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
data Opaque = forall a. O a
type String = [Char]
data NonEmpty a = a :| [a]
class (Alternative m, Monad m) => MonadPlus m where
- mzero :: m a
- mplus :: m a -> m a -> m a
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]
(<**>) :: Applicative f => f a -> f (a -> b) -> f b
liftA :: Applicative f => (a -> b) -> f a -> f b
liftA3 :: Applicative f => (a -> b -> c -> d) -> f a -> f b -> f c -> f d
(=<<) :: Monad m => (a -> m b) -> m a -> m b
when :: Applicative f => Bool -> f () -> f ()
sequence :: Monad m => [m a] -> m [a]
mapM :: Monad m => (a -> m b) -> [a] -> m [b]
liftM :: Monad m => (a1 -> r) -> m a1 -> m r
liftM2 :: Monad m => (a1 -> a2 -> r) -> m a1 -> m a2 -> m r
liftM3 :: Monad m => (a1 -> a2 -> a3 -> r) -> m a1 -> m a2 -> m a3 -> m r
liftM4 :: Monad m => (a1 -> a2 -> a3 -> a4 -> r) -> m a1 -> m a2 -> m a3 -> m a4 -> m r
liftM5 :: Monad m => (a1 -> a2 -> a3 -> a4 -> a5 -> r) -> m a1 -> m a2 -> m a3 -> m a4 -> m a5 -> m r
ap :: Monad m => m (a -> b) -> m a -> m b
mapFB :: (elt -> lst -> lst) -> (a -> elt) -> a -> lst -> lst
unsafeChr :: Int -> Char
ord :: Char -> Int
minInt :: Int
maxInt :: Int
id :: a -> a
const :: a -> b -> a
(.) :: (b -> c) -> (a -> b) -> a -> c
flip :: (a -> b -> c) -> b -> a -> c
($!) :: forall r a (b :: TYPE r). (a -> b) -> a -> b
until :: (a -> Bool) -> (a -> a) -> a -> a
asTypeOf :: a -> a -> a
failIO :: String -> IO a
unIO :: IO a -> State# RealWorld -> (# State# RealWorld, a #)
getTag :: a -> Int#
quotInt :: Int -> Int -> Int
remInt :: Int -> Int -> Int
divInt :: Int -> Int -> Int
modInt :: Int -> Int -> Int
quotRemInt :: Int -> Int -> (Int, Int)
divModInt :: Int -> Int -> (Int, Int)
divModInt# :: Int# -> Int# -> (# Int#, Int# #)
shiftL# :: Word# -> Int# -> Word#
shiftRL# :: Word# -> Int# -> Word#
iShiftL# :: Int# -> Int# -> Int#
iShiftRA# :: Int# -> Int# -> Int#
iShiftRL# :: Int# -> Int# -> Int#
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]

($) :: 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 [] Source #	Since: base-2.1
Instance details Defined in GHC.Base Methods (>>=) :: [a] -> (a -> [b]) -> [b] Source # (>>) :: [a] -> [b] -> [b] Source # return :: a -> [a] Source #
Monad Maybe Source #	Since: base-2.1
Instance details Defined in GHC.Base Methods (>>=) :: Maybe a -> (a -> Maybe b) -> Maybe b Source # (>>) :: Maybe a -> Maybe b -> Maybe b Source # return :: a -> Maybe a Source #
Monad IO Source #	Since: base-2.1
Instance details Defined in GHC.Base Methods (>>=) :: IO a -> (a -> IO b) -> IO b Source # (>>) :: IO a -> IO b -> IO b Source # return :: a -> IO a Source #
Monad Par1 Source #	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods (>>=) :: Par1 a -> (a -> Par1 b) -> Par1 b Source # (>>) :: Par1 a -> Par1 b -> Par1 b Source # return :: a -> Par1 a Source #
Monad NonEmpty Source #	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (>>=) :: NonEmpty a -> (a -> NonEmpty b) -> NonEmpty b Source # (>>) :: NonEmpty a -> NonEmpty b -> NonEmpty b Source # return :: a -> NonEmpty a Source #
Monad NoIO Source #	Since: base-4.4.0.0
Instance details Defined in GHC.GHCi Methods (>>=) :: NoIO a -> (a -> NoIO b) -> NoIO b Source # (>>) :: NoIO a -> NoIO b -> NoIO b Source # return :: a -> NoIO a Source #
Monad ReadP Source #	Since: base-2.1
Instance details Defined in Text.ParserCombinators.ReadP Methods (>>=) :: ReadP a -> (a -> ReadP b) -> ReadP b Source # (>>) :: ReadP a -> ReadP b -> ReadP b Source # return :: a -> ReadP a Source #
Monad ReadPrec Source #	Since: base-2.1
Instance details Defined in Text.ParserCombinators.ReadPrec Methods (>>=) :: ReadPrec a -> (a -> ReadPrec b) -> ReadPrec b Source # (>>) :: ReadPrec a -> ReadPrec b -> ReadPrec b Source # return :: a -> ReadPrec a Source #
Monad Down Source #	Since: base-4.11.0.0
Instance details Defined in Data.Ord Methods (>>=) :: Down a -> (a -> Down b) -> Down b Source # (>>) :: Down a -> Down b -> Down b Source # return :: a -> Down a Source #
Monad Product Source #	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods (>>=) :: Product a -> (a -> Product b) -> Product b Source # (>>) :: Product a -> Product b -> Product b Source # return :: a -> Product a Source #
Monad Sum Source #	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods (>>=) :: Sum a -> (a -> Sum b) -> Sum b Source # (>>) :: Sum a -> Sum b -> Sum b Source # return :: a -> Sum a Source #
Monad Dual Source #	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods (>>=) :: Dual a -> (a -> Dual b) -> Dual b Source # (>>) :: Dual a -> Dual b -> Dual b Source # return :: a -> Dual a Source #
Monad Last Source #	Since: base-4.8.0.0
Instance details Defined in Data.Monoid Methods (>>=) :: Last a -> (a -> Last b) -> Last b Source # (>>) :: Last a -> Last b -> Last b Source # return :: a -> Last a Source #
Monad First Source #	Since: base-4.8.0.0
Instance details Defined in Data.Monoid Methods (>>=) :: First a -> (a -> First b) -> First b Source # (>>) :: First a -> First b -> First b Source # return :: a -> First a Source #
Monad STM Source #	Since: base-4.3.0.0
Instance details Defined in GHC.Conc.Sync Methods (>>=) :: STM a -> (a -> STM b) -> STM b Source # (>>) :: STM a -> STM b -> STM b Source # return :: a -> STM a Source #
Monad Identity Source #	Since: base-4.8.0.0
Instance details Defined in Data.Functor.Identity Methods (>>=) :: Identity a -> (a -> Identity b) -> Identity b Source # (>>) :: Identity a -> Identity b -> Identity b Source # return :: a -> Identity a Source #
Monad Option Source #	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (>>=) :: Option a -> (a -> Option b) -> Option b Source # (>>) :: Option a -> Option b -> Option b Source # return :: a -> Option a Source #
Monad Last Source #	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (>>=) :: Last a -> (a -> Last b) -> Last b Source # (>>) :: Last a -> Last b -> Last b Source # return :: a -> Last a Source #
Monad First Source #	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (>>=) :: First a -> (a -> First b) -> First b Source # (>>) :: First a -> First b -> First b Source # return :: a -> First a Source #
Monad Max Source #	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (>>=) :: Max a -> (a -> Max b) -> Max b Source # (>>) :: Max a -> Max b -> Max b Source # return :: a -> Max a Source #
Monad Min Source #	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (>>=) :: Min a -> (a -> Min b) -> Min b Source # (>>) :: Min a -> Min b -> Min b Source # return :: a -> Min a Source #
Monad Complex Source #	Since: base-4.9.0.0
Instance details Defined in Data.Complex Methods (>>=) :: Complex a -> (a -> Complex b) -> Complex b Source # (>>) :: Complex a -> Complex b -> Complex b Source # return :: a -> Complex a Source #
Monad (Either e) Source #	Since: base-4.4.0.0
Instance details Defined in Data.Either Methods (>>=) :: Either e a -> (a -> Either e b) -> Either e b Source # (>>) :: Either e a -> Either e b -> Either e b Source # return :: a -> Either e a Source #
Monad (U1 :: Type -> Type) Source #	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods (>>=) :: U1 a -> (a -> U1 b) -> U1 b Source # (>>) :: U1 a -> U1 b -> U1 b Source # return :: a -> U1 a Source #
Monoid a => Monad ((,) a) Source #	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (>>=) :: (a, a0) -> (a0 -> (a, b)) -> (a, b) Source # (>>) :: (a, a0) -> (a, b) -> (a, b) Source # return :: a0 -> (a, a0) Source #
Monad (ST s) Source #	Since: base-2.1
Instance details Defined in GHC.ST Methods (>>=) :: ST s a -> (a -> ST s b) -> ST s b Source # (>>) :: ST s a -> ST s b -> ST s b Source # return :: a -> ST s a Source #
Monad (Proxy :: Type -> Type) Source #	Since: base-4.7.0.0
Instance details Defined in Data.Proxy Methods (>>=) :: Proxy a -> (a -> Proxy b) -> Proxy b Source # (>>) :: Proxy a -> Proxy b -> Proxy b Source # return :: a -> Proxy a Source #
ArrowApply a => Monad (ArrowMonad a) Source #	Since: base-2.1
Instance details Defined in Control.Arrow Methods (>>=) :: ArrowMonad a a0 -> (a0 -> ArrowMonad a b) -> ArrowMonad a b Source # (>>) :: ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a b Source # return :: a0 -> ArrowMonad a a0 Source #
Monad m => Monad (WrappedMonad m) Source #	Since: base-4.7.0.0
Instance details Defined in Control.Applicative Methods (>>=) :: WrappedMonad m a -> (a -> WrappedMonad m b) -> WrappedMonad m b Source # (>>) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m b Source # return :: a -> WrappedMonad m a Source #
Monad (ST s) Source #	Since: base-2.1
Instance details Defined in Control.Monad.ST.Lazy.Imp Methods (>>=) :: ST s a -> (a -> ST s b) -> ST s b Source # (>>) :: ST s a -> ST s b -> ST s b Source # return :: a -> ST s a Source #
Monad f => Monad (Rec1 f) Source #	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods (>>=) :: Rec1 f a -> (a -> Rec1 f b) -> Rec1 f b Source # (>>) :: Rec1 f a -> Rec1 f b -> Rec1 f b Source # return :: a -> Rec1 f a Source #
(Monoid a, Monoid b) => Monad ((,,) a b) Source #	Since: base-4.14.0.0
Instance details Defined in GHC.Base Methods (>>=) :: (a, b, a0) -> (a0 -> (a, b, b0)) -> (a, b, b0) Source # (>>) :: (a, b, a0) -> (a, b, b0) -> (a, b, b0) Source # return :: a0 -> (a, b, a0) Source #
Monad f => Monad (Alt f) Source #	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods (>>=) :: Alt f a -> (a -> Alt f b) -> Alt f b Source # (>>) :: Alt f a -> Alt f b -> Alt f b Source # return :: a -> Alt f a Source #
Monad f => Monad (Ap f) Source #	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods (>>=) :: Ap f a -> (a -> Ap f b) -> Ap f b Source # (>>) :: Ap f a -> Ap f b -> Ap f b Source # return :: a -> Ap f a Source #
Monad m => Monad (Kleisli m a) Source #	Since: base-4.14.0.0
Instance details Defined in Control.Arrow Methods (>>=) :: Kleisli m a a0 -> (a0 -> Kleisli m a b) -> Kleisli m a b Source # (>>) :: Kleisli m a a0 -> Kleisli m a b -> Kleisli m a b Source # return :: a0 -> Kleisli m a a0 Source #
Monad ((->) r :: Type -> Type) Source #	Since: base-2.1
Instance details Defined in GHC.Base Methods (>>=) :: (r -> a) -> (a -> r -> b) -> r -> b Source # (>>) :: (r -> a) -> (r -> b) -> r -> b Source # return :: a -> r -> a Source #
(Monad f, Monad g) => Monad (f :*: g) Source #	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods (>>=) :: (f :: g) a -> (a -> (f :: g) b) -> (f :: g) b Source # (>>) :: (f :: g) a -> (f :: g) b -> (f :: g) b Source # return :: a -> (f :*: g) a Source #
(Monoid a, Monoid b, Monoid c) => Monad ((,,,) a b c) Source #	Since: base-4.14.0.0
Instance details Defined in GHC.Base Methods (>>=) :: (a, b, c, a0) -> (a0 -> (a, b, c, b0)) -> (a, b, c, b0) Source # (>>) :: (a, b, c, a0) -> (a, b, c, b0) -> (a, b, c, b0) Source # return :: a0 -> (a, b, c, a0) Source #
(Monad f, Monad g) => Monad (Product f g) Source #	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods (>>=) :: Product f g a -> (a -> Product f g b) -> Product f g b Source # (>>) :: Product f g a -> Product f g b -> Product f g b Source # return :: a -> Product f g a Source #
Monad f => Monad (M1 i c f) Source #	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods (>>=) :: M1 i c f a -> (a -> M1 i c f b) -> M1 i c f b Source # (>>) :: M1 i c f a -> M1 i c f b -> M1 i c f b Source # return :: a -> M1 i c f a Source #

class Functor f where Source #

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

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

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

Minimal complete definition

fmap

Methods

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

Using ApplicativeDo: 'fmap f as' can be understood as the do expression

do a <- as
   pure (f a)

with an inferred Functor constraint.

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

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

Using ApplicativeDo: 'a <$ bs' can be understood as the do expression

do bs
   pure a

with an inferred Functor constraint.

Instances

Instances details

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

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.

Using ApplicativeDo: 'fs <*> as' can be understood as the do expression

do f <- fs
   a <- as
   pure (f a)

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

Lift a binary function to actions.

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

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

Using ApplicativeDo: 'liftA2 f as bs' can be understood as the do expression

do a <- as
   b <- bs
   pure (f a b)

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

Sequence actions, discarding the value of the first argument.

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

do as
   bs

This is a tad complicated for our ApplicativeDo extension which will give it a Monad constraint. For an Applicative constraint we write it of the form

do _ <- as
   b <- bs
   pure b

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

Sequence actions, discarding the value of the second argument.

Using ApplicativeDo: 'as <* bs' can be understood as the do expression

do a <- as
   bs
   pure a

Instances

Instances details

Applicative [] Source #	Since: base-2.1
Instance details Defined in GHC.Base Methods pure :: a -> [a] Source # (<>) :: [a -> b] -> [a] -> [b] Source # liftA2 :: (a -> b -> c) -> [a] -> [b] -> [c] Source # (>) :: [a] -> [b] -> [b] Source # (<*) :: [a] -> [b] -> [a] Source #
Applicative Maybe Source #	Since: base-2.1
Instance details Defined in GHC.Base Methods pure :: a -> Maybe a Source # (<>) :: Maybe (a -> b) -> Maybe a -> Maybe b Source # liftA2 :: (a -> b -> c) -> Maybe a -> Maybe b -> Maybe c Source # (>) :: Maybe a -> Maybe b -> Maybe b Source # (<*) :: Maybe a -> Maybe b -> Maybe a Source #
Applicative IO Source #	Since: base-2.1
Instance details Defined in GHC.Base Methods pure :: a -> IO a Source # (<>) :: IO (a -> b) -> IO a -> IO b Source # liftA2 :: (a -> b -> c) -> IO a -> IO b -> IO c Source # (>) :: IO a -> IO b -> IO b Source # (<*) :: IO a -> IO b -> IO a Source #
Applicative Par1 Source #	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods pure :: a -> Par1 a Source # (<>) :: Par1 (a -> b) -> Par1 a -> Par1 b Source # liftA2 :: (a -> b -> c) -> Par1 a -> Par1 b -> Par1 c Source # (>) :: Par1 a -> Par1 b -> Par1 b Source # (<*) :: Par1 a -> Par1 b -> Par1 a Source #
Applicative NonEmpty Source #	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods pure :: a -> NonEmpty a Source # (<>) :: NonEmpty (a -> b) -> NonEmpty a -> NonEmpty b Source # liftA2 :: (a -> b -> c) -> NonEmpty a -> NonEmpty b -> NonEmpty c Source # (>) :: NonEmpty a -> NonEmpty b -> NonEmpty b Source # (<*) :: NonEmpty a -> NonEmpty b -> NonEmpty a Source #
Applicative NoIO Source #	Since: base-4.8.0.0
Instance details Defined in GHC.GHCi Methods pure :: a -> NoIO a Source # (<>) :: NoIO (a -> b) -> NoIO a -> NoIO b Source # liftA2 :: (a -> b -> c) -> NoIO a -> NoIO b -> NoIO c Source # (>) :: NoIO a -> NoIO b -> NoIO b Source # (<*) :: NoIO a -> NoIO b -> NoIO a Source #
Applicative ReadP Source #	Since: base-4.6.0.0
Instance details Defined in Text.ParserCombinators.ReadP Methods pure :: a -> ReadP a Source # (<>) :: ReadP (a -> b) -> ReadP a -> ReadP b Source # liftA2 :: (a -> b -> c) -> ReadP a -> ReadP b -> ReadP c Source # (>) :: ReadP a -> ReadP b -> ReadP b Source # (<*) :: ReadP a -> ReadP b -> ReadP a Source #
Applicative ReadPrec Source #	Since: base-4.6.0.0
Instance details Defined in Text.ParserCombinators.ReadPrec Methods pure :: a -> ReadPrec a Source # (<>) :: ReadPrec (a -> b) -> ReadPrec a -> ReadPrec b Source # liftA2 :: (a -> b -> c) -> ReadPrec a -> ReadPrec b -> ReadPrec c Source # (>) :: ReadPrec a -> ReadPrec b -> ReadPrec b Source # (<*) :: ReadPrec a -> ReadPrec b -> ReadPrec a Source #
Applicative Down Source #	Since: base-4.11.0.0
Instance details Defined in Data.Ord Methods pure :: a -> Down a Source # (<>) :: Down (a -> b) -> Down a -> Down b Source # liftA2 :: (a -> b -> c) -> Down a -> Down b -> Down c Source # (>) :: Down a -> Down b -> Down b Source # (<*) :: Down a -> Down b -> Down a Source #
Applicative Product Source #	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods pure :: a -> Product a Source # (<>) :: Product (a -> b) -> Product a -> Product b Source # liftA2 :: (a -> b -> c) -> Product a -> Product b -> Product c Source # (>) :: Product a -> Product b -> Product b Source # (<*) :: Product a -> Product b -> Product a Source #
Applicative Sum Source #	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods pure :: a -> Sum a Source # (<>) :: Sum (a -> b) -> Sum a -> Sum b Source # liftA2 :: (a -> b -> c) -> Sum a -> Sum b -> Sum c Source # (>) :: Sum a -> Sum b -> Sum b Source # (<*) :: Sum a -> Sum b -> Sum a Source #
Applicative Dual Source #	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods pure :: a -> Dual a Source # (<>) :: Dual (a -> b) -> Dual a -> Dual b Source # liftA2 :: (a -> b -> c) -> Dual a -> Dual b -> Dual c Source # (>) :: Dual a -> Dual b -> Dual b Source # (<*) :: Dual a -> Dual b -> Dual a Source #
Applicative Last Source #	Since: base-4.8.0.0
Instance details Defined in Data.Monoid Methods pure :: a -> Last a Source # (<>) :: Last (a -> b) -> Last a -> Last b Source # liftA2 :: (a -> b -> c) -> Last a -> Last b -> Last c Source # (>) :: Last a -> Last b -> Last b Source # (<*) :: Last a -> Last b -> Last a Source #
Applicative First Source #	Since: base-4.8.0.0
Instance details Defined in Data.Monoid Methods pure :: a -> First a Source # (<>) :: First (a -> b) -> First a -> First b Source # liftA2 :: (a -> b -> c) -> First a -> First b -> First c Source # (>) :: First a -> First b -> First b Source # (<*) :: First a -> First b -> First a Source #
Applicative STM Source #	Since: base-4.8.0.0
Instance details Defined in GHC.Conc.Sync Methods pure :: a -> STM a Source # (<>) :: STM (a -> b) -> STM a -> STM b Source # liftA2 :: (a -> b -> c) -> STM a -> STM b -> STM c Source # (>) :: STM a -> STM b -> STM b Source # (<*) :: STM a -> STM b -> STM a Source #
Applicative Identity Source #	Since: base-4.8.0.0
Instance details Defined in Data.Functor.Identity Methods pure :: a -> Identity a Source # (<>) :: Identity (a -> b) -> Identity a -> Identity b Source # liftA2 :: (a -> b -> c) -> Identity a -> Identity b -> Identity c Source # (>) :: Identity a -> Identity b -> Identity b Source # (<*) :: Identity a -> Identity b -> Identity a Source #
Applicative ZipList Source #	f <$> ZipList xs1 <> ... <> ZipList xsN = ZipList (zipWithN f xs1 ... xsN) where `zipWithN` refers to the `zipWith` function of the appropriate arity (`zipWith`, `zipWith3`, `zipWith4`, ...). For example: (\a b c -> stimes c [a, b]) <$> ZipList "abcd" <> ZipList "567" <> ZipList [1..] = ZipList (zipWith3 (\a b c -> stimes c [a, b]) "abcd" "567" [1..]) = ZipList {getZipList = ["a5","b6b6","c7c7c7"]} Since: base-2.1
Instance details Defined in Control.Applicative Methods pure :: a -> ZipList a Source # (<>) :: ZipList (a -> b) -> ZipList a -> ZipList b Source # liftA2 :: (a -> b -> c) -> ZipList a -> ZipList b -> ZipList c Source # (>) :: ZipList a -> ZipList b -> ZipList b Source # (<*) :: ZipList a -> ZipList b -> ZipList a Source #
Applicative Option Source #	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods pure :: a -> Option a Source # (<>) :: Option (a -> b) -> Option a -> Option b Source # liftA2 :: (a -> b -> c) -> Option a -> Option b -> Option c Source # (>) :: Option a -> Option b -> Option b Source # (<*) :: Option a -> Option b -> Option a Source #
Applicative Last Source #	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods pure :: a -> Last a Source # (<>) :: Last (a -> b) -> Last a -> Last b Source # liftA2 :: (a -> b -> c) -> Last a -> Last b -> Last c Source # (>) :: Last a -> Last b -> Last b Source # (<*) :: Last a -> Last b -> Last a Source #
Applicative First Source #	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods pure :: a -> First a Source # (<>) :: First (a -> b) -> First a -> First b Source # liftA2 :: (a -> b -> c) -> First a -> First b -> First c Source # (>) :: First a -> First b -> First b Source # (<*) :: First a -> First b -> First a Source #
Applicative Max Source #	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods pure :: a -> Max a Source # (<>) :: Max (a -> b) -> Max a -> Max b Source # liftA2 :: (a -> b -> c) -> Max a -> Max b -> Max c Source # (>) :: Max a -> Max b -> Max b Source # (<*) :: Max a -> Max b -> Max a Source #
Applicative Min Source #	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods pure :: a -> Min a Source # (<>) :: Min (a -> b) -> Min a -> Min b Source # liftA2 :: (a -> b -> c) -> Min a -> Min b -> Min c Source # (>) :: Min a -> Min b -> Min b Source # (<*) :: Min a -> Min b -> Min a Source #
Applicative Complex Source #	Since: base-4.9.0.0
Instance details Defined in Data.Complex Methods pure :: a -> Complex a Source # (<>) :: Complex (a -> b) -> Complex a -> Complex b Source # liftA2 :: (a -> b -> c) -> Complex a -> Complex b -> Complex c Source # (>) :: Complex a -> Complex b -> Complex b Source # (<*) :: Complex a -> Complex b -> Complex a Source #
Applicative (Either e) Source #	Since: base-3.0
Instance details Defined in Data.Either Methods pure :: a -> Either e a Source # (<>) :: Either e (a -> b) -> Either e a -> Either e b Source # liftA2 :: (a -> b -> c) -> Either e a -> Either e b -> Either e c Source # (>) :: Either e a -> Either e b -> Either e b Source # (<*) :: Either e a -> Either e b -> Either e a Source #
Applicative (U1 :: Type -> Type) Source #	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods pure :: a -> U1 a Source # (<>) :: U1 (a -> b) -> U1 a -> U1 b Source # liftA2 :: (a -> b -> c) -> U1 a -> U1 b -> U1 c Source # (>) :: U1 a -> U1 b -> U1 b Source # (<*) :: U1 a -> U1 b -> U1 a Source #
Monoid a => Applicative ((,) a) Source #	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 #
Applicative (ST s) Source #	Since: base-4.4.0.0
Instance details Defined in GHC.ST Methods pure :: a -> ST s a Source # (<>) :: ST s (a -> b) -> ST s a -> ST s b Source # liftA2 :: (a -> b -> c) -> ST s a -> ST s b -> ST s c Source # (>) :: ST s a -> ST s b -> ST s b Source # (<*) :: ST s a -> ST s b -> ST s a Source #
Applicative (Proxy :: Type -> Type) Source #	Since: base-4.7.0.0
Instance details Defined in Data.Proxy Methods pure :: a -> Proxy a Source # (<>) :: Proxy (a -> b) -> Proxy a -> Proxy b Source # liftA2 :: (a -> b -> c) -> Proxy a -> Proxy b -> Proxy c Source # (>) :: Proxy a -> Proxy b -> Proxy b Source # (<*) :: Proxy a -> Proxy b -> Proxy a Source #
Arrow a => Applicative (ArrowMonad a) Source #	Since: base-4.6.0.0
Instance details Defined in Control.Arrow Methods pure :: a0 -> ArrowMonad a a0 Source # (<>) :: ArrowMonad a (a0 -> b) -> ArrowMonad a a0 -> ArrowMonad a b Source # liftA2 :: (a0 -> b -> c) -> ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a c Source # (>) :: ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a b Source # (<*) :: ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a a0 Source #
Monad m => Applicative (WrappedMonad m) Source #	Since: base-2.1
Instance details Defined in Control.Applicative Methods pure :: a -> WrappedMonad m a Source # (<>) :: WrappedMonad m (a -> b) -> WrappedMonad m a -> WrappedMonad m b Source # liftA2 :: (a -> b -> c) -> WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m c Source # (>) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m b Source # (<*) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m a Source #
Applicative (ST s) Source #	Since: base-2.1
Instance details Defined in Control.Monad.ST.Lazy.Imp Methods pure :: a -> ST s a Source # (<>) :: ST s (a -> b) -> ST s a -> ST s b Source # liftA2 :: (a -> b -> c) -> ST s a -> ST s b -> ST s c Source # (>) :: ST s a -> ST s b -> ST s b Source # (<*) :: ST s a -> ST s b -> ST s a Source #
Applicative f => Applicative (Rec1 f) Source #	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods pure :: a -> Rec1 f a Source # (<>) :: Rec1 f (a -> b) -> Rec1 f a -> Rec1 f b Source # liftA2 :: (a -> b -> c) -> Rec1 f a -> Rec1 f b -> Rec1 f c Source # (>) :: Rec1 f a -> Rec1 f b -> Rec1 f b Source # (<*) :: Rec1 f a -> Rec1 f b -> Rec1 f a Source #
(Monoid a, Monoid b) => Applicative ((,,) a b) Source #	Since: base-4.14.0.0
Instance details Defined in GHC.Base Methods pure :: a0 -> (a, b, a0) Source # (<>) :: (a, b, a0 -> b0) -> (a, b, a0) -> (a, b, b0) Source # liftA2 :: (a0 -> b0 -> c) -> (a, b, a0) -> (a, b, b0) -> (a, b, c) Source # (>) :: (a, b, a0) -> (a, b, b0) -> (a, b, b0) Source # (<*) :: (a, b, a0) -> (a, b, b0) -> (a, b, a0) Source #
Applicative f => Applicative (Alt f) Source #	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods pure :: a -> Alt f a Source # (<>) :: Alt f (a -> b) -> Alt f a -> Alt f b Source # liftA2 :: (a -> b -> c) -> Alt f a -> Alt f b -> Alt f c Source # (>) :: Alt f a -> Alt f b -> Alt f b Source # (<*) :: Alt f a -> Alt f b -> Alt f a Source #
Applicative f => Applicative (Ap f) Source #	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods pure :: a -> Ap f a Source # (<>) :: Ap f (a -> b) -> Ap f a -> Ap f b Source # liftA2 :: (a -> b -> c) -> Ap f a -> Ap f b -> Ap f c Source # (>) :: Ap f a -> Ap f b -> Ap f b Source # (<*) :: Ap f a -> Ap f b -> Ap f a Source #
Monoid m => Applicative (Const m :: Type -> Type) Source #	Since: base-2.0.1
Instance details Defined in Data.Functor.Const Methods pure :: a -> Const m a Source # (<>) :: Const m (a -> b) -> Const m a -> Const m b Source # liftA2 :: (a -> b -> c) -> Const m a -> Const m b -> Const m c Source # (>) :: Const m a -> Const m b -> Const m b Source # (<*) :: Const m a -> Const m b -> Const m a Source #
Applicative m => Applicative (Kleisli m a) Source #	Since: base-4.14.0.0
Instance details Defined in Control.Arrow Methods pure :: a0 -> Kleisli m a a0 Source # (<>) :: Kleisli m a (a0 -> b) -> Kleisli m a a0 -> Kleisli m a b Source # liftA2 :: (a0 -> b -> c) -> Kleisli m a a0 -> Kleisli m a b -> Kleisli m a c Source # (>) :: Kleisli m a a0 -> Kleisli m a b -> Kleisli m a b Source # (<*) :: Kleisli m a a0 -> Kleisli m a b -> Kleisli m a a0 Source #
Arrow a => Applicative (WrappedArrow a b) Source #	Since: base-2.1
Instance details Defined in Control.Applicative Methods pure :: a0 -> WrappedArrow a b a0 Source # (<>) :: WrappedArrow a b (a0 -> b0) -> WrappedArrow a b a0 -> WrappedArrow a b b0 Source # liftA2 :: (a0 -> b0 -> c) -> WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b c Source # (>) :: WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b b0 Source # (<*) :: WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0 Source #
Applicative ((->) r :: Type -> Type) Source #	Since: base-2.1
Instance details Defined in GHC.Base Methods pure :: a -> r -> a Source # (<>) :: (r -> (a -> b)) -> (r -> a) -> r -> b Source # liftA2 :: (a -> b -> c) -> (r -> a) -> (r -> b) -> r -> c Source # (>) :: (r -> a) -> (r -> b) -> r -> b Source # (<*) :: (r -> a) -> (r -> b) -> r -> a Source #
Monoid c => Applicative (K1 i c :: Type -> Type) Source #	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods pure :: a -> K1 i c a Source # (<>) :: K1 i c (a -> b) -> K1 i c a -> K1 i c b Source # liftA2 :: (a -> b -> c0) -> K1 i c a -> K1 i c b -> K1 i c c0 Source # (>) :: K1 i c a -> K1 i c b -> K1 i c b Source # (<*) :: K1 i c a -> K1 i c b -> K1 i c a Source #
(Applicative f, Applicative g) => Applicative (f :*: g) Source #	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods pure :: a -> (f :: g) a Source # (<>) :: (f :: g) (a -> b) -> (f :: g) a -> (f :: g) b Source # liftA2 :: (a -> b -> c) -> (f :: g) a -> (f :: g) b -> (f :: g) c Source # (>) :: (f :: g) a -> (f :: g) b -> (f :: g) b Source # (<) :: (f :: g) a -> (f :: g) b -> (f :: g) a Source #
(Monoid a, Monoid b, Monoid c) => Applicative ((,,,) a b c) Source #	Since: base-4.14.0.0
Instance details Defined in GHC.Base Methods pure :: a0 -> (a, b, c, a0) Source # (<>) :: (a, b, c, a0 -> b0) -> (a, b, c, a0) -> (a, b, c, b0) Source # liftA2 :: (a0 -> b0 -> c0) -> (a, b, c, a0) -> (a, b, c, b0) -> (a, b, c, c0) Source # (>) :: (a, b, c, a0) -> (a, b, c, b0) -> (a, b, c, b0) Source # (<*) :: (a, b, c, a0) -> (a, b, c, b0) -> (a, b, c, a0) Source #
(Applicative f, Applicative g) => Applicative (Product f g) Source #	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods pure :: a -> Product f g a Source # (<>) :: Product f g (a -> b) -> Product f g a -> Product f g b Source # liftA2 :: (a -> b -> c) -> Product f g a -> Product f g b -> Product f g c Source # (>) :: Product f g a -> Product f g b -> Product f g b Source # (<*) :: Product f g a -> Product f g b -> Product f g a Source #
Applicative f => Applicative (M1 i c f) Source #	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods pure :: a -> M1 i c f a Source # (<>) :: M1 i c f (a -> b) -> M1 i c f a -> M1 i c f b Source # liftA2 :: (a -> b -> c0) -> M1 i c f a -> M1 i c f b -> M1 i c f c0 Source # (>) :: M1 i c f a -> M1 i c f b -> M1 i c f b Source # (<*) :: M1 i c f a -> M1 i c f b -> M1 i c f a Source #
(Applicative f, Applicative g) => Applicative (f :.: g) Source #	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods pure :: a -> (f :.: g) a Source # (<>) :: (f :.: g) (a -> b) -> (f :.: g) a -> (f :.: g) b Source # liftA2 :: (a -> b -> c) -> (f :.: g) a -> (f :.: g) b -> (f :.: g) c Source # (>) :: (f :.: g) a -> (f :.: g) b -> (f :.: g) b Source # (<*) :: (f :.: g) a -> (f :.: g) b -> (f :.: g) a Source #
(Applicative f, Applicative g) => Applicative (Compose f g) Source #	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Compose Methods pure :: a -> Compose f g a Source # (<>) :: Compose f g (a -> b) -> Compose f g a -> Compose f g b Source # liftA2 :: (a -> b -> c) -> Compose f g a -> Compose f g b -> Compose f g c Source # (>) :: Compose f g a -> Compose f g b -> Compose f g b Source # (<*) :: Compose f g a -> Compose f g b -> Compose f g a Source #

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
>>> 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 Ordering Source #	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 () Source #	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: () -> () -> () Source # sconcat :: NonEmpty () -> () Source # stimes :: Integral b => b -> () -> () Source #
Semigroup Any Source #	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Any -> Any -> Any Source # sconcat :: NonEmpty Any -> Any Source # stimes :: Integral b => b -> Any -> Any Source #
Semigroup All Source #	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: All -> All -> All Source # sconcat :: NonEmpty All -> All Source # stimes :: Integral b => b -> All -> All Source #
Semigroup Lifetime Source #	Since: base-4.10.0.0
Instance details Defined in GHC.Event.Internal Methods (<>) :: Lifetime -> Lifetime -> Lifetime Source # sconcat :: NonEmpty Lifetime -> Lifetime Source # stimes :: Integral b => b -> Lifetime -> Lifetime Source #
Semigroup Event Source #	Since: base-4.10.0.0
Instance details Defined in GHC.Event.Internal Methods (<>) :: Event -> Event -> Event Source # sconcat :: NonEmpty Event -> Event Source # stimes :: Integral b => b -> Event -> Event Source #
Semigroup Void Source #	Since: base-4.9.0.0
Instance details Defined in Data.Void Methods (<>) :: Void -> Void -> Void Source # sconcat :: NonEmpty Void -> Void Source # stimes :: Integral b => b -> Void -> Void Source #
Semigroup [a] Source #	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: [a] -> [a] -> [a] Source # sconcat :: NonEmpty [a] -> [a] Source # stimes :: Integral b => b -> [a] -> [a] Source #
Semigroup a => Semigroup (Maybe a) Source #	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: Maybe a -> Maybe a -> Maybe a Source # sconcat :: NonEmpty (Maybe a) -> Maybe a Source # stimes :: Integral b => b -> Maybe a -> Maybe a Source #
Semigroup a => Semigroup (IO a) Source #	Since: base-4.10.0.0
Instance details Defined in GHC.Base Methods (<>) :: IO a -> IO a -> IO a Source # sconcat :: NonEmpty (IO a) -> IO a Source # stimes :: Integral b => b -> IO a -> IO a Source #
Semigroup p => Semigroup (Par1 p) Source #	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods (<>) :: Par1 p -> Par1 p -> Par1 p Source # sconcat :: NonEmpty (Par1 p) -> Par1 p Source # stimes :: Integral b => b -> Par1 p -> Par1 p Source #
Semigroup (NonEmpty a) Source #	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 a => Semigroup (Down a) Source #	Since: base-4.11.0.0
Instance details Defined in Data.Ord Methods (<>) :: Down a -> Down a -> Down a Source # sconcat :: NonEmpty (Down a) -> Down a Source # stimes :: Integral b => b -> Down a -> Down a Source #
Num a => Semigroup (Product a) Source #	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Product a -> Product a -> Product a Source # sconcat :: NonEmpty (Product a) -> Product a Source # stimes :: Integral b => b -> Product a -> Product a Source #
Num a => Semigroup (Sum a) Source #	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Sum a -> Sum a -> Sum a Source # sconcat :: NonEmpty (Sum a) -> Sum a Source # stimes :: Integral b => b -> Sum a -> Sum a Source #
Semigroup (Endo a) Source #	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Endo a -> Endo a -> Endo a Source # sconcat :: NonEmpty (Endo a) -> Endo a Source # stimes :: Integral b => b -> Endo a -> Endo a Source #
Semigroup a => Semigroup (Dual a) Source #	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Dual a -> Dual a -> Dual a Source # sconcat :: NonEmpty (Dual a) -> Dual a Source # stimes :: Integral b => b -> Dual a -> Dual a Source #
Semigroup (Last a) Source #	Since: base-4.9.0.0
Instance details Defined in Data.Monoid Methods (<>) :: Last a -> Last a -> Last a Source # sconcat :: NonEmpty (Last a) -> Last a Source # stimes :: Integral b => b -> Last a -> Last a Source #
Semigroup (First a) Source #	Since: base-4.9.0.0
Instance details Defined in Data.Monoid Methods (<>) :: First a -> First a -> First a Source # sconcat :: NonEmpty (First a) -> First a Source # stimes :: Integral b => b -> First a -> First a Source #
Semigroup a => Semigroup (Identity a) Source #	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 a => Semigroup (Option a) Source #	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (<>) :: Option a -> Option a -> Option a Source # sconcat :: NonEmpty (Option a) -> Option a Source # stimes :: Integral b => b -> Option a -> Option a Source #
Monoid m => Semigroup (WrappedMonoid m) Source #	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 (Last a) Source #	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (<>) :: Last a -> Last a -> Last a Source # sconcat :: NonEmpty (Last a) -> Last a Source # stimes :: Integral b => b -> Last a -> Last a Source #
Semigroup (First a) Source #	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (<>) :: First a -> First a -> First a Source # sconcat :: NonEmpty (First a) -> First a Source # stimes :: Integral b => b -> First a -> First a Source #
Ord a => Semigroup (Max a) Source #	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (<>) :: Max a -> Max a -> Max a Source # sconcat :: NonEmpty (Max a) -> Max a Source # stimes :: Integral b => b -> Max a -> Max a Source #
Ord a => Semigroup (Min a) Source #	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (<>) :: Min a -> Min a -> Min a Source # sconcat :: NonEmpty (Min a) -> Min a Source # stimes :: Integral b => b -> Min a -> Min a Source #
Semigroup (Equivalence a) Source #
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 (Comparison a) Source #
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 (Predicate a) Source #
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 b => Semigroup (a -> b) Source #	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: (a -> b) -> (a -> b) -> a -> b Source # sconcat :: NonEmpty (a -> b) -> a -> b Source # stimes :: Integral b0 => b0 -> (a -> b) -> a -> b Source #
Semigroup (Either a b) Source #	Since: base-4.9.0.0
Instance details Defined in Data.Either Methods (<>) :: Either a b -> Either a b -> Either a b Source # sconcat :: NonEmpty (Either a b) -> Either a b Source # stimes :: Integral b0 => b0 -> Either a b -> Either a b Source #
Semigroup (V1 p) Source #	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods (<>) :: V1 p -> V1 p -> V1 p Source # sconcat :: NonEmpty (V1 p) -> V1 p Source # stimes :: Integral b => b -> V1 p -> V1 p Source #
Semigroup (U1 p) Source #	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods (<>) :: U1 p -> U1 p -> U1 p Source # sconcat :: NonEmpty (U1 p) -> U1 p Source # stimes :: Integral b => b -> U1 p -> U1 p Source #
(Semigroup a, Semigroup b) => Semigroup (a, b) Source #	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: (a, b) -> (a, b) -> (a, b) Source # sconcat :: NonEmpty (a, b) -> (a, b) Source # stimes :: Integral b0 => b0 -> (a, b) -> (a, b) Source #
Semigroup a => Semigroup (ST s a) Source #	Since: base-4.11.0.0
Instance details Defined in GHC.ST Methods (<>) :: ST s a -> ST s a -> ST s a Source # sconcat :: NonEmpty (ST s a) -> ST s a Source # stimes :: Integral b => b -> ST s a -> ST s a Source #
Semigroup (Proxy s) Source #	Since: base-4.9.0.0
Instance details Defined in Data.Proxy Methods (<>) :: Proxy s -> Proxy s -> Proxy s Source # sconcat :: NonEmpty (Proxy s) -> Proxy s Source # stimes :: Integral b => b -> Proxy s -> Proxy s Source #
Semigroup a => Semigroup (Op a b) Source #
Instance details Defined in Data.Functor.Contravariant Methods (<>) :: Op a b -> Op a b -> Op a b Source # sconcat :: NonEmpty (Op a b) -> Op a b Source # stimes :: Integral b0 => b0 -> Op a b -> Op a b Source #
Semigroup (f p) => Semigroup (Rec1 f p) Source #	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods (<>) :: Rec1 f p -> Rec1 f p -> Rec1 f p Source # sconcat :: NonEmpty (Rec1 f p) -> Rec1 f p Source # stimes :: Integral b => b -> Rec1 f p -> Rec1 f p Source #
(Semigroup a, Semigroup b, Semigroup c) => Semigroup (a, b, c) Source #	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: (a, b, c) -> (a, b, c) -> (a, b, c) Source # sconcat :: NonEmpty (a, b, c) -> (a, b, c) Source # stimes :: Integral b0 => b0 -> (a, b, c) -> (a, b, c) Source #
Alternative f => Semigroup (Alt f a) Source #	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Alt f a -> Alt f a -> Alt f a Source # sconcat :: NonEmpty (Alt f a) -> Alt f a Source # stimes :: Integral b => b -> Alt f a -> Alt f a Source #
(Applicative f, Semigroup a) => Semigroup (Ap f a) Source #	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods (<>) :: Ap f a -> Ap f a -> Ap f a Source # sconcat :: NonEmpty (Ap f a) -> Ap f a Source # stimes :: Integral b => b -> Ap f a -> Ap f a Source #
Semigroup a => Semigroup (Const a b) Source #	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods (<>) :: Const a b -> Const a b -> Const a b Source # sconcat :: NonEmpty (Const a b) -> Const a b Source # stimes :: Integral b0 => b0 -> Const a b -> Const a b Source #
Semigroup c => Semigroup (K1 i c p) Source #	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods (<>) :: K1 i c p -> K1 i c p -> K1 i c p Source # sconcat :: NonEmpty (K1 i c p) -> K1 i c p Source # stimes :: Integral b => b -> K1 i c p -> K1 i c p Source #
(Semigroup (f p), Semigroup (g p)) => Semigroup ((f :*: g) p) Source #	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods (<>) :: (f :: g) p -> (f :: g) p -> (f :: g) p Source # sconcat :: NonEmpty ((f :: g) p) -> (f :: g) p Source # stimes :: Integral b => b -> (f :: g) p -> (f :*: g) p Source #
(Semigroup a, Semigroup b, Semigroup c, Semigroup d) => Semigroup (a, b, c, d) Source #	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) Source # sconcat :: NonEmpty (a, b, c, d) -> (a, b, c, d) Source # stimes :: Integral b0 => b0 -> (a, b, c, d) -> (a, b, c, d) Source #
Semigroup (f p) => Semigroup (M1 i c f p) Source #	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods (<>) :: M1 i c f p -> M1 i c f p -> M1 i c f p Source # sconcat :: NonEmpty (M1 i c f p) -> M1 i c f p Source # stimes :: Integral b => b -> M1 i c f p -> M1 i c f p Source #
Semigroup (f (g p)) => Semigroup ((f :.: g) p) Source #	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods (<>) :: (f :.: g) p -> (f :.: g) p -> (f :.: g) p Source # sconcat :: NonEmpty ((f :.: g) p) -> (f :.: g) p Source # stimes :: Integral b => b -> (f :.: g) p -> (f :.: g) p Source #
(Semigroup a, Semigroup b, Semigroup c, Semigroup d, Semigroup e) => Semigroup (a, b, c, d, e) Source #	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) Source # sconcat :: NonEmpty (a, b, c, d, e) -> (a, b, c, d, e) Source # stimes :: Integral b0 => b0 -> (a, b, c, d, e) -> (a, b, c, d, e) Source #

class Semigroup a => Monoid a where Source #

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

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

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

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

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

Minimal complete definition

mempty

Methods

mempty :: a Source #

Identity of mappend

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

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

An associative operation

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

mconcat :: [a] -> a Source #

Fold a list using the monoid.

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

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

Instances

Instances details

Monoid Ordering Source #	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: Ordering Source # mappend :: Ordering -> Ordering -> Ordering Source # mconcat :: [Ordering] -> Ordering Source #
Monoid () Source #	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: () Source # mappend :: () -> () -> () Source # mconcat :: [()] -> () Source #
Monoid Any Source #	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Any Source # mappend :: Any -> Any -> Any Source # mconcat :: [Any] -> Any Source #
Monoid All Source #	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: All Source # mappend :: All -> All -> All Source # mconcat :: [All] -> All Source #
Monoid Lifetime Source #	`mappend` takes the longer of two lifetimes. Since: base-4.8.0.0
Instance details Defined in GHC.Event.Internal Methods mempty :: Lifetime Source # mappend :: Lifetime -> Lifetime -> Lifetime Source # mconcat :: [Lifetime] -> Lifetime Source #
Monoid Event Source #	Since: base-4.4.0.0
Instance details Defined in GHC.Event.Internal Methods mempty :: Event Source # mappend :: Event -> Event -> Event Source # mconcat :: [Event] -> Event Source #
Monoid [a] Source #	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: [a] Source # mappend :: [a] -> [a] -> [a] Source # mconcat :: [[a]] -> [a] Source #
Semigroup a => Monoid (Maybe a) Source #	Lift a semigroup into `Maybe` forming a `Monoid` according to http://en.wikipedia.org/wiki/Monoid: "Any semigroup `S` may be turned into a monoid simply by adjoining an element `e` not in `S` and defining `ee = e` and `es = s = se` for all `s ∈ S`." Since 4.11.0: constraint on inner `a` value generalised from `Monoid` to `Semigroup`. Since: base-2.1*
Instance details Defined in GHC.Base Methods mempty :: Maybe a Source # mappend :: Maybe a -> Maybe a -> Maybe a Source # mconcat :: [Maybe a] -> Maybe a Source #
Monoid a => Monoid (IO a) Source #	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods mempty :: IO a Source # mappend :: IO a -> IO a -> IO a Source # mconcat :: [IO a] -> IO a Source #
Monoid p => Monoid (Par1 p) Source #	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods mempty :: Par1 p Source # mappend :: Par1 p -> Par1 p -> Par1 p Source # mconcat :: [Par1 p] -> Par1 p Source #
Monoid a => Monoid (Down a) Source #	Since: base-4.11.0.0
Instance details Defined in Data.Ord Methods mempty :: Down a Source # mappend :: Down a -> Down a -> Down a Source # mconcat :: [Down a] -> Down a Source #
Num a => Monoid (Product a) Source #	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) Source #	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Sum a Source # mappend :: Sum a -> Sum a -> Sum a Source # mconcat :: [Sum a] -> Sum a Source #
Monoid (Endo a) Source #	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Endo a Source # mappend :: Endo a -> Endo a -> Endo a Source # mconcat :: [Endo a] -> Endo a Source #
Monoid a => Monoid (Dual a) Source #	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Dual a Source # mappend :: Dual a -> Dual a -> Dual a Source # mconcat :: [Dual a] -> Dual a Source #
Monoid (Last a) Source #	Since: base-2.1
Instance details Defined in Data.Monoid Methods mempty :: Last a Source # mappend :: Last a -> Last a -> Last a Source # mconcat :: [Last a] -> Last a Source #
Monoid (First a) Source #	Since: base-2.1
Instance details Defined in Data.Monoid Methods mempty :: First a Source # mappend :: First a -> First a -> First a Source # mconcat :: [First a] -> First a Source #
Monoid a => Monoid (Identity a) Source #	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 #
Semigroup a => Monoid (Option a) Source #	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods mempty :: Option a Source # mappend :: Option a -> Option a -> Option a Source # mconcat :: [Option a] -> Option a Source #
Monoid m => Monoid (WrappedMonoid m) Source #	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 #
(Ord a, Bounded a) => Monoid (Max a) Source #	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods mempty :: Max a Source # mappend :: Max a -> Max a -> Max a Source # mconcat :: [Max a] -> Max a Source #
(Ord a, Bounded a) => Monoid (Min a) Source #	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods mempty :: Min a Source # mappend :: Min a -> Min a -> Min a Source # mconcat :: [Min a] -> Min a Source #
Monoid (Equivalence a) Source #
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 (Comparison a) Source #
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 (Predicate a) Source #
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 b => Monoid (a -> b) Source #	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: a -> b Source # mappend :: (a -> b) -> (a -> b) -> a -> b Source # mconcat :: [a -> b] -> a -> b Source #
Monoid (U1 p) Source #	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods mempty :: U1 p Source # mappend :: U1 p -> U1 p -> U1 p Source # mconcat :: [U1 p] -> U1 p Source #
(Monoid a, Monoid b) => Monoid (a, b) Source #	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: (a, b) Source # mappend :: (a, b) -> (a, b) -> (a, b) Source # mconcat :: [(a, b)] -> (a, b) Source #
Monoid a => Monoid (ST s a) Source #	Since: base-4.11.0.0
Instance details Defined in GHC.ST Methods mempty :: ST s a Source # mappend :: ST s a -> ST s a -> ST s a Source # mconcat :: [ST s a] -> ST s a Source #
Monoid (Proxy s) Source #	Since: base-4.7.0.0
Instance details Defined in Data.Proxy Methods mempty :: Proxy s Source # mappend :: Proxy s -> Proxy s -> Proxy s Source # mconcat :: [Proxy s] -> Proxy s Source #
Monoid a => Monoid (Op a b) Source #
Instance details Defined in Data.Functor.Contravariant Methods mempty :: Op a b Source # mappend :: Op a b -> Op a b -> Op a b Source # mconcat :: [Op a b] -> Op a b Source #
Monoid (f p) => Monoid (Rec1 f p) Source #	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods mempty :: Rec1 f p Source # mappend :: Rec1 f p -> Rec1 f p -> Rec1 f p Source # mconcat :: [Rec1 f p] -> Rec1 f p Source #
(Monoid a, Monoid b, Monoid c) => Monoid (a, b, c) Source #	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: (a, b, c) Source # mappend :: (a, b, c) -> (a, b, c) -> (a, b, c) Source # mconcat :: [(a, b, c)] -> (a, b, c) Source #
Alternative f => Monoid (Alt f a) Source #	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Alt f a Source # mappend :: Alt f a -> Alt f a -> Alt f a Source # mconcat :: [Alt f a] -> Alt f a Source #
(Applicative f, Monoid a) => Monoid (Ap f a) Source #	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods mempty :: Ap f a Source # mappend :: Ap f a -> Ap f a -> Ap f a Source # mconcat :: [Ap f a] -> Ap f a Source #
Monoid a => Monoid (Const a b) Source #	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods mempty :: Const a b Source # mappend :: Const a b -> Const a b -> Const a b Source # mconcat :: [Const a b] -> Const a b Source #
Monoid c => Monoid (K1 i c p) Source #	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods mempty :: K1 i c p Source # mappend :: K1 i c p -> K1 i c p -> K1 i c p Source # mconcat :: [K1 i c p] -> K1 i c p Source #
(Monoid (f p), Monoid (g p)) => Monoid ((f :*: g) p) Source #	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods mempty :: (f :: g) p Source # mappend :: (f :: g) p -> (f :: g) p -> (f :: g) p Source # mconcat :: [(f :: g) p] -> (f :: g) p Source #
(Monoid a, Monoid b, Monoid c, Monoid d) => Monoid (a, b, c, d) Source #	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: (a, b, c, d) Source # mappend :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) Source # mconcat :: [(a, b, c, d)] -> (a, b, c, d) Source #
Monoid (f p) => Monoid (M1 i c f p) Source #	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods mempty :: M1 i c f p Source # mappend :: M1 i c f p -> M1 i c f p -> M1 i c f p Source # mconcat :: [M1 i c f p] -> M1 i c f p Source #
Monoid (f (g p)) => Monoid ((f :.: g) p) Source #	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods mempty :: (f :.: g) p Source # mappend :: (f :.: g) p -> (f :.: g) p -> (f :.: g) p Source # mconcat :: [(f :.: g) p] -> (f :.: g) p Source #
(Monoid a, Monoid b, Monoid c, Monoid d, Monoid e) => Monoid (a, b, c, d, e) Source #	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: (a, b, c, d, e) Source # mappend :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) Source # mconcat :: [(a, b, c, d, e)] -> (a, b, c, d, e) Source #

data Opaque Source #

Constructors

forall a. O a

type String = [Char] Source #

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

See Data.List for operations on lists.

data NonEmpty a Source #

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

Since: base-4.9.0.0

Constructors

a :| [a] infixr 5

Instances

Instances details

Monad NonEmpty Source #	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (>>=) :: NonEmpty a -> (a -> NonEmpty b) -> NonEmpty b Source # (>>) :: NonEmpty a -> NonEmpty b -> NonEmpty b Source # return :: a -> NonEmpty a Source #
Functor NonEmpty Source #	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods fmap :: (a -> b) -> NonEmpty a -> NonEmpty b Source # (<$) :: a -> NonEmpty b -> NonEmpty a Source #
MonadFix NonEmpty Source #	Since: base-4.9.0.0
Instance details Defined in Control.Monad.Fix Methods mfix :: (a -> NonEmpty a) -> NonEmpty a Source #
Applicative NonEmpty Source #	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods pure :: a -> NonEmpty a Source # (<>) :: NonEmpty (a -> b) -> NonEmpty a -> NonEmpty b Source # liftA2 :: (a -> b -> c) -> NonEmpty a -> NonEmpty b -> NonEmpty c Source # (>) :: NonEmpty a -> NonEmpty b -> NonEmpty b Source # (<*) :: NonEmpty a -> NonEmpty b -> NonEmpty a Source #
Foldable NonEmpty Source #	Since: base-4.9.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => NonEmpty m -> m Source # foldMap :: Monoid m => (a -> m) -> NonEmpty a -> m Source # foldMap' :: Monoid m => (a -> m) -> NonEmpty a -> m Source # foldr :: (a -> b -> b) -> b -> NonEmpty a -> b Source # foldr' :: (a -> b -> b) -> b -> NonEmpty a -> b Source # foldl :: (b -> a -> b) -> b -> NonEmpty a -> b Source # foldl' :: (b -> a -> b) -> b -> NonEmpty a -> b Source # foldr1 :: (a -> a -> a) -> NonEmpty a -> a Source # foldl1 :: (a -> a -> a) -> NonEmpty a -> a Source # toList :: NonEmpty a -> [a] Source # null :: NonEmpty a -> Bool Source # length :: NonEmpty a -> Int Source # elem :: Eq a => a -> NonEmpty a -> Bool Source # maximum :: Ord a => NonEmpty a -> a Source # minimum :: Ord a => NonEmpty a -> a Source # sum :: Num a => NonEmpty a -> a Source # product :: Num a => NonEmpty a -> a Source #
Traversable NonEmpty Source #	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> NonEmpty a -> f (NonEmpty b) Source # sequenceA :: Applicative f => NonEmpty (f a) -> f (NonEmpty a) Source # mapM :: Monad m => (a -> m b) -> NonEmpty a -> m (NonEmpty b) Source # sequence :: Monad m => NonEmpty (m a) -> m (NonEmpty a) Source #
MonadZip NonEmpty Source #	Since: base-4.9.0.0
Instance details Defined in Control.Monad.Zip Methods mzip :: NonEmpty a -> NonEmpty b -> NonEmpty (a, b) Source # mzipWith :: (a -> b -> c) -> NonEmpty a -> NonEmpty b -> NonEmpty c Source # munzip :: NonEmpty (a, b) -> (NonEmpty a, NonEmpty b) Source #
Show1 NonEmpty Source #	Since: base-4.10.0.0
Instance details Defined in Data.Functor.Classes Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> NonEmpty a -> ShowS Source # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [NonEmpty a] -> ShowS Source #
Read1 NonEmpty Source #	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 #
Ord1 NonEmpty Source #	Since: base-4.10.0.0
Instance details Defined in Data.Functor.Classes Methods liftCompare :: (a -> b -> Ordering) -> NonEmpty a -> NonEmpty b -> Ordering Source #
Eq1 NonEmpty Source #	Since: base-4.10.0.0
Instance details Defined in Data.Functor.Classes Methods liftEq :: (a -> b -> Bool) -> NonEmpty a -> NonEmpty b -> Bool Source #
IsList (NonEmpty a) Source #	Since: base-4.9.0.0
Instance details Defined in GHC.Exts Associated Types type Item (NonEmpty a) Source # Methods fromList :: [Item (NonEmpty a)] -> NonEmpty a Source # fromListN :: Int -> [Item (NonEmpty a)] -> NonEmpty a Source # toList :: NonEmpty a -> [Item (NonEmpty a)] Source #
Eq a => Eq (NonEmpty a) Source #	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (==) :: NonEmpty a -> NonEmpty a -> Bool Source # (/=) :: NonEmpty a -> NonEmpty a -> Bool Source #
Data a => Data (NonEmpty a) Source #	Since: base-4.9.0.0
Instance details Defined in Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> NonEmpty a -> c (NonEmpty a) Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (NonEmpty a) Source # toConstr :: NonEmpty a -> Constr Source # dataTypeOf :: NonEmpty a -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (NonEmpty a)) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (NonEmpty a)) Source # gmapT :: (forall b. Data b => b -> b) -> NonEmpty a -> NonEmpty a Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> NonEmpty a -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> NonEmpty a -> r Source # gmapQ :: (forall d. Data d => d -> u) -> NonEmpty a -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> NonEmpty a -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> NonEmpty a -> m (NonEmpty a) Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> NonEmpty a -> m (NonEmpty a) Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> NonEmpty a -> m (NonEmpty a) Source #
Ord a => Ord (NonEmpty a) Source #	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 #
Read a => Read (NonEmpty a) Source #	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) Source #	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 #
Generic (NonEmpty a) Source #	Since: base-4.6.0.0
Instance details Defined in GHC.Generics Associated Types type Rep (NonEmpty a) :: Type -> Type Source # Methods from :: NonEmpty a -> Rep (NonEmpty a) x Source # to :: Rep (NonEmpty a) x -> NonEmpty a Source #
Semigroup (NonEmpty a) Source #	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 #
Generic1 NonEmpty Source #	Since: base-4.6.0.0
Instance details Defined in GHC.Generics Associated Types type Rep1 NonEmpty :: k -> Type Source # Methods from1 :: forall (a :: k). NonEmpty a -> Rep1 NonEmpty a Source # to1 :: forall (a :: k). Rep1 NonEmpty a -> NonEmpty a Source #
type Rep (NonEmpty a) Source #
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 Item (NonEmpty a) Source #
Instance details Defined in GHC.Exts type Item (NonEmpty a) = a
type Rep1 NonEmpty Source #
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 [])))

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

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 [] Source #	Since: base-2.1
Instance details Defined in GHC.Base Methods empty :: [a] Source # (<\|>) :: [a] -> [a] -> [a] Source # some :: [a] -> [[a]] Source # many :: [a] -> [[a]] Source #
Alternative Maybe Source #	Since: base-2.1
Instance details Defined in GHC.Base Methods empty :: Maybe a Source # (<\|>) :: Maybe a -> Maybe a -> Maybe a Source # some :: Maybe a -> Maybe [a] Source # many :: Maybe a -> Maybe [a] Source #
Alternative IO Source #	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods empty :: IO a Source # (<\|>) :: IO a -> IO a -> IO a Source # some :: IO a -> IO [a] Source # many :: IO a -> IO [a] Source #
Alternative ReadP Source #	Since: base-4.6.0.0
Instance details Defined in Text.ParserCombinators.ReadP Methods empty :: ReadP a Source # (<\|>) :: ReadP a -> ReadP a -> ReadP a Source # some :: ReadP a -> ReadP [a] Source # many :: ReadP a -> ReadP [a] Source #
Alternative ReadPrec Source #	Since: base-4.6.0.0
Instance details Defined in Text.ParserCombinators.ReadPrec 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 STM Source #	Since: base-4.8.0.0
Instance details Defined in GHC.Conc.Sync Methods empty :: STM a Source # (<\|>) :: STM a -> STM a -> STM a Source # some :: STM a -> STM [a] Source # many :: STM a -> STM [a] Source #
Alternative ZipList Source #	Since: base-4.11.0.0
Instance details Defined in Control.Applicative Methods empty :: ZipList a Source # (<\|>) :: ZipList a -> ZipList a -> ZipList a Source # some :: ZipList a -> ZipList [a] Source # many :: ZipList a -> ZipList [a] Source #
Alternative Option Source #	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods empty :: Option a Source # (<\|>) :: Option a -> Option a -> Option a Source # some :: Option a -> Option [a] Source # many :: Option a -> Option [a] Source #
Alternative (U1 :: Type -> Type) Source #	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods empty :: U1 a Source # (<\|>) :: U1 a -> U1 a -> U1 a Source # some :: U1 a -> U1 [a] Source # many :: U1 a -> U1 [a] Source #
Alternative (Proxy :: Type -> Type) Source #	Since: base-4.9.0.0
Instance details Defined in Data.Proxy Methods empty :: Proxy a Source # (<\|>) :: Proxy a -> Proxy a -> Proxy a Source # some :: Proxy a -> Proxy [a] Source # many :: Proxy a -> Proxy [a] Source #
ArrowPlus a => Alternative (ArrowMonad a) Source #	Since: base-4.6.0.0
Instance details Defined in Control.Arrow Methods empty :: ArrowMonad a a0 Source # (<\|>) :: ArrowMonad a a0 -> ArrowMonad a a0 -> ArrowMonad a a0 Source # some :: ArrowMonad a a0 -> ArrowMonad a [a0] Source # many :: ArrowMonad a a0 -> ArrowMonad a [a0] Source #
MonadPlus m => Alternative (WrappedMonad m) Source #	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 #
Alternative f => Alternative (Rec1 f) Source #	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods empty :: Rec1 f a Source # (<\|>) :: Rec1 f a -> Rec1 f a -> Rec1 f a Source # some :: Rec1 f a -> Rec1 f [a] Source # many :: Rec1 f a -> Rec1 f [a] Source #
Alternative f => Alternative (Alt f) Source #	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods empty :: Alt f a Source # (<\|>) :: Alt f a -> Alt f a -> Alt f a Source # some :: Alt f a -> Alt f [a] Source # many :: Alt f a -> Alt f [a] Source #
Alternative f => Alternative (Ap f) Source #	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods empty :: Ap f a Source # (<\|>) :: Ap f a -> Ap f a -> Ap f a Source # some :: Ap f a -> Ap f [a] Source # many :: Ap f a -> Ap f [a] Source #
Alternative m => Alternative (Kleisli m a) Source #	Since: base-4.14.0.0
Instance details Defined in Control.Arrow Methods empty :: Kleisli m a a0 Source # (<\|>) :: Kleisli m a a0 -> Kleisli m a a0 -> Kleisli m a a0 Source # some :: Kleisli m a a0 -> Kleisli m a [a0] Source # many :: Kleisli m a a0 -> Kleisli m a [a0] Source #
(ArrowZero a, ArrowPlus a) => Alternative (WrappedArrow a b) Source #	Since: base-2.1
Instance details Defined in Control.Applicative Methods empty :: WrappedArrow a b a0 Source # (<\|>) :: WrappedArrow a b a0 -> WrappedArrow a b a0 -> WrappedArrow a b a0 Source # some :: WrappedArrow a b a0 -> WrappedArrow a b [a0] Source # many :: WrappedArrow a b a0 -> WrappedArrow a b [a0] Source #
(Alternative f, Alternative g) => Alternative (f :*: g) Source #	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods empty :: (f :: g) a Source # (<\|>) :: (f :: g) a -> (f :: g) a -> (f :: g) a Source # some :: (f :: g) a -> (f :: g) [a] Source # many :: (f :: g) a -> (f :: g) [a] Source #
(Alternative f, Alternative g) => Alternative (Product f g) Source #	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods empty :: Product f g a Source # (<\|>) :: Product f g a -> Product f g a -> Product f g a Source # some :: Product f g a -> Product f g [a] Source # many :: Product f g a -> Product f g [a] Source #
Alternative f => Alternative (M1 i c f) Source #	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods empty :: M1 i c f a Source # (<\|>) :: M1 i c f a -> M1 i c f a -> M1 i c f a Source # some :: M1 i c f a -> M1 i c f [a] Source # many :: M1 i c f a -> M1 i c f [a] Source #
(Alternative f, Applicative g) => Alternative (f :.: g) Source #	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods empty :: (f :.: g) a Source # (<\|>) :: (f :.: g) a -> (f :.: g) a -> (f :.: g) a Source # some :: (f :.: g) a -> (f :.: g) [a] Source # many :: (f :.: g) a -> (f :.: g) [a] Source #
(Alternative f, Applicative g) => Alternative (Compose f g) Source #	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Compose Methods empty :: Compose f g a Source # (<\|>) :: Compose f g a -> Compose f g a -> Compose f g a Source # some :: Compose f g a -> Compose f g [a] Source # many :: Compose f g a -> Compose f g [a] Source #

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

A variant of <*> with the arguments reversed.

Using ApplicativeDo: 'as <**> fs' can be understood as the do expression

do a <- as
   f <- fs
   pure (f a)

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

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

| Using ApplicativeDo: 'liftA f as' can be understood as the do expression

do a <- as
   pure (f a)

with an inferred Functor constraint, weaker than Applicative.

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

Lift a ternary function to actions.

Using ApplicativeDo: 'liftA3 f as bs cs' can be understood as the do expression

do a <- as
   b <- bs
   c <- cs
   pure (f a b c)

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

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

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

Conditional execution of Applicative expressions. For example,

when debug (putStrLn "Debugging")

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

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

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

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

mapM f is equivalent to sequence . map f.

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

Promote a function to a monad.

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

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

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

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

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

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

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

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

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

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

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

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

is equivalent to

liftMn f x1 x2 ... xn

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

unsafeChr :: Int -> Char Source #

ord :: Char -> Int Source #

The fromEnum method restricted to the type Char.

minInt :: Int Source #

maxInt :: Int Source #

id :: a -> a Source #

Identity function.

id x = x

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

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

>>> const 42 "hello"
42

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

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

Function composition.

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

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

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

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

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

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

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

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

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

failIO :: String -> IO a Source #

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

getTag :: a -> Int# Source #

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

module GHC.Classes

module GHC.CString

module GHC.Magic

module GHC.Types

module GHC.Prim

module GHC.Prim.Ext

module GHC.Err

module GHC.Maybe