GHC.Base

base-4.16.0.0: Basic libraries

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

- augment :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a] -> [a]
- (++) :: [a] -> [a] -> [a]
- build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
- foldr :: (a -> b -> b) -> b -> [a] -> b
- eqString :: String -> String -> Bool
- bindIO :: IO a -> (a -> IO b) -> IO b
- returnIO :: a -> IO a
- otherwise :: Bool
- assert :: Bool -> a -> a
- thenIO :: IO a -> IO b -> IO b
- breakpoint :: a -> a
- breakpointCond :: Bool -> a -> a
- map :: (a -> b) -> [a] -> [b]
- ($) :: forall r a (b :: TYPE r). (a -> b) -> a -> b
- join :: Monad m => m (m a) -> m a
- class Applicative m => Monad m where
  - (>>=) :: forall a b. m a -> (a -> m b) -> m b
  - (>>) :: forall a b. m a -> m b -> m b
  - return :: a -> m a
- class Functor f where
  - fmap :: (a -> b) -> f a -> f b
  - (<$) :: a -> f b -> f a
- class Functor f => Applicative f where
  - pure :: a -> f a
  - (<*>) :: f (a -> b) -> f a -> f b
  - liftA2 :: (a -> b -> c) -> f a -> f b -> f c
  - (*>) :: f a -> f b -> f b
  - (<*) :: f a -> f b -> f a
- class Semigroup a where
  - (<>) :: a -> a -> a
  - sconcat :: NonEmpty a -> a
  - stimes :: Integral b => b -> a -> a
- class Semigroup a => Monoid a where
  - mempty :: a
  - mappend :: a -> a -> a
  - mconcat :: [a] -> a
- type String = [Char]
- data Opaque = forall a. O a
- ($!) :: forall r a (b :: TYPE r). (a -> b) -> a -> b
- (.) :: (b -> c) -> (a -> b) -> a -> c
- (<**>) :: Applicative f => f a -> f (a -> b) -> f b
- (=<<) :: Monad m => (a -> m b) -> m a -> m b
- ap :: Monad m => m (a -> b) -> m a -> m b
- asTypeOf :: a -> a -> a
- const :: a -> b -> a
- divInt :: Int -> Int -> Int
- divModInt :: Int -> Int -> (Int, Int)
- divModInt# :: Int# -> Int# -> (# Int#, Int# #)
- failIO :: String -> IO a
- flip :: (a -> b -> c) -> b -> a -> c
- getTag :: a -> Int#
- iShiftL# :: Int# -> Int# -> Int#
- iShiftRA# :: Int# -> Int# -> Int#
- iShiftRL# :: Int# -> Int# -> Int#
- id :: a -> a
- liftA :: Applicative f => (a -> b) -> f a -> f b
- liftA3 :: Applicative f => (a -> b -> c -> d) -> f a -> f b -> f c -> f d
- 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
- mapFB :: (elt -> lst -> lst) -> (a -> elt) -> a -> lst -> lst
- mapM :: Monad m => (a -> m b) -> [a] -> m [b]
- maxInt :: Int
- minInt :: Int
- modInt :: Int -> Int -> Int
- ord :: Char -> Int
- quotInt :: Int -> Int -> Int
- quotRemInt :: Int -> Int -> (Int, Int)
- remInt :: Int -> Int -> Int
- sequence :: Monad m => [m a] -> m [a]
- shiftL# :: Word# -> Int# -> Word#
- shiftRL# :: Word# -> Int# -> Word#
- unIO :: IO a -> State# RealWorld -> (# State# RealWorld, a #)
- unsafeChr :: Int -> Char
- until :: (a -> Bool) -> (a -> a) -> a -> a
- when :: Applicative f => Bool -> f () -> f ()
- class Applicative f => Alternative f where
  - empty :: f a
  - (<|>) :: f a -> f a -> f a
  - some :: f a -> f [a]
  - many :: f a -> f [a]
- class (Alternative m, Monad m) => MonadPlus m where
  - mzero :: m a
  - mplus :: m a -> m a -> m a
- data NonEmpty a = a :| [a]
- 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

# Documentation

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

A list producer that can be fused with `foldr`. This function is merely

       augment g xs = g (:) xs

but GHC's simplifier will transform an expression of the form ``foldr` k z (`augment` g xs)`, which may arise after inlining, to `g k (`foldr` k z xs)`, which avoids producing an intermediate list.

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

Append two lists, i.e.,

    [x1, ..., xm] ++ [y1, ..., yn] == [x1, ..., xm, y1, ..., yn]
    [x1, ..., xm] ++ [y1, ...] == [x1, ..., xm, y1, ...]

If the first list is not finite, the result is the first list.

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

A list producer that can be fused with `foldr`. This function is merely

       build g = g (:) []

but GHC's simplifier will transform an expression of the form ``foldr` k z (`build` g)`, which may arise after inlining, to `g k z`, which avoids producing an intermediate list.

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

`foldr`, applied to a binary operator, a starting value (typically the right-identity of the operator), and a list, reduces the list using the binary operator, from right to left:

    foldr f z [x1, x2, ..., xn] == x1 `f` (x2 `f` ... (xn `f` z)...)

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

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

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

returnIO :: a -> IO a Source #

otherwise :: Bool Source #

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

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

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

If the first argument evaluates to `True`, then the result is the second argument. Otherwise an `AssertionFailed` exception is raised, containing a `String` with the source file and line number of the call to `assert`.

Assertions can normally be turned on or off with a compiler flag (for GHC, assertions are normally on unless optimisation is turned on with `-O` or the `-fignore-asserts` option is given). When assertions are turned off, the first argument to `assert` is ignored, and the second argument is returned as the result.

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

breakpoint :: a -> a Source #

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]
    [2,3,4]

($) :: forall r a (b :: TYPE r). (a -> b) -> a -> b infixr 0 Source #

Application operator. This operator is redundant, since ordinary application `(f x)` means the same as `(f `$` x)`. However, `$` has low, right-associative binding precedence, so it sometimes allows parentheses to be omitted; for example:

    f $ g $ h x  =  f (g (h x))

It is also useful in higher-order situations, such as ``map` (`$` 0) xs`, or ``zipWith` (`$`) fs xs`.

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

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

The `join` function is the conventional monad join operator. It is used to remove one level of monadic structure, projecting its bound argument into the outer level.

'``join` bss`' can be understood as the `do` expression

    do bs <- bss
       bs

#### Examples

Expand

A common use of `join` is to run an `IO` computation returned from an `STM` transaction, since `STM` transactions can't perform `IO` directly. Recall that

    atomically :: STM a -> IO a

is used to run `STM` transactions atomically. So, by specializing the types of `atomically` and `join` to

    atomically :: STM (IO b) -> IO (IO b)
    join       :: IO (IO b)  -> IO b

we can compose them as

    join . atomically :: STM (IO b) -> IO b

to run an `STM` transaction and the `IO` action it returns.

class Applicative m => Monad m where Source #

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

Instances of `Monad` should satisfy the following:

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

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

-     pure = return

-     m1 <*> m2 = m1 >>= (x1 -> m2 >>= (x2 -> return (x1 x2)))

The above laws imply:

-     fmap f xs  =  xs >>= return . f

-     (>>) = (*>)

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

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

Minimal complete definition

(>>=)

Methods

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

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

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

    do a <- as
       bs a

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

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

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

    do as
       bs

return :: a -> m a Source #

Inject a value into the monadic type.

#### Instances

Instances details

Monad Complex # | Since: base-4.9.0.0
Instance details Defined in Data.Complex Methods (>>=) :: Complex a -> (a -> Complex b) -> Complex b Source # (>>) :: Complex a -> Complex b -> Complex b Source # return :: a -> Complex a Source #
Monad Identity # | Since: base-4.8.0.0
Instance details Defined in Data.Functor.Identity Methods (>>=) :: Identity a -> (a -> Identity b) -> Identity b Source # (>>) :: Identity a -> Identity b -> Identity b Source # return :: a -> Identity a Source #
Monad First # | Since: base-4.8.0.0
Instance details Defined in Data.Monoid Methods (>>=) :: First a -> (a -> First b) -> First b Source # (>>) :: First a -> First b -> First b Source # return :: a -> First a Source #
Monad Last # | Since: base-4.8.0.0
Instance details Defined in Data.Monoid Methods (>>=) :: Last a -> (a -> Last b) -> Last b Source # (>>) :: Last a -> Last b -> Last b Source # return :: a -> Last a Source #
Monad Down # | Since: base-4.11.0.0
Instance details Defined in Data.Ord Methods (>>=) :: Down a -> (a -> Down b) -> Down b Source # (>>) :: Down a -> Down b -> Down b Source # return :: a -> Down a Source #
Monad First # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (>>=) :: First a -> (a -> First b) -> First b Source # (>>) :: First a -> First b -> First b Source # return :: a -> First a Source #
Monad Last # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (>>=) :: Last a -> (a -> Last b) -> Last b Source # (>>) :: Last a -> Last b -> Last b Source # return :: a -> Last a Source #
Monad Max # | 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 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 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 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 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 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 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 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 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 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 Solo # | Since: base-4.15
Instance details Defined in GHC.Base Methods (>>=) :: Solo a -> (a -> Solo b) -> Solo b Source # (>>) :: Solo a -> Solo b -> Solo b Source # return :: a -> Solo a Source #
Monad [] # | Since: base-2.1
Instance details Defined in GHC.Base Methods (>>=) :: [a] -> (a -> [b]) -> [b] Source # (>>) :: [a] -> [b] -> [b] Source # return :: a -> [a] Source #
Monad m => Monad (WrappedMonad m) # | Since: base-4.7.0.0
Instance details Defined in Control.Applicative Methods (>>=) :: WrappedMonad m a -> (a -> WrappedMonad m b) -> WrappedMonad m b Source # (>>) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m b Source # return :: a -> WrappedMonad m a Source #
ArrowApply a => Monad (ArrowMonad a) # | Since: base-2.1
Instance details Defined in Control.Arrow Methods (>>=) :: ArrowMonad a a0 -> (a0 -> ArrowMonad a b) -> ArrowMonad a b Source # (>>) :: ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a b Source # return :: a0 -> ArrowMonad a a0 Source #
Monad (ST s) # | Since: base-2.1
Instance details Defined in Control.Monad.ST.Lazy.Imp Methods (>>=) :: ST s a -> (a -> ST s b) -> ST s b Source # (>>) :: ST s a -> ST s b -> ST s b Source # return :: a -> ST s a Source #
Monad (Either e) # | Since: base-4.4.0.0
Instance details Defined in Data.Either Methods (>>=) :: Either e a -> (a -> Either e b) -> Either e b Source # (>>) :: Either e a -> Either e b -> Either e b Source # return :: a -> Either e a Source #
Monad (Proxy :: Type -> Type) # | Since: base-4.7.0.0
Instance details Defined in Data.Proxy Methods (>>=) :: Proxy a -> (a -> Proxy b) -> Proxy b Source # (>>) :: Proxy a -> Proxy b -> Proxy b Source # return :: a -> Proxy a Source #
Monad (U1 :: Type -> Type) # | Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods (>>=) :: U1 a -> (a -> U1 b) -> U1 b Source # (>>) :: U1 a -> U1 b -> U1 b Source # return :: a -> U1 a Source #
Monad (ST s) # | Since: base-2.1
Instance details Defined in GHC.ST Methods (>>=) :: ST s a -> (a -> ST s b) -> ST s b Source # (>>) :: ST s a -> ST s b -> ST s b Source # return :: a -> ST s a Source #
Monoid a => Monad ((,) a) # | Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (>>=) :: (a, a0) -> (a0 -> (a, b)) -> (a, b) Source # (>>) :: (a, a0) -> (a, b) -> (a, b) Source # return :: a0 -> (a, a0) Source #
Monad m => Monad (Kleisli m a) # | Since: base-4.14.0.0
Instance details Defined in Control.Arrow Methods (>>=) :: Kleisli m a a0 -> (a0 -> Kleisli m a b) -> Kleisli m a b Source # (>>) :: Kleisli m a a0 -> Kleisli m a b -> Kleisli m a b Source # return :: a0 -> Kleisli m a a0 Source #
Monad f => Monad (Ap f) # | Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods (>>=) :: Ap f a -> (a -> Ap f b) -> Ap f b Source # (>>) :: Ap f a -> Ap f b -> Ap f b Source # return :: a -> Ap f a Source #
Monad f => Monad (Alt f) # | Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods (>>=) :: Alt f a -> (a -> Alt f b) -> Alt f b Source # (>>) :: Alt f a -> Alt f b -> Alt f b Source # return :: a -> Alt f a Source #
Monad f => Monad (Rec1 f) # | Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods (>>=) :: Rec1 f a -> (a -> Rec1 f b) -> Rec1 f b Source # (>>) :: Rec1 f a -> Rec1 f b -> Rec1 f b Source # return :: a -> Rec1 f a Source #
(Monoid a, Monoid b) => Monad ((,,) a b) # | Since: base-4.14.0.0
Instance details Defined in GHC.Base Methods (>>=) :: (a, b, a0) -> (a0 -> (a, b, b0)) -> (a, b, b0) Source # (>>) :: (a, b, a0) -> (a, b, b0) -> (a, b, b0) Source # return :: a0 -> (a, b, a0) Source #
(Monad f, Monad g) => Monad (Product f g) # | Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods (>>=) :: Product f g a -> (a -> Product f g b) -> Product f g b Source # (>>) :: Product f g a -> Product f g b -> Product f g b Source # return :: a -> Product f g a Source #
(Monad f, Monad g) => Monad (f :*: g) # | Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods (>>=) :: (f :*: g) a -> (a -> (f :*: g) b) -> (f :*: g) b Source # (>>) :: (f :*: g) a -> (f :*: g) b -> (f :*: g) b Source # return :: a -> (f :*: g) a Source #
(Monoid a, Monoid b, Monoid c) => Monad ((,,,) a b c) # | Since: base-4.14.0.0
Instance details Defined in GHC.Base Methods (>>=) :: (a, b, c, a0) -> (a0 -> (a, b, c, b0)) -> (a, b, c, b0) Source # (>>) :: (a, b, c, a0) -> (a, b, c, b0) -> (a, b, c, b0) Source # return :: a0 -> (a, b, c, a0) Source #
Monad ((->) r) # | Since: base-2.1
Instance details Defined in GHC.Base Methods (>>=) :: (r -> a) -> (a -> r -> b) -> r -> b Source # (>>) :: (r -> a) -> (r -> b) -> r -> b Source # return :: a -> r -> a Source #
Monad f => Monad (M1 i c f) # | Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods (>>=) :: M1 i c f a -> (a -> M1 i c f b) -> M1 i c f b Source # (>>) :: M1 i c f a -> M1 i c f b -> M1 i c f b Source # return :: a -> M1 i c f a Source #

class Functor f where Source #

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

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

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

Minimal complete definition

fmap

Methods

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

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

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

#### Examples

Expand

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

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

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

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

Double each element of a list:

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

Apply `even` to the second element of a pair:

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

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

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

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

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

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

#### Instances

Instances details

Functor ZipList # | Since: base-2.1
Instance details Defined in Control.Applicative Methods fmap :: (a -> b) -> ZipList a -> ZipList b Source # (<$) :: a -> ZipList b -> ZipList a Source #
Functor Handler # | Since: base-4.6.0.0
Instance details Defined in Control.Exception Methods fmap :: (a -> b) -> Handler a -> Handler b Source # (<$) :: a -> Handler b -> Handler a Source #
Functor Complex # | Since: base-4.9.0.0
Instance details Defined in Data.Complex Methods fmap :: (a -> b) -> Complex a -> Complex b Source # (<$) :: a -> Complex b -> Complex a Source #
Functor Identity # | Since: base-4.8.0.0
Instance details Defined in Data.Functor.Identity Methods fmap :: (a -> b) -> Identity a -> Identity b Source # (<$) :: a -> Identity b -> Identity a Source #
Functor First # | Since: base-4.8.0.0
Instance details Defined in Data.Monoid Methods fmap :: (a -> b) -> First a -> First b Source # (<$) :: a -> First b -> First a Source #
Functor Last # | Since: base-4.8.0.0
Instance details Defined in Data.Monoid Methods fmap :: (a -> b) -> Last a -> Last b Source # (<$) :: a -> Last b -> Last a Source #
Functor Down # | Since: base-4.11.0.0
Instance details Defined in Data.Ord Methods fmap :: (a -> b) -> Down a -> Down b Source # (<$) :: a -> Down b -> Down a Source #
Functor First # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fmap :: (a -> b) -> First a -> First b Source # (<$) :: a -> First b -> First a Source #
Functor Last # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fmap :: (a -> b) -> Last a -> Last b Source # (<$) :: a -> Last b -> Last a Source #
Functor Max # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fmap :: (a -> b) -> Max a -> Max b Source # (<$) :: 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 # (<$) :: a -> Min b -> Min a Source #
Functor Dual # | Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods fmap :: (a -> b) -> Dual a -> Dual b Source # (<$) :: a -> Dual b -> Dual a Source #
Functor 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 NonEmpty # | Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods fmap :: (a -> b) -> NonEmpty a -> NonEmpty b Source # (<$) :: a -> NonEmpty b -> NonEmpty a Source #
Functor STM # | Since: base-4.3.0.0
Instance details Defined in GHC.Conc.Sync Methods fmap :: (a -> b) -> STM a -> STM b Source # (<$) :: a -> STM b -> STM a Source #
Functor NoIO # | Since: base-4.8.0.0
Instance details Defined in GHC.GHCi Methods fmap :: (a -> b) -> NoIO a -> NoIO b Source # (<$) :: a -> NoIO b -> NoIO a Source #
Functor Par1 # | Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> Par1 a -> Par1 b Source # (<$) :: a -> Par1 b -> Par1 a Source #
Functor ArgDescr # | Since: base-4.6.0.0
Instance details Defined in System.Console.GetOpt Methods fmap :: (a -> b) -> ArgDescr a -> ArgDescr b Source # (<$) :: a -> ArgDescr b -> ArgDescr a Source #
Functor ArgOrder # | Since: base-4.6.0.0
Instance details Defined in System.Console.GetOpt Methods fmap :: (a -> b) -> ArgOrder a -> ArgOrder b Source # (<$) :: a -> ArgOrder b -> ArgOrder a Source #
Functor OptDescr # | Since: base-4.6.0.0
Instance details Defined in System.Console.GetOpt Methods fmap :: (a -> b) -> OptDescr a -> OptDescr b Source # (<$) :: a -> OptDescr b -> OptDescr a Source #
Functor ReadP # | Since: base-2.1
Instance details Defined in Text.ParserCombinators.ReadP Methods fmap :: (a -> b) -> ReadP a -> ReadP b Source # (<$) :: 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 # (<$) :: a -> ReadPrec b -> ReadPrec a Source #
Functor IO # | Since: base-2.1
Instance details Defined in GHC.Base Methods fmap :: (a -> b) -> IO a -> IO b Source # (<$) :: a -> IO b -> IO a Source #
Functor Maybe # | Since: base-2.1
Instance details Defined in GHC.Base Methods fmap :: (a -> b) -> Maybe a -> Maybe b Source # (<$) :: a -> Maybe b -> Maybe a Source #
Functor Solo # | Since: base-4.15
Instance details Defined in GHC.Base Methods fmap :: (a -> b) -> Solo a -> Solo b Source # (<$) :: a -> Solo b -> Solo a Source #
Functor [] # | Since: base-2.1
Instance details Defined in GHC.Base Methods fmap :: (a -> b) -> [a] -> [b] Source # (<$) :: a -> [b] -> [a] Source #
Monad m => Functor (WrappedMonad m) # | Since: base-2.1
Instance details Defined in Control.Applicative Methods fmap :: (a -> b) -> WrappedMonad m a -> WrappedMonad m b Source # (<$) :: a -> WrappedMonad m b -> WrappedMonad m a Source #
Arrow a => Functor (ArrowMonad a) # | Since: base-4.6.0.0
Instance details Defined in Control.Arrow Methods fmap :: (a0 -> b) -> ArrowMonad a a0 -> ArrowMonad a b Source # (<$) :: a0 -> ArrowMonad a b -> ArrowMonad a a0 Source #
Functor (ST s) # | Since: base-2.1
Instance details Defined in Control.Monad.ST.Lazy.Imp Methods fmap :: (a -> b) -> ST s a -> ST s b Source # (<$) :: a -> ST s b -> ST s a Source #
Functor (Either a) # | Since: base-3.0
Instance details Defined in Data.Either Methods fmap :: (a0 -> b) -> Either a a0 -> Either a b Source # (<$) :: a0 -> Either a b -> Either a a0 Source #
Functor (Proxy :: Type -> Type) # | Since: base-4.7.0.0
Instance details Defined in Data.Proxy Methods fmap :: (a -> b) -> Proxy a -> Proxy b Source # (<$) :: a -> Proxy b -> Proxy a Source #
Functor (Arg a) # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fmap :: (a0 -> b) -> Arg a a0 -> Arg a b Source # (<$) :: a0 -> Arg a b -> Arg a a0 Source #
Functor (Array i) # | Since: base-2.1
Instance details Defined in GHC.Arr Methods fmap :: (a -> b) -> Array i a -> Array i b Source # (<$) :: a -> Array i b -> Array i a Source #
Functor (U1 :: Type -> Type) # | Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> U1 a -> U1 b Source # (<$) :: a -> U1 b -> U1 a Source #
Functor (V1 :: TYPE LiftedRep -> Type) # | Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> V1 a -> V1 b Source # (<$) :: a -> V1 b -> V1 a Source #
Functor (ST s) # | Since: base-2.1
Instance details Defined in GHC.ST Methods fmap :: (a -> b) -> ST s a -> ST s b Source # (<$) :: a -> ST s b -> ST s a Source #
Functor ((,) a) # | Since: base-2.1
Instance details Defined in GHC.Base Methods fmap :: (a0 -> b) -> (a, a0) -> (a, b) Source # (<$) :: a0 -> (a, b) -> (a, a0) Source #
Arrow a => Functor (WrappedArrow a b) # | Since: base-2.1
Instance details Defined in Control.Applicative Methods fmap :: (a0 -> b0) -> WrappedArrow a b a0 -> WrappedArrow a b b0 Source # (<$) :: a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0 Source #
Functor m => Functor (Kleisli m a) # | Since: base-4.14.0.0
Instance details Defined in Control.Arrow Methods fmap :: (a0 -> b) -> Kleisli m a a0 -> Kleisli m a b Source # (<$) :: a0 -> Kleisli m a b -> Kleisli m a a0 Source #
Functor (Const m :: Type -> Type) # | Since: base-2.1
Instance details Defined in Data.Functor.Const Methods fmap :: (a -> b) -> Const m a -> Const m b Source # (<$) :: a -> Const m b -> Const m a Source #
Functor f => Functor (Ap f) # | Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods fmap :: (a -> b) -> Ap f a -> Ap f b Source # (<$) :: a -> Ap f b -> Ap f a Source #
Functor f => Functor (Alt f) # | Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods fmap :: (a -> b) -> Alt f a -> Alt f b Source # (<$) :: a -> Alt f b -> Alt f a Source #
Functor f => Functor (Rec1 f) # | Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> Rec1 f a -> Rec1 f b Source # (<$) :: a -> Rec1 f b -> Rec1 f a Source #
Functor (URec (Ptr ()) :: TYPE LiftedRep -> Type) # | Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> URec (Ptr ()) a -> URec (Ptr ()) b Source # (<$) :: a -> URec (Ptr ()) b -> URec (Ptr ()) a Source #
Functor (URec Char :: TYPE LiftedRep -> Type) # | Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> URec Char a -> URec Char b Source # (<$) :: a -> URec Char b -> URec Char a Source #
Functor (URec Double :: TYPE LiftedRep -> Type) # | Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> URec Double a -> URec Double b Source # (<$) :: a -> URec Double b -> URec Double a Source #
Functor (URec Float :: TYPE LiftedRep -> Type) # | Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> URec Float a -> URec Float b Source # (<$) :: a -> URec Float b -> URec Float a Source #
Functor (URec Int :: TYPE LiftedRep -> Type) # | Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> URec Int a -> URec Int b Source # (<$) :: a -> URec Int b -> URec Int a Source #
Functor (URec Word :: TYPE LiftedRep -> Type) # | Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> URec Word a -> URec Word b Source # (<$) :: a -> URec Word b -> URec Word a Source #
Functor ((,,) a b) # | Since: base-4.14.0.0
Instance details Defined in GHC.Base Methods fmap :: (a0 -> b0) -> (a, b, a0) -> (a, b, b0) Source # (<$) :: a0 -> (a, b, b0) -> (a, b, a0) Source #
(Functor f, Functor g) => Functor (Product f g) # | Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods fmap :: (a -> b) -> Product f g a -> Product f g b Source # (<$) :: a -> Product f g b -> Product f g a Source #
(Functor f, Functor g) => Functor (Sum f g) # | Since: base-4.9.0.0
Instance details Defined in Data.Functor.Sum Methods fmap :: (a -> b) -> Sum f g a -> Sum f g b Source # (<$) :: a -> Sum f g b -> Sum f g a Source #
(Functor f, Functor g) => Functor (f :*: g) # | Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> (f :*: g) a -> (f :*: g) b Source # (<$) :: 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 # (<$) :: a -> (f :+: g) b -> (f :+: g) a Source #
Functor (K1 i c :: TYPE LiftedRep -> Type) # | Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> K1 i c a -> K1 i c b Source # (<$) :: a -> K1 i c b -> K1 i c a Source #
Functor ((,,,) a b c) # | Since: base-4.14.0.0
Instance details Defined in GHC.Base Methods fmap :: (a0 -> b0) -> (a, b, c, a0) -> (a, b, c, b0) Source # (<$) :: a0 -> (a, b, c, b0) -> (a, b, c, a0) Source #
Functor ((->) r) # | Since: base-2.1
Instance details Defined in GHC.Base Methods fmap :: (a -> b) -> (r -> a) -> r -> b Source # (<$) :: a -> (r -> b) -> r -> a Source #
(Functor f, Functor g) => Functor (Compose f g) # | Since: base-4.9.0.0
Instance details Defined in Data.Functor.Compose Methods fmap :: (a -> b) -> Compose f g a -> Compose f g b Source # (<$) :: a -> Compose f g b -> Compose f g a Source #
(Functor f, Functor g) => Functor (f :.: g) # | Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> (f :.: g) a -> (f :.: g) b Source # (<$) :: a -> (f :.: g) b -> (f :.: g) a Source #
Functor f => Functor (M1 i c f) # | Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> M1 i c f a -> M1 i c f b Source # (<$) :: a -> M1 i c f b -> M1 i c f a Source #

class Functor f => Applicative f where Source #

A functor with application, providing operations to

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

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

    (<*>) = liftA2 id

    liftA2 f x y = f <$> x <*> y

Further, any definition must satisfy the following:

Identity

      pure id <*> v = v

Composition

      pure (.) <*> u <*> v <*> w = u <*> (v <*> w)

Homomorphism

      pure f <*> pure x = pure (f x)

Interchange

      u <*> pure y = pure ($ y) <*> u

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

-     u *> v = (id <$ u) <*> v

-     u <* v = liftA2 const u v

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

-     fmap f x = pure f <*> x

It may be useful to note that supposing

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

it follows from the above that

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

If `f` is also a `Monad`, it should satisfy

-     pure = return

-     m1 <*> m2 = m1 >>= (x1 -> m2 >>= (x2 -> return (x1 x2)))

-     (*>) = (>>)

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

Minimal complete definition

pure, ((<*>) | liftA2)

Methods

pure :: a -> f a Source #

Lift a value.

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

Sequential application.

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

#### Example

Expand

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

    >>> data MyState = MyState {arg1 :: Foo, arg2 :: Bar, arg3 :: Baz}

    >>> produceFoo :: Applicative f => f Foo

    >>> produceBar :: Applicative f => f Bar
    >>> produceBaz :: Applicative f => f Baz

    >>> mkState :: Applicative f => f MyState
    >>> mkState = MyState <$> produceFoo <*> produceBar <*> produceBaz

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

Lift a binary function to actions.

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

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

#### Example

Expand

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

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

Sequence actions, discarding the value of the first argument.

#### Examples

Expand

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

    >>> Just 2 *> Just 3
    Just 3

    >>> Nothing *> Just 3
    Nothing

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

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

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

Sequence actions, discarding the value of the second argument.

#### Instances

Instances details

Applicative ZipList # |
    f <$> ZipList xs1 <*> ... <*> ZipList xsN
        = ZipList (zipWithN f xs1 ... xsN)
where `zipWithN` refers to the `zipWith` function of the appropriate arity (`zipWith`, `zipWith3`, `zipWith4`, ...). For example:
    (\a b c -> stimes c [a, b]) <$> ZipList "abcd" <*> ZipList "567" <*> ZipList [1..]
        = ZipList (zipWith3 (\a b c -> stimes c [a, b]) "abcd" "567" [1..])
        = ZipList {getZipList = ["a5","b6b6","c7c7c7"]}
Since: base-2.1
Instance details Defined in Control.Applicative Methods pure :: a -> ZipList a Source # (<*>) :: ZipList (a -> b) -> ZipList a -> ZipList b Source # liftA2 :: (a -> b -> c) -> ZipList a -> ZipList b -> ZipList c Source # (*>) :: ZipList a -> ZipList b -> ZipList b Source # (<*) :: ZipList a -> ZipList b -> ZipList a Source #
Applicative Complex # | Since: base-4.9.0.0
Instance details Defined in Data.Complex Methods pure :: a -> Complex a Source # (<*>) :: Complex (a -> b) -> Complex a -> Complex b Source # liftA2 :: (a -> b -> c) -> Complex a -> Complex b -> Complex c Source # (*>) :: Complex a -> Complex b -> Complex b Source # (<*) :: Complex a -> Complex b -> Complex a Source #
Applicative Identity # | Since: base-4.8.0.0
Instance details Defined in Data.Functor.Identity Methods pure :: a -> Identity a Source # (<*>) :: Identity (a -> b) -> Identity a -> Identity b Source # liftA2 :: (a -> b -> c) -> Identity a -> Identity b -> Identity c Source # (*>) :: Identity a -> Identity b -> Identity b Source # (<*) :: Identity a -> Identity b -> Identity a Source #
Applicative First # | Since: base-4.8.0.0
Instance details Defined in Data.Monoid Methods pure :: a -> First a Source # (<*>) :: First (a -> b) -> First a -> First b Source # liftA2 :: (a -> b -> c) -> First a -> First b -> First c Source # (*>) :: First a -> First b -> First b Source # (<*) :: First a -> First b -> First a Source #
Applicative Last # | Since: base-4.8.0.0
Instance details Defined in Data.Monoid Methods pure :: a -> Last a Source # (<*>) :: Last (a -> b) -> Last a -> Last b Source # liftA2 :: (a -> b -> c) -> Last a -> Last b -> Last c Source # (*>) :: Last a -> Last b -> Last b Source # (<*) :: Last a -> Last b -> Last a Source #
Applicative Down # | Since: base-4.11.0.0
Instance details Defined in Data.Ord Methods pure :: a -> Down a Source # (<*>) :: Down (a -> b) -> Down a -> Down b Source # liftA2 :: (a -> b -> c) -> Down a -> Down b -> Down c Source # (*>) :: Down a -> Down b -> Down b Source # (<*) :: Down a -> Down b -> Down a Source #
Applicative First # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods pure :: a -> First a Source # (<*>) :: First (a -> b) -> First a -> First b Source # liftA2 :: (a -> b -> c) -> First a -> First b -> First c Source # (*>) :: First a -> First b -> First b Source # (<*) :: First a -> First b -> First a Source #
Applicative Last # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods pure :: a -> Last a Source # (<*>) :: Last (a -> b) -> Last a -> Last b Source # liftA2 :: (a -> b -> c) -> Last a -> Last b -> Last c Source # (*>) :: Last a -> Last b -> Last b Source # (<*) :: Last a -> Last b -> Last a Source #
Applicative Max # | 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 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 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 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 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 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 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 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 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 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 Solo # | Since: base-4.15
Instance details Defined in GHC.Base Methods pure :: a -> Solo a Source # (<*>) :: Solo (a -> b) -> Solo a -> Solo b Source # liftA2 :: (a -> b -> c) -> Solo a -> Solo b -> Solo c Source # (*>) :: Solo a -> Solo b -> Solo b Source # (<*) :: Solo a -> Solo b -> Solo a Source #
Applicative [] # | Since: base-2.1
Instance details Defined in GHC.Base Methods pure :: a -> [a] Source # (<*>) :: [a -> b] -> [a] -> [b] Source # liftA2 :: (a -> b -> c) -> [a] -> [b] -> [c] Source # (*>) :: [a] -> [b] -> [b] Source # (<*) :: [a] -> [b] -> [a] Source #
Monad m => Applicative (WrappedMonad m) # | Since: base-2.1
Instance details Defined in Control.Applicative Methods pure :: a -> WrappedMonad m a Source # (<*>) :: WrappedMonad m (a -> b) -> WrappedMonad m a -> WrappedMonad m b Source # liftA2 :: (a -> b -> c) -> WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m c Source # (*>) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m b Source # (<*) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m a Source #
Arrow a => Applicative (ArrowMonad a) # | Since: base-4.6.0.0
Instance details Defined in Control.Arrow Methods pure :: a0 -> ArrowMonad a a0 Source # (<*>) :: ArrowMonad a (a0 -> b) -> ArrowMonad a a0 -> ArrowMonad a b Source # liftA2 :: (a0 -> b -> c) -> ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a c Source # (*>) :: ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a b Source # (<*) :: ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a a0 Source #
Applicative (ST s) # | Since: base-2.1
Instance details Defined in Control.Monad.ST.Lazy.Imp Methods pure :: a -> ST s a Source # (<*>) :: ST s (a -> b) -> ST s a -> ST s b Source # liftA2 :: (a -> b -> c) -> ST s a -> ST s b -> ST s c Source # (*>) :: ST s a -> ST s b -> ST s b Source # (<*) :: ST s a -> ST s b -> ST s a Source #
Applicative (Either e) # | Since: base-3.0
Instance details Defined in Data.Either Methods pure :: a -> Either e a Source # (<*>) :: Either e (a -> b) -> Either e a -> Either e b Source # liftA2 :: (a -> b -> c) -> Either e a -> Either e b -> Either e c Source # (*>) :: Either e a -> Either e b -> Either e b Source # (<*) :: Either e a -> Either e b -> Either e a Source #
Applicative (Proxy :: Type -> Type) # | Since: base-4.7.0.0
Instance details Defined in Data.Proxy Methods pure :: a -> Proxy a Source # (<*>) :: Proxy (a -> b) -> Proxy a -> Proxy b Source # liftA2 :: (a -> b -> c) -> Proxy a -> Proxy b -> Proxy c Source # (*>) :: Proxy a -> Proxy b -> Proxy b Source # (<*) :: Proxy a -> Proxy b -> Proxy a Source #
Applicative (U1 :: Type -> Type) # | Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods pure :: a -> U1 a Source # (<*>) :: U1 (a -> b) -> U1 a -> U1 b Source # liftA2 :: (a -> b -> c) -> U1 a -> U1 b -> U1 c Source # (*>) :: U1 a -> U1 b -> U1 b Source # (<*) :: U1 a -> U1 b -> U1 a Source #
Applicative (ST s) # | Since: base-4.4.0.0
Instance details Defined in GHC.ST Methods pure :: a -> ST s a Source # (<*>) :: ST s (a -> b) -> ST s a -> ST s b Source # liftA2 :: (a -> b -> c) -> ST s a -> ST s b -> ST s c Source # (*>) :: ST s a -> ST s b -> ST s b Source # (<*) :: ST s a -> ST s b -> ST s a Source #
Monoid a => Applicative ((,) a) # | For tuples, the `Monoid` constraint on `a` determines how the first values merge. For example, `String`s concatenate:
    ("hello ", (+15)) <*> ("world!", 2002)
    ("hello world!",2017)
Since: base-2.1
Instance details Defined in GHC.Base Methods pure :: a0 -> (a, a0) Source # (<*>) :: (a, a0 -> b) -> (a, a0) -> (a, b) Source # liftA2 :: (a0 -> b -> c) -> (a, a0) -> (a, b) -> (a, c) Source # (*>) :: (a, a0) -> (a, b) -> (a, b) Source # (<*) :: (a, a0) -> (a, b) -> (a, a0) Source #
Arrow a => Applicative (WrappedArrow a b) # | Since: base-2.1
Instance details Defined in Control.Applicative Methods pure :: a0 -> WrappedArrow a b a0 Source # (<*>) :: WrappedArrow a b (a0 -> b0) -> WrappedArrow a b a0 -> WrappedArrow a b b0 Source # liftA2 :: (a0 -> b0 -> c) -> WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b c Source # (*>) :: WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b b0 Source # (<*) :: WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0 Source #
Applicative m => Applicative (Kleisli m a) # | Since: base-4.14.0.0
Instance details Defined in Control.Arrow Methods pure :: a0 -> Kleisli m a a0 Source # (<*>) :: Kleisli m a (a0 -> b) -> Kleisli m a a0 -> Kleisli m a b Source # liftA2 :: (a0 -> b -> c) -> Kleisli m a a0 -> Kleisli m a b -> Kleisli m a c Source # (*>) :: Kleisli m a a0 -> Kleisli m a b -> Kleisli m a b Source # (<*) :: Kleisli m a a0 -> Kleisli m a b -> Kleisli m a a0 Source #
Monoid m => Applicative (Const m :: Type -> Type) # | Since: base-2.0.1
Instance details Defined in Data.Functor.Const Methods pure :: a -> Const m a Source # (<*>) :: Const m (a -> b) -> Const m a -> Const m b Source # liftA2 :: (a -> b -> c) -> Const m a -> Const m b -> Const m c Source # (*>) :: Const m a -> Const m b -> Const m b Source # (<*) :: Const m a -> Const m b -> Const m a Source #
Applicative f => Applicative (Ap f) # | Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods pure :: a -> Ap f a Source # (<*>) :: Ap f (a -> b) -> Ap f a -> Ap f b Source # liftA2 :: (a -> b -> c) -> Ap f a -> Ap f b -> Ap f c Source # (*>) :: Ap f a -> Ap f b -> Ap f b Source # (<*) :: Ap f a -> Ap f b -> Ap f a Source #
Applicative f => Applicative (Alt f) # | Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods pure :: a -> Alt f a Source # (<*>) :: Alt f (a -> b) -> Alt f a -> Alt f b Source # liftA2 :: (a -> b -> c) -> Alt f a -> Alt f b -> Alt f c Source # (*>) :: Alt f a -> Alt f b -> Alt f b Source # (<*) :: Alt f a -> Alt f b -> Alt f a Source #
Applicative f => Applicative (Rec1 f) # | Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods pure :: a -> Rec1 f a Source # (<*>) :: Rec1 f (a -> b) -> Rec1 f a -> Rec1 f b Source # liftA2 :: (a -> b -> c) -> Rec1 f a -> Rec1 f b -> Rec1 f c Source # (*>) :: Rec1 f a -> Rec1 f b -> Rec1 f b Source # (<*) :: Rec1 f a -> Rec1 f b -> Rec1 f a Source #
(Monoid a, Monoid b) => Applicative ((,,) a b) # | Since: base-4.14.0.0
Instance details Defined in GHC.Base Methods pure :: a0 -> (a, b, a0) Source # (<*>) :: (a, b, a0 -> b0) -> (a, b, a0) -> (a, b, b0) Source # liftA2 :: (a0 -> b0 -> c) -> (a, b, a0) -> (a, b, b0) -> (a, b, c) Source # (*>) :: (a, b, a0) -> (a, b, b0) -> (a, b, b0) Source # (<*) :: (a, b, a0) -> (a, b, b0) -> (a, b, a0) Source #
(Applicative f, Applicative g) => Applicative (Product f g) # | Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods pure :: a -> Product f g a Source # (<*>) :: Product f g (a -> b) -> Product f g a -> Product f g b Source # liftA2 :: (a -> b -> c) -> Product f g a -> Product f g b -> Product f g c Source # (*>) :: Product f g a -> Product f g b -> Product f g b Source # (<*) :: Product f g a -> Product f g b -> Product f g a Source #
(Applicative f, Applicative g) => Applicative (f :*: g) # | Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods pure :: a -> (f :*: g) a Source # (<*>) :: (f :*: g) (a -> b) -> (f :*: g) a -> (f :*: g) b Source # liftA2 :: (a -> b -> c) -> (f :*: g) a -> (f :*: g) b -> (f :*: g) c Source # (*>) :: (f :*: g) a -> (f :*: g) b -> (f :*: g) b Source # (<*) :: (f :*: g) a -> (f :*: g) b -> (f :*: g) a Source #
Monoid c => Applicative (K1 i c :: Type -> Type) # | Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods pure :: a -> K1 i c a Source # (<*>) :: K1 i c (a -> b) -> K1 i c a -> K1 i c b Source # liftA2 :: (a -> b -> c0) -> K1 i c a -> K1 i c b -> K1 i c c0 Source # (*>) :: K1 i c a -> K1 i c b -> K1 i c b Source # (<*) :: K1 i c a -> K1 i c b -> K1 i c a Source #
(Monoid a, Monoid b, Monoid c) => Applicative ((,,,) a b c) # | Since: base-4.14.0.0
Instance details Defined in GHC.Base Methods pure :: a0 -> (a, b, c, a0) Source # (<*>) :: (a, b, c, a0 -> b0) -> (a, b, c, a0) -> (a, b, c, b0) Source # liftA2 :: (a0 -> b0 -> c0) -> (a, b, c, a0) -> (a, b, c, b0) -> (a, b, c, c0) Source # (*>) :: (a, b, c, a0) -> (a, b, c, b0) -> (a, b, c, b0) Source # (<*) :: (a, b, c, a0) -> (a, b, c, b0) -> (a, b, c, a0) Source #
Applicative ((->) r) # | Since: base-2.1
Instance details Defined in GHC.Base Methods pure :: a -> r -> a Source # (<*>) :: (r -> (a -> b)) -> (r -> a) -> r -> b Source # liftA2 :: (a -> b -> c) -> (r -> a) -> (r -> b) -> r -> c Source # (*>) :: (r -> a) -> (r -> b) -> r -> b Source # (<*) :: (r -> a) -> (r -> b) -> r -> a Source #
(Applicative f, Applicative g) => Applicative (Compose f g) # | Since: base-4.9.0.0
Instance details Defined in Data.Functor.Compose Methods pure :: a -> Compose f g a Source # (<*>) :: Compose f g (a -> b) -> Compose f g a -> Compose f g b Source # liftA2 :: (a -> b -> c) -> Compose f g a -> Compose f g b -> Compose f g c Source # (*>) :: Compose f g a -> Compose f g b -> Compose f g b Source # (<*) :: Compose f g a -> Compose f g b -> Compose f g a Source #
(Applicative f, Applicative g) => Applicative (f :.: g) # | Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods pure :: a -> (f :.: g) a Source # (<*>) :: (f :.: g) (a -> b) -> (f :.: g) a -> (f :.: g) b Source # liftA2 :: (a -> b -> c) -> (f :.: g) a -> (f :.: g) b -> (f :.: g) c Source # (*>) :: (f :.: g) a -> (f :.: g) b -> (f :.: g) b Source # (<*) :: (f :.: g) a -> (f :.: g) b -> (f :.: g) a Source #
Applicative f => Applicative (M1 i c f) # | Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods pure :: a -> M1 i c f a Source # (<*>) :: M1 i c f (a -> b) -> M1 i c f a -> M1 i c f b Source # liftA2 :: (a -> b -> c0) -> M1 i c f a -> M1 i c f b -> M1 i c f c0 Source # (*>) :: M1 i c f a -> M1 i c f b -> M1 i c f b Source # (<*) :: M1 i c f a -> M1 i c f b -> M1 i c f a Source #

class Semigroup a where Source #

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

Instances should satisfy the following:

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

Since: base-4.9.0.0

Minimal complete definition

(<>)

Methods

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

An associative operation.

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

sconcat :: NonEmpty a -> a Source #

Reduce a non-empty list with `<>`

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

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

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

Repeat a value `n` times.

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

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

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

#### Instances

Instances details

Semigroup All # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: All -> All -> All Source # sconcat :: NonEmpty All -> All Source # stimes :: Integral b => b -> All -> All Source #
Semigroup Any # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Any -> Any -> Any Source # sconcat :: NonEmpty Any -> Any Source # stimes :: Integral b => b -> Any -> Any Source #
Semigroup Void # | 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 Event # | Since: base-4.10.0.0
Instance details Defined in GHC.Event.Internal.Types Methods (<>) :: Event -> Event -> Event Source # sconcat :: NonEmpty Event -> Event Source # stimes :: Integral b => b -> Event -> Event Source #
Semigroup Lifetime # | Since: base-4.10.0.0
Instance details Defined in GHC.Event.Internal.Types Methods (<>) :: Lifetime -> Lifetime -> Lifetime Source # sconcat :: NonEmpty Lifetime -> Lifetime Source # stimes :: Integral b => b -> Lifetime -> Lifetime Source #
Semigroup Ordering # | Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: Ordering -> Ordering -> Ordering Source # sconcat :: NonEmpty Ordering -> Ordering Source # stimes :: Integral b => b -> Ordering -> Ordering Source #
Semigroup () # | Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: () -> () -> () Source # sconcat :: NonEmpty () -> () Source # stimes :: Integral b => b -> () -> () Source #
Bits a => Semigroup (And a) # | Since: base-4.16
Instance details Defined in Data.Bits Methods (<>) :: And a -> And a -> And a Source # sconcat :: NonEmpty (And a) -> And a Source # stimes :: Integral b => b -> And a -> And a Source #
FiniteBits a => Semigroup (Iff a) # | This constraint is arguably too strong. However, as some types (such as `Natural`) have undefined `complement`, this is the only safe choice. Since: base-4.16
Instance details Defined in Data.Bits Methods (<>) :: Iff a -> Iff a -> Iff a Source # sconcat :: NonEmpty (Iff a) -> Iff a Source # stimes :: Integral b => b -> Iff a -> Iff a Source #
Bits a => Semigroup (Ior a) # | Since: base-4.16
Instance details Defined in Data.Bits Methods (<>) :: Ior a -> Ior a -> Ior a Source # sconcat :: NonEmpty (Ior a) -> Ior a Source # stimes :: Integral b => b -> Ior a -> Ior a Source #
Bits a => Semigroup (Xor a) # | Since: base-4.16
Instance details Defined in Data.Bits Methods (<>) :: Xor a -> Xor a -> Xor a Source # sconcat :: NonEmpty (Xor a) -> Xor a Source # stimes :: Integral b => b -> Xor a -> Xor a Source #
Semigroup (Comparison a) # | `(`<>`)` on comparisons combines results with `(`<>`) @Ordering`. Without newtypes this equals ``liftA2` (`liftA2` (`<>`))`.
    (<>) :: Comparison a -> Comparison a -> Comparison a
    Comparison cmp <> Comparison cmp' = Comparison a a' ->
      cmp a a' <> cmp a a'
Instance details Defined in Data.Functor.Contravariant 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) # | `(`<>`)` on equivalences uses logical conjunction `(`&&`)` on the results. Without newtypes this equals ``liftA2` (`liftA2` (&&))`.
    (<>) :: Equivalence a -> Equivalence a -> Equivalence a
    Equivalence equiv <> Equivalence equiv' = Equivalence a b ->
      equiv a b && equiv a b
Instance details Defined in Data.Functor.Contravariant 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) # | `(`<>`)` on predicates uses logical conjunction `(`&&`)` on the results. Without newtypes this equals ``liftA2` (&&)`.
    (<>) :: Predicate a -> Predicate a -> Predicate a
    Predicate pred <> Predicate pred' = Predicate a ->
      pred a && pred' a
Instance details Defined in Data.Functor.Contravariant Methods (<>) :: Predicate a -> Predicate a -> Predicate a Source # sconcat :: NonEmpty (Predicate a) -> Predicate a Source # stimes :: Integral b => b -> Predicate a -> Predicate a Source #
Semigroup a => Semigroup (Identity a) # | Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods (<>) :: Identity a -> Identity a -> Identity a Source # sconcat :: NonEmpty (Identity a) -> Identity a Source # stimes :: Integral b => b -> Identity a -> Identity 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 (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 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 #
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 #
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 #
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 #
Monoid m => Semigroup (WrappedMonoid m) # | Since: base-4.9.0.0
Instance details 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) # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Dual a -> Dual a -> Dual a Source # sconcat :: NonEmpty (Dual a) -> Dual a Source # stimes :: Integral b => b -> Dual a -> Dual a Source #
Semigroup (Endo a) # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Endo a -> Endo a -> Endo a Source # sconcat :: NonEmpty (Endo a) -> Endo a Source # stimes :: Integral b => b -> Endo a -> Endo a Source #
Num a => Semigroup (Product a) # | 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 (NonEmpty a) # | Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: NonEmpty a -> NonEmpty a -> NonEmpty a Source # sconcat :: NonEmpty (NonEmpty a) -> NonEmpty a Source # stimes :: Integral b => b -> NonEmpty a -> NonEmpty 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 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 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 (a) # | Since: base-4.15
Instance details Defined in GHC.Base Methods (<>) :: (a) -> (a) -> (a) Source # sconcat :: NonEmpty (a) -> (a) Source # stimes :: Integral b => b -> (a) -> (a) Source #
Semigroup [a] # | Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: [a] -> [a] -> [a] Source # sconcat :: NonEmpty [a] -> [a] Source # stimes :: Integral b => b -> [a] -> [a] Source #
Semigroup (Either a b) # | Since: base-4.9.0.0
Instance details Defined in Data.Either Methods (<>) :: Either a b -> Either a b -> Either a b Source # sconcat :: NonEmpty (Either a b) -> Either a b Source # stimes :: Integral b0 => b0 -> Either a b -> Either a b Source #
Semigroup a => Semigroup (Op a b) # | `(`<>`) @(Op a b)` without newtypes is `(`<>`) @(b->a)` = `liftA2 (`<>`)`. This lifts the `Semigroup` operation `(`<>`)` over the output of `a`.
    (<>) :: Op a b -> Op a b -> Op a b
    Op f <> Op g = Op a -> f a <> g a
Instance details Defined in Data.Functor.Contravariant Methods (<>) :: Op a b -> Op a b -> Op a b Source # sconcat :: NonEmpty (Op a b) -> Op a b Source # stimes :: Integral b0 => b0 -> Op a b -> Op a b Source #
Semigroup (Proxy s) # | Since: base-4.9.0.0
Instance details Defined in Data.Proxy Methods (<>) :: Proxy s -> Proxy s -> Proxy s Source # sconcat :: NonEmpty (Proxy s) -> Proxy s Source # stimes :: Integral b => b -> Proxy s -> Proxy s Source #
Semigroup (U1 p) # | Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods (<>) :: U1 p -> U1 p -> U1 p Source # sconcat :: NonEmpty (U1 p) -> U1 p Source # stimes :: Integral b => b -> U1 p -> U1 p Source #
Semigroup (V1 p) # | Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods (<>) :: V1 p -> V1 p -> V1 p Source # sconcat :: NonEmpty (V1 p) -> V1 p Source # stimes :: Integral b => b -> V1 p -> V1 p Source #
Semigroup a => Semigroup (ST s a) # | Since: base-4.11.0.0
Instance details Defined in GHC.ST Methods (<>) :: ST s a -> ST s a -> ST s a Source # sconcat :: NonEmpty (ST s a) -> ST s a Source # stimes :: Integral b => b -> ST s a -> ST s a Source #
Semigroup b => Semigroup (a -> b) # | Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: (a -> b) -> (a -> b) -> a -> b Source # sconcat :: NonEmpty (a -> b) -> a -> b Source # stimes :: Integral b0 => b0 -> (a -> b) -> a -> b Source #
(Semigroup a, Semigroup b) => Semigroup (a, b) # | Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: (a, b) -> (a, b) -> (a, b) Source # sconcat :: NonEmpty (a, b) -> (a, b) Source # stimes :: Integral b0 => b0 -> (a, b) -> (a, b) Source #
Semigroup a => Semigroup (Const a b) # | Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods (<>) :: Const a b -> Const a b -> Const a b Source # sconcat :: NonEmpty (Const a b) -> Const a b Source # stimes :: Integral b0 => b0 -> Const a b -> Const a b Source #
(Applicative f, Semigroup a) => Semigroup (Ap f a) # | Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods (<>) :: Ap f a -> Ap f a -> Ap f a Source # sconcat :: NonEmpty (Ap f a) -> Ap f a Source # stimes :: Integral b => b -> Ap f a -> Ap f a Source #
Alternative f => Semigroup (Alt f a) # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Alt f a -> Alt f a -> Alt f a Source # sconcat :: NonEmpty (Alt f a) -> Alt f a Source # stimes :: Integral b => b -> Alt f a -> Alt f a Source #
Semigroup (f p) => Semigroup (Rec1 f p) # | 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 #
(Semigroup (f a), Semigroup (g a)) => Semigroup (Product f g a) # | Since: base-4.16.0.0
Instance details Defined in Data.Functor.Product Methods (<>) :: Product f g a -> Product f g a -> Product f g a Source # sconcat :: NonEmpty (Product f g a) -> Product f g a Source # stimes :: Integral b => b -> Product f g a -> Product f g a Source #
(Semigroup (f p), Semigroup (g p)) => Semigroup ((f :*: g) p) # | Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods (<>) :: (f :*: g) p -> (f :*: g) p -> (f :*: g) p Source # sconcat :: NonEmpty ((f :*: g) p) -> (f :*: g) p Source # stimes :: Integral b => b -> (f :*: g) p -> (f :*: g) p Source #
Semigroup c => Semigroup (K1 i c p) # | Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods (<>) :: K1 i c p -> K1 i c p -> K1 i c p Source # sconcat :: NonEmpty (K1 i c p) -> K1 i c p Source # stimes :: Integral b => b -> K1 i c p -> K1 i c p Source #
(Semigroup a, Semigroup b, Semigroup c, Semigroup d) => Semigroup (a, b, c, d) # | Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) Source # sconcat :: NonEmpty (a, b, c, d) -> (a, b, c, d) Source # stimes :: Integral b0 => b0 -> (a, b, c, d) -> (a, b, c, d) Source #
Semigroup (f (g a)) => Semigroup (Compose f g a) # | Since: base-4.16.0.0
Instance details Defined in Data.Functor.Compose Methods (<>) :: Compose f g a -> Compose f g a -> Compose f g a Source # sconcat :: NonEmpty (Compose f g a) -> Compose f g a Source # stimes :: Integral b => b -> Compose f g a -> Compose f g a Source #
Semigroup (f (g p)) => Semigroup ((f :.: g) p) # | Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods (<>) :: (f :.: g) p -> (f :.: g) p -> (f :.: g) p Source # sconcat :: NonEmpty ((f :.: g) p) -> (f :.: g) p Source # stimes :: Integral b => b -> (f :.: g) p -> (f :.: g) p Source #
Semigroup (f p) => Semigroup (M1 i c f p) # | Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods (<>) :: M1 i c f p -> M1 i c f p -> M1 i c f p Source # sconcat :: NonEmpty (M1 i c f p) -> M1 i c f p Source # stimes :: Integral b => b -> M1 i c f p -> M1 i c f p Source #
(Semigroup a, Semigroup b, Semigroup c, Semigroup d, Semigroup e) => Semigroup (a, b, c, d, e) # | 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 `newtype`s and make those instances of `Monoid`, e.g. `Sum` and `Product`.

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

Minimal complete definition

mempty

Methods

mempty :: a Source #

Identity of `mappend`

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

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

An associative operation

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

mconcat :: [a] -> a Source #

Fold a list using the monoid.

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

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

#### Instances

Instances details

Monoid All # | 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 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 Event # | Since: base-4.4.0.0
Instance details Defined in GHC.Event.Internal.Types Methods mempty :: Event Source # mappend :: Event -> Event -> Event Source # mconcat :: [Event] -> Event Source #
Monoid Lifetime # | `mappend` takes the longer of two lifetimes. Since: base-4.8.0.0
Instance details Defined in GHC.Event.Internal.Types Methods mempty :: Lifetime Source # mappend :: Lifetime -> Lifetime -> Lifetime Source # mconcat :: [Lifetime] -> Lifetime Source #
Monoid Ordering # | Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: Ordering Source # mappend :: Ordering -> Ordering -> Ordering Source # mconcat :: [Ordering] -> Ordering Source #
Monoid () # | Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: () Source # mappend :: () -> () -> () Source # mconcat :: [()] -> () Source #
FiniteBits a => Monoid (And a) # | This constraint is arguably too strong. However, as some types (such as `Natural`) have undefined `complement`, this is the only safe choice. Since: base-4.16
Instance details Defined in Data.Bits Methods mempty :: And a Source # mappend :: And a -> And a -> And a Source # mconcat :: [And a] -> And a Source #
FiniteBits a => Monoid (Iff a) # | This constraint is arguably too strong. However, as some types (such as `Natural`) have undefined `complement`, this is the only safe choice. Since: base-4.16
Instance details Defined in Data.Bits Methods mempty :: Iff a Source # mappend :: Iff a -> Iff a -> Iff a Source # mconcat :: [Iff a] -> Iff a Source #
Bits a => Monoid (Ior a) # | Since: base-4.16
Instance details Defined in Data.Bits Methods mempty :: Ior a Source # mappend :: Ior a -> Ior a -> Ior a Source # mconcat :: [Ior a] -> Ior a Source #
Bits a => Monoid (Xor a) # | Since: base-4.16
Instance details Defined in Data.Bits Methods mempty :: Xor a Source # mappend :: Xor a -> Xor a -> Xor a Source # mconcat :: [Xor a] -> Xor a Source #
Monoid (Comparison a) # | ``mempty`` on comparisons always returns `EQ`. Without newtypes this equals ``pure` (`pure` EQ)`.
    mempty :: Comparison a
    mempty = Comparison _ _ -> EQ
Instance details Defined in Data.Functor.Contravariant Methods mempty :: Comparison a Source # mappend :: Comparison a -> Comparison a -> Comparison a Source # mconcat :: [Comparison a] -> Comparison a Source #
Monoid (Equivalence a) # | ``mempty`` on equivalences always returns `True`. Without newtypes this equals ``pure` (`pure` True)`.
    mempty :: Equivalence a
    mempty = Equivalence _ _ -> True
Instance details Defined in Data.Functor.Contravariant Methods mempty :: Equivalence a Source # mappend :: Equivalence a -> Equivalence a -> Equivalence a Source # mconcat :: [Equivalence a] -> Equivalence a Source #
Monoid (Predicate a) # | ``mempty`` on predicates always returns `True`. Without newtypes this equals ``pure` True`.
    mempty :: Predicate a
    mempty = _ -> True
Instance details Defined in Data.Functor.Contravariant Methods mempty :: Predicate a Source # mappend :: Predicate a -> Predicate a -> Predicate a Source # mconcat :: [Predicate a] -> Predicate a Source #
Monoid a => Monoid (Identity a) # | Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods mempty :: Identity a Source # mappend :: Identity a -> Identity a -> Identity a Source # mconcat :: [Identity a] -> Identity 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 (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 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 #
(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 m => Monoid (WrappedMonoid m) # | Since: base-4.9.0.0
Instance details 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) # | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Dual a Source # mappend :: Dual a -> Dual a -> Dual a Source # mconcat :: [Dual a] -> Dual a Source #
Monoid (Endo a) # | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Endo a Source # mappend :: Endo a -> Endo a -> Endo a Source # mconcat :: [Endo a] -> Endo a Source #
Num a => Monoid (Product a) # | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Product a Source # mappend :: Product a -> Product a -> Product a Source # mconcat :: [Product a] -> Product a Source #
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 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 (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 #
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 (a) # | Since: base-4.15
Instance details Defined in GHC.Base Methods mempty :: (a) Source # mappend :: (a) -> (a) -> (a) Source # mconcat :: [(a)] -> (a) Source #
Monoid [a] # | Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: [a] Source # mappend :: [a] -> [a] -> [a] Source # mconcat :: [[a]] -> [a] Source #
Monoid a => Monoid (Op a b) # | ``mempty` @(Op a b)` without newtypes is `mempty @(b->a)` = `_ -> mempty`.
    mempty :: Op a b
    mempty = Op _ -> mempty
Instance details Defined in Data.Functor.Contravariant Methods mempty :: Op a b Source # mappend :: Op a b -> Op a b -> Op a b Source # mconcat :: [Op a b] -> Op a b Source #
Monoid (Proxy s) # | Since: base-4.7.0.0
Instance details Defined in Data.Proxy Methods mempty :: Proxy s Source # mappend :: Proxy s -> Proxy s -> Proxy s Source # mconcat :: [Proxy s] -> Proxy s Source #
Monoid (U1 p) # | Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods mempty :: U1 p Source # mappend :: U1 p -> U1 p -> U1 p Source # mconcat :: [U1 p] -> U1 p Source #
Monoid a => Monoid (ST s a) # | Since: base-4.11.0.0
Instance details Defined in GHC.ST Methods mempty :: ST s a Source # mappend :: ST s a -> ST s a -> ST s a Source # mconcat :: [ST s a] -> ST s a Source #
Monoid b => Monoid (a -> b) # | Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: a -> b Source # mappend :: (a -> b) -> (a -> b) -> a -> b Source # mconcat :: [a -> b] -> a -> b Source #
(Monoid a, Monoid b) => Monoid (a, b) # | Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: (a, b) Source # mappend :: (a, b) -> (a, b) -> (a, b) Source # mconcat :: [(a, b)] -> (a, b) Source #
Monoid a => Monoid (Const a b) # | Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods mempty :: Const a b Source # mappend :: Const a b -> Const a b -> Const a b Source # mconcat :: [Const a b] -> Const a b Source #
(Applicative f, Monoid a) => Monoid (Ap f a) # | Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods mempty :: Ap f a Source # mappend :: Ap f a -> Ap f a -> Ap f a Source # mconcat :: [Ap f a] -> Ap f a Source #
Alternative f => Monoid (Alt f a) # | Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Alt f a Source # mappend :: Alt f a -> Alt f a -> Alt f a Source # mconcat :: [Alt f a] -> Alt f a Source #
Monoid (f p) => Monoid (Rec1 f p) # | 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 #
(Monoid (f a), Monoid (g a)) => Monoid (Product f g a) # | Since: base-4.16.0.0
Instance details Defined in Data.Functor.Product Methods mempty :: Product f g a Source # mappend :: Product f g a -> Product f g a -> Product f g a Source # mconcat :: [Product f g a] -> Product f g a Source #
(Monoid (f p), Monoid (g p)) => Monoid ((f :*: g) p) # | Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods mempty :: (f :*: g) p Source # mappend :: (f :*: g) p -> (f :*: g) p -> (f :*: g) p Source # mconcat :: [(f :*: g) p] -> (f :*: g) p Source #
Monoid c => Monoid (K1 i c p) # | Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods mempty :: K1 i c p Source # mappend :: K1 i c p -> K1 i c p -> K1 i c p Source # mconcat :: [K1 i c p] -> K1 i c p Source #
(Monoid a, Monoid b, Monoid c, Monoid d) => Monoid (a, b, c, d) # | Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: (a, b, c, d) Source # mappend :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) Source # mconcat :: [(a, b, c, d)] -> (a, b, c, d) Source #
Monoid (f (g a)) => Monoid (Compose f g a) # | Since: base-4.16.0.0
Instance details Defined in Data.Functor.Compose Methods mempty :: Compose f g a Source # mappend :: Compose f g a -> Compose f g a -> Compose f g a Source # mconcat :: [Compose f g a] -> Compose f g a Source #
Monoid (f (g p)) => Monoid ((f :.: g) p) # | Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods mempty :: (f :.: g) p Source # mappend :: (f :.: g) p -> (f :.: g) p -> (f :.: g) p Source # mconcat :: [(f :.: g) p] -> (f :.: g) p Source #
Monoid (f p) => Monoid (M1 i c f p) # | Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods mempty :: M1 i c f p Source # mappend :: M1 i c f p -> M1 i c f p -> M1 i c f p Source # mconcat :: [M1 i c f p] -> M1 i c f p Source #
(Monoid a, Monoid b, Monoid c, Monoid d, Monoid e) => Monoid (a, b, c, d, e) # | Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: (a, b, c, d, e) Source # mappend :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) Source # mconcat :: [(a, b, c, d, e)] -> (a, b, c, d, e) Source #

type String = [Char] Source #

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

See Data.List for operations on lists.

data Opaque Source #

Constructors

forall a. O a |

($!) :: forall r a (b :: TYPE r). (a -> b) -> a -> b infixr 0 Source #

Strict (call-by-value) application operator. It takes a function and an argument, evaluates the argument to weak head normal form (WHNF), then calls the function with that value.

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

Function composition.

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

A variant of `<*>` with the arguments reversed.

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

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

ap :: Monad m => m (a -> b) -> m a -> m b Source #

In many situations, the `liftM` operations can be replaced by uses of `ap`, which promotes function application.

    return f `ap` x1 `ap` ... `ap` xn

is equivalent to

    liftMn f x1 x2 ... xn

asTypeOf :: a -> a -> a Source #

`asTypeOf` is a type-restricted version of `const`. It is usually used as an infix operator, and its typing forces its first argument (which is usually overloaded) to have the same type as the second.

const :: a -> b -> a Source #

`const x` is a unary function which evaluates to `x` for all inputs.

    >>> const 42 "hello"
    42

    >>> map (const 42) [0..3]
    [42,42,42,42]

divInt :: Int -> Int -> Int Source #

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

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

failIO :: String -> IO a Source #

flip :: (a -> b -> c) -> b -> a -> c Source #

``flip` f` takes its (first) two arguments in the reverse order of `f`.

    >>> flip (++) "hello" "world"
    "worldhello"

getTag :: a -> Int# Source #

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

iShiftL# :: Int# -> Int# -> Int# Source #

Shift the argument left by the specified number of bits (which must be non-negative).

iShiftRA# :: Int# -> Int# -> Int# Source #

Shift the argument right (signed) by the specified number of bits (which must be non-negative). The RA means "right, arithmetic" (as opposed to RL for logical)

iShiftRL# :: Int# -> Int# -> Int# Source #

Shift the argument right (unsigned) by the specified number of bits (which must be non-negative). The RL means "right, logical" (as opposed to RA for arithmetic)

id :: a -> a Source #

Identity function.

    id x = x

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

Lift a function to actions. Equivalent to Functor's `fmap` but implemented using only `Applicative`'s methods: `liftA f a = pure f * a`

As such this function may be used to implement a `Functor` instance from an `Applicative` one.

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

Lift a ternary function to actions.

liftM :: Monad m => (a1 -> r) -> m a1 -> m r Source #

Promote a function to a monad.

liftM2 :: Monad m => (a1 -> a2 -> r) -> m a1 -> m a2 -> m r Source #

Promote a function to a monad, scanning the monadic arguments from left to right. For example,

    liftM2 (+) [0,1] [0,2] = [0,2,1,3]
    liftM2 (+) (Just 1) Nothing = Nothing

liftM3 :: Monad m => (a1 -> a2 -> a3 -> r) -> m a1 -> m a2 -> m a3 -> m r Source #

Promote a function to a monad, scanning the monadic arguments from left to right (cf. `liftM2`).

liftM4 :: Monad m => (a1 -> a2 -> a3 -> a4 -> r) -> m a1 -> m a2 -> m a3 -> m a4 -> m r Source #

Promote a function to a monad, scanning the monadic arguments from left to right (cf. `liftM2`).

liftM5 :: Monad m => (a1 -> a2 -> a3 -> a4 -> a5 -> r) -> m a1 -> m a2 -> m a3 -> m a4 -> m a5 -> m r Source #

Promote a function to a monad, scanning the monadic arguments from left to right (cf. `liftM2`).

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

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

``mapM` f` is equivalent to ``sequence` . `map` f`.

maxInt :: Int Source #

minInt :: Int Source #

modInt :: Int -> Int -> Int Source #

ord :: Char -> Int Source #

The `fromEnum` method restricted to the type `Char`.

quotInt :: Int -> Int -> Int Source #

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

remInt :: Int -> Int -> Int Source #

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

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

shiftL# :: Word# -> Int# -> Word# Source #

Shift the argument left by the specified number of bits (which must be non-negative).

shiftRL# :: Word# -> Int# -> Word# Source #

Shift the argument right by the specified number of bits (which must be non-negative). The RL means "right, logical" (as opposed to RA for arithmetic) (although an arithmetic right shift wouldn't make sense for Word#)

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

unsafeChr :: Int -> Char Source #

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

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

when :: Applicative f => Bool -> f () -> f () Source #

Conditional execution of `Applicative` expressions. For example,

    when debug (putStrLn "Debugging")

will output the string `Debugging` if the Boolean value `debug` is `True`, and otherwise do nothing.

class Applicative f => Alternative f where Source #

A monoid on applicative functors.

If defined, `some` and `many` should be the least solutions of the equations:

-     some v = (:) <$> v <*> many v

-     many v = some v <|> pure []

Minimal complete definition

empty, (<|>)

Methods

empty :: f a Source #

The identity of `<|>`

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

An associative binary operation

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

One or more.

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

Zero or more.

#### Instances

Instances details

Alternative ZipList # | 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 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 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 Methods empty :: ReadPrec a Source # (<|>) :: ReadPrec a -> ReadPrec a -> ReadPrec a Source # some :: ReadPrec a -> ReadPrec [a] Source # many :: ReadPrec a -> ReadPrec [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 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 [] # | Since: base-2.1
Instance details Defined in GHC.Base Methods empty :: [a] Source # (<|>) :: [a] -> [a] -> [a] Source # some :: [a] -> [[a]] Source # many :: [a] -> [[a]] Source #
MonadPlus m => Alternative (WrappedMonad m) # | Since: base-2.1
Instance details Defined in Control.Applicative Methods empty :: WrappedMonad m a Source # (<|>) :: WrappedMonad m a -> WrappedMonad m a -> WrappedMonad m a Source # some :: WrappedMonad m a -> WrappedMonad m [a] Source # many :: WrappedMonad m a -> WrappedMonad m [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 #
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 #
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 #
(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 m => Alternative (Kleisli m a) # | Since: base-4.14.0.0
Instance details Defined in Control.Arrow Methods empty :: Kleisli m a a0 Source # (<|>) :: Kleisli m a a0 -> Kleisli m a a0 -> Kleisli m a a0 Source # some :: Kleisli m a a0 -> Kleisli m a [a0] Source # many :: Kleisli m a a0 -> Kleisli m a [a0] Source #
Alternative f => Alternative (Ap f) # | Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods empty :: Ap f a Source # (<|>) :: Ap f a -> Ap f a -> Ap f a Source # some :: Ap f a -> Ap f [a] Source # many :: Ap f a -> Ap f [a] Source #
Alternative f => Alternative (Alt f) # | Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods empty :: Alt f a Source # (<|>) :: Alt f a -> Alt f a -> Alt f a Source # some :: Alt f a -> Alt f [a] Source # many :: Alt f a -> Alt f [a] Source #
Alternative f => Alternative (Rec1 f) # | Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods empty :: Rec1 f a Source # (<|>) :: Rec1 f a -> Rec1 f a -> Rec1 f a Source # some :: Rec1 f a -> Rec1 f [a] Source # many :: Rec1 f a -> Rec1 f [a] Source #
(Alternative f, Alternative g) => Alternative (Product f g) # | Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods empty :: Product f g a Source # (<|>) :: Product f g a -> Product f g a -> Product f g a Source # some :: Product f g a -> Product f g [a] Source # many :: Product f g a -> Product f g [a] Source #
(Alternative f, Alternative g) => Alternative (f :*: g) # | 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 #
(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 => 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 #

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

Monads that also support choice and failure.

Minimal complete definition

Nothing

Methods

mzero :: m a Source #

The identity of `mplus`. It should also satisfy the equations

    mzero >>= f  =  mzero
    v >> mzero   =  mzero

The default definition is

    mzero = empty

mplus :: m a -> m a -> m a Source #

An associative operation. The default definition is

    mplus = (<|>)

#### Instances

Instances details

MonadPlus STM # | Since: base-4.3.0.0
Instance details Defined in GHC.Conc.Sync Methods mzero :: STM a Source # mplus :: STM a -> STM a -> STM a Source #
MonadPlus ReadP # | 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 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 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 [] # | Since: base-2.1
Instance details Defined in GHC.Base Methods mzero :: [a] Source # mplus :: [a] -> [a] -> [a] Source #
(ArrowApply a, ArrowPlus a) => MonadPlus (ArrowMonad a) # | Since: base-4.6.0.0
Instance details Defined in Control.Arrow Methods mzero :: ArrowMonad a a0 Source # mplus :: ArrowMonad a a0 -> ArrowMonad a a0 -> ArrowMonad a a0 Source #
MonadPlus (Proxy :: Type -> Type) # | Since: base-4.9.0.0
Instance details Defined in Data.Proxy Methods mzero :: Proxy a Source # mplus :: Proxy a -> Proxy a -> Proxy a Source #
MonadPlus (U1 :: Type -> Type) # | Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods mzero :: U1 a Source # mplus :: U1 a -> U1 a -> U1 a Source #
MonadPlus m => MonadPlus (Kleisli m a) # | Since: base-4.14.0.0
Instance details Defined in Control.Arrow Methods mzero :: Kleisli m a a0 Source # mplus :: Kleisli m a a0 -> Kleisli m a a0 -> Kleisli m a a0 Source #
MonadPlus f => MonadPlus (Ap f) # | Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods mzero :: Ap f a Source # mplus :: Ap f a -> Ap f a -> Ap f a Source #
MonadPlus f => MonadPlus (Alt f) # | Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods mzero :: Alt f a Source # mplus :: Alt f a -> Alt f a -> Alt f a Source #
MonadPlus f => MonadPlus (Rec1 f) # | Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods mzero :: Rec1 f a Source # mplus :: Rec1 f a -> Rec1 f a -> Rec1 f a Source #
(MonadPlus f, MonadPlus g) => MonadPlus (Product f g) # | Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods mzero :: Product f g a Source # mplus :: Product f g a -> Product f g a -> Product f g a Source #
(MonadPlus f, MonadPlus g) => MonadPlus (f :*: g) # | Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods mzero :: (f :*: g) a Source # mplus :: (f :*: g) a -> (f :*: g) a -> (f :*: g) a Source #
MonadPlus f => MonadPlus (M1 i c f) # | 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 #

data NonEmpty a Source #

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

Since: base-4.9.0.0

Constructors

a :| [a] infixr 5 |

#### Instances

Instances details

MonadFix NonEmpty # | Since: base-4.9.0.0
Instance details Defined in Control.Monad.Fix Methods mfix :: (a -> NonEmpty a) -> 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 #
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 #
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 #
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 #
Read1 NonEmpty # | Since: base-4.10.0.0
Instance details 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 # | Since: base-4.10.0.0
Instance details Defined in Data.Functor.Classes Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> NonEmpty a -> ShowS Source # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [NonEmpty a] -> ShowS Source #
Traversable NonEmpty # | Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> NonEmpty a -> f (NonEmpty b) Source # sequenceA :: Applicative f => NonEmpty (f a) -> f (NonEmpty a) Source # mapM :: Monad m => (a -> m b) -> NonEmpty a -> m (NonEmpty b) Source # sequence :: Monad m => NonEmpty (m a) -> m (NonEmpty a) Source #
Applicative NonEmpty # | Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods pure :: a -> NonEmpty a Source # (<*>) :: NonEmpty (a -> b) -> NonEmpty a -> NonEmpty b Source # liftA2 :: (a -> b -> c) -> NonEmpty a -> NonEmpty b -> NonEmpty c Source # (*>) :: NonEmpty a -> NonEmpty b -> NonEmpty b Source # (<*) :: NonEmpty a -> NonEmpty b -> NonEmpty a Source #
Functor NonEmpty # | Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods fmap :: (a -> b) -> NonEmpty a -> NonEmpty b Source # (<$) :: a -> NonEmpty b -> NonEmpty a Source #
Monad NonEmpty # | 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 #
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 #
Semigroup (NonEmpty a) # | Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: NonEmpty a -> NonEmpty a -> NonEmpty a Source # sconcat :: NonEmpty (NonEmpty a) -> NonEmpty a Source # stimes :: Integral b => b -> NonEmpty a -> NonEmpty a 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 #
Generic (NonEmpty a) # |
Instance details Defined in GHC.Generics Associated Types type Rep (NonEmpty a) :: Type -> Type Source # Methods from :: NonEmpty a -> Rep (NonEmpty a) x Source # to :: Rep (NonEmpty a) x -> NonEmpty a Source #
Read a => Read (NonEmpty a) # | Since: base-4.11.0.0
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS (NonEmpty a) Source # readList :: ReadS [NonEmpty a] Source # readPrec :: ReadPrec (NonEmpty a) Source # readListPrec :: ReadPrec [NonEmpty a] Source #
Show a => Show (NonEmpty a) # | Since: base-4.11.0.0
Instance details Defined in GHC.Show Methods showsPrec :: Int -> NonEmpty a -> ShowS Source # show :: NonEmpty a -> String Source # showList :: [NonEmpty a] -> ShowS 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 #
Ord a => Ord (NonEmpty a) # | Since: base-4.9.0.0
Instance details 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 # max :: NonEmpty a -> NonEmpty a -> NonEmpty a Source # min :: NonEmpty a -> NonEmpty a -> NonEmpty a Source #
Generic1 NonEmpty # |
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 Item (NonEmpty a) # |
Instance details Defined in GHC.Exts type Item (NonEmpty a) = a
type Rep (NonEmpty a) # | Since: base-4.6.0.0
Instance details 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 # | Since: base-4.6.0.0
Instance details 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 [])))

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