base-4.14.0.0: Basic libraries
Copyright(c) Andy Gill 2001
(c) Oregon Graduate Institute of Science and Technology 2001
LicenseBSD-style (see the file libraries/base/LICENSE)
Maintainerlibraries@haskell.org
Stabilityexperimental
Portabilityportable
Safe HaskellTrustworthy
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:

>>> mempty :: Sum Int
Sum 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

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

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

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

Minimal complete definition

mempty

Methods

mempty :: a Source #

Identity of mappend

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

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

An associative operation

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

mconcat :: [a] -> a Source #

Fold a list using the monoid.

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

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

Instances

Instances details
Monoid Ordering #

Since: base-2.1

Instance details

Defined in GHC.Base

Monoid () #

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

mempty :: () Source #

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

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

Monoid Any #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Monoid All #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Monoid Lifetime #

mappend takes the longer of two lifetimes.

Since: base-4.8.0.0

Instance details

Defined in GHC.Event.Internal

Monoid Event #

Since: base-4.4.0.0

Instance details

Defined in GHC.Event.Internal

Monoid [a] #

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

mempty :: [a] Source #

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

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

Semigroup a => Monoid (Maybe a) #

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

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

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

mempty :: Maybe a Source #

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

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

Monoid a => Monoid (IO a) #

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Methods

mempty :: IO a Source #

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

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

Monoid p => Monoid (Par1 p) #

Since: base-4.12.0.0

Instance details

Defined in GHC.Generics

Methods

mempty :: Par1 p Source #

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

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

Monoid a => Monoid (Down a) #

Since: base-4.11.0.0

Instance details

Defined in Data.Ord

Methods

mempty :: Down a Source #

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

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

Num a => Monoid (Product a) #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Num a => Monoid (Sum a) #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

mempty :: Sum a Source #

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

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

Monoid (Endo a) #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

mempty :: Endo a Source #

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

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

Monoid a => Monoid (Dual a) #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

mempty :: Dual a Source #

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

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

Monoid (Last a) #

Since: base-2.1

Instance details

Defined in Data.Monoid

Methods

mempty :: Last a Source #

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

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

Monoid (First a) #

Since: base-2.1

Instance details

Defined in Data.Monoid

Methods

mempty :: First a Source #

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

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

Monoid a => Monoid (Identity a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Identity

Semigroup a => Monoid (Option a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Monoid m => Monoid (WrappedMonoid m) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

(Ord a, Bounded a) => Monoid (Max a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

mempty :: Max a Source #

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

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

(Ord a, Bounded a) => Monoid (Min a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

mempty :: Min a Source #

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

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

Monoid (Equivalence a) #

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

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

Defined in Data.Functor.Contravariant

Monoid (Comparison a) #

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

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

Defined in Data.Functor.Contravariant

Monoid (Predicate a) #

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

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

Defined in Data.Functor.Contravariant

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

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

mempty :: a -> b Source #

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

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

Monoid (U1 p) #

Since: base-4.12.0.0

Instance details

Defined in GHC.Generics

Methods

mempty :: U1 p Source #

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

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

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

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

mempty :: (a, b) Source #

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

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

Monoid a => Monoid (ST s a) #

Since: base-4.11.0.0

Instance details

Defined in GHC.ST

Methods

mempty :: ST s a Source #

mappend :: ST s a -> ST s a -> ST s a Source #

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

Monoid (Proxy s) #

Since: base-4.7.0.0

Instance details

Defined in Data.Proxy

Methods

mempty :: Proxy s Source #

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

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

Monoid a => Monoid (Op a b) #

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

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

Defined in Data.Functor.Contravariant

Methods

mempty :: Op a b Source #

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

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

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

Since: base-4.12.0.0

Instance details

Defined in GHC.Generics

Methods

mempty :: Rec1 f p Source #

mappend :: Rec1 f p -> Rec1 f p -> Rec1 f p Source #

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

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

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

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

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

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

Alternative f => Monoid (Alt f a) #

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

mempty :: Alt f a Source #

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

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

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

Since: base-4.12.0.0

Instance details

Defined in Data.Monoid

Methods

mempty :: Ap f a Source #

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

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

Monoid a => Monoid (Const a b) #

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Const

Methods

mempty :: Const a b Source #

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

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

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

Since: base-4.12.0.0

Instance details

Defined in GHC.Generics

Methods

mempty :: K1 i c p Source #

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

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

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

Since: base-4.12.0.0

Instance details

Defined in GHC.Generics

Methods

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

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

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

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

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

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

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

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

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

Since: base-4.12.0.0

Instance details

Defined in GHC.Generics

Methods

mempty :: M1 i c f p Source #

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

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

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

Since: base-4.12.0.0

Instance details

Defined in GHC.Generics

Methods

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

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

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

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

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

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

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

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

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

An associative operation.

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

newtype Dual a Source #

The dual of a Monoid, obtained by swapping the arguments of mappend.

>>> getDual (mappend (Dual "Hello") (Dual "World"))
"WorldHello"

Constructors

Dual 

Fields

Instances

Instances details
Monad Dual #

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

return :: a -> Dual a Source #

Functor Dual #

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

MonadFix Dual #

Since: base-4.8.0.0

Instance details

Defined in Control.Monad.Fix

Methods

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

Applicative Dual #

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

pure :: a -> Dual a Source #

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

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

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

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

Foldable Dual #

Since: base-4.8.0.0

Instance details

Defined in 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 #

Since: base-4.8.0.0

Instance details

Defined in 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 #

MonadZip Dual #

Since: base-4.8.0.0

Instance details

Defined in 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 #

Bounded a => Bounded (Dual a) #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Eq a => Eq (Dual a) #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

Data a => Data (Dual a) #

Since: base-4.8.0.0

Instance details

Defined in Data.Data

Methods

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

Ord a => Ord (Dual a) #

Since: base-2.1

Instance details

Defined in 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 #

Read a => Read (Dual a) #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Show a => Show (Dual a) #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

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

show :: Dual a -> String Source #

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

Generic (Dual a) # 
Instance details

Defined in Data.Semigroup.Internal

Associated Types

type Rep (Dual a) :: Type -> Type Source #

Methods

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

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

Semigroup a => Semigroup (Dual a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

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

Monoid a => Monoid (Dual a) #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

mempty :: Dual a Source #

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

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

Generic1 Dual # 
Instance details

Defined in Data.Semigroup.Internal

Associated Types

type Rep1 Dual :: k -> Type Source #

Methods

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

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

type Rep (Dual a) #

Since: base-4.7.0.0

Instance details

Defined in Data.Semigroup.Internal

type Rep (Dual a) = D1 ('MetaData "Dual" "Data.Semigroup.Internal" "base" 'True) (C1 ('MetaCons "Dual" 'PrefixI 'True) (S1 ('MetaSel ('Just "getDual") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))
type Rep1 Dual #

Since: base-4.7.0.0

Instance details

Defined in Data.Semigroup.Internal

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

newtype Endo a Source #

The monoid of endomorphisms under composition.

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

Constructors

Endo 

Fields

Instances

Instances details
Generic (Endo a) # 
Instance details

Defined in Data.Semigroup.Internal

Associated Types

type Rep (Endo a) :: Type -> Type Source #

Methods

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

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

Semigroup (Endo a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

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

Monoid (Endo a) #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

mempty :: Endo a Source #

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

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

type Rep (Endo a) #

Since: base-4.7.0.0

Instance details

Defined in Data.Semigroup.Internal

type Rep (Endo a) = D1 ('MetaData "Endo" "Data.Semigroup.Internal" "base" '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 (&&).

>>> getAll (All True <> mempty <> All False)
False
>>> getAll (mconcat (map (\x -> All (even x)) [2,4,6,7,8]))
False

Constructors

All 

Fields

Instances

Instances details
Bounded All #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Eq All #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

Data All #

Since: base-4.8.0.0

Instance details

Defined in Data.Data

Methods

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

Ord All #

Since: base-2.1

Instance details

Defined in 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 #

Read All #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Show All #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Generic All # 
Instance details

Defined in Data.Semigroup.Internal

Associated Types

type Rep All :: Type -> Type Source #

Methods

from :: All -> Rep All x Source #

to :: Rep All x -> All Source #

Semigroup All #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

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

sconcat :: NonEmpty All -> All Source #

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

Monoid All #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

type Rep All #

Since: base-4.7.0.0

Instance details

Defined in Data.Semigroup.Internal

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

newtype Any Source #

Boolean monoid under disjunction (||).

>>> getAny (Any True <> mempty <> Any False)
True
>>> getAny (mconcat (map (\x -> Any (even x)) [2,4,6,7,8]))
True

Constructors

Any 

Fields

Instances

Instances details
Bounded Any #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Eq Any #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

Data Any #

Since: base-4.8.0.0

Instance details

Defined in Data.Data

Methods

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

Ord Any #

Since: base-2.1

Instance details

Defined in 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 #

Read Any #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Show Any #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Generic Any # 
Instance details

Defined in Data.Semigroup.Internal

Associated Types

type Rep Any :: Type -> Type Source #

Methods

from :: Any -> Rep Any x Source #

to :: Rep Any x -> Any Source #

Semigroup Any #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

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

sconcat :: NonEmpty Any -> Any Source #

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

Monoid Any #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

type Rep Any #

Since: base-4.7.0.0

Instance details

Defined in Data.Semigroup.Internal

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

Num wrappers

newtype Sum a Source #

Monoid under addition.

>>> getSum (Sum 1 <> Sum 2 <> mempty)
3

Constructors

Sum 

Fields

Instances

Instances details
Monad Sum #

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

return :: a -> Sum a Source #

Functor Sum #

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

MonadFix Sum #

Since: base-4.8.0.0

Instance details

Defined in Control.Monad.Fix

Methods

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

Applicative Sum #

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

pure :: a -> Sum a Source #

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

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

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

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

Foldable Sum #

Since: base-4.8.0.0

Instance details

Defined in 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 #

Since: base-4.8.0.0

Instance details

Defined in 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 #

MonadZip Sum #

Since: base-4.8.0.0

Instance details

Defined in 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 #

Bounded a => Bounded (Sum a) #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Eq a => Eq (Sum a) #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

Data a => Data (Sum a) #

Since: base-4.8.0.0

Instance details

Defined in Data.Data

Methods

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

Num a => Num (Sum a) #

Since: base-4.7.0.0

Instance details

Defined in 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 #

Ord a => Ord (Sum a) #

Since: base-2.1

Instance details

Defined in 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 #

Read a => Read (Sum a) #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Show a => Show (Sum a) #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

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

show :: Sum a -> String Source #

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

Generic (Sum a) # 
Instance details

Defined in Data.Semigroup.Internal

Associated Types

type Rep (Sum a) :: Type -> Type Source #

Methods

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

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

Num a => Semigroup (Sum a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

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

Num a => Monoid (Sum a) #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

mempty :: Sum a Source #

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

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

Generic1 Sum # 
Instance details

Defined in Data.Semigroup.Internal

Associated Types

type Rep1 Sum :: k -> Type Source #

Methods

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

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

type Rep (Sum a) #

Since: base-4.7.0.0

Instance details

Defined in Data.Semigroup.Internal

type Rep (Sum a) = D1 ('MetaData "Sum" "Data.Semigroup.Internal" "base" 'True) (C1 ('MetaCons "Sum" 'PrefixI 'True) (S1 ('MetaSel ('Just "getSum") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))
type Rep1 Sum #

Since: base-4.7.0.0

Instance details

Defined in Data.Semigroup.Internal

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

newtype Product a Source #

Monoid under multiplication.

>>> getProduct (Product 3 <> Product 4 <> mempty)
12

Constructors

Product 

Fields

Instances

Instances details
Monad Product #

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

return :: a -> Product a Source #

Functor Product #

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

MonadFix Product #

Since: base-4.8.0.0

Instance details

Defined in Control.Monad.Fix

Methods

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

Applicative Product #

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

pure :: a -> Product a Source #

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

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

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

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

Foldable Product #

Since: base-4.8.0.0

Instance details

Defined in 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 #

Since: base-4.8.0.0

Instance details

Defined in 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 #

MonadZip Product #

Since: base-4.8.0.0

Instance details

Defined in 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 #

Bounded a => Bounded (Product a) #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Eq a => Eq (Product a) #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

Data a => Data (Product a) #

Since: base-4.8.0.0

Instance details

Defined in Data.Data

Methods

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

Num a => Num (Product a) #

Since: base-4.7.0.0

Instance details

Defined in Data.Semigroup.Internal

Ord a => Ord (Product a) #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Read a => Read (Product a) #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Show a => Show (Product a) #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Generic (Product a) # 
Instance details

Defined in Data.Semigroup.Internal

Associated Types

type Rep (Product a) :: Type -> Type Source #

Methods

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

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

Num a => Semigroup (Product a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

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

Num a => Monoid (Product a) #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Generic1 Product # 
Instance details

Defined in Data.Semigroup.Internal

Associated Types

type Rep1 Product :: k -> Type Source #

Methods

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

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

type Rep (Product a) #

Since: base-4.7.0.0

Instance details

Defined in Data.Semigroup.Internal

type Rep (Product a) = D1 ('MetaData "Product" "Data.Semigroup.Internal" "base" 'True) (C1 ('MetaCons "Product" 'PrefixI 'True) (S1 ('MetaSel ('Just "getProduct") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))
type Rep1 Product #

Since: base-4.7.0.0

Instance details

Defined in Data.Semigroup.Internal

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

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 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 Source #

Maybe monoid returning the leftmost non-Nothing value.

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

>>> getFirst (First (Just "hello") <> First Nothing <> First (Just "world"))
Just "hello"

Use of this type is discouraged. Note the following equivalence:

Data.Monoid.First x === Maybe (Data.Semigroup.First x)

In addition to being equivalent in the structural sense, the two also have Monoid instances that behave the same. This type will be marked deprecated in GHC 8.8, and removed in GHC 8.10. Users are advised to use the variant from Data.Semigroup and wrap it in Maybe.

Constructors

First 

Fields

Instances

Instances details
Monad First #

Since: base-4.8.0.0

Instance details

Defined in Data.Monoid

Methods

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

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

return :: a -> First a Source #

Functor First #

Since: base-4.8.0.0

Instance details

Defined in Data.Monoid

Methods

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

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

MonadFix First #

Since: base-4.8.0.0

Instance details

Defined in Control.Monad.Fix

Methods

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

Applicative First #

Since: base-4.8.0.0

Instance details

Defined in Data.Monoid

Methods

pure :: a -> First a Source #

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

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

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

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

Foldable First #

Since: base-4.8.0.0

Instance details

Defined in 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 #

Since: base-4.8.0.0

Instance details

Defined in 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 #

MonadZip First #

Since: base-4.8.0.0

Instance details

Defined in 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 #

Eq a => Eq (First a) #

Since: base-2.1

Instance details

Defined in Data.Monoid

Methods

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

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

Data a => Data (First a) #

Since: base-4.8.0.0

Instance details

Defined in Data.Data

Methods

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

Ord a => Ord (First a) #

Since: base-2.1

Instance details

Defined in 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 #

Read a => Read (First a) #

Since: base-2.1

Instance details

Defined in Data.Monoid

Show a => Show (First a) #

Since: base-2.1

Instance details

Defined in Data.Monoid

Generic (First a) # 
Instance details

Defined in Data.Monoid

Associated Types

type Rep (First a) :: Type -> Type Source #

Methods

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

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

Semigroup (First a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Monoid

Methods

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

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

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

Monoid (First a) #

Since: base-2.1

Instance details

Defined in Data.Monoid

Methods

mempty :: First a Source #

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

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

Generic1 First # 
Instance details

Defined in Data.Monoid

Associated Types

type Rep1 First :: k -> Type Source #

Methods

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

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

type Rep (First a) #

Since: base-4.7.0.0

Instance details

Defined in Data.Monoid

type Rep (First a) = D1 ('MetaData "First" "Data.Monoid" "base" 'True) (C1 ('MetaCons "First" 'PrefixI 'True) (S1 ('MetaSel ('Just "getFirst") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (Maybe a))))
type Rep1 First #

Since: base-4.7.0.0

Instance details

Defined in Data.Monoid

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

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)

>>> getLast (Last (Just "hello") <> Last Nothing <> Last (Just "world"))
Just "world"

Use of this type is discouraged. Note the following equivalence:

Data.Monoid.Last x === Maybe (Data.Semigroup.Last x)

In addition to being equivalent in the structural sense, the two also have Monoid instances that behave the same. This type will be marked deprecated in GHC 8.8, and removed in GHC 8.10. Users are advised to use the variant from Data.Semigroup and wrap it in Maybe.

Constructors

Last 

Fields

Instances

Instances details
Monad Last #

Since: base-4.8.0.0

Instance details

Defined in Data.Monoid

Methods

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

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

return :: a -> Last a Source #

Functor Last #

Since: base-4.8.0.0

Instance details

Defined in Data.Monoid

Methods

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

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

MonadFix Last #

Since: base-4.8.0.0

Instance details

Defined in Control.Monad.Fix

Methods

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

Applicative Last #

Since: base-4.8.0.0

Instance details

Defined in Data.Monoid

Methods

pure :: a -> Last a Source #

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

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

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

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

Foldable Last #

Since: base-4.8.0.0

Instance details

Defined in 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 #

Since: base-4.8.0.0

Instance details

Defined in 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 #

MonadZip Last #

Since: base-4.8.0.0

Instance details

Defined in 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 #

Eq a => Eq (Last a) #

Since: base-2.1

Instance details

Defined in Data.Monoid

Methods

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

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

Data a => Data (Last a) #

Since: base-4.8.0.0

Instance details

Defined in Data.Data

Methods

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

Ord a => Ord (Last a) #

Since: base-2.1

Instance details

Defined in 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 #

Read a => Read (Last a) #

Since: base-2.1

Instance details

Defined in Data.Monoid

Show a => Show (Last a) #

Since: base-2.1

Instance details

Defined in Data.Monoid

Methods

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

show :: Last a -> String Source #

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

Generic (Last a) # 
Instance details

Defined in Data.Monoid

Associated Types

type Rep (Last a) :: Type -> Type Source #

Methods

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

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

Semigroup (Last a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Monoid

Methods

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

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

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

Monoid (Last a) #

Since: base-2.1

Instance details

Defined in Data.Monoid

Methods

mempty :: Last a Source #

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

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

Generic1 Last # 
Instance details

Defined in Data.Monoid

Associated Types

type Rep1 Last :: k -> Type Source #

Methods

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

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

type Rep (Last a) #

Since: base-4.7.0.0

Instance details

Defined in Data.Monoid

type Rep (Last a) = D1 ('MetaData "Last" "Data.Monoid" "base" 'True) (C1 ('MetaCons "Last" 'PrefixI 'True) (S1 ('MetaSel ('Just "getLast") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (Maybe a))))
type Rep1 Last #

Since: base-4.7.0.0

Instance details

Defined in Data.Monoid

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

Alternative wrapper

newtype Alt f a Source #

Monoid under <|>.

>>> getAlt (Alt (Just 12) <> Alt (Just 24))
Just 12
>>> getAlt $ Alt Nothing <> Alt (Just 24)
Just 24

Since: base-4.8.0.0

Constructors

Alt 

Fields

Instances

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

Defined in Data.Semigroup.Internal

Associated Types

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

Methods

from1 :: forall (a :: k0). Alt f a -> Rep1 (Alt f) a Source #

to1 :: forall (a :: k0). Rep1 (Alt f) a -> Alt f a Source #

Monad f => Monad (Alt f) #

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

return :: a -> Alt f a Source #

Functor f => Functor (Alt f) #

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

MonadFix f => MonadFix (Alt f) #

Since: base-4.8.0.0

Instance details

Defined in Control.Monad.Fix

Methods

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

Applicative f => Applicative (Alt f) #

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

pure :: a -> Alt f a Source #

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

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

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

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

Foldable f => Foldable (Alt f) #

Since: base-4.12.0.0

Instance details

Defined in 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) #

Since: base-4.12.0.0

Instance details

Defined in 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 #

MonadPlus f => MonadPlus (Alt f) #

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

mzero :: Alt f a Source #

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

Alternative f => Alternative (Alt f) #

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

empty :: Alt f a Source #

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

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

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

MonadZip f => MonadZip (Alt f) #

Since: base-4.8.0.0

Instance details

Defined in 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 #

Contravariant f => Contravariant (Alt f) # 
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 #

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

Since: base-4.8.0.0

Instance details

Defined in 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 #

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

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

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

Since: base-4.8.0.0

Instance details

Defined in Data.Data

Methods

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

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

Since: base-4.8.0.0

Instance details

Defined in 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 #

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

Since: base-4.8.0.0

Instance details

Defined in 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 #

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

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

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

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

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

show :: Alt f a -> String Source #

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

Generic (Alt f a) # 
Instance details

Defined in Data.Semigroup.Internal

Associated Types

type Rep (Alt f a) :: Type -> Type Source #

Methods

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

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

Alternative f => Semigroup (Alt f a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

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

Alternative f => Monoid (Alt f a) #

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

mempty :: Alt f a Source #

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

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

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

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

type Rep1 (Alt f :: k -> Type) = D1 ('MetaData "Alt" "Data.Semigroup.Internal" "base" '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

Instance details

Defined in Data.Semigroup.Internal

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

Applicative wrapper

newtype Ap f a Source #

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

Since: base-4.12.0.0

Constructors

Ap 

Fields

Instances

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

Defined in Data.Monoid

Associated Types

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

Methods

from1 :: forall (a :: k0). Ap f a -> Rep1 (Ap f) a Source #

to1 :: forall (a :: k0). Rep1 (Ap f) a -> Ap f a Source #

Monad f => Monad (Ap f) #

Since: base-4.12.0.0

Instance details

Defined in Data.Monoid

Methods

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

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

return :: a -> Ap f a Source #

Functor f => Functor (Ap f) #

Since: base-4.12.0.0

Instance details

Defined in Data.Monoid

Methods

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

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

MonadFix f => MonadFix (Ap f) #

Since: base-4.12.0.0

Instance details

Defined in Control.Monad.Fix

Methods

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

MonadFail f => MonadFail (Ap f) #

Since: base-4.12.0.0

Instance details

Defined in Data.Monoid

Methods

fail :: String -> Ap f a Source #

Applicative f => Applicative (Ap f) #

Since: base-4.12.0.0

Instance details

Defined in Data.Monoid

Methods

pure :: a -> Ap f a Source #

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

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

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

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

Foldable f => Foldable (Ap f) #

Since: base-4.12.0.0

Instance details

Defined in 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) #

Since: base-4.12.0.0

Instance details

Defined in 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 #

MonadPlus f => MonadPlus (Ap f) #

Since: base-4.12.0.0

Instance details

Defined in Data.Monoid

Methods

mzero :: Ap f a Source #

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

Alternative f => Alternative (Ap f) #

Since: base-4.12.0.0

Instance details

Defined in Data.Monoid

Methods

empty :: Ap f a Source #

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

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

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

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

Since: base-4.12.0.0

Instance details

Defined in Data.Monoid

Methods

minBound :: Ap f a Source #

maxBound :: Ap f a Source #

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

Since: base-4.12.0.0

Instance details

Defined in 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 #

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

Since: base-4.12.0.0

Instance details

Defined in Data.Monoid

Methods

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

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

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

Since: base-4.12.0.0

Instance details

Defined in Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> 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, 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

Instance details

Defined in 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 #

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

Since: base-4.12.0.0

Instance details

Defined in 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 #

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

Since: base-4.12.0.0

Instance details

Defined in Data.Monoid

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

Since: base-4.12.0.0

Instance details

Defined in Data.Monoid

Methods

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

show :: Ap f a -> String Source #

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

Generic (Ap f a) # 
Instance details

Defined in Data.Monoid

Associated Types

type Rep (Ap f a) :: Type -> Type Source #

Methods

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

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

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

Since: base-4.12.0.0

Instance details

Defined in Data.Monoid

Methods

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

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

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

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

Since: base-4.12.0.0

Instance details

Defined in Data.Monoid

Methods

mempty :: Ap f a Source #

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

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

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

Since: base-4.12.0.0

Instance details

Defined in Data.Monoid

type Rep1 (Ap f :: k -> Type) = D1 ('MetaData "Ap" "Data.Monoid" "base" '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

Instance details

Defined in Data.Monoid

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