonadFix NonEmpty | Since: base-4.9.0.0 |
Defined in Control.Monad.Fix | |
| Applicative NonEmpty | Since: base-4.9.0.0 |
Defined in GHC.Base | |
| Foldable NonEmpty | Since: base-4.9.0.0 |
Defined in Data.Foldable Methodsfold :: 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 | |
| Traversable NonEmpty | Since: base-4.9.0.0 |
Defined in Data.Traversable | |
| MonadZip NonEmpty | Since: base-4.9.0.0 |
| Show1 NonEmpty | Since: base-4.10.0.0 |
| Read1 NonEmpty | Since: base-4.10.0.0 |
Defined in Data.Functor.Classes MethodsliftReadsPrec :: (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 | |
| Ord1 NonEmpty | Since: base-4.10.0.0 |
Defined in Data.Functor.Classes | |
| Eq1 NonEmpty | Since: base-4.10.0.0 |
| IsList (NonEmpty a) | Since: base-4.9.0.0 |
| Eq a => Eq (NonEmpty a) | Since: base-4.9.0.0 |
| Data a => Data (NonEmpty a) | Since: base-4.9.0.0 |
Defined in Data.Data Methodsgfoldl :: (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 |
Defined in GHC.Base Methodscompare :: 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 | |
| Read a => Read (NonEmpty a) | Since: base-4.11.0.0 |
| Show a => Show (NonEmpty a) | Since: base-4.11.0.0 |
| Generic (NonEmpty a) | Since: base-4.6.0.0 |
| Semigroup (NonEmpty a) | Since: base-4.9.0.0 |
| Generic1 NonEmpty | Since: base-4.6.0.0 |
| type Rep (NonEmpty a) | |
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 Item (NonEmpty a) | |
| type Rep1 NonEmpty | |
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 (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 [] | Since: base-2.1 |
| MonadPlus Maybe | Since: base-2.1 |
| MonadPlus IO | Since: base-4.9.0.0 |
| MonadPlus ReadP | Since: base-2.1 |
| MonadPlus ReadPrec | Since: base-2.1 |
| MonadPlus STM | Since: base-4.3.0.0 |
| MonadPlus Option | Since: base-4.9.0.0 |
| MonadPlus (U1 :: Type -> Type) | Since: base-4.9.0.0 |
| MonadPlus (Proxy :: Type -> Type) | Since: base-4.9.0.0 |
| (ArrowApply a, ArrowPlus a) => MonadPlus (ArrowMonad a) | Since: base-4.6.0.0 |
Defined in Control.Arrow Methodsmzero :: 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 |
| MonadPlus f => MonadPlus (Alt f) | Since: base-4.8.0.0 |
| MonadPlus f => MonadPlus (Ap f) | Since: base-4.12.0.0 |
| MonadPlus m => MonadPlus (Kleisli m a) | Since: base-4.14.0.0 |
| (MonadPlus f, MonadPlus g) => MonadPlus (f :*: g) | Since: base-4.9.0.0 |
| (MonadPlus f, MonadPlus g) => MonadPlus (Product f g) | Since: base-4.9.0.0 |
| MonadPlus f => MonadPlus (M1 i c f) | Since: base-4.9.0.0 |
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
(<**>) :: Applicative f => f a -> f (a -> b) -> f b infixl 4 Source
A variant of <*> with the arguments reversed.
Using ApplicativeDo: 'as <**> fs' can be understood as the do expression
do a <- as f <- fs pure (f a)
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.
| Using ApplicativeDo: 'liftA f as' can be understood as the do expression
do a <- as pure (f a)
with an inferred Functor constraint, weaker than Applicative.
liftA3 :: Applicative f => (a -> b -> c -> d) -> f a -> f b -> f c -> f d Source
Lift a ternary function to actions.
Using ApplicativeDo: 'liftA3 f as bs cs' can be understood as the do expression
do a <- as b <- bs c <- cs pure (f a b c)
(=<<) :: 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
The fromEnum method restricted to the type Char.
Identity function.
id x = x
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.
failIO :: String -> IO a Source
unIO :: IO a -> State# RealWorld -> (# State# RealWorld, a #) 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.Prim.Ext
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/8.10.2/docs/html/libraries/base-4.14.1.0/GHC-Base.html