base-4.21.0.0: Core data structures and operations
Copyright(c) Andy Gill 2001
(c) Oregon Graduate Institute of Science and Technology 2001
LicenseBSD-style (see the file libraries/base/LICENSE)
Maintainer[email protected]
Stabilitystable
Portabilityportable
Safe HaskellSafe
LanguageHaskell2010

Data.Monoid

Description

A type a is a Monoid if it provides an associative function (<>) that lets you combine any two values of type a into one, and a neutral element (mempty) such that

a <> mempty == mempty <> a == a

A Monoid is a Semigroup with the added requirement of a neutral element. Thus any Monoid is a Semigroup, but not the other way around.

Examples

Expand

The Sum monoid is defined by the numerical addition operator and `0` as neutral element:

>>> import Data.Int
>>> mempty :: Sum Int
Sum {getSum = 0}
>>> Sum 1 <> Sum 2 <> Sum 3 <> Sum 4 :: Sum Int
Sum {getSum = 10}

We can combine multiple values in a list into a single value using the mconcat function. Note that we have to specify the type here since Int is a monoid under several different operations:

>>> mconcat [1,2,3,4] :: Sum Int
Sum {getSum = 10}
>>> mconcat [] :: Sum Int
Sum {getSum = 0}

Another valid monoid instance of Int is Product It is defined by multiplication and `1` as neutral element:

>>> Product 1 <> Product 2 <> Product 3 <> Product 4 :: Product Int
Product {getProduct = 24}
>>> mconcat [1,2,3,4] :: Product Int
Product {getProduct = 24}
>>> mconcat [] :: Product Int
Product {getProduct = 1}
Synopsis

Monoid typeclass

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

You can alternatively define mconcat instead of mempty, in which case the laws are:

Unit
mconcat (pure x) = x
Multiplication
mconcat (join xss) = mconcat (fmap mconcat xss)
Subclass
mconcat (toList xs) = sconcat xs

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 | mconcat

Methods

mempty :: a Source #

Identity of mappend

Examples

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

>>> mempty <> [1, 2, 3]
[1,2,3]

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 ByteArray Source #

Since: base-4.17.0.0

Instance details

Defined in Data.Array.Byte

Methods

mempty :: ByteArray Source #

mappend :: ByteArray -> ByteArray -> ByteArray Source #

mconcat :: [ByteArray] -> ByteArray Source #

Monoid All Source #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

mempty :: All Source #

mappend :: All -> All -> All Source #

mconcat :: [All] -> All Source #

Monoid Any Source #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

mempty :: Any Source #

mappend :: Any -> Any -> Any Source #

mconcat :: [Any] -> Any Source #

Monoid Event Source #

Since: base-4.4.0.0

Instance details

Defined in GHC.Internal.Event.Internal.Types

Methods

mempty :: Event Source #

mappend :: Event -> Event -> Event Source #

mconcat :: [Event] -> Event Source #

Monoid EventLifetime Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Event.Internal.Types

Methods

mempty :: EventLifetime Source #

mappend :: EventLifetime -> EventLifetime -> EventLifetime Source #

mconcat :: [EventLifetime] -> EventLifetime Source #

Monoid Lifetime Source #

mappend takes the longer of two lifetimes.

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Event.Internal.Types

Methods

mempty :: Lifetime Source #

mappend :: Lifetime -> Lifetime -> Lifetime Source #

mconcat :: [Lifetime] -> Lifetime Source #

Monoid ExceptionContext Source # 
Instance details

Defined in GHC.Internal.Exception.Context

Methods

mempty :: ExceptionContext Source #

mappend :: ExceptionContext -> ExceptionContext -> ExceptionContext Source #

mconcat :: [ExceptionContext] -> ExceptionContext Source #

Monoid Ordering Source #

Since: base-2.1

Instance details

Defined in GHC.Internal.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.Internal.Base

Methods

mempty :: () Source #

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

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

Monoid (Comparison a) Source #

mempty on comparisons always returns EQ. Without newtypes this equals pure (pure EQ).

mempty :: Comparison a
mempty = Comparison _ _ -> EQ
Instance details

Defined in Data.Functor.Contravariant

Methods

mempty :: Comparison a Source #

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

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

Monoid (Equivalence a) Source #

mempty on equivalences always returns True. Without newtypes this equals pure (pure True).

mempty :: Equivalence a
mempty = Equivalence _ _ -> True
Instance details

Defined in Data.Functor.Contravariant

Methods

mempty :: Equivalence a Source #

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

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

Monoid (Predicate a) Source #

mempty on predicates always returns True. Without newtypes this equals pure True.

mempty :: Predicate a
mempty = _ -> True
Instance details

Defined in Data.Functor.Contravariant

Methods

mempty :: Predicate a Source #

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

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

(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 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 #

Monoid a => Monoid (STM a) Source #

Since: base-4.17.0.0

Instance details

Defined in GHC.Internal.Conc.Sync

Methods

mempty :: STM a Source #

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

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

FiniteBits a => Monoid (And a) Source #

This constraint is arguably too strong. However, as some types (such as Natural) have undefined complement, this is the only safe choice.

Since: base-4.16

Instance details

Defined in GHC.Internal.Data.Bits

Methods

mempty :: And a Source #

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

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

FiniteBits a => Monoid (Iff a) Source #

This constraint is arguably too strong. However, as some types (such as Natural) have undefined complement, this is the only safe choice.

Since: base-4.16

Instance details

Defined in GHC.Internal.Data.Bits

Methods

mempty :: Iff a Source #

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

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

Bits a => Monoid (Ior a) Source #

Since: base-4.16

Instance details

Defined in GHC.Internal.Data.Bits

Methods

mempty :: Ior a Source #

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

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

Bits a => Monoid (Xor a) Source #

Since: base-4.16

Instance details

Defined in GHC.Internal.Data.Bits

Methods

mempty :: Xor a Source #

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

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

Monoid a => Monoid (Identity a) Source #

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Identity

Methods

mempty :: Identity a Source #

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

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

Ord a => Monoid (Max a) Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Utils

Methods

mempty :: Max a Source #

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

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

Ord a => Monoid (Min a) Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Utils

Methods

mempty :: Min a Source #

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

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

Monoid (First a) Source #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Monoid

Methods

mempty :: First a Source #

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

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

Monoid (Last a) Source #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Monoid

Methods

mempty :: Last a Source #

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

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

Monoid a => Monoid (Down a) Source #

Since: base-4.11.0.0

Instance details

Defined in GHC.Internal.Data.Ord

Methods

mempty :: Down a Source #

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

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

Monoid a => Monoid (Dual a) Source #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

mempty :: Dual a Source #

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

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

Monoid (Endo a) Source #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

mempty :: Endo a Source #

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

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

Num a => Monoid (Product a) Source #

Since: base-2.1

Instance details

Defined in GHC.Internal.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 GHC.Internal.Data.Semigroup.Internal

Methods

mempty :: Sum a Source #

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

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

(Generic a, Monoid (Rep a ())) => Monoid (Generically a) Source #

Since: base-4.17.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

mempty :: Generically a Source #

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

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

Monoid p => Monoid (Par1 p) Source #

Since: base-4.12.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

mempty :: Par1 p Source #

mappend :: Par1 p -> Par1 p -> Par1 p Source #

mconcat :: [Par1 p] -> Par1 p Source #

Monoid a => Monoid (Q a) Source #

Since: ghc-internal-2.17.0.0

Instance details

Defined in GHC.Internal.TH.Syntax

Methods

mempty :: Q a Source #

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

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

Monoid a => Monoid (IO a) Source #

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Base

Methods

mempty :: IO a Source #

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

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

Semigroup a => Monoid (Maybe a) 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 e*e = e and e*s = s = s*e for all s ∈ S."

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

Since: base-2.1

Instance details

Defined in GHC.Internal.Base

Methods

mempty :: Maybe a Source #

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

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

Monoid a => Monoid (Solo a) Source #

Since: base-4.15

Instance details

Defined in GHC.Internal.Base

Methods

mempty :: Solo a Source #

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

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

Monoid [a] Source #

Since: base-2.1

Instance details

Defined in GHC.Internal.Base

Methods

mempty :: [a] Source #

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

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

Monoid a => Monoid (Op a b) Source #

mempty @(Op a b) without newtypes is mempty @(b->a) = _ -> mempty.

mempty :: Op a b
mempty = Op _ -> mempty
Instance details

Defined in Data.Functor.Contravariant

Methods

mempty :: Op a b Source #

mappend :: Op a b -> Op a b -> Op a b Source #

mconcat :: [Op a b] -> Op a b Source #

Monoid (Proxy s) Source #

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Proxy

Methods

mempty :: Proxy s Source #

mappend :: Proxy s -> Proxy s -> Proxy s Source #

mconcat :: [Proxy s] -> Proxy s Source #

Monoid (U1 p) Source #

Since: base-4.12.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

mempty :: U1 p Source #

mappend :: U1 p -> U1 p -> U1 p Source #

mconcat :: [U1 p] -> U1 p Source #

Monoid a => Monoid (ST s a) Source #

Since: base-4.11.0.0

Instance details

Defined in GHC.Internal.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 a, Monoid b) => Monoid (a, b) Source #

Since: base-2.1

Instance details

Defined in GHC.Internal.Base

Methods

mempty :: (a, b) Source #

mappend :: (a, b) -> (a, b) -> (a, b) Source #

mconcat :: [(a, b)] -> (a, b) Source #

Monoid b => Monoid (a -> b) Source #

Since: base-2.1

Instance details

Defined in GHC.Internal.Base

Methods

mempty :: a -> b Source #

mappend :: (a -> b) -> (a -> b) -> a -> b Source #

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

Monoid a => Monoid (Const a b) Source #

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Const

Methods

mempty :: Const a b Source #

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

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

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

Since: base-4.12.0.0

Instance details

Defined in GHC.Internal.Data.Monoid

Methods

mempty :: Ap f a Source #

mappend :: Ap f a -> Ap f a -> Ap f a Source #

mconcat :: [Ap f a] -> Ap f a Source #

Alternative f => Monoid (Alt f a) Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

mempty :: Alt f a Source #

mappend :: Alt f a -> Alt f a -> Alt f a Source #

mconcat :: [Alt f a] -> Alt f a Source #

Monoid (f p) => Monoid (Rec1 f p) Source #

Since: base-4.12.0.0

Instance details

Defined in GHC.Internal.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.Internal.Base

Methods

mempty :: (a, b, c) Source #

mappend :: (a, b, c) -> (a, b, c) -> (a, b, c) Source #

mconcat :: [(a, b, c)] -> (a, b, c) Source #

(Monoid (f a), Monoid (g a)) => Monoid (Product f g a) Source #

Since: base-4.16.0.0

Instance details

Defined in Data.Functor.Product

Methods

mempty :: Product f g a Source #

mappend :: Product f g a -> Product f g a -> Product f g a Source #

mconcat :: [Product f g a] -> Product f g a Source #

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

Since: base-4.12.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

mempty :: (f :*: g) p Source #

mappend :: (f :*: g) p -> (f :*: g) p -> (f :*: g) p Source #

mconcat :: [(f :*: g) p] -> (f :*: g) p Source #

Monoid c => Monoid (K1 i c p) Source #

Since: base-4.12.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

mempty :: K1 i c p Source #

mappend :: K1 i c p -> K1 i c p -> K1 i c p Source #

mconcat :: [K1 i c p] -> K1 i c p Source #

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

Since: base-2.1

Instance details

Defined in GHC.Internal.Base

Methods

mempty :: (a, b, c, d) Source #

mappend :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) Source #

mconcat :: [(a, b, c, d)] -> (a, b, c, d) Source #

Monoid (f (g a)) => Monoid (Compose f g a) Source #

Since: base-4.16.0.0

Instance details

Defined in Data.Functor.Compose

Methods

mempty :: Compose f g a Source #

mappend :: Compose f g a -> Compose f g a -> Compose f g a Source #

mconcat :: [Compose f g a] -> Compose f g a Source #

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

Since: base-4.12.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

mempty :: (f :.: g) p Source #

mappend :: (f :.: g) p -> (f :.: g) p -> (f :.: g) p Source #

mconcat :: [(f :.: g) p] -> (f :.: g) p Source #

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

Since: base-4.12.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

mempty :: M1 i c f p Source #

mappend :: M1 i c f p -> M1 i c f p -> M1 i c f p Source #

mconcat :: [M1 i c f p] -> M1 i c f p Source #

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

Since: base-2.1

Instance details

Defined in GHC.Internal.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 #

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

An associative operation.

Examples

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

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

>>> putStr "Hello, " <> putStrLn "World!"
Hello, World!

newtype Dual a Source #

The dual of a Monoid, obtained by swapping the arguments of (<>).

Dual a <> Dual b == Dual (b <> a)

Examples

Expand
>>> Dual "Hello" <> Dual "World"
Dual {getDual = "WorldHello"}

>>> Dual (Dual "Hello") <> Dual (Dual "World")
Dual {getDual = Dual {getDual = "HelloWorld"}}

Constructors

Dual 

Fields

Instances

Instances details
Foldable1 Dual Source #

Since: base-4.18.0.0

Instance details

Defined in Data.Foldable1

Methods

fold1 :: Semigroup m => Dual m -> m Source #

foldMap1 :: Semigroup m => (a -> m) -> Dual a -> m Source #

foldMap1' :: Semigroup m => (a -> m) -> Dual a -> m Source #

toNonEmpty :: Dual a -> NonEmpty a Source #

maximum :: Ord a => Dual a -> a Source #

minimum :: Ord a => Dual a -> a Source #

head :: Dual a -> a Source #

last :: Dual a -> a Source #

foldrMap1 :: (a -> b) -> (a -> b -> b) -> Dual a -> b Source #

foldlMap1' :: (a -> b) -> (b -> a -> b) -> Dual a -> b Source #

foldlMap1 :: (a -> b) -> (b -> a -> b) -> Dual a -> b Source #

foldrMap1' :: (a -> b) -> (a -> b -> b) -> Dual a -> b Source #

Applicative Dual Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.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 #

Functor Dual Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

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

(<$) :: a -> Dual b -> Dual a Source #

Monad Dual Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

(>>=) :: Dual a -> (a -> Dual b) -> Dual b Source #

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

return :: a -> Dual a Source #

MonadFix Dual Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Control.Monad.Fix

Methods

mfix :: (a -> Dual a) -> Dual a Source #

MonadZip Dual Source #

Since: ghc-internal-4.8.0.0

Instance details

Defined in GHC.Internal.Control.Monad.Zip

Methods

mzip :: Dual a -> Dual b -> Dual (a, b) Source #

mzipWith :: (a -> b -> c) -> Dual a -> Dual b -> Dual c Source #

munzip :: Dual (a, b) -> (Dual a, Dual b) Source #

Foldable Dual Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Foldable

Methods

fold :: Monoid m => Dual m -> m Source #

foldMap :: Monoid m => (a -> m) -> Dual a -> m Source #

foldMap' :: Monoid m => (a -> m) -> Dual a -> m Source #

foldr :: (a -> b -> b) -> b -> Dual a -> b Source #

foldr' :: (a -> b -> b) -> b -> Dual a -> b Source #

foldl :: (b -> a -> b) -> b -> Dual a -> b Source #

foldl' :: (b -> a -> b) -> b -> Dual a -> b Source #

foldr1 :: (a -> a -> a) -> Dual a -> a Source #

foldl1 :: (a -> a -> a) -> Dual a -> a Source #

toList :: Dual a -> [a] Source #

null :: Dual a -> Bool Source #

length :: Dual a -> Int Source #

elem :: Eq a => a -> Dual a -> Bool Source #

maximum :: Ord a => Dual a -> a Source #

minimum :: Ord a => Dual a -> a Source #

sum :: Num a => Dual a -> a Source #

product :: Num a => Dual a -> a Source #

Traversable Dual Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Traversable

Methods

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

sequenceA :: Applicative f => Dual (f a) -> f (Dual a) Source #

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

sequence :: Monad m => Dual (m a) -> m (Dual a) Source #

Generic1 Dual Source # 
Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Associated Types

type Rep1 Dual

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

type Rep1 Dual = D1 ('MetaData "Dual" "GHC.Internal.Data.Semigroup.Internal" "ghc-internal" 'True) (C1 ('MetaCons "Dual" 'PrefixI 'True) (S1 ('MetaSel ('Just "getDual") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))

Methods

from1 :: Dual a -> Rep1 Dual a Source #

to1 :: Rep1 Dual a -> Dual a Source #

Monoid a => Monoid (Dual a) Source #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

mempty :: Dual a Source #

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

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

Semigroup a => Semigroup (Dual a) Source #

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.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 #

Data a => Data (Dual a) Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Dual a -> c (Dual a) Source #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Dual a) Source #

toConstr :: Dual a -> Constr Source #

dataTypeOf :: Dual a -> DataType Source #

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Dual a)) Source #

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Dual a)) Source #

gmapT :: (forall b. Data b => b -> b) -> Dual a -> Dual a Source #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Dual a -> r Source #

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Dual a -> r Source #

gmapQ :: (forall d. Data d => d -> u) -> Dual a -> [u] Source #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Dual a -> u Source #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Dual a -> m (Dual a) Source #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Dual a -> m (Dual a) Source #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Dual a -> m (Dual a) Source #

Bounded a => Bounded (Dual a) Source #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

minBound :: Dual a Source #

maxBound :: Dual a Source #

Generic (Dual a) Source # 
Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Associated Types

type Rep (Dual a)

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

type Rep (Dual a) = D1 ('MetaData "Dual" "GHC.Internal.Data.Semigroup.Internal" "ghc-internal" 'True) (C1 ('MetaCons "Dual" 'PrefixI 'True) (S1 ('MetaSel ('Just "getDual") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))

Methods

from :: Dual a -> Rep (Dual a) x Source #

to :: Rep (Dual a) x -> Dual a Source #

Read a => Read (Dual a) Source #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

readsPrec :: Int -> ReadS (Dual a) Source #

readList :: ReadS [Dual a] Source #

readPrec :: ReadPrec (Dual a) Source #

readListPrec :: ReadPrec [Dual a] Source #

Show a => Show (Dual a) Source #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

showsPrec :: Int -> Dual a -> ShowS Source #

show :: Dual a -> String Source #

showList :: [Dual a] -> ShowS Source #

Eq a => Eq (Dual a) Source #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

(==) :: Dual a -> Dual a -> Bool Source #

(/=) :: Dual a -> Dual a -> Bool Source #

Ord a => Ord (Dual a) Source #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

compare :: Dual a -> Dual a -> Ordering Source #

(<) :: Dual a -> Dual a -> Bool Source #

(<=) :: Dual a -> Dual a -> Bool Source #

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

(>=) :: Dual a -> Dual a -> Bool Source #

max :: Dual a -> Dual a -> Dual a Source #

min :: Dual a -> Dual a -> Dual a Source #

type Rep1 Dual Source #

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

type Rep1 Dual = D1 ('MetaData "Dual" "GHC.Internal.Data.Semigroup.Internal" "ghc-internal" 'True) (C1 ('MetaCons "Dual" 'PrefixI 'True) (S1 ('MetaSel ('Just "getDual") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))
type Rep (Dual a) Source #

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

type Rep (Dual a) = D1 ('MetaData "Dual" "GHC.Internal.Data.Semigroup.Internal" "ghc-internal" 'True) (C1 ('MetaCons "Dual" 'PrefixI 'True) (S1 ('MetaSel ('Just "getDual") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))

newtype Endo a Source #

The monoid of endomorphisms under composition.

Endo f <> Endo g == Endo (f . g)

Examples

Expand
>>> let computation = Endo ("Hello, " ++) <> Endo (++ "!")
>>> appEndo computation "Haskell"
"Hello, Haskell!"

>>> let computation = Endo (*3) <> Endo (+1)
>>> appEndo computation 1
6

Constructors

Endo 

Fields

Instances

Instances details
Monoid (Endo a) Source #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

mempty :: Endo a Source #

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

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

Semigroup (Endo a) Source #

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.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 #

Generic (Endo a) Source # 
Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Associated Types

type Rep (Endo a)

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

type Rep (Endo a) = D1 ('MetaData "Endo" "GHC.Internal.Data.Semigroup.Internal" "ghc-internal" 'True) (C1 ('MetaCons "Endo" 'PrefixI 'True) (S1 ('MetaSel ('Just "appEndo") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (a -> a))))

Methods

from :: Endo a -> Rep (Endo a) x Source #

to :: Rep (Endo a) x -> Endo a Source #

type Rep (Endo a) Source #

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

type Rep (Endo a) = D1 ('MetaData "Endo" "GHC.Internal.Data.Semigroup.Internal" "ghc-internal" 'True) (C1 ('MetaCons "Endo" 'PrefixI 'True) (S1 ('MetaSel ('Just "appEndo") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (a -> a))))

Bool wrappers

newtype All Source #

Boolean monoid under conjunction (&&).

All x <> All y = All (x && y)

Examples

Expand
>>> All True <> mempty <> All False)
All {getAll = False}

>>> mconcat (map (\x -> All (even x)) [2,4,6,7,8])
All {getAll = False}

>>> All True <> mempty
All {getAll = True}

Constructors

All 

Fields

Instances

Instances details
Monoid All Source #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

mempty :: All Source #

mappend :: All -> All -> All Source #

mconcat :: [All] -> All Source #

Semigroup All Source #

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

(<>) :: All -> All -> All Source #

sconcat :: NonEmpty All -> All Source #

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

Data All Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> All -> c All Source #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c All Source #

toConstr :: All -> Constr Source #

dataTypeOf :: All -> DataType Source #

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c All) Source #

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c All) Source #

gmapT :: (forall b. Data b => b -> b) -> All -> All Source #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> All -> r Source #

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> All -> r Source #

gmapQ :: (forall d. Data d => d -> u) -> All -> [u] Source #

gmapQi :: Int -> (forall d. Data d => d -> u) -> All -> u Source #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> All -> m All Source #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> All -> m All Source #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> All -> m All Source #

Bounded All Source #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

minBound :: All Source #

maxBound :: All Source #

Generic All Source # 
Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Associated Types

type Rep All

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

type Rep All = D1 ('MetaData "All" "GHC.Internal.Data.Semigroup.Internal" "ghc-internal" 'True) (C1 ('MetaCons "All" 'PrefixI 'True) (S1 ('MetaSel ('Just "getAll") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 Bool)))

Methods

from :: All -> Rep All x Source #

to :: Rep All x -> All Source #

Read All Source #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

readsPrec :: Int -> ReadS All Source #

readList :: ReadS [All] Source #

readPrec :: ReadPrec All Source #

readListPrec :: ReadPrec [All] Source #

Show All Source #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

showsPrec :: Int -> All -> ShowS Source #

show :: All -> String Source #

showList :: [All] -> ShowS Source #

Eq All Source #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

(==) :: All -> All -> Bool Source #

(/=) :: All -> All -> Bool Source #

Ord All Source #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

compare :: All -> All -> Ordering Source #

(<) :: All -> All -> Bool Source #

(<=) :: All -> All -> Bool Source #

(>) :: All -> All -> Bool Source #

(>=) :: All -> All -> Bool Source #

max :: All -> All -> All Source #

min :: All -> All -> All Source #

type Rep All Source #

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

type Rep All = D1 ('MetaData "All" "GHC.Internal.Data.Semigroup.Internal" "ghc-internal" 'True) (C1 ('MetaCons "All" 'PrefixI 'True) (S1 ('MetaSel ('Just "getAll") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 Bool)))

newtype Any Source #

Boolean monoid under disjunction (||).

Any x <> Any y = Any (x || y)

Examples

Expand
>>> Any True <> mempty <> Any False
Any {getAny = True}

>>> mconcat (map (\x -> Any (even x)) [2,4,6,7,8])
Any {getAny = True}

>>> Any False <> mempty
Any {getAny = False}

Constructors

Any 

Fields

Instances

Instances details
Monoid Any Source #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

mempty :: Any Source #

mappend :: Any -> Any -> Any Source #

mconcat :: [Any] -> Any Source #

Semigroup Any Source #

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

(<>) :: Any -> Any -> Any Source #

sconcat :: NonEmpty Any -> Any Source #

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

Data Any Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Any -> c Any Source #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Any Source #

toConstr :: Any -> Constr Source #

dataTypeOf :: Any -> DataType Source #

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Any) Source #

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Any) Source #

gmapT :: (forall b. Data b => b -> b) -> Any -> Any Source #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Any -> r Source #

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Any -> r Source #

gmapQ :: (forall d. Data d => d -> u) -> Any -> [u] Source #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Any -> u Source #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Any -> m Any Source #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Any -> m Any Source #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Any -> m Any Source #

Bounded Any Source #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

minBound :: Any Source #

maxBound :: Any Source #

Generic Any Source # 
Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Associated Types

type Rep Any

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

type Rep Any = D1 ('MetaData "Any" "GHC.Internal.Data.Semigroup.Internal" "ghc-internal" 'True) (C1 ('MetaCons "Any" 'PrefixI 'True) (S1 ('MetaSel ('Just "getAny") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 Bool)))

Methods

from :: Any -> Rep Any x Source #

to :: Rep Any x -> Any Source #

Read Any Source #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

readsPrec :: Int -> ReadS Any Source #

readList :: ReadS [Any] Source #

readPrec :: ReadPrec Any Source #

readListPrec :: ReadPrec [Any] Source #

Show Any Source #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

showsPrec :: Int -> Any -> ShowS Source #

show :: Any -> String Source #

showList :: [Any] -> ShowS Source #

Eq Any Source #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

(==) :: Any -> Any -> Bool Source #

(/=) :: Any -> Any -> Bool Source #

Ord Any Source #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

compare :: Any -> Any -> Ordering Source #

(<) :: Any -> Any -> Bool Source #

(<=) :: Any -> Any -> Bool Source #

(>) :: Any -> Any -> Bool Source #

(>=) :: Any -> Any -> Bool Source #

max :: Any -> Any -> Any Source #

min :: Any -> Any -> Any Source #

type Rep Any Source #

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

type Rep Any = D1 ('MetaData "Any" "GHC.Internal.Data.Semigroup.Internal" "ghc-internal" 'True) (C1 ('MetaCons "Any" 'PrefixI 'True) (S1 ('MetaSel ('Just "getAny") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 Bool)))

Num wrappers

newtype Sum a Source #

Monoid under addition.

Sum a <> Sum b = Sum (a + b)

Examples

Expand
>>> Sum 1 <> Sum 2 <> mempty
Sum {getSum = 3}

>>> mconcat [ Sum n | n <- [3 .. 9]]
Sum {getSum = 42}

Constructors

Sum 

Fields

Instances

Instances details
Foldable1 Sum Source #

Since: base-4.18.0.0

Instance details

Defined in Data.Foldable1

Methods

fold1 :: Semigroup m => Sum m -> m Source #

foldMap1 :: Semigroup m => (a -> m) -> Sum a -> m Source #

foldMap1' :: Semigroup m => (a -> m) -> Sum a -> m Source #

toNonEmpty :: Sum a -> NonEmpty a Source #

maximum :: Ord a => Sum a -> a Source #

minimum :: Ord a => Sum a -> a Source #

head :: Sum a -> a Source #

last :: Sum a -> a Source #

foldrMap1 :: (a -> b) -> (a -> b -> b) -> Sum a -> b Source #

foldlMap1' :: (a -> b) -> (b -> a -> b) -> Sum a -> b Source #

foldlMap1 :: (a -> b) -> (b -> a -> b) -> Sum a -> b Source #

foldrMap1' :: (a -> b) -> (a -> b -> b) -> Sum a -> b Source #

Applicative Sum Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.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 #

Functor Sum Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

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

(<$) :: a -> Sum b -> Sum a Source #

Monad Sum Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

(>>=) :: Sum a -> (a -> Sum b) -> Sum b Source #

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

return :: a -> Sum a Source #

MonadFix Sum Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Control.Monad.Fix

Methods

mfix :: (a -> Sum a) -> Sum a Source #

MonadZip Sum Source #

Since: ghc-internal-4.8.0.0

Instance details

Defined in GHC.Internal.Control.Monad.Zip

Methods

mzip :: Sum a -> Sum b -> Sum (a, b) Source #

mzipWith :: (a -> b -> c) -> Sum a -> Sum b -> Sum c Source #

munzip :: Sum (a, b) -> (Sum a, Sum b) Source #

Foldable Sum Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Foldable

Methods

fold :: Monoid m => Sum m -> m Source #

foldMap :: Monoid m => (a -> m) -> Sum a -> m Source #

foldMap' :: Monoid m => (a -> m) -> Sum a -> m Source #

foldr :: (a -> b -> b) -> b -> Sum a -> b Source #

foldr' :: (a -> b -> b) -> b -> Sum a -> b Source #

foldl :: (b -> a -> b) -> b -> Sum a -> b Source #

foldl' :: (b -> a -> b) -> b -> Sum a -> b Source #

foldr1 :: (a -> a -> a) -> Sum a -> a Source #

foldl1 :: (a -> a -> a) -> Sum a -> a Source #

toList :: Sum a -> [a] Source #

null :: Sum a -> Bool Source #

length :: Sum a -> Int Source #

elem :: Eq a => a -> Sum a -> Bool Source #

maximum :: Ord a => Sum a -> a Source #

minimum :: Ord a => Sum a -> a Source #

sum :: Num a => Sum a -> a Source #

product :: Num a => Sum a -> a Source #

Traversable Sum Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Traversable

Methods

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

sequenceA :: Applicative f => Sum (f a) -> f (Sum a) Source #

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

sequence :: Monad m => Sum (m a) -> m (Sum a) Source #

Generic1 Sum Source # 
Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Associated Types

type Rep1 Sum

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

type Rep1 Sum = D1 ('MetaData "Sum" "GHC.Internal.Data.Semigroup.Internal" "ghc-internal" 'True) (C1 ('MetaCons "Sum" 'PrefixI 'True) (S1 ('MetaSel ('Just "getSum") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))

Methods

from1 :: Sum a -> Rep1 Sum a Source #

to1 :: Rep1 Sum a -> Sum a Source #

Num a => Monoid (Sum a) Source #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

mempty :: Sum a Source #

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

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

Num a => Semigroup (Sum a) Source #

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.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 #

Data a => Data (Sum a) Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Sum a -> c (Sum a) Source #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Sum a) Source #

toConstr :: Sum a -> Constr Source #

dataTypeOf :: Sum a -> DataType Source #

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Sum a)) Source #

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Sum a)) Source #

gmapT :: (forall b. Data b => b -> b) -> Sum a -> Sum a Source #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Sum a -> r Source #

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Sum a -> r Source #

gmapQ :: (forall d. Data d => d -> u) -> Sum a -> [u] Source #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Sum a -> u Source #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Sum a -> m (Sum a) Source #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Sum a -> m (Sum a) Source #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Sum a -> m (Sum a) Source #

Bounded a => Bounded (Sum a) Source #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

minBound :: Sum a Source #

maxBound :: Sum a Source #

Generic (Sum a) Source # 
Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Associated Types

type Rep (Sum a)

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

type Rep (Sum a) = D1 ('MetaData "Sum" "GHC.Internal.Data.Semigroup.Internal" "ghc-internal" 'True) (C1 ('MetaCons "Sum" 'PrefixI 'True) (S1 ('MetaSel ('Just "getSum") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))

Methods

from :: Sum a -> Rep (Sum a) x Source #

to :: Rep (Sum a) x -> Sum a Source #

Num a => Num (Sum a) Source #

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

(+) :: Sum a -> Sum a -> Sum a Source #

(-) :: Sum a -> Sum a -> Sum a Source #

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

negate :: Sum a -> Sum a Source #

abs :: Sum a -> Sum a Source #

signum :: Sum a -> Sum a Source #

fromInteger :: Integer -> Sum a Source #

Read a => Read (Sum a) Source #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

readsPrec :: Int -> ReadS (Sum a) Source #

readList :: ReadS [Sum a] Source #

readPrec :: ReadPrec (Sum a) Source #

readListPrec :: ReadPrec [Sum a] Source #

Show a => Show (Sum a) Source #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

showsPrec :: Int -> Sum a -> ShowS Source #

show :: Sum a -> String Source #

showList :: [Sum a] -> ShowS Source #

Eq a => Eq (Sum a) Source #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

(==) :: Sum a -> Sum a -> Bool Source #

(/=) :: Sum a -> Sum a -> Bool Source #

Ord a => Ord (Sum a) Source #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

compare :: Sum a -> Sum a -> Ordering Source #

(<) :: Sum a -> Sum a -> Bool Source #

(<=) :: Sum a -> Sum a -> Bool Source #

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

(>=) :: Sum a -> Sum a -> Bool Source #

max :: Sum a -> Sum a -> Sum a Source #

min :: Sum a -> Sum a -> Sum a Source #

type Rep1 Sum Source #

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

type Rep1 Sum = D1 ('MetaData "Sum" "GHC.Internal.Data.Semigroup.Internal" "ghc-internal" 'True) (C1 ('MetaCons "Sum" 'PrefixI 'True) (S1 ('MetaSel ('Just "getSum") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))
type Rep (Sum a) Source #

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

type Rep (Sum a) = D1 ('MetaData "Sum" "GHC.Internal.Data.Semigroup.Internal" "ghc-internal" 'True) (C1 ('MetaCons "Sum" 'PrefixI 'True) (S1 ('MetaSel ('Just "getSum") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))

newtype Product a Source #

Monoid under multiplication.

Product x <> Product y == Product (x * y)

Examples

Expand
>>> Product 3 <> Product 4 <> mempty
Product {getProduct = 12}

>>> mconcat [ Product n | n <- [2 .. 10]]
Product {getProduct = 3628800}

Constructors

Product 

Fields

Instances

Instances details
Foldable1 Product Source #

Since: base-4.18.0.0

Instance details

Defined in Data.Foldable1

Methods

fold1 :: Semigroup m => Product m -> m Source #

foldMap1 :: Semigroup m => (a -> m) -> Product a -> m Source #

foldMap1' :: Semigroup m => (a -> m) -> Product a -> m Source #

toNonEmpty :: Product a -> NonEmpty a Source #

maximum :: Ord a => Product a -> a Source #

minimum :: Ord a => Product a -> a Source #

head :: Product a -> a Source #

last :: Product a -> a Source #

foldrMap1 :: (a -> b) -> (a -> b -> b) -> Product a -> b Source #

foldlMap1' :: (a -> b) -> (b -> a -> b) -> Product a -> b Source #

foldlMap1 :: (a -> b) -> (b -> a -> b) -> Product a -> b Source #

foldrMap1' :: (a -> b) -> (a -> b -> b) -> Product a -> b Source #

Applicative Product Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.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 #

Functor Product Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

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

(<$) :: a -> Product b -> Product a Source #

Monad Product Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

(>>=) :: Product a -> (a -> Product b) -> Product b Source #

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

return :: a -> Product a Source #

MonadFix Product Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Control.Monad.Fix

Methods

mfix :: (a -> Product a) -> Product a Source #

MonadZip Product Source #

Since: ghc-internal-4.8.0.0

Instance details

Defined in GHC.Internal.Control.Monad.Zip

Methods

mzip :: Product a -> Product b -> Product (a, b) Source #

mzipWith :: (a -> b -> c) -> Product a -> Product b -> Product c Source #

munzip :: Product (a, b) -> (Product a, Product b) Source #

Foldable Product Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Foldable

Methods

fold :: Monoid m => Product m -> m Source #

foldMap :: Monoid m => (a -> m) -> Product a -> m Source #

foldMap' :: Monoid m => (a -> m) -> Product a -> m Source #

foldr :: (a -> b -> b) -> b -> Product a -> b Source #

foldr' :: (a -> b -> b) -> b -> Product a -> b Source #

foldl :: (b -> a -> b) -> b -> Product a -> b Source #

foldl' :: (b -> a -> b) -> b -> Product a -> b Source #

foldr1 :: (a -> a -> a) -> Product a -> a Source #

foldl1 :: (a -> a -> a) -> Product a -> a Source #

toList :: Product a -> [a] Source #

null :: Product a -> Bool Source #

length :: Product a -> Int Source #

elem :: Eq a => a -> Product a -> Bool Source #

maximum :: Ord a => Product a -> a Source #

minimum :: Ord a => Product a -> a Source #

sum :: Num a => Product a -> a Source #

product :: Num a => Product a -> a Source #

Traversable Product Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Traversable

Methods

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

sequenceA :: Applicative f => Product (f a) -> f (Product a) Source #

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

sequence :: Monad m => Product (m a) -> m (Product a) Source #

Generic1 Product Source # 
Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Associated Types

type Rep1 Product

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

type Rep1 Product = D1 ('MetaData "Product" "GHC.Internal.Data.Semigroup.Internal" "ghc-internal" 'True) (C1 ('MetaCons "Product" 'PrefixI 'True) (S1 ('MetaSel ('Just "getProduct") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))

Methods

from1 :: Product a -> Rep1 Product a Source #

to1 :: Rep1 Product a -> Product a Source #

Num a => Monoid (Product a) Source #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

mempty :: Product a Source #

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

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

Num a => Semigroup (Product a) Source #

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.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 #

Data a => Data (Product a) Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Product a -> c (Product a) Source #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Product a) Source #

toConstr :: Product a -> Constr Source #

dataTypeOf :: Product a -> DataType Source #

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Product a)) Source #

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Product a)) Source #

gmapT :: (forall b. Data b => b -> b) -> Product a -> Product a Source #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Product a -> r Source #

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Product a -> r Source #

gmapQ :: (forall d. Data d => d -> u) -> Product a -> [u] Source #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Product a -> u Source #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Product a -> m (Product a) Source #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Product a -> m (Product a) Source #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Product a -> m (Product a) Source #

Bounded a => Bounded (Product a) Source #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

minBound :: Product a Source #

maxBound :: Product a Source #

Generic (Product a) Source # 
Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Associated Types

type Rep (Product a)

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

type Rep (Product a) = D1 ('MetaData "Product" "GHC.Internal.Data.Semigroup.Internal" "ghc-internal" 'True) (C1 ('MetaCons "Product" 'PrefixI 'True) (S1 ('MetaSel ('Just "getProduct") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))

Methods

from :: Product a -> Rep (Product a) x Source #

to :: Rep (Product a) x -> Product a Source #

Num a => Num (Product a) Source #

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

(+) :: Product a -> Product a -> Product a Source #

(-) :: Product a -> Product a -> Product a Source #

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

negate :: Product a -> Product a Source #

abs :: Product a -> Product a Source #

signum :: Product a -> Product a Source #

fromInteger :: Integer -> Product a Source #

Read a => Read (Product a) Source #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

readsPrec :: Int -> ReadS (Product a) Source #

readList :: ReadS [Product a] Source #

readPrec :: ReadPrec (Product a) Source #

readListPrec :: ReadPrec [Product a] Source #

Show a => Show (Product a) Source #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

showsPrec :: Int -> Product a -> ShowS Source #

show :: Product a -> String Source #

showList :: [Product a] -> ShowS Source #

Eq a => Eq (Product a) Source #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

(==) :: Product a -> Product a -> Bool Source #

(/=) :: Product a -> Product a -> Bool Source #

Ord a => Ord (Product a) Source #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

compare :: Product a -> Product a -> Ordering Source #

(<) :: Product a -> Product a -> Bool Source #

(<=) :: Product a -> Product a -> Bool Source #

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

(>=) :: Product a -> Product a -> Bool Source #

max :: Product a -> Product a -> Product a Source #

min :: Product a -> Product a -> Product a Source #

type Rep1 Product Source #

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

type Rep1 Product = D1 ('MetaData "Product" "GHC.Internal.Data.Semigroup.Internal" "ghc-internal" 'True) (C1 ('MetaCons "Product" 'PrefixI 'True) (S1 ('MetaSel ('Just "getProduct") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))
type Rep (Product a) Source #

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

type Rep (Product a) = D1 ('MetaData "Product" "GHC.Internal.Data.Semigroup.Internal" "ghc-internal" 'True) (C1 ('MetaCons "Product" 'PrefixI 'True) (S1 ('MetaSel ('Just "getProduct") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))

Maybe wrappers

newtype First a Source #

Maybe monoid returning the leftmost non-Nothing value.

First a is isomorphic to Alt Maybe a, but precedes it historically.

Beware that Data.Monoid.First is different from Data.Semigroup.First. The former returns the first non-Nothing, so Data.Monoid.First Nothing <> x = x. The latter simply returns the first value, thus Data.Semigroup.First Nothing <> x = Data.Semigroup.First Nothing.

Examples

Expand
>>> First (Just "hello") <> First Nothing <> First (Just "world")
First {getFirst = Just "hello"}

>>> First Nothing <> mempty
First {getFirst = Nothing}

Constructors

First 

Fields

Instances

Instances details
Applicative First Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.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 #

Functor First Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Monoid

Methods

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

(<$) :: a -> First b -> First a Source #

Monad First Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Monoid

Methods

(>>=) :: First a -> (a -> First b) -> First b Source #

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

return :: a -> First a Source #

MonadFix First Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Control.Monad.Fix

Methods

mfix :: (a -> First a) -> First a Source #

MonadZip First Source #

Since: ghc-internal-4.8.0.0

Instance details

Defined in GHC.Internal.Control.Monad.Zip

Methods

mzip :: First a -> First b -> First (a, b) Source #

mzipWith :: (a -> b -> c) -> First a -> First b -> First c Source #

munzip :: First (a, b) -> (First a, First b) Source #

Foldable First Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Foldable

Methods

fold :: Monoid m => First m -> m Source #

foldMap :: Monoid m => (a -> m) -> First a -> m Source #

foldMap' :: Monoid m => (a -> m) -> First a -> m Source #

foldr :: (a -> b -> b) -> b -> First a -> b Source #

foldr' :: (a -> b -> b) -> b -> First a -> b Source #

foldl :: (b -> a -> b) -> b -> First a -> b Source #

foldl' :: (b -> a -> b) -> b -> First a -> b Source #

foldr1 :: (a -> a -> a) -> First a -> a Source #

foldl1 :: (a -> a -> a) -> First a -> a Source #

toList :: First a -> [a] Source #

null :: First a -> Bool Source #

length :: First a -> Int Source #

elem :: Eq a => a -> First a -> Bool Source #

maximum :: Ord a => First a -> a Source #

minimum :: Ord a => First a -> a Source #

sum :: Num a => First a -> a Source #

product :: Num a => First a -> a Source #

Traversable First Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Traversable

Methods

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

sequenceA :: Applicative f => First (f a) -> f (First a) Source #

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

sequence :: Monad m => First (m a) -> m (First a) Source #

Generic1 First Source # 
Instance details

Defined in GHC.Internal.Data.Monoid

Associated Types

type Rep1 First

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Monoid

type Rep1 First = D1 ('MetaData "First" "GHC.Internal.Data.Monoid" "ghc-internal" 'True) (C1 ('MetaCons "First" 'PrefixI 'True) (S1 ('MetaSel ('Just "getFirst") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 Maybe)))

Methods

from1 :: First a -> Rep1 First a Source #

to1 :: Rep1 First a -> First a Source #

Monoid (First a) Source #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Monoid

Methods

mempty :: First a Source #

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

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

Semigroup (First a) Source #

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.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 #

Data a => Data (First a) Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> First a -> c (First a) Source #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (First a) Source #

toConstr :: First a -> Constr Source #

dataTypeOf :: First a -> DataType Source #

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (First a)) Source #

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (First a)) Source #

gmapT :: (forall b. Data b => b -> b) -> First a -> First a Source #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> First a -> r Source #

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> First a -> r Source #

gmapQ :: (forall d. Data d => d -> u) -> First a -> [u] Source #

gmapQi :: Int -> (forall d. Data d => d -> u) -> First a -> u Source #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> First a -> m (First a) Source #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> First a -> m (First a) Source #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> First a -> m (First a) Source #

Generic (First a) Source # 
Instance details

Defined in GHC.Internal.Data.Monoid

Associated Types

type Rep (First a)

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Monoid

type Rep (First a) = D1 ('MetaData "First" "GHC.Internal.Data.Monoid" "ghc-internal" 'True) (C1 ('MetaCons "First" 'PrefixI 'True) (S1 ('MetaSel ('Just "getFirst") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (Maybe a))))

Methods

from :: First a -> Rep (First a) x Source #

to :: Rep (First a) x -> First a Source #

Read a => Read (First a) Source #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Monoid

Methods

readsPrec :: Int -> ReadS (First a) Source #

readList :: ReadS [First a] Source #

readPrec :: ReadPrec (First a) Source #

readListPrec :: ReadPrec [First a] Source #

Show a => Show (First a) Source #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Monoid

Methods

showsPrec :: Int -> First a -> ShowS Source #

show :: First a -> String Source #

showList :: [First a] -> ShowS Source #

Eq a => Eq (First a) Source #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Monoid

Methods

(==) :: First a -> First a -> Bool Source #

(/=) :: First a -> First a -> Bool Source #

Ord a => Ord (First a) Source #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Monoid

Methods

compare :: First a -> First a -> Ordering Source #

(<) :: First a -> First a -> Bool Source #

(<=) :: First a -> First a -> Bool Source #

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

(>=) :: First a -> First a -> Bool Source #

max :: First a -> First a -> First a Source #

min :: First a -> First a -> First a Source #

type Rep1 First Source #

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Monoid

type Rep1 First = D1 ('MetaData "First" "GHC.Internal.Data.Monoid" "ghc-internal" 'True) (C1 ('MetaCons "First" 'PrefixI 'True) (S1 ('MetaSel ('Just "getFirst") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 Maybe)))
type Rep (First a) Source #

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Monoid

type Rep (First a) = D1 ('MetaData "First" "GHC.Internal.Data.Monoid" "ghc-internal" 'True) (C1 ('MetaCons "First" 'PrefixI 'True) (S1 ('MetaSel ('Just "getFirst") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (Maybe a))))

newtype Last a Source #

Maybe monoid returning the rightmost non-Nothing value.

Last a is isomorphic to Dual (First a), and thus to Dual (Alt Maybe a)

Data.Semigroup.Last. The former returns the last non-Nothing, so x <> Data.Monoid.Last Nothing = x. The latter simply returns the last value, thus x <> Data.Semigroup.Last Nothing = Data.Semigroup.Last Nothing.

Examples

Expand
>>> Last (Just "hello") <> Last Nothing <> Last (Just "world")
Last {getLast = Just "world"}

>>> Last Nothing <> mempty
Last {getLast = Nothing}

Constructors

Last 

Fields

Instances

Instances details
Applicative Last Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.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 #

Functor Last Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Monoid

Methods

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

(<$) :: a -> Last b -> Last a Source #

Monad Last Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Monoid

Methods

(>>=) :: Last a -> (a -> Last b) -> Last b Source #

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

return :: a -> Last a Source #

MonadFix Last Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Control.Monad.Fix

Methods

mfix :: (a -> Last a) -> Last a Source #

MonadZip Last Source #

Since: ghc-internal-4.8.0.0

Instance details

Defined in GHC.Internal.Control.Monad.Zip

Methods

mzip :: Last a -> Last b -> Last (a, b) Source #

mzipWith :: (a -> b -> c) -> Last a -> Last b -> Last c Source #

munzip :: Last (a, b) -> (Last a, Last b) Source #

Foldable Last Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Foldable

Methods

fold :: Monoid m => Last m -> m Source #

foldMap :: Monoid m => (a -> m) -> Last a -> m Source #

foldMap' :: Monoid m => (a -> m) -> Last a -> m Source #

foldr :: (a -> b -> b) -> b -> Last a -> b Source #

foldr' :: (a -> b -> b) -> b -> Last a -> b Source #

foldl :: (b -> a -> b) -> b -> Last a -> b Source #

foldl' :: (b -> a -> b) -> b -> Last a -> b Source #

foldr1 :: (a -> a -> a) -> Last a -> a Source #

foldl1 :: (a -> a -> a) -> Last a -> a Source #

toList :: Last a -> [a] Source #

null :: Last a -> Bool Source #

length :: Last a -> Int Source #

elem :: Eq a => a -> Last a -> Bool Source #

maximum :: Ord a => Last a -> a Source #

minimum :: Ord a => Last a -> a Source #

sum :: Num a => Last a -> a Source #

product :: Num a => Last a -> a Source #

Traversable Last Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Traversable

Methods

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

sequenceA :: Applicative f => Last (f a) -> f (Last a) Source #

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

sequence :: Monad m => Last (m a) -> m (Last a) Source #

Generic1 Last Source # 
Instance details

Defined in GHC.Internal.Data.Monoid

Associated Types

type Rep1 Last

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Monoid

type Rep1 Last = D1 ('MetaData "Last" "GHC.Internal.Data.Monoid" "ghc-internal" 'True) (C1 ('MetaCons "Last" 'PrefixI 'True) (S1 ('MetaSel ('Just "getLast") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 Maybe)))

Methods

from1 :: Last a -> Rep1 Last a Source #

to1 :: Rep1 Last a -> Last a Source #

Monoid (Last a) Source #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Monoid

Methods

mempty :: Last a Source #

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

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

Semigroup (Last a) Source #

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.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 #

Data a => Data (Last a) Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Last a -> c (Last a) Source #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Last a) Source #

toConstr :: Last a -> Constr Source #

dataTypeOf :: Last a -> DataType Source #

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Last a)) Source #

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Last a)) Source #

gmapT :: (forall b. Data b => b -> b) -> Last a -> Last a Source #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Last a -> r Source #

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Last a -> r Source #

gmapQ :: (forall d. Data d => d -> u) -> Last a -> [u] Source #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Last a -> u Source #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Last a -> m (Last a) Source #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Last a -> m (Last a) Source #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Last a -> m (Last a) Source #

Generic (Last a) Source # 
Instance details

Defined in GHC.Internal.Data.Monoid

Associated Types

type Rep (Last a)

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Monoid

type Rep (Last a) = D1 ('MetaData "Last" "GHC.Internal.Data.Monoid" "ghc-internal" 'True) (C1 ('MetaCons "Last" 'PrefixI 'True) (S1 ('MetaSel ('Just "getLast") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (Maybe a))))

Methods

from :: Last a -> Rep (Last a) x Source #

to :: Rep (Last a) x -> Last a Source #

Read a => Read (Last a) Source #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Monoid

Methods

readsPrec :: Int -> ReadS (Last a) Source #

readList :: ReadS [Last a] Source #

readPrec :: ReadPrec (Last a) Source #

readListPrec :: ReadPrec [Last a] Source #

Show a => Show (Last a) Source #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Monoid

Methods

showsPrec :: Int -> Last a -> ShowS Source #

show :: Last a -> String Source #

showList :: [Last a] -> ShowS Source #

Eq a => Eq (Last a) Source #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Monoid

Methods

(==) :: Last a -> Last a -> Bool Source #

(/=) :: Last a -> Last a -> Bool Source #

Ord a => Ord (Last a) Source #

Since: base-2.1

Instance details

Defined in GHC.Internal.Data.Monoid

Methods

compare :: Last a -> Last a -> Ordering Source #

(<) :: Last a -> Last a -> Bool Source #

(<=) :: Last a -> Last a -> Bool Source #

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

(>=) :: Last a -> Last a -> Bool Source #

max :: Last a -> Last a -> Last a Source #

min :: Last a -> Last a -> Last a Source #

type Rep1 Last Source #

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Monoid

type Rep1 Last = D1 ('MetaData "Last" "GHC.Internal.Data.Monoid" "ghc-internal" 'True) (C1 ('MetaCons "Last" 'PrefixI 'True) (S1 ('MetaSel ('Just "getLast") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 Maybe)))
type Rep (Last a) Source #

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Monoid

type Rep (Last a) = D1 ('MetaData "Last" "GHC.Internal.Data.Monoid" "ghc-internal" 'True) (C1 ('MetaCons "Last" 'PrefixI 'True) (S1 ('MetaSel ('Just "getLast") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (Maybe a))))

Alternative wrapper

newtype Alt (f :: k -> Type) (a :: k) Source #

Monoid under <|>.

Alt l <> Alt r == Alt (l <|> r)

Examples

Expand
>>> Alt (Just 12) <> Alt (Just 24)
Alt {getAlt = Just 12}

>>> Alt Nothing <> Alt (Just 24)
Alt {getAlt = Just 24}

Since: base-4.8.0.0

Constructors

Alt 

Fields

Instances

Instances details
Generic1 (Alt f :: k -> Type) Source # 
Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Associated Types

type Rep1 (Alt f :: k -> Type)

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

type Rep1 (Alt f :: k -> Type) = D1 ('MetaData "Alt" "GHC.Internal.Data.Semigroup.Internal" "ghc-internal" 'True) (C1 ('MetaCons "Alt" 'PrefixI 'True) (S1 ('MetaSel ('Just "getAlt") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 f)))

Methods

from1 :: forall (a :: k). Alt f a -> Rep1 (Alt f) a Source #

to1 :: forall (a :: k). Rep1 (Alt f) a -> Alt f a Source #

Foldable1 f => Foldable1 (Alt f) Source #

Since: base-4.18.0.0

Instance details

Defined in Data.Foldable1

Methods

fold1 :: Semigroup m => Alt f m -> m Source #

foldMap1 :: Semigroup m => (a -> m) -> Alt f a -> m Source #

foldMap1' :: Semigroup m => (a -> m) -> Alt f a -> m Source #

toNonEmpty :: Alt f a -> NonEmpty a Source #

maximum :: Ord a => Alt f a -> a Source #

minimum :: Ord a => Alt f a -> a Source #

head :: Alt f a -> a Source #

last :: Alt f a -> a Source #

foldrMap1 :: (a -> b) -> (a -> b -> b) -> Alt f a -> b Source #

foldlMap1' :: (a -> b) -> (b -> a -> b) -> Alt f a -> b Source #

foldlMap1 :: (a -> b) -> (b -> a -> b) -> Alt f a -> b Source #

foldrMap1' :: (a -> b) -> (a -> b -> b) -> Alt f a -> b Source #

Contravariant f => Contravariant (Alt f) Source # 
Instance details

Defined in Data.Functor.Contravariant

Methods

contramap :: (a' -> a) -> Alt f a -> Alt f a' Source #

(>$) :: b -> Alt f b -> Alt f a Source #

Alternative f => Alternative (Alt f) Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.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 #

Applicative f => Applicative (Alt f) Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.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 #

Functor f => Functor (Alt f) Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

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

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

Monad f => Monad (Alt f) Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.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 #

MonadPlus f => MonadPlus (Alt f) Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

mzero :: Alt f a Source #

mplus :: Alt f a -> Alt f a -> Alt f a Source #

MonadFix f => MonadFix (Alt f) Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Control.Monad.Fix

Methods

mfix :: (a -> Alt f a) -> Alt f a Source #

MonadZip f => MonadZip (Alt f) Source #

Since: ghc-internal-4.8.0.0

Instance details

Defined in GHC.Internal.Control.Monad.Zip

Methods

mzip :: Alt f a -> Alt f b -> Alt f (a, b) Source #

mzipWith :: (a -> b -> c) -> Alt f a -> Alt f b -> Alt f c Source #

munzip :: Alt f (a, b) -> (Alt f a, Alt f b) Source #

Foldable f => Foldable (Alt f) Source #

Since: base-4.12.0.0

Instance details

Defined in GHC.Internal.Data.Foldable

Methods

fold :: Monoid m => Alt f m -> m Source #

foldMap :: Monoid m => (a -> m) -> Alt f a -> m Source #

foldMap' :: Monoid m => (a -> m) -> Alt f a -> m Source #

foldr :: (a -> b -> b) -> b -> Alt f a -> b Source #

foldr' :: (a -> b -> b) -> b -> Alt f a -> b Source #

foldl :: (b -> a -> b) -> b -> Alt f a -> b Source #

foldl' :: (b -> a -> b) -> b -> Alt f a -> b Source #

foldr1 :: (a -> a -> a) -> Alt f a -> a Source #

foldl1 :: (a -> a -> a) -> Alt f a -> a Source #

toList :: Alt f a -> [a] Source #

null :: Alt f a -> Bool Source #

length :: Alt f a -> Int Source #

elem :: Eq a => a -> Alt f a -> Bool Source #

maximum :: Ord a => Alt f a -> a Source #

minimum :: Ord a => Alt f a -> a Source #

sum :: Num a => Alt f a -> a Source #

product :: Num a => Alt f a -> a Source #

Traversable f => Traversable (Alt f) Source #

Since: base-4.12.0.0

Instance details

Defined in GHC.Internal.Data.Traversable

Methods

traverse :: Applicative f0 => (a -> f0 b) -> Alt f a -> f0 (Alt f b) Source #

sequenceA :: Applicative f0 => Alt f (f0 a) -> f0 (Alt f a) Source #

mapM :: Monad m => (a -> m b) -> Alt f a -> m (Alt f b) Source #

sequence :: Monad m => Alt f (m a) -> m (Alt f a) Source #

Alternative f => Monoid (Alt f a) Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.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 #

Alternative f => Semigroup (Alt f a) Source #

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.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 #

(Data (f a), Data a, Typeable f) => Data (Alt f a) Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Alt f a -> c (Alt f a) Source #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Alt f a) Source #

toConstr :: Alt f a -> Constr Source #

dataTypeOf :: Alt f a -> DataType Source #

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Alt f a)) Source #

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Alt f a)) Source #

gmapT :: (forall b. Data b => b -> b) -> Alt f a -> Alt f a Source #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Alt f a -> r Source #

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Alt f a -> r Source #

gmapQ :: (forall d. Data d => d -> u) -> Alt f a -> [u] Source #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Alt f a -> u Source #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Alt f a -> m (Alt f a) Source #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Alt f a -> m (Alt f a) Source #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Alt f a -> m (Alt f a) Source #

Enum (f a) => Enum (Alt f a) Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

succ :: Alt f a -> Alt f a Source #

pred :: Alt f a -> Alt f a Source #

toEnum :: Int -> Alt f a Source #

fromEnum :: Alt f a -> Int Source #

enumFrom :: Alt f a -> [Alt f a] Source #

enumFromThen :: Alt f a -> Alt f a -> [Alt f a] Source #

enumFromTo :: Alt f a -> Alt f a -> [Alt f a] Source #

enumFromThenTo :: Alt f a -> Alt f a -> Alt f a -> [Alt f a] Source #

Generic (Alt f a) Source # 
Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Associated Types

type Rep (Alt f a)

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

type Rep (Alt f a) = D1 ('MetaData "Alt" "GHC.Internal.Data.Semigroup.Internal" "ghc-internal" 'True) (C1 ('MetaCons "Alt" 'PrefixI 'True) (S1 ('MetaSel ('Just "getAlt") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (f a))))

Methods

from :: Alt f a -> Rep (Alt f a) x Source #

to :: Rep (Alt f a) x -> Alt f a Source #

Num (f a) => Num (Alt f a) Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

(+) :: Alt f a -> Alt f a -> Alt f a Source #

(-) :: Alt f a -> Alt f a -> Alt f a Source #

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

negate :: Alt f a -> Alt f a Source #

abs :: Alt f a -> Alt f a Source #

signum :: Alt f a -> Alt f a Source #

fromInteger :: Integer -> Alt f a Source #

Read (f a) => Read (Alt f a) Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

readsPrec :: Int -> ReadS (Alt f a) Source #

readList :: ReadS [Alt f a] Source #

readPrec :: ReadPrec (Alt f a) Source #

readListPrec :: ReadPrec [Alt f a] Source #

Show (f a) => Show (Alt f a) Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

showsPrec :: Int -> Alt f a -> ShowS Source #

show :: Alt f a -> String Source #

showList :: [Alt f a] -> ShowS Source #

Eq (f a) => Eq (Alt f a) Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

(==) :: Alt f a -> Alt f a -> Bool Source #

(/=) :: Alt f a -> Alt f a -> Bool Source #

Ord (f a) => Ord (Alt f a) Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

compare :: Alt f a -> Alt f a -> Ordering Source #

(<) :: Alt f a -> Alt f a -> Bool Source #

(<=) :: Alt f a -> Alt f a -> Bool Source #

(>) :: Alt f a -> Alt f a -> Bool Source #

(>=) :: Alt f a -> Alt f a -> Bool Source #

max :: Alt f a -> Alt f a -> Alt f a Source #

min :: Alt f a -> Alt f a -> Alt f a Source #

type Rep1 (Alt f :: k -> Type) Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

type Rep1 (Alt f :: k -> Type) = D1 ('MetaData "Alt" "GHC.Internal.Data.Semigroup.Internal" "ghc-internal" 'True) (C1 ('MetaCons "Alt" 'PrefixI 'True) (S1 ('MetaSel ('Just "getAlt") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 f)))
type Rep (Alt f a) Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

type Rep (Alt f a) = D1 ('MetaData "Alt" "GHC.Internal.Data.Semigroup.Internal" "ghc-internal" 'True) (C1 ('MetaCons "Alt" 'PrefixI 'True) (S1 ('MetaSel ('Just "getAlt") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (f a))))

Applicative wrapper

newtype Ap (f :: k -> Type) (a :: k) Source #

This data type witnesses the lifting of a Monoid into an Applicative pointwise.

Examples

Expand
>>> Ap (Just [1, 2, 3]) <> Ap Nothing
Ap {getAp = Nothing}

>>> Ap [Sum 10, Sum 20] <> Ap [Sum 1, Sum 2]
Ap {getAp = [Sum {getSum = 11},Sum {getSum = 12},Sum {getSum = 21},Sum {getSum = 22}]}

Since: base-4.12.0.0

Constructors

Ap 

Fields

Instances

Instances details
Generic1 (Ap f :: k -> Type) Source # 
Instance details

Defined in GHC.Internal.Data.Monoid

Associated Types

type Rep1 (Ap f :: k -> Type)

Since: base-4.12.0.0

Instance details

Defined in GHC.Internal.Data.Monoid

type Rep1 (Ap f :: k -> Type) = D1 ('MetaData "Ap" "GHC.Internal.Data.Monoid" "ghc-internal" 'True) (C1 ('MetaCons "Ap" 'PrefixI 'True) (S1 ('MetaSel ('Just "getAp") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 f)))

Methods

from1 :: forall (a :: k). Ap f a -> Rep1 (Ap f) a Source #

to1 :: forall (a :: k). Rep1 (Ap f) a -> Ap f a Source #

Foldable1 f => Foldable1 (Ap f) Source #

Since: base-4.18.0.0

Instance details

Defined in Data.Foldable1

Methods

fold1 :: Semigroup m => Ap f m -> m Source #

foldMap1 :: Semigroup m => (a -> m) -> Ap f a -> m Source #

foldMap1' :: Semigroup m => (a -> m) -> Ap f a -> m Source #

toNonEmpty :: Ap f a -> NonEmpty a Source #

maximum :: Ord a => Ap f a -> a Source #

minimum :: Ord a => Ap f a -> a Source #

head :: Ap f a -> a Source #

last :: Ap f a -> a Source #

foldrMap1 :: (a -> b) -> (a -> b -> b) -> Ap f a -> b Source #

foldlMap1' :: (a -> b) -> (b -> a -> b) -> Ap f a -> b Source #

foldlMap1 :: (a -> b) -> (b -> a -> b) -> Ap f a -> b Source #

foldrMap1' :: (a -> b) -> (a -> b -> b) -> Ap f a -> b Source #

Alternative f => Alternative (Ap f) Source #

Since: base-4.12.0.0

Instance details

Defined in GHC.Internal.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 #

Applicative f => Applicative (Ap f) Source #

Since: base-4.12.0.0

Instance details

Defined in GHC.Internal.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 #

Functor f => Functor (Ap f) Source #

Since: base-4.12.0.0

Instance details

Defined in GHC.Internal.Data.Monoid

Methods

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

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

Monad f => Monad (Ap f) Source #

Since: base-4.12.0.0

Instance details

Defined in GHC.Internal.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 #

MonadPlus f => MonadPlus (Ap f) Source #

Since: base-4.12.0.0

Instance details

Defined in GHC.Internal.Data.Monoid

Methods

mzero :: Ap f a Source #

mplus :: Ap f a -> Ap f a -> Ap f a Source #

MonadFail f => MonadFail (Ap f) Source #

Since: base-4.12.0.0

Instance details

Defined in GHC.Internal.Data.Monoid

Methods

fail :: String -> Ap f a Source #

MonadFix f => MonadFix (Ap f) Source #

Since: base-4.12.0.0

Instance details

Defined in GHC.Internal.Control.Monad.Fix

Methods

mfix :: (a -> Ap f a) -> Ap f a Source #

Foldable f => Foldable (Ap f) Source #

Since: base-4.12.0.0

Instance details

Defined in GHC.Internal.Data.Foldable

Methods

fold :: Monoid m => Ap f m -> m Source #

foldMap :: Monoid m => (a -> m) -> Ap f a -> m Source #

foldMap' :: Monoid m => (a -> m) -> Ap f a -> m Source #

foldr :: (a -> b -> b) -> b -> Ap f a -> b Source #

foldr' :: (a -> b -> b) -> b -> Ap f a -> b Source #

foldl :: (b -> a -> b) -> b -> Ap f a -> b Source #

foldl' :: (b -> a -> b) -> b -> Ap f a -> b Source #

foldr1 :: (a -> a -> a) -> Ap f a -> a Source #

foldl1 :: (a -> a -> a) -> Ap f a -> a Source #

toList :: Ap f a -> [a] Source #

null :: Ap f a -> Bool Source #

length :: Ap f a -> Int Source #

elem :: Eq a => a -> Ap f a -> Bool Source #

maximum :: Ord a => Ap f a -> a Source #

minimum :: Ord a => Ap f a -> a Source #

sum :: Num a => Ap f a -> a Source #

product :: Num a => Ap f a -> a Source #

Traversable f => Traversable (Ap f) Source #

Since: base-4.12.0.0

Instance details

Defined in GHC.Internal.Data.Traversable

Methods

traverse :: Applicative f0 => (a -> f0 b) -> Ap f a -> f0 (Ap f b) Source #

sequenceA :: Applicative f0 => Ap f (f0 a) -> f0 (Ap f a) Source #

mapM :: Monad m => (a -> m b) -> Ap f a -> m (Ap f b) Source #

sequence :: Monad m => Ap f (m a) -> m (Ap f a) Source #

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

Since: base-4.12.0.0

Instance details

Defined in GHC.Internal.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 #

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

Since: base-4.12.0.0

Instance details

Defined in GHC.Internal.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 #

(Data (f a), Data a, Typeable f) => Data (Ap f a) Source #

Since: base-4.12.0.0

Instance details

Defined in GHC.Internal.Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Ap f a -> c (Ap f a) Source #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Ap f a) Source #

toConstr :: Ap f a -> Constr Source #

dataTypeOf :: Ap f a -> DataType Source #

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Ap f a)) Source #

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Ap f a)) Source #

gmapT :: (forall b. Data b => b -> b) -> Ap f a -> Ap f a Source #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Ap f a -> r Source #

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Ap f a -> r Source #

gmapQ :: (forall d. Data d => d -> u) -> Ap f a -> [u] Source #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Ap f a -> u Source #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Ap f a -> m (Ap f a) Source #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Ap f a -> m (Ap f a) Source #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Ap f a -> m (Ap f a) Source #

(Applicative f, Bounded a) => Bounded (Ap f a) Source #

Since: base-4.12.0.0

Instance details

Defined in GHC.Internal.Data.Monoid

Methods

minBound :: Ap f a Source #

maxBound :: Ap f a Source #

Enum (f a) => Enum (Ap f a) Source #

Since: base-4.12.0.0

Instance details

Defined in GHC.Internal.Data.Monoid

Methods

succ :: Ap f a -> Ap f a Source #

pred :: Ap f a -> Ap f a Source #

toEnum :: Int -> Ap f a Source #

fromEnum :: Ap f a -> Int Source #

enumFrom :: Ap f a -> [Ap f a] Source #

enumFromThen :: Ap f a -> Ap f a -> [Ap f a] Source #

enumFromTo :: Ap f a -> Ap f a -> [Ap f a] Source #

enumFromThenTo :: Ap f a -> Ap f a -> Ap f a -> [Ap f a] Source #

Generic (Ap f a) Source # 
Instance details

Defined in GHC.Internal.Data.Monoid

Associated Types

type Rep (Ap f a)

Since: base-4.12.0.0

Instance details

Defined in GHC.Internal.Data.Monoid

type Rep (Ap f a) = D1 ('MetaData "Ap" "GHC.Internal.Data.Monoid" "ghc-internal" 'True) (C1 ('MetaCons "Ap" 'PrefixI 'True) (S1 ('MetaSel ('Just "getAp") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (f a))))

Methods

from :: Ap f a -> Rep (Ap f a) x Source #

to :: Rep (Ap f a) x -> Ap f a Source #

(Applicative f, Num a) => Num (Ap f a) Source #

Note that even if the underlying Num and Applicative instances are lawful, for most Applicatives, this instance will not be lawful. If you use this instance with the list Applicative, the following customary laws will not hold:

Commutativity:

>>> Ap [10,20] + Ap [1,2]
Ap {getAp = [11,12,21,22]}
>>> Ap [1,2] + Ap [10,20]
Ap {getAp = [11,21,12,22]}

Additive inverse:

>>> Ap [] + negate (Ap [])
Ap {getAp = []}
>>> fromInteger 0 :: Ap [] Int
Ap {getAp = [0]}

Distributivity:

>>> Ap [1,2] * (3 + 4)
Ap {getAp = [7,14]}
>>> (Ap [1,2] * 3) + (Ap [1,2] * 4)
Ap {getAp = [7,11,10,14]}

Since: base-4.12.0.0

Instance details

Defined in GHC.Internal.Data.Monoid

Methods

(+) :: Ap f a -> Ap f a -> Ap f a Source #

(-) :: Ap f a -> Ap f a -> Ap f a Source #

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

negate :: Ap f a -> Ap f a Source #

abs :: Ap f a -> Ap f a Source #

signum :: Ap f a -> Ap f a Source #

fromInteger :: Integer -> Ap f a Source #

Read (f a) => Read (Ap f a) Source #

Since: base-4.12.0.0

Instance details

Defined in GHC.Internal.Data.Monoid

Methods

readsPrec :: Int -> ReadS (Ap f a) Source #

readList :: ReadS [Ap f a] Source #

readPrec :: ReadPrec (Ap f a) Source #

readListPrec :: ReadPrec [Ap f a] Source #

Show (f a) => Show (Ap f a) Source #

Since: base-4.12.0.0

Instance details

Defined in GHC.Internal.Data.Monoid

Methods

showsPrec :: Int -> Ap f a -> ShowS Source #

show :: Ap f a -> String Source #

showList :: [Ap f a] -> ShowS Source #

Eq (f a) => Eq (Ap f a) Source #

Since: base-4.12.0.0

Instance details

Defined in GHC.Internal.Data.Monoid

Methods

(==) :: Ap f a -> Ap f a -> Bool Source #

(/=) :: Ap f a -> Ap f a -> Bool Source #

Ord (f a) => Ord (Ap f a) Source #

Since: base-4.12.0.0

Instance details

Defined in GHC.Internal.Data.Monoid

Methods

compare :: Ap f a -> Ap f a -> Ordering Source #

(<) :: Ap f a -> Ap f a -> Bool Source #

(<=) :: Ap f a -> Ap f a -> Bool Source #

(>) :: Ap f a -> Ap f a -> Bool Source #

(>=) :: Ap f a -> Ap f a -> Bool Source #

max :: Ap f a -> Ap f a -> Ap f a Source #

min :: Ap f a -> Ap f a -> Ap f a Source #

type Rep1 (Ap f :: k -> Type) Source #

Since: base-4.12.0.0

Instance details

Defined in GHC.Internal.Data.Monoid

type Rep1 (Ap f :: k -> Type) = D1 ('MetaData "Ap" "GHC.Internal.Data.Monoid" "ghc-internal" 'True) (C1 ('MetaCons "Ap" 'PrefixI 'True) (S1 ('MetaSel ('Just "getAp") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 f)))
type Rep (Ap f a) Source #

Since: base-4.12.0.0

Instance details

Defined in GHC.Internal.Data.Monoid

type Rep (Ap f a) = D1 ('MetaData "Ap" "GHC.Internal.Data.Monoid" "ghc-internal" 'True) (C1 ('MetaCons "Ap" 'PrefixI 'True) (S1 ('MetaSel ('Just "getAp") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (f a))))