GHC.Internal.Data.Monoid

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

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

>>> 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}

Monoid typeclass

class Semigroup a => Monoid a where

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

Identity of mappend

Examples

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

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

mappend :: a -> a -> a

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

Fold a list using the monoid.

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

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

Instances

Monoid All

Since: base-2.1

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

mempty :: All

mappend :: All -> All -> All

mconcat :: [All] -> All

Monoid Any

Since: base-2.1

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

mempty :: Any

mappend :: Any -> Any -> Any

mconcat :: [Any] -> Any

Monoid Event

Since: base-4.4.0.0

Defined in GHC.Internal.Event.Internal.Types

Methods

mempty :: Event

mappend :: Event -> Event -> Event

mconcat :: [Event] -> Event

Monoid Lifetime

mappend takes the longer of two lifetimes.

Since: base-4.8.0.0

Defined in GHC.Internal.Event.Internal.Types

Methods

mempty :: Lifetime

mappend :: Lifetime -> Lifetime -> Lifetime

mconcat :: [Lifetime] -> Lifetime

Monoid ExceptionContext

Defined in GHC.Internal.Exception.Context

Methods

mempty :: ExceptionContext

mappend :: ExceptionContext -> ExceptionContext -> ExceptionContext

mconcat :: [ExceptionContext] -> ExceptionContext

Monoid Ordering

Since: base-2.1

Defined in GHC.Internal.Base

Methods

mempty :: Ordering

mappend :: Ordering -> Ordering -> Ordering

mconcat :: [Ordering] -> Ordering

Monoid ()

Since: base-2.1

Defined in GHC.Internal.Base

Methods

mempty :: ()

mappend :: () -> () -> ()

mconcat :: [()] -> ()

Monoid a => Monoid (STM a)

Since: base-4.17.0.0

Defined in GHC.Internal.Conc.Sync

Methods

mempty :: STM a

mappend :: STM a -> STM a -> STM a

mconcat :: [STM a] -> STM a

FiniteBits a => Monoid (And a)

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

Since: base-4.16

Defined in GHC.Internal.Data.Bits

Methods

mempty :: And a

mappend :: And a -> And a -> And a

mconcat :: [And a] -> And a

FiniteBits a => Monoid (Iff a)

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

Since: base-4.16

Defined in GHC.Internal.Data.Bits

Methods

mempty :: Iff a

mappend :: Iff a -> Iff a -> Iff a

mconcat :: [Iff a] -> Iff a

Bits a => Monoid (Ior a)

Since: base-4.16

Defined in GHC.Internal.Data.Bits

Methods

mempty :: Ior a

mappend :: Ior a -> Ior a -> Ior a

mconcat :: [Ior a] -> Ior a

Bits a => Monoid (Xor a)

Since: base-4.16

Defined in GHC.Internal.Data.Bits

Methods

mempty :: Xor a

mappend :: Xor a -> Xor a -> Xor a

mconcat :: [Xor a] -> Xor a

Monoid a => Monoid (Identity a)

Since: base-4.9.0.0

Defined in GHC.Internal.Data.Functor.Identity

Methods

mempty :: Identity a

mappend :: Identity a -> Identity a -> Identity a

mconcat :: [Identity a] -> Identity a

Ord a => Monoid (Max a)

Since: base-4.8.0.0

Defined in GHC.Internal.Data.Functor.Utils

Methods

mempty :: Max a

mappend :: Max a -> Max a -> Max a

mconcat :: [Max a] -> Max a

Ord a => Monoid (Min a)

Since: base-4.8.0.0

Defined in GHC.Internal.Data.Functor.Utils

Methods

mempty :: Min a

mappend :: Min a -> Min a -> Min a

mconcat :: [Min a] -> Min a

Monoid (First a)

Since: base-2.1

Defined in GHC.Internal.Data.Monoid

Methods

mempty :: First a

mappend :: First a -> First a -> First a

mconcat :: [First a] -> First a

Monoid (Last a)

Since: base-2.1

Defined in GHC.Internal.Data.Monoid

Methods

mempty :: Last a

mappend :: Last a -> Last a -> Last a

mconcat :: [Last a] -> Last a

Monoid a => Monoid (Down a)

Since: base-4.11.0.0

Defined in GHC.Internal.Data.Ord

Methods

mempty :: Down a

mappend :: Down a -> Down a -> Down a

mconcat :: [Down a] -> Down a

Monoid a => Monoid (Dual a)

Since: base-2.1

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

mempty :: Dual a

mappend :: Dual a -> Dual a -> Dual a

mconcat :: [Dual a] -> Dual a

Monoid (Endo a)

Since: base-2.1

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

mempty :: Endo a

mappend :: Endo a -> Endo a -> Endo a

mconcat :: [Endo a] -> Endo a

Num a => Monoid (Product a)

Since: base-2.1

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

mempty :: Product a

mappend :: Product a -> Product a -> Product a

mconcat :: [Product a] -> Product a

Num a => Monoid (Sum a)

Since: base-2.1

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

mempty :: Sum a

mappend :: Sum a -> Sum a -> Sum a

mconcat :: [Sum a] -> Sum a

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

Since: base-4.17.0.0

Defined in GHC.Internal.Generics

Methods

mempty :: Generically a

mappend :: Generically a -> Generically a -> Generically a

mconcat :: [Generically a] -> Generically a

Monoid p => Monoid (Par1 p)

Since: base-4.12.0.0

Defined in GHC.Internal.Generics

Methods

mempty :: Par1 p

mappend :: Par1 p -> Par1 p -> Par1 p

mconcat :: [Par1 p] -> Par1 p

Monoid a => Monoid (IO a)

Since: base-4.9.0.0

Defined in GHC.Internal.Base

Methods

mempty :: IO a

mappend :: IO a -> IO a -> IO a

mconcat :: [IO a] -> IO a

Semigroup a => Monoid (Maybe a)

Lift a semigroup into Maybe forming a Monoid according to http://en.wikipedia.org/wiki/Monoid: "Any semigroup S may be turned into a monoid simply by adjoining an element e not in S and defining e*e = e and e*s = s = s*e for all s ∈ S."

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

Since: base-2.1

Defined in GHC.Internal.Base

Methods

mempty :: Maybe a

mappend :: Maybe a -> Maybe a -> Maybe a

mconcat :: [Maybe a] -> Maybe a

Monoid a => Monoid (Solo a)

Since: base-4.15

Defined in GHC.Internal.Base

Methods

mempty :: Solo a

mappend :: Solo a -> Solo a -> Solo a

mconcat :: [Solo a] -> Solo a

Monoid [a]

Since: base-2.1

Defined in GHC.Internal.Base

Methods

mempty :: [a]

mappend :: [a] -> [a] -> [a]

mconcat :: [[a]] -> [a]

Monoid (Proxy s)

Since: base-4.7.0.0

Defined in GHC.Internal.Data.Proxy

Methods

mempty :: Proxy s

mappend :: Proxy s -> Proxy s -> Proxy s

mconcat :: [Proxy s] -> Proxy s

Monoid (U1 p)

Since: base-4.12.0.0

Defined in GHC.Internal.Generics

Methods

mempty :: U1 p

mappend :: U1 p -> U1 p -> U1 p

mconcat :: [U1 p] -> U1 p

Monoid a => Monoid (ST s a)

Since: base-4.11.0.0

Defined in GHC.Internal.ST

Methods

mempty :: ST s a

mappend :: ST s a -> ST s a -> ST s a

mconcat :: [ST s a] -> ST s a

(Monoid a, Monoid b) => Monoid (a, b)

Since: base-2.1

Defined in GHC.Internal.Base

Methods

mempty :: (a, b)

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

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

Monoid b => Monoid (a -> b)

Since: base-2.1

Defined in GHC.Internal.Base

Methods

mempty :: a -> b

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

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

Monoid a => Monoid (Const a b)

Since: base-4.9.0.0

Defined in GHC.Internal.Data.Functor.Const

Methods

mempty :: Const a b

mappend :: Const a b -> Const a b -> Const a b

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

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

Since: base-4.12.0.0

Defined in GHC.Internal.Data.Monoid

Methods

mempty :: Ap f a

mappend :: Ap f a -> Ap f a -> Ap f a

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

Alternative f => Monoid (Alt f a)

Since: base-4.8.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

mempty :: Alt f a

mappend :: Alt f a -> Alt f a -> Alt f a

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

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

Since: base-4.12.0.0

Defined in GHC.Internal.Generics

Methods

mempty :: Rec1 f p

mappend :: Rec1 f p -> Rec1 f p -> Rec1 f p

mconcat :: [Rec1 f p] -> Rec1 f p

(Monoid a, Monoid b, Monoid c) => Monoid (a, b, c)

Since: base-2.1

Defined in GHC.Internal.Base

Methods

mempty :: (a, b, c)

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

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

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

Since: base-4.12.0.0

Defined in GHC.Internal.Generics

Methods

mempty :: (f :*: g) p

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

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

Monoid c => Monoid (K1 i c p)

Since: base-4.12.0.0

Defined in GHC.Internal.Generics

Methods

mempty :: K1 i c p

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

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

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

Since: base-2.1

Defined in GHC.Internal.Base

Methods

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

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

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

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

Since: base-4.12.0.0

Defined in GHC.Internal.Generics

Methods

mempty :: (f :.: g) p

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

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

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

Since: base-4.12.0.0

Defined in GHC.Internal.Generics

Methods

mempty :: M1 i c f p

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

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

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

Since: base-2.1

Defined in GHC.Internal.Base

Methods

mempty :: (a, b, c, d, e)

mappend :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e)

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

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

An associative operation.

Examples

>>> [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

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

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

Examples

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

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

Constructors

Dual

Fields

• getDual :: a

Instances

Applicative Dual

Since: base-4.8.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

pure :: a -> Dual a

(<*>) :: Dual (a -> b) -> Dual a -> Dual b

liftA2 :: (a -> b -> c) -> Dual a -> Dual b -> Dual c

(*>) :: Dual a -> Dual b -> Dual b

(<*) :: Dual a -> Dual b -> Dual a

Functor Dual

Since: base-4.8.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

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

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

Monad Dual

Since: base-4.8.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

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

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

return :: a -> Dual a

MonadFix Dual

Since: base-4.8.0.0

Defined in GHC.Internal.Control.Monad.Fix

Methods

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

Foldable Dual

Since: base-4.8.0.0

Defined in GHC.Internal.Data.Foldable

Methods

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

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

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

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

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

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

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

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

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

toList :: Dual a -> [a]

null :: Dual a -> Bool

length :: Dual a -> Int

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

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

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

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

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

Traversable Dual

Since: base-4.8.0.0

Defined in GHC.Internal.Data.Traversable

Methods

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

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

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

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

Generic1 Dual

Defined in GHC.Internal.Data.Semigroup.Internal

Associated Types

type Rep1 Dual

Since: base-4.7.0.0

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

to1 :: Rep1 Dual a -> Dual a

Monoid a => Monoid (Dual a)

Since: base-2.1

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

mempty :: Dual a

mappend :: Dual a -> Dual a -> Dual a

mconcat :: [Dual a] -> Dual a

Semigroup a => Semigroup (Dual a)

Since: base-4.9.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

(<>) :: Dual a -> Dual a -> Dual a

sconcat :: NonEmpty (Dual a) -> Dual a

stimes :: Integral b => b -> Dual a -> Dual a

Data a => Data (Dual a)

Since: base-4.8.0.0

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)

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

toConstr :: Dual a -> Constr

dataTypeOf :: Dual a -> DataType

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

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

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

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

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

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

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

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

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

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

Bounded a => Bounded (Dual a)

Since: base-2.1

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

minBound :: Dual a

maxBound :: Dual a

Generic (Dual a)

Defined in GHC.Internal.Data.Semigroup.Internal

Associated Types

type Rep (Dual a)

Since: base-4.7.0.0

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

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

Read a => Read (Dual a)

Since: base-2.1

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

readsPrec :: Int -> ReadS (Dual a)

readList :: ReadS [Dual a]

readPrec :: ReadPrec (Dual a)

readListPrec :: ReadPrec [Dual a]

Show a => Show (Dual a)

Since: base-2.1

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

showsPrec :: Int -> Dual a -> ShowS

show :: Dual a -> String

showList :: [Dual a] -> ShowS

Eq a => Eq (Dual a)

Since: base-2.1

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

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

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

Ord a => Ord (Dual a)

Since: base-2.1

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

compare :: Dual a -> Dual a -> Ordering

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

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

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

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

max :: Dual a -> Dual a -> Dual a

min :: Dual a -> Dual a -> Dual a

type Rep1 Dual

Since: base-4.7.0.0

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)

Since: base-4.7.0.0

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

The monoid of endomorphisms under composition.

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

Examples

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

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

Constructors

Endo

Fields

• appEndo :: a -> a

Instances

Monoid (Endo a)

Since: base-2.1

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

mempty :: Endo a

mappend :: Endo a -> Endo a -> Endo a

mconcat :: [Endo a] -> Endo a

Semigroup (Endo a)

Since: base-4.9.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

(<>) :: Endo a -> Endo a -> Endo a

sconcat :: NonEmpty (Endo a) -> Endo a

stimes :: Integral b => b -> Endo a -> Endo a

Generic (Endo a)

Defined in GHC.Internal.Data.Semigroup.Internal

Associated Types

type Rep (Endo a)

Since: base-4.7.0.0

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

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

type Rep (Endo a)

Since: base-4.7.0.0

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

Boolean monoid under conjunction (&&).

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

Examples

>>> 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

• getAll :: Bool

Instances

Monoid All

Since: base-2.1

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

mempty :: All

mappend :: All -> All -> All

mconcat :: [All] -> All

Semigroup All

Since: base-4.9.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

(<>) :: All -> All -> All

sconcat :: NonEmpty All -> All

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

Data All

Since: base-4.8.0.0

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

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

toConstr :: All -> Constr

dataTypeOf :: All -> DataType

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

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

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

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

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

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

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

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

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

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

Bounded All

Since: base-2.1

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

minBound :: All

maxBound :: All

Generic All

Defined in GHC.Internal.Data.Semigroup.Internal

Associated Types

type Rep All

Since: base-4.7.0.0

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

to :: Rep All x -> All

Read All

Since: base-2.1

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

readsPrec :: Int -> ReadS All

readList :: ReadS [All]

readPrec :: ReadPrec All

readListPrec :: ReadPrec [All]

Show All

Since: base-2.1

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

showsPrec :: Int -> All -> ShowS

show :: All -> String

showList :: [All] -> ShowS

Eq All

Since: base-2.1

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

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

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

Ord All

Since: base-2.1

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

compare :: All -> All -> Ordering

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

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

(>) :: All -> All -> Bool

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

max :: All -> All -> All

min :: All -> All -> All

type Rep All

Since: base-4.7.0.0

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

Boolean monoid under disjunction (||).

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

Examples

>>> 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

• getAny :: Bool

Instances

Monoid Any

Since: base-2.1

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

mempty :: Any

mappend :: Any -> Any -> Any

mconcat :: [Any] -> Any

Semigroup Any

Since: base-4.9.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

(<>) :: Any -> Any -> Any

sconcat :: NonEmpty Any -> Any

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

Data Any

Since: base-4.8.0.0

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

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

toConstr :: Any -> Constr

dataTypeOf :: Any -> DataType

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

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

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

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

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

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

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

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

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

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

Bounded Any

Since: base-2.1

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

minBound :: Any

maxBound :: Any

Generic Any

Defined in GHC.Internal.Data.Semigroup.Internal

Associated Types

type Rep Any

Since: base-4.7.0.0

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

to :: Rep Any x -> Any

Read Any

Since: base-2.1

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

readsPrec :: Int -> ReadS Any

readList :: ReadS [Any]

readPrec :: ReadPrec Any

readListPrec :: ReadPrec [Any]

Show Any

Since: base-2.1

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

showsPrec :: Int -> Any -> ShowS

show :: Any -> String

showList :: [Any] -> ShowS

Eq Any

Since: base-2.1

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

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

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

Ord Any

Since: base-2.1

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

compare :: Any -> Any -> Ordering

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

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

(>) :: Any -> Any -> Bool

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

max :: Any -> Any -> Any

min :: Any -> Any -> Any

type Rep Any

Since: base-4.7.0.0

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

Monoid under addition.

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

Examples

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

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

Constructors

Sum

Fields

• getSum :: a

Instances

Applicative Sum

Since: base-4.8.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

pure :: a -> Sum a

(<*>) :: Sum (a -> b) -> Sum a -> Sum b

liftA2 :: (a -> b -> c) -> Sum a -> Sum b -> Sum c

(*>) :: Sum a -> Sum b -> Sum b

(<*) :: Sum a -> Sum b -> Sum a

Functor Sum

Since: base-4.8.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

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

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

Monad Sum

Since: base-4.8.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

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

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

return :: a -> Sum a

MonadFix Sum

Since: base-4.8.0.0

Defined in GHC.Internal.Control.Monad.Fix

Methods

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

Foldable Sum

Since: base-4.8.0.0

Defined in GHC.Internal.Data.Foldable

Methods

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

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

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

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

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

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

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

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

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

toList :: Sum a -> [a]

null :: Sum a -> Bool

length :: Sum a -> Int

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

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

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

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

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

Traversable Sum

Since: base-4.8.0.0

Defined in GHC.Internal.Data.Traversable

Methods

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

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

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

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

Generic1 Sum

Defined in GHC.Internal.Data.Semigroup.Internal

Associated Types

type Rep1 Sum

Since: base-4.7.0.0

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

to1 :: Rep1 Sum a -> Sum a

Num a => Monoid (Sum a)

Since: base-2.1

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

mempty :: Sum a

mappend :: Sum a -> Sum a -> Sum a

mconcat :: [Sum a] -> Sum a

Num a => Semigroup (Sum a)

Since: base-4.9.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

(<>) :: Sum a -> Sum a -> Sum a

sconcat :: NonEmpty (Sum a) -> Sum a

stimes :: Integral b => b -> Sum a -> Sum a

Data a => Data (Sum a)

Since: base-4.8.0.0

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)

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

toConstr :: Sum a -> Constr

dataTypeOf :: Sum a -> DataType

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

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

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

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

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

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

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

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

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

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

Bounded a => Bounded (Sum a)

Since: base-2.1

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

minBound :: Sum a

maxBound :: Sum a

Generic (Sum a)

Defined in GHC.Internal.Data.Semigroup.Internal

Associated Types

type Rep (Sum a)

Since: base-4.7.0.0

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

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

Num a => Num (Sum a)

Since: base-4.7.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

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

(-) :: Sum a -> Sum a -> Sum a

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

negate :: Sum a -> Sum a

abs :: Sum a -> Sum a

signum :: Sum a -> Sum a

fromInteger :: Integer -> Sum a

Read a => Read (Sum a)

Since: base-2.1

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

readsPrec :: Int -> ReadS (Sum a)

readList :: ReadS [Sum a]

readPrec :: ReadPrec (Sum a)

readListPrec :: ReadPrec [Sum a]

Show a => Show (Sum a)

Since: base-2.1

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

showsPrec :: Int -> Sum a -> ShowS

show :: Sum a -> String

showList :: [Sum a] -> ShowS

Eq a => Eq (Sum a)

Since: base-2.1

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

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

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

Ord a => Ord (Sum a)

Since: base-2.1

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

compare :: Sum a -> Sum a -> Ordering

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

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

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

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

max :: Sum a -> Sum a -> Sum a

min :: Sum a -> Sum a -> Sum a

type Rep1 Sum

Since: base-4.7.0.0

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)

Since: base-4.7.0.0

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

Monoid under multiplication.

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

Examples

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

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

Constructors

Product

Fields

• getProduct :: a

Instances

Applicative Product

Since: base-4.8.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

pure :: a -> Product a

(<*>) :: Product (a -> b) -> Product a -> Product b

liftA2 :: (a -> b -> c) -> Product a -> Product b -> Product c

(*>) :: Product a -> Product b -> Product b

(<*) :: Product a -> Product b -> Product a

Functor Product

Since: base-4.8.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

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

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

Monad Product

Since: base-4.8.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

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

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

return :: a -> Product a

MonadFix Product

Since: base-4.8.0.0

Defined in GHC.Internal.Control.Monad.Fix

Methods

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

Foldable Product

Since: base-4.8.0.0

Defined in GHC.Internal.Data.Foldable

Methods

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

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

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

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

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

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

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

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

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

toList :: Product a -> [a]

null :: Product a -> Bool

length :: Product a -> Int

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

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

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

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

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

Traversable Product

Since: base-4.8.0.0

Defined in GHC.Internal.Data.Traversable

Methods

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

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

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

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

Generic1 Product

Defined in GHC.Internal.Data.Semigroup.Internal

Associated Types

type Rep1 Product

Since: base-4.7.0.0

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

to1 :: Rep1 Product a -> Product a

Num a => Monoid (Product a)

Since: base-2.1

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

mempty :: Product a

mappend :: Product a -> Product a -> Product a

mconcat :: [Product a] -> Product a

Num a => Semigroup (Product a)

Since: base-4.9.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

(<>) :: Product a -> Product a -> Product a

sconcat :: NonEmpty (Product a) -> Product a

stimes :: Integral b => b -> Product a -> Product a

Data a => Data (Product a)

Since: base-4.8.0.0

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)

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

toConstr :: Product a -> Constr

dataTypeOf :: Product a -> DataType

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

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

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

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

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

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

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

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

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

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

Bounded a => Bounded (Product a)

Since: base-2.1

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

minBound :: Product a

maxBound :: Product a

Generic (Product a)

Defined in GHC.Internal.Data.Semigroup.Internal

Associated Types

type Rep (Product a)

Since: base-4.7.0.0

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

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

Num a => Num (Product a)

Since: base-4.7.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

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

(-) :: Product a -> Product a -> Product a

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

negate :: Product a -> Product a

abs :: Product a -> Product a

signum :: Product a -> Product a

fromInteger :: Integer -> Product a

Read a => Read (Product a)

Since: base-2.1

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

readsPrec :: Int -> ReadS (Product a)

readList :: ReadS [Product a]

readPrec :: ReadPrec (Product a)

readListPrec :: ReadPrec [Product a]

Show a => Show (Product a)

Since: base-2.1

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

showsPrec :: Int -> Product a -> ShowS

show :: Product a -> String

showList :: [Product a] -> ShowS

Eq a => Eq (Product a)

Since: base-2.1

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

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

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

Ord a => Ord (Product a)

Since: base-2.1

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

compare :: Product a -> Product a -> Ordering

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

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

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

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

max :: Product a -> Product a -> Product a

min :: Product a -> Product a -> Product a

type Rep1 Product

Since: base-4.7.0.0

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)

Since: base-4.7.0.0

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

To implement find or findLast on any Foldable:

findLast :: Foldable t => (a -> Bool) -> t a -> Maybe a
findLast pred = getLast . foldMap (x -> if pred x
                                           then Last (Just x)
                                           else Last Nothing)

Much of Maps interface can be implemented with alter. Some of the rest can be implemented with a new alterF function and either First or Last:

alterF :: (Functor f, Ord k) =>
          (Maybe a -> f (Maybe a)) -> k -> Map k a -> f (Map k a)

instance Monoid a => Functor ((,) a)  -- from GHC.Internal.Data.Functor

insertLookupWithKey :: Ord k => (k -> v -> v -> v) -> k -> v
                    -> Map k v -> (Maybe v, Map k v)
insertLookupWithKey combine key value =
  Arrow.first getFirst . alterF doChange key
  where
  doChange Nothing = (First Nothing, Just value)
  doChange (Just oldValue) =
    (First (Just oldValue),
     Just (combine key value oldValue))

newtype First a

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

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

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

Constructors

First

Fields

• getFirst :: Maybe a

Instances

Applicative First

Since: base-4.8.0.0

Defined in GHC.Internal.Data.Monoid

Methods

pure :: a -> First a

(<*>) :: First (a -> b) -> First a -> First b

liftA2 :: (a -> b -> c) -> First a -> First b -> First c

(*>) :: First a -> First b -> First b

(<*) :: First a -> First b -> First a

Functor First

Since: base-4.8.0.0

Defined in GHC.Internal.Data.Monoid

Methods

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

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

Monad First

Since: base-4.8.0.0

Defined in GHC.Internal.Data.Monoid

Methods

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

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

return :: a -> First a

MonadFix First

Since: base-4.8.0.0

Defined in GHC.Internal.Control.Monad.Fix

Methods

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

Foldable First

Since: base-4.8.0.0

Defined in GHC.Internal.Data.Foldable

Methods

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

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

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

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

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

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

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

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

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

toList :: First a -> [a]

null :: First a -> Bool

length :: First a -> Int

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

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

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

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

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

Traversable First

Since: base-4.8.0.0

Defined in GHC.Internal.Data.Traversable

Methods

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

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

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

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

Generic1 First

Defined in GHC.Internal.Data.Monoid

Associated Types

type Rep1 First

Since: base-4.7.0.0

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

to1 :: Rep1 First a -> First a

Monoid (First a)

Since: base-2.1

Defined in GHC.Internal.Data.Monoid

Methods

mempty :: First a

mappend :: First a -> First a -> First a

mconcat :: [First a] -> First a

Semigroup (First a)

Since: base-4.9.0.0

Defined in GHC.Internal.Data.Monoid

Methods

(<>) :: First a -> First a -> First a

sconcat :: NonEmpty (First a) -> First a

stimes :: Integral b => b -> First a -> First a

Data a => Data (First a)

Since: base-4.8.0.0

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)

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

toConstr :: First a -> Constr

dataTypeOf :: First a -> DataType

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

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

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

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

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

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

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

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

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

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

Generic (First a)

Defined in GHC.Internal.Data.Monoid

Associated Types

type Rep (First a)

Since: base-4.7.0.0

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

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

Read a => Read (First a)

Since: base-2.1

Defined in GHC.Internal.Data.Monoid

Methods

readsPrec :: Int -> ReadS (First a)

readList :: ReadS [First a]

readPrec :: ReadPrec (First a)

readListPrec :: ReadPrec [First a]

Show a => Show (First a)

Since: base-2.1

Defined in GHC.Internal.Data.Monoid

Methods

showsPrec :: Int -> First a -> ShowS

show :: First a -> String

showList :: [First a] -> ShowS

Eq a => Eq (First a)

Since: base-2.1

Defined in GHC.Internal.Data.Monoid

Methods

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

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

Ord a => Ord (First a)

Since: base-2.1

Defined in GHC.Internal.Data.Monoid

Methods

compare :: First a -> First a -> Ordering

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

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

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

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

max :: First a -> First a -> First a

min :: First a -> First a -> First a

type Rep1 First

Since: base-4.7.0.0

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)

Since: base-4.7.0.0

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

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

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

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

Constructors

Last

Fields

• getLast :: Maybe a

Instances

Applicative Last

Since: base-4.8.0.0

Defined in GHC.Internal.Data.Monoid

Methods

pure :: a -> Last a

(<*>) :: Last (a -> b) -> Last a -> Last b

liftA2 :: (a -> b -> c) -> Last a -> Last b -> Last c

(*>) :: Last a -> Last b -> Last b

(<*) :: Last a -> Last b -> Last a

Functor Last

Since: base-4.8.0.0

Defined in GHC.Internal.Data.Monoid

Methods

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

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

Monad Last

Since: base-4.8.0.0

Defined in GHC.Internal.Data.Monoid

Methods

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

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

return :: a -> Last a

MonadFix Last

Since: base-4.8.0.0

Defined in GHC.Internal.Control.Monad.Fix

Methods

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

Foldable Last

Since: base-4.8.0.0

Defined in GHC.Internal.Data.Foldable

Methods

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

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

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

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

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

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

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

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

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

toList :: Last a -> [a]

null :: Last a -> Bool

length :: Last a -> Int

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

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

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

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

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

Traversable Last

Since: base-4.8.0.0

Defined in GHC.Internal.Data.Traversable

Methods

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

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

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

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

Generic1 Last

Defined in GHC.Internal.Data.Monoid

Associated Types

type Rep1 Last

Since: base-4.7.0.0

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

to1 :: Rep1 Last a -> Last a

Monoid (Last a)

Since: base-2.1

Defined in GHC.Internal.Data.Monoid

Methods

mempty :: Last a

mappend :: Last a -> Last a -> Last a

mconcat :: [Last a] -> Last a

Semigroup (Last a)

Since: base-4.9.0.0

Defined in GHC.Internal.Data.Monoid

Methods

(<>) :: Last a -> Last a -> Last a

sconcat :: NonEmpty (Last a) -> Last a

stimes :: Integral b => b -> Last a -> Last a

Data a => Data (Last a)

Since: base-4.8.0.0

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)

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

toConstr :: Last a -> Constr

dataTypeOf :: Last a -> DataType

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

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

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

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

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

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

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

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

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

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

Generic (Last a)

Defined in GHC.Internal.Data.Monoid

Associated Types

type Rep (Last a)

Since: base-4.7.0.0

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

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

Read a => Read (Last a)

Since: base-2.1

Defined in GHC.Internal.Data.Monoid

Methods

readsPrec :: Int -> ReadS (Last a)

readList :: ReadS [Last a]

readPrec :: ReadPrec (Last a)

readListPrec :: ReadPrec [Last a]

Show a => Show (Last a)

Since: base-2.1

Defined in GHC.Internal.Data.Monoid

Methods

showsPrec :: Int -> Last a -> ShowS

show :: Last a -> String

showList :: [Last a] -> ShowS

Eq a => Eq (Last a)

Since: base-2.1

Defined in GHC.Internal.Data.Monoid

Methods

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

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

Ord a => Ord (Last a)

Since: base-2.1

Defined in GHC.Internal.Data.Monoid

Methods

compare :: Last a -> Last a -> Ordering

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

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

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

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

max :: Last a -> Last a -> Last a

min :: Last a -> Last a -> Last a

type Rep1 Last

Since: base-4.7.0.0

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)

Since: base-4.7.0.0

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)

Monoid under <|>.

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

Examples

>>> 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

• getAlt :: f a

Instances

Generic1 (Alt f :: k -> Type)

Defined in GHC.Internal.Data.Semigroup.Internal

Associated Types

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

Since: base-4.8.0.0

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

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

Alternative f => Alternative (Alt f)

Since: base-4.8.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

empty :: Alt f a

(<|>) :: Alt f a -> Alt f a -> Alt f a

some :: Alt f a -> Alt f [a]

many :: Alt f a -> Alt f [a]

Applicative f => Applicative (Alt f)

Since: base-4.8.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

pure :: a -> Alt f a

(<*>) :: Alt f (a -> b) -> Alt f a -> Alt f b

liftA2 :: (a -> b -> c) -> Alt f a -> Alt f b -> Alt f c

(*>) :: Alt f a -> Alt f b -> Alt f b

(<*) :: Alt f a -> Alt f b -> Alt f a

Functor f => Functor (Alt f)

Since: base-4.8.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

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

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

Monad f => Monad (Alt f)

Since: base-4.8.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

(>>=) :: Alt f a -> (a -> Alt f b) -> Alt f b

(>>) :: Alt f a -> Alt f b -> Alt f b

return :: a -> Alt f a

MonadPlus f => MonadPlus (Alt f)

Since: base-4.8.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

mzero :: Alt f a

mplus :: Alt f a -> Alt f a -> Alt f a

MonadFix f => MonadFix (Alt f)

Since: base-4.8.0.0

Defined in GHC.Internal.Control.Monad.Fix

Methods

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

Foldable f => Foldable (Alt f)

Since: base-4.12.0.0

Defined in GHC.Internal.Data.Foldable

Methods

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

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

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

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

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

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

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

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

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

toList :: Alt f a -> [a]

null :: Alt f a -> Bool

length :: Alt f a -> Int

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

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

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

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

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

Traversable f => Traversable (Alt f)

Since: base-4.12.0.0

Defined in GHC.Internal.Data.Traversable

Methods

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

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

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

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

Alternative f => Monoid (Alt f a)

Since: base-4.8.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

mempty :: Alt f a

mappend :: Alt f a -> Alt f a -> Alt f a

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

Alternative f => Semigroup (Alt f a)

Since: base-4.9.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

(<>) :: Alt f a -> Alt f a -> Alt f a

sconcat :: NonEmpty (Alt f a) -> Alt f a

stimes :: Integral b => b -> Alt f a -> Alt f a

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

Since: base-4.8.0.0

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)

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

toConstr :: Alt f a -> Constr

dataTypeOf :: Alt f a -> DataType

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

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

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

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

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

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

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

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

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

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

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

Since: base-4.8.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

succ :: Alt f a -> Alt f a

pred :: Alt f a -> Alt f a

toEnum :: Int -> Alt f a

fromEnum :: Alt f a -> Int

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

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

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

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

Generic (Alt f a)

Defined in GHC.Internal.Data.Semigroup.Internal

Associated Types

type Rep (Alt f a)

Since: base-4.8.0.0

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

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

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

Since: base-4.8.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

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

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

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

negate :: Alt f a -> Alt f a

abs :: Alt f a -> Alt f a

signum :: Alt f a -> Alt f a

fromInteger :: Integer -> Alt f a

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

Since: base-4.8.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

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

readList :: ReadS [Alt f a]

readPrec :: ReadPrec (Alt f a)

readListPrec :: ReadPrec [Alt f a]

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

Since: base-4.8.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

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

show :: Alt f a -> String

showList :: [Alt f a] -> ShowS

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

Since: base-4.8.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

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

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

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

Since: base-4.8.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

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

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

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

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

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

max :: Alt f a -> Alt f a -> Alt f a

min :: Alt f a -> Alt f a -> Alt f a

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

Since: base-4.8.0.0

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)

Since: base-4.8.0.0

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)

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

Examples

>>> 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

• getAp :: f a

Instances

Generic1 (Ap f :: k -> Type)

Defined in GHC.Internal.Data.Monoid

Associated Types

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

Since: base-4.12.0.0

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

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

Alternative f => Alternative (Ap f)

Since: base-4.12.0.0

Defined in GHC.Internal.Data.Monoid

Methods

empty :: Ap f a

(<|>) :: Ap f a -> Ap f a -> Ap f a

some :: Ap f a -> Ap f [a]

many :: Ap f a -> Ap f [a]

Applicative f => Applicative (Ap f)

Since: base-4.12.0.0

Defined in GHC.Internal.Data.Monoid

Methods

pure :: a -> Ap f a

(<*>) :: Ap f (a -> b) -> Ap f a -> Ap f b

liftA2 :: (a -> b -> c) -> Ap f a -> Ap f b -> Ap f c

(*>) :: Ap f a -> Ap f b -> Ap f b

(<*) :: Ap f a -> Ap f b -> Ap f a

Functor f => Functor (Ap f)

Since: base-4.12.0.0

Defined in GHC.Internal.Data.Monoid

Methods

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

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

Monad f => Monad (Ap f)

Since: base-4.12.0.0

Defined in GHC.Internal.Data.Monoid

Methods

(>>=) :: Ap f a -> (a -> Ap f b) -> Ap f b

(>>) :: Ap f a -> Ap f b -> Ap f b

return :: a -> Ap f a

MonadPlus f => MonadPlus (Ap f)

Since: base-4.12.0.0

Defined in GHC.Internal.Data.Monoid

Methods

mzero :: Ap f a

mplus :: Ap f a -> Ap f a -> Ap f a

MonadFail f => MonadFail (Ap f)

Since: base-4.12.0.0

Defined in GHC.Internal.Data.Monoid

Methods

fail :: String -> Ap f a

MonadFix f => MonadFix (Ap f)

Since: base-4.12.0.0

Defined in GHC.Internal.Control.Monad.Fix

Methods

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

Foldable f => Foldable (Ap f)

Since: base-4.12.0.0

Defined in GHC.Internal.Data.Foldable

Methods

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

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

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

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

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

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

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

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

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

toList :: Ap f a -> [a]

null :: Ap f a -> Bool

length :: Ap f a -> Int

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

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

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

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

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

Traversable f => Traversable (Ap f)

Since: base-4.12.0.0

Defined in GHC.Internal.Data.Traversable

Methods

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

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

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

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

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

Since: base-4.12.0.0

Defined in GHC.Internal.Data.Monoid

Methods

mempty :: Ap f a

mappend :: Ap f a -> Ap f a -> Ap f a

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

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

Since: base-4.12.0.0

Defined in GHC.Internal.Data.Monoid

Methods

(<>) :: Ap f a -> Ap f a -> Ap f a

sconcat :: NonEmpty (Ap f a) -> Ap f a

stimes :: Integral b => b -> Ap f a -> Ap f a

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

Since: base-4.12.0.0

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)

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

toConstr :: Ap f a -> Constr

dataTypeOf :: Ap f a -> DataType

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

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

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

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

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

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

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

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

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

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

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

Since: base-4.12.0.0

Defined in GHC.Internal.Data.Monoid

Methods

minBound :: Ap f a

maxBound :: Ap f a

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

Since: base-4.12.0.0

Defined in GHC.Internal.Data.Monoid

Methods

succ :: Ap f a -> Ap f a

pred :: Ap f a -> Ap f a

toEnum :: Int -> Ap f a

fromEnum :: Ap f a -> Int

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

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

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

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

Generic (Ap f a)

Defined in GHC.Internal.Data.Monoid

Associated Types

type Rep (Ap f a)

Since: base-4.12.0.0

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

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

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

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

Defined in GHC.Internal.Data.Monoid

Methods

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

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

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

negate :: Ap f a -> Ap f a

abs :: Ap f a -> Ap f a

signum :: Ap f a -> Ap f a

fromInteger :: Integer -> Ap f a

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

Since: base-4.12.0.0

Defined in GHC.Internal.Data.Monoid

Methods

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

readList :: ReadS [Ap f a]

readPrec :: ReadPrec (Ap f a)

readListPrec :: ReadPrec [Ap f a]

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

Since: base-4.12.0.0

Defined in GHC.Internal.Data.Monoid

Methods

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

show :: Ap f a -> String

showList :: [Ap f a] -> ShowS

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

Since: base-4.12.0.0

Defined in GHC.Internal.Data.Monoid

Methods

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

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

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

Since: base-4.12.0.0

Defined in GHC.Internal.Data.Monoid

Methods

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

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

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

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

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

max :: Ap f a -> Ap f a -> Ap f a

min :: Ap f a -> Ap f a -> Ap f a

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

Since: base-4.12.0.0

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)

Since: base-4.12.0.0

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))))