Data.Monoid

Copyright	(c) Andy Gill 2001 (c) Oregon Graduate Institute of Science and Technology 2001
License	BSD-style (see the file libraries/base/LICENSE)
Maintainer	libraries@haskell.org
Stability	stable
Portability	portable
Safe Haskell	Trustworthy
Language	Haskell2010

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 {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 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 ByteArray Source	Since: base-4.17.0.0
Instance details Defined in Data.Array.Byte Methods mempty :: ByteArray Source mappend :: ByteArray -> ByteArray -> ByteArray Source mconcat :: [ByteArray] -> ByteArray Source
Monoid All Source	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: All Source mappend :: All -> All -> All Source mconcat :: [All] -> All Source
Monoid Any Source	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Any Source mappend :: Any -> Any -> Any Source mconcat :: [Any] -> Any Source
Monoid Event Source	Since: base-4.4.0.0
Instance details Defined in GHC.Event.Internal.Types Methods mempty :: Event Source mappend :: Event -> Event -> Event Source mconcat :: [Event] -> Event Source
Monoid Lifetime Source	`mappend` takes the longer of two lifetimes. Since: base-4.8.0.0
Instance details Defined in GHC.Event.Internal.Types Methods mempty :: Lifetime Source mappend :: Lifetime -> Lifetime -> Lifetime Source mconcat :: [Lifetime] -> Lifetime Source
Monoid Ordering Source	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: Ordering Source mappend :: Ordering -> Ordering -> Ordering Source mconcat :: [Ordering] -> Ordering Source
Monoid () Source	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: () Source mappend :: () -> () -> () Source mconcat :: [()] -> () Source
FiniteBits a => Monoid (And a) Source	This constraint is arguably too strong. However, as some types (such as `Natural`) have undefined `complement`, this is the only safe choice. Since: base-4.16
Instance details Defined in Data.Bits Methods mempty :: And a Source mappend :: And a -> And a -> And a Source mconcat :: [And a] -> And a Source
FiniteBits a => Monoid (Iff a) Source	This constraint is arguably too strong. However, as some types (such as `Natural`) have undefined `complement`, this is the only safe choice. Since: base-4.16
Instance details Defined in Data.Bits Methods mempty :: Iff a Source mappend :: Iff a -> Iff a -> Iff a Source mconcat :: [Iff a] -> Iff a Source
Bits a => Monoid (Ior a) Source	Since: base-4.16
Instance details Defined in Data.Bits Methods mempty :: Ior a Source mappend :: Ior a -> Ior a -> Ior a Source mconcat :: [Ior a] -> Ior a Source
Bits a => Monoid (Xor a) Source	Since: base-4.16
Instance details Defined in Data.Bits Methods mempty :: Xor a Source mappend :: Xor a -> Xor a -> Xor a Source mconcat :: [Xor a] -> Xor a Source
Monoid (Comparison a) Source	`mempty` on comparisons always returns `EQ`. Without newtypes this equals `pure (pure EQ)`. `mempty :: Comparison a mempty = Comparison _ _ -> EQ`
Instance details Defined in Data.Functor.Contravariant Methods mempty :: Comparison a Source mappend :: Comparison a -> Comparison a -> Comparison a Source mconcat :: [Comparison a] -> Comparison a Source
Monoid (Equivalence a) Source	`mempty` on equivalences always returns `True`. Without newtypes this equals `pure (pure True)`. `mempty :: Equivalence a mempty = Equivalence _ _ -> True`
Instance details Defined in Data.Functor.Contravariant Methods mempty :: Equivalence a Source mappend :: Equivalence a -> Equivalence a -> Equivalence a Source mconcat :: [Equivalence a] -> Equivalence a Source
Monoid (Predicate a) Source	`mempty` on predicates always returns `True`. Without newtypes this equals `pure True`. `mempty :: Predicate a mempty = _ -> True`
Instance details Defined in Data.Functor.Contravariant Methods mempty :: Predicate a Source mappend :: Predicate a -> Predicate a -> Predicate a Source mconcat :: [Predicate a] -> Predicate a Source
Monoid a => Monoid (Identity a) Source	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods mempty :: Identity a Source mappend :: Identity a -> Identity a -> Identity a Source mconcat :: [Identity a] -> Identity a Source
Monoid (First a) Source	Since: base-2.1
Instance details Defined in Data.Monoid Methods mempty :: First a Source mappend :: First a -> First a -> First a Source mconcat :: [First a] -> First a Source
Monoid (Last a) Source	Since: base-2.1
Instance details Defined in Data.Monoid Methods mempty :: Last a Source mappend :: Last a -> Last a -> Last a Source mconcat :: [Last a] -> Last a Source
Monoid a => Monoid (Down a) Source	Since: base-4.11.0.0
Instance details Defined in Data.Ord Methods mempty :: Down a Source mappend :: Down a -> Down a -> Down a Source mconcat :: [Down a] -> Down a Source
(Ord a, Bounded a) => Monoid (Max a) Source	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods mempty :: Max a Source mappend :: Max a -> Max a -> Max a Source mconcat :: [Max a] -> Max a Source
(Ord a, Bounded a) => Monoid (Min a) Source	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods mempty :: Min a Source mappend :: Min a -> Min a -> Min a Source mconcat :: [Min a] -> Min a Source
Monoid m => Monoid (WrappedMonoid m) Source	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods mempty :: WrappedMonoid m Source mappend :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m Source mconcat :: [WrappedMonoid m] -> WrappedMonoid m Source
Monoid a => Monoid (Dual a) Source	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Dual a Source mappend :: Dual a -> Dual a -> Dual a Source mconcat :: [Dual a] -> Dual a Source
Monoid (Endo a) Source	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Endo a Source mappend :: Endo a -> Endo a -> Endo a Source mconcat :: [Endo a] -> Endo a Source
Num a => Monoid (Product a) Source	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Product a Source mappend :: Product a -> Product a -> Product a Source mconcat :: [Product a] -> Product a Source
Num a => Monoid (Sum a) Source	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Sum a Source mappend :: Sum a -> Sum a -> Sum a Source mconcat :: [Sum a] -> Sum a Source
Monoid a => Monoid (STM a) Source	Since: base-4.17.0.0
Instance details Defined in GHC.Conc.Sync Methods mempty :: STM a Source mappend :: STM a -> STM a -> STM a Source mconcat :: [STM a] -> STM a Source
(Generic a, Monoid (Rep a ())) => Monoid (Generically a) Source	Since: base-4.17.0.0
Instance details Defined in GHC.Generics Methods mempty :: Generically a Source mappend :: Generically a -> Generically a -> Generically a Source mconcat :: [Generically a] -> Generically a Source
Monoid p => Monoid (Par1 p) Source	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods mempty :: Par1 p Source mappend :: Par1 p -> Par1 p -> Par1 p Source mconcat :: [Par1 p] -> Par1 p Source
Monoid a => Monoid (IO a) Source	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods mempty :: IO a Source mappend :: IO a -> IO a -> IO a Source mconcat :: [IO a] -> IO a Source
Semigroup a => Monoid (Maybe a) Source	Lift a semigroup into `Maybe` forming a `Monoid` according to http://en.wikipedia.org/wiki/Monoid: "Any semigroup `S` may be turned into a monoid simply by adjoining an element `e` not in `S` and defining `ee = e` and `es = s = s*e` for all `s ∈ S`." Since 4.11.0: constraint on inner `a` value generalised from `Monoid` to `Semigroup`. Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: Maybe a Source mappend :: Maybe a -> Maybe a -> Maybe a Source mconcat :: [Maybe a] -> Maybe a Source
Monoid a => Monoid (a) Source	Since: base-4.15
Instance details Defined in GHC.Base Methods mempty :: (a) Source mappend :: (a) -> (a) -> (a) Source mconcat :: [(a)] -> (a) Source
Monoid [a] Source	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: [a] Source mappend :: [a] -> [a] -> [a] Source mconcat :: [[a]] -> [a] Source
Monoid a => Monoid (Op a b) Source	`mempty @(Op a b)` without newtypes is `mempty @(b->a)` = `_ -> mempty`. `mempty :: Op a b mempty = Op _ -> mempty`
Instance details Defined in Data.Functor.Contravariant Methods mempty :: Op a b Source mappend :: Op a b -> Op a b -> Op a b Source mconcat :: [Op a b] -> Op a b Source
Monoid (Proxy s) Source	Since: base-4.7.0.0
Instance details Defined in Data.Proxy Methods mempty :: Proxy s Source mappend :: Proxy s -> Proxy s -> Proxy s Source mconcat :: [Proxy s] -> Proxy s Source
Monoid (U1 p) Source	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods mempty :: U1 p Source mappend :: U1 p -> U1 p -> U1 p Source mconcat :: [U1 p] -> U1 p Source
Monoid a => Monoid (ST s a) Source	Since: base-4.11.0.0
Instance details Defined in GHC.ST Methods mempty :: ST s a Source mappend :: ST s a -> ST s a -> ST s a Source mconcat :: [ST s a] -> ST s a Source
Monoid b => Monoid (a -> b) Source	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: a -> b Source mappend :: (a -> b) -> (a -> b) -> a -> b Source mconcat :: [a -> b] -> a -> b Source
(Monoid a, Monoid b) => Monoid (a, b) Source	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: (a, b) Source mappend :: (a, b) -> (a, b) -> (a, b) Source mconcat :: [(a, b)] -> (a, b) Source
Monoid a => Monoid (Const a b) Source	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods mempty :: Const a b Source mappend :: Const a b -> Const a b -> Const a b Source mconcat :: [Const a b] -> Const a b Source
(Applicative f, Monoid a) => Monoid (Ap f a) Source	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods mempty :: Ap f a Source mappend :: Ap f a -> Ap f a -> Ap f a Source mconcat :: [Ap f a] -> Ap f a Source
Alternative f => Monoid (Alt f a) Source	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Alt f a Source mappend :: Alt f a -> Alt f a -> Alt f a Source mconcat :: [Alt f a] -> Alt f a Source
Monoid (f p) => Monoid (Rec1 f p) Source	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods mempty :: Rec1 f p Source mappend :: Rec1 f p -> Rec1 f p -> Rec1 f p Source mconcat :: [Rec1 f p] -> Rec1 f p Source
(Monoid a, Monoid b, Monoid c) => Monoid (a, b, c) Source	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: (a, b, c) Source mappend :: (a, b, c) -> (a, b, c) -> (a, b, c) Source mconcat :: [(a, b, c)] -> (a, b, c) Source
(Monoid (f a), Monoid (g a)) => Monoid (Product f g a) Source	Since: base-4.16.0.0
Instance details Defined in Data.Functor.Product Methods mempty :: Product f g a Source mappend :: Product f g a -> Product f g a -> Product f g a Source mconcat :: [Product f g a] -> Product f g a Source
(Monoid (f p), Monoid (g p)) => Monoid ((f :*: g) p) Source	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods mempty :: (f :: g) p Source mappend :: (f :: g) p -> (f :: g) p -> (f :: g) p Source mconcat :: [(f :: g) p] -> (f :: g) p Source
Monoid c => Monoid (K1 i c p) Source	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods mempty :: K1 i c p Source mappend :: K1 i c p -> K1 i c p -> K1 i c p Source mconcat :: [K1 i c p] -> K1 i c p Source
(Monoid a, Monoid b, Monoid c, Monoid d) => Monoid (a, b, c, d) Source	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: (a, b, c, d) Source mappend :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) Source mconcat :: [(a, b, c, d)] -> (a, b, c, d) Source
Monoid (f (g a)) => Monoid (Compose f g a) Source	Since: base-4.16.0.0
Instance details Defined in Data.Functor.Compose Methods mempty :: Compose f g a Source mappend :: Compose f g a -> Compose f g a -> Compose f g a Source mconcat :: [Compose f g a] -> Compose f g a Source
Monoid (f (g p)) => Monoid ((f :.: g) p) Source	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods mempty :: (f :.: g) p Source mappend :: (f :.: g) p -> (f :.: g) p -> (f :.: g) p Source mconcat :: [(f :.: g) p] -> (f :.: g) p Source
Monoid (f p) => Monoid (M1 i c f p) Source	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods mempty :: M1 i c f p Source mappend :: M1 i c f p -> M1 i c f p -> M1 i c f p Source mconcat :: [M1 i c f p] -> M1 i c f p Source
(Monoid a, Monoid b, Monoid c, Monoid d, Monoid e) => Monoid (a, b, c, d, e) Source	Since: base-2.1
Instance details Defined in GHC.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 getDual :: a

Instances

Instances details

MonadFix Dual Source	Since: base-4.8.0.0
Instance details Defined in Control.Monad.Fix Methods mfix :: (a -> Dual a) -> Dual a Source
MonadZip Dual Source	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
Foldable Dual Source	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 Source	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
Applicative Dual Source	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods pure :: a -> Dual a Source (<>) :: Dual (a -> b) -> Dual a -> Dual b Source liftA2 :: (a -> b -> c) -> Dual a -> Dual b -> Dual c Source (>) :: Dual a -> Dual b -> Dual b Source (<*) :: Dual a -> Dual b -> Dual a Source
Functor Dual Source	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods fmap :: (a -> b) -> Dual a -> Dual b Source (<$) :: a -> Dual b -> Dual a Source
Monad Dual Source	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods (>>=) :: Dual a -> (a -> Dual b) -> Dual b Source (>>) :: Dual a -> Dual b -> Dual b Source return :: a -> Dual a Source
Generic1 Dual Source
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
Data a => Data (Dual a) Source	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
Monoid a => Monoid (Dual a) Source	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Dual a Source mappend :: Dual a -> Dual a -> Dual a Source mconcat :: [Dual a] -> Dual a Source
Semigroup a => Semigroup (Dual a) Source	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Dual a -> Dual a -> Dual a Source sconcat :: NonEmpty (Dual a) -> Dual a Source stimes :: Integral b => b -> Dual a -> Dual a Source
Bounded a => Bounded (Dual a) Source	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods minBound :: Dual a Source maxBound :: Dual a Source
Generic (Dual a) Source
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
Read a => Read (Dual a) Source	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods readsPrec :: Int -> ReadS (Dual a) Source readList :: ReadS [Dual a] Source readPrec :: ReadPrec (Dual a) Source readListPrec :: ReadPrec [Dual a] Source
Show a => Show (Dual a) Source	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods showsPrec :: Int -> Dual a -> ShowS Source show :: Dual a -> String Source showList :: [Dual a] -> ShowS Source
Eq a => Eq (Dual a) Source	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods (==) :: Dual a -> Dual a -> Bool Source (/=) :: Dual a -> Dual a -> Bool Source
Ord a => Ord (Dual a) Source	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods compare :: Dual a -> Dual a -> Ordering Source (<) :: Dual a -> Dual a -> Bool Source (<=) :: Dual a -> Dual a -> Bool Source (>) :: Dual a -> Dual a -> Bool Source (>=) :: Dual a -> Dual a -> Bool Source max :: Dual a -> Dual a -> Dual a Source min :: Dual a -> Dual a -> Dual a Source
type Rep1 Dual Source	Since: base-4.7.0.0
Instance details Defined in 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))
type Rep (Dual a) Source	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)))

newtype Endo a Source

The monoid of endomorphisms under composition.

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

Constructors

Endo
Fields appEndo :: a -> a

Instances

Instances details

Monoid (Endo a) Source	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Endo a Source mappend :: Endo a -> Endo a -> Endo a Source mconcat :: [Endo a] -> Endo a Source
Semigroup (Endo a) Source	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Endo a -> Endo a -> Endo a Source sconcat :: NonEmpty (Endo a) -> Endo a Source stimes :: Integral b => b -> Endo a -> Endo a Source
Generic (Endo a) Source
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
type Rep (Endo a) Source	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 getAll :: Bool

Instances

Instances details

Data All Source	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
Monoid All Source	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: All Source mappend :: All -> All -> All Source mconcat :: [All] -> All Source
Semigroup All Source	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: All -> All -> All Source sconcat :: NonEmpty All -> All Source stimes :: Integral b => b -> All -> All Source
Bounded All Source	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods minBound :: All Source maxBound :: All Source
Generic All Source
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
Read All Source	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods readsPrec :: Int -> ReadS All Source readList :: ReadS [All] Source readPrec :: ReadPrec All Source readListPrec :: ReadPrec [All] Source
Show All Source	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods showsPrec :: Int -> All -> ShowS Source show :: All -> String Source showList :: [All] -> ShowS Source
Eq All Source	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods (==) :: All -> All -> Bool Source (/=) :: All -> All -> Bool Source
Ord All Source	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
type Rep All Source	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 getAny :: Bool

Instances

Instances details

Data Any Source	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
Monoid Any Source	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Any Source mappend :: Any -> Any -> Any Source mconcat :: [Any] -> Any Source
Semigroup Any Source	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Any -> Any -> Any Source sconcat :: NonEmpty Any -> Any Source stimes :: Integral b => b -> Any -> Any Source
Bounded Any Source	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods minBound :: Any Source maxBound :: Any Source
Generic Any Source
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
Read Any Source	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods readsPrec :: Int -> ReadS Any Source readList :: ReadS [Any] Source readPrec :: ReadPrec Any Source readListPrec :: ReadPrec [Any] Source
Show Any Source	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods showsPrec :: Int -> Any -> ShowS Source show :: Any -> String Source showList :: [Any] -> ShowS Source
Eq Any Source	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods (==) :: Any -> Any -> Bool Source (/=) :: Any -> Any -> Bool Source
Ord Any Source	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
type Rep Any Source	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 getSum :: a

Instances

Instances details

MonadFix Sum Source	Since: base-4.8.0.0
Instance details Defined in Control.Monad.Fix Methods mfix :: (a -> Sum a) -> Sum a Source
MonadZip Sum Source	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
Foldable Sum Source	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 Source	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
Applicative Sum Source	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods pure :: a -> Sum a Source (<>) :: Sum (a -> b) -> Sum a -> Sum b Source liftA2 :: (a -> b -> c) -> Sum a -> Sum b -> Sum c Source (>) :: Sum a -> Sum b -> Sum b Source (<*) :: Sum a -> Sum b -> Sum a Source
Functor Sum Source	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods fmap :: (a -> b) -> Sum a -> Sum b Source (<$) :: a -> Sum b -> Sum a Source
Monad Sum Source	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods (>>=) :: Sum a -> (a -> Sum b) -> Sum b Source (>>) :: Sum a -> Sum b -> Sum b Source return :: a -> Sum a Source
Generic1 Sum Source
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
Data a => Data (Sum a) Source	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 => Monoid (Sum a) Source	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Sum a Source mappend :: Sum a -> Sum a -> Sum a Source mconcat :: [Sum a] -> Sum a Source
Num a => Semigroup (Sum a) Source	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Sum a -> Sum a -> Sum a Source sconcat :: NonEmpty (Sum a) -> Sum a Source stimes :: Integral b => b -> Sum a -> Sum a Source
Bounded a => Bounded (Sum a) Source	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods minBound :: Sum a Source maxBound :: Sum a Source
Generic (Sum a) Source
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 => Num (Sum a) Source	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
Read a => Read (Sum a) Source	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods readsPrec :: Int -> ReadS (Sum a) Source readList :: ReadS [Sum a] Source readPrec :: ReadPrec (Sum a) Source readListPrec :: ReadPrec [Sum a] Source
Show a => Show (Sum a) Source	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods showsPrec :: Int -> Sum a -> ShowS Source show :: Sum a -> String Source showList :: [Sum a] -> ShowS Source
Eq a => Eq (Sum a) Source	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods (==) :: Sum a -> Sum a -> Bool Source (/=) :: Sum a -> Sum a -> Bool Source
Ord a => Ord (Sum a) Source	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods compare :: Sum a -> Sum a -> Ordering Source (<) :: Sum a -> Sum a -> Bool Source (<=) :: Sum a -> Sum a -> Bool Source (>) :: Sum a -> Sum a -> Bool Source (>=) :: Sum a -> Sum a -> Bool Source max :: Sum a -> Sum a -> Sum a Source min :: Sum a -> Sum a -> Sum a Source
type Rep1 Sum Source	Since: base-4.7.0.0
Instance details Defined in 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))
type Rep (Sum a) Source	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)))

newtype Product a Source

Monoid under multiplication.

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

Constructors

Product
Fields getProduct :: a

Instances

Instances details

MonadFix Product Source	Since: base-4.8.0.0
Instance details Defined in Control.Monad.Fix Methods mfix :: (a -> Product a) -> Product a Source
MonadZip Product Source	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
Foldable Product Source	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 Source	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
Applicative Product Source	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods pure :: a -> Product a Source (<>) :: Product (a -> b) -> Product a -> Product b Source liftA2 :: (a -> b -> c) -> Product a -> Product b -> Product c Source (>) :: Product a -> Product b -> Product b Source (<*) :: Product a -> Product b -> Product a Source
Functor Product Source	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods fmap :: (a -> b) -> Product a -> Product b Source (<$) :: a -> Product b -> Product a Source
Monad Product Source	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods (>>=) :: Product a -> (a -> Product b) -> Product b Source (>>) :: Product a -> Product b -> Product b Source return :: a -> Product a Source
Generic1 Product Source
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
Data a => Data (Product a) Source	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 => Monoid (Product a) Source	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Product a Source mappend :: Product a -> Product a -> Product a Source mconcat :: [Product a] -> Product a Source
Num a => Semigroup (Product a) Source	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Product a -> Product a -> Product a Source sconcat :: NonEmpty (Product a) -> Product a Source stimes :: Integral b => b -> Product a -> Product a Source
Bounded a => Bounded (Product a) Source	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods minBound :: Product a Source maxBound :: Product a Source
Generic (Product a) Source
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 => Num (Product a) Source	Since: base-4.7.0.0
Instance details Defined in Data.Semigroup.Internal Methods (+) :: Product a -> Product a -> Product a Source (-) :: Product a -> Product a -> Product a Source (*) :: Product a -> Product a -> Product a Source negate :: Product a -> Product a Source abs :: Product a -> Product a Source signum :: Product a -> Product a Source fromInteger :: Integer -> Product a Source
Read a => Read (Product a) Source	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods readsPrec :: Int -> ReadS (Product a) Source readList :: ReadS [Product a] Source readPrec :: ReadPrec (Product a) Source readListPrec :: ReadPrec [Product a] Source
Show a => Show (Product a) Source	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods showsPrec :: Int -> Product a -> ShowS Source show :: Product a -> String Source showList :: [Product a] -> ShowS Source
Eq a => Eq (Product a) Source	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods (==) :: Product a -> Product a -> Bool Source (/=) :: Product a -> Product a -> Bool Source
Ord a => Ord (Product a) Source	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods compare :: Product a -> Product a -> Ordering Source (<) :: Product a -> Product a -> Bool Source (<=) :: Product a -> Product a -> Bool Source (>) :: Product a -> Product a -> Bool Source (>=) :: Product a -> Product a -> Bool Source max :: Product a -> Product a -> Product a Source min :: Product a -> Product a -> Product a Source
type Rep1 Product Source	Since: base-4.7.0.0
Instance details Defined in 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))
type Rep (Product a) Source	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)))

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"

Constructors

First
Fields getFirst :: Maybe a

Instances

Instances details

MonadFix First Source	Since: base-4.8.0.0
Instance details Defined in Control.Monad.Fix Methods mfix :: (a -> First a) -> First a Source
MonadZip First Source	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
Foldable First Source	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 Source	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
Applicative First Source	Since: base-4.8.0.0
Instance details Defined in Data.Monoid Methods pure :: a -> First a Source (<>) :: First (a -> b) -> First a -> First b Source liftA2 :: (a -> b -> c) -> First a -> First b -> First c Source (>) :: First a -> First b -> First b Source (<*) :: First a -> First b -> First a Source
Functor First Source	Since: base-4.8.0.0
Instance details Defined in Data.Monoid Methods fmap :: (a -> b) -> First a -> First b Source (<$) :: a -> First b -> First a Source
Monad First Source	Since: base-4.8.0.0
Instance details Defined in Data.Monoid Methods (>>=) :: First a -> (a -> First b) -> First b Source (>>) :: First a -> First b -> First b Source return :: a -> First a Source
Generic1 First Source
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
Data a => Data (First a) Source	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
Monoid (First a) Source	Since: base-2.1
Instance details Defined in Data.Monoid Methods mempty :: First a Source mappend :: First a -> First a -> First a Source mconcat :: [First a] -> First a Source
Semigroup (First a) Source	Since: base-4.9.0.0
Instance details Defined in Data.Monoid Methods (<>) :: First a -> First a -> First a Source sconcat :: NonEmpty (First a) -> First a Source stimes :: Integral b => b -> First a -> First a Source
Generic (First a) Source
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
Read a => Read (First a) Source	Since: base-2.1
Instance details Defined in Data.Monoid Methods readsPrec :: Int -> ReadS (First a) Source readList :: ReadS [First a] Source readPrec :: ReadPrec (First a) Source readListPrec :: ReadPrec [First a] Source
Show a => Show (First a) Source	Since: base-2.1
Instance details Defined in Data.Monoid Methods showsPrec :: Int -> First a -> ShowS Source show :: First a -> String Source showList :: [First a] -> ShowS Source
Eq a => Eq (First a) Source	Since: base-2.1
Instance details Defined in Data.Monoid Methods (==) :: First a -> First a -> Bool Source (/=) :: First a -> First a -> Bool Source
Ord a => Ord (First a) Source	Since: base-2.1
Instance details Defined in Data.Monoid Methods compare :: First a -> First a -> Ordering Source (<) :: First a -> First a -> Bool Source (<=) :: First a -> First a -> Bool Source (>) :: First a -> First a -> Bool Source (>=) :: First a -> First a -> Bool Source max :: First a -> First a -> First a Source min :: First a -> First a -> First a Source
type Rep1 First Source	Since: base-4.7.0.0
Instance details Defined in 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)))
type Rep (First a) Source	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))))

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"

Constructors

Last
Fields getLast :: Maybe a

Instances

Instances details

MonadFix Last Source	Since: base-4.8.0.0
Instance details Defined in Control.Monad.Fix Methods mfix :: (a -> Last a) -> Last a Source
MonadZip Last Source	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
Foldable Last Source	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 Source	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
Applicative Last Source	Since: base-4.8.0.0
Instance details Defined in Data.Monoid Methods pure :: a -> Last a Source (<>) :: Last (a -> b) -> Last a -> Last b Source liftA2 :: (a -> b -> c) -> Last a -> Last b -> Last c Source (>) :: Last a -> Last b -> Last b Source (<*) :: Last a -> Last b -> Last a Source
Functor Last Source	Since: base-4.8.0.0
Instance details Defined in Data.Monoid Methods fmap :: (a -> b) -> Last a -> Last b Source (<$) :: a -> Last b -> Last a Source
Monad Last Source	Since: base-4.8.0.0
Instance details Defined in Data.Monoid Methods (>>=) :: Last a -> (a -> Last b) -> Last b Source (>>) :: Last a -> Last b -> Last b Source return :: a -> Last a Source
Generic1 Last Source
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
Data a => Data (Last a) Source	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
Monoid (Last a) Source	Since: base-2.1
Instance details Defined in Data.Monoid Methods mempty :: Last a Source mappend :: Last a -> Last a -> Last a Source mconcat :: [Last a] -> Last a Source
Semigroup (Last a) Source	Since: base-4.9.0.0
Instance details Defined in Data.Monoid Methods (<>) :: Last a -> Last a -> Last a Source sconcat :: NonEmpty (Last a) -> Last a Source stimes :: Integral b => b -> Last a -> Last a Source
Generic (Last a) Source
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
Read a => Read (Last a) Source	Since: base-2.1
Instance details Defined in Data.Monoid Methods readsPrec :: Int -> ReadS (Last a) Source readList :: ReadS [Last a] Source readPrec :: ReadPrec (Last a) Source readListPrec :: ReadPrec [Last a] Source
Show a => Show (Last a) Source	Since: base-2.1
Instance details Defined in Data.Monoid Methods showsPrec :: Int -> Last a -> ShowS Source show :: Last a -> String Source showList :: [Last a] -> ShowS Source
Eq a => Eq (Last a) Source	Since: base-2.1
Instance details Defined in Data.Monoid Methods (==) :: Last a -> Last a -> Bool Source (/=) :: Last a -> Last a -> Bool Source
Ord a => Ord (Last a) Source	Since: base-2.1
Instance details Defined in Data.Monoid Methods compare :: Last a -> Last a -> Ordering Source (<) :: Last a -> Last a -> Bool Source (<=) :: Last a -> Last a -> Bool Source (>) :: Last a -> Last a -> Bool Source (>=) :: Last a -> Last a -> Bool Source max :: Last a -> Last a -> Last a Source min :: Last a -> Last a -> Last a Source
type Rep1 Last Source	Since: base-4.7.0.0
Instance details Defined in 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)))
type Rep (Last a) Source	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))))

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 getAlt :: f a

Instances

Instances details

Generic1 (Alt f :: k -> Type) Source
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
MonadFix f => MonadFix (Alt f) Source	Since: base-4.8.0.0
Instance details Defined in Control.Monad.Fix Methods mfix :: (a -> Alt f a) -> Alt f a Source
MonadZip f => MonadZip (Alt f) Source	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
Foldable f => Foldable (Alt f) Source	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
Contravariant f => Contravariant (Alt f) Source
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a' -> a) -> Alt f a -> Alt f a' Source (>$) :: b -> Alt f b -> Alt f a Source
Traversable f => Traversable (Alt f) Source	Since: base-4.12.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> Alt f a -> f0 (Alt f b) Source sequenceA :: Applicative f0 => Alt f (f0 a) -> f0 (Alt f a) Source mapM :: Monad m => (a -> m b) -> Alt f a -> m (Alt f b) Source sequence :: Monad m => Alt f (m a) -> m (Alt f a) Source
Alternative f => Alternative (Alt f) Source	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods empty :: Alt f a Source (<\|>) :: Alt f a -> Alt f a -> Alt f a Source some :: Alt f a -> Alt f [a] Source many :: Alt f a -> Alt f [a] Source
Applicative f => Applicative (Alt f) Source	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods pure :: a -> Alt f a Source (<>) :: Alt f (a -> b) -> Alt f a -> Alt f b Source liftA2 :: (a -> b -> c) -> Alt f a -> Alt f b -> Alt f c Source (>) :: Alt f a -> Alt f b -> Alt f b Source (<*) :: Alt f a -> Alt f b -> Alt f a Source
Functor f => Functor (Alt f) Source	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods fmap :: (a -> b) -> Alt f a -> Alt f b Source (<$) :: a -> Alt f b -> Alt f a Source
Monad f => Monad (Alt f) Source	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods (>>=) :: Alt f a -> (a -> Alt f b) -> Alt f b Source (>>) :: Alt f a -> Alt f b -> Alt f b Source return :: a -> Alt f a Source
MonadPlus f => MonadPlus (Alt f) Source	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods mzero :: Alt f a Source mplus :: Alt f a -> Alt f a -> Alt f a Source
(Data (f a), Data a, Typeable f) => Data (Alt f a) Source	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
Alternative f => Monoid (Alt f a) Source	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Alt f a Source mappend :: Alt f a -> Alt f a -> Alt f a Source mconcat :: [Alt f a] -> Alt f a Source
Alternative f => Semigroup (Alt f a) Source	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Alt f a -> Alt f a -> Alt f a Source sconcat :: NonEmpty (Alt f a) -> Alt f a Source stimes :: Integral b => b -> Alt f a -> Alt f a Source
Enum (f a) => Enum (Alt f a) Source	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
Generic (Alt f a) Source
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
Num (f a) => Num (Alt f a) Source	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
Read (f a) => Read (Alt f a) Source	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods readsPrec :: Int -> ReadS (Alt f a) Source readList :: ReadS [Alt f a] Source readPrec :: ReadPrec (Alt f a) Source readListPrec :: ReadPrec [Alt f a] Source
Show (f a) => Show (Alt f a) Source	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods showsPrec :: Int -> Alt f a -> ShowS Source show :: Alt f a -> String Source showList :: [Alt f a] -> ShowS Source
Eq (f a) => Eq (Alt f a) Source	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods (==) :: Alt f a -> Alt f a -> Bool Source (/=) :: Alt f a -> Alt f a -> Bool Source
Ord (f a) => Ord (Alt f a) Source	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods compare :: Alt f a -> Alt f a -> Ordering Source (<) :: Alt f a -> Alt f a -> Bool Source (<=) :: Alt f a -> Alt f a -> Bool Source (>) :: Alt f a -> Alt f a -> Bool Source (>=) :: Alt f a -> Alt f a -> Bool Source max :: Alt f a -> Alt f a -> Alt f a Source min :: Alt f a -> Alt f a -> Alt f a Source
type Rep1 (Alt f :: k -> Type) Source	Since: base-4.8.0.0
Instance details Defined in 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) Source	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 getAp :: f a

Instances

Instances details

Generic1 (Ap f :: k -> Type) Source
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
MonadFail f => MonadFail (Ap f) Source	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods fail :: String -> Ap f a Source
MonadFix f => MonadFix (Ap f) Source	Since: base-4.12.0.0
Instance details Defined in Control.Monad.Fix Methods mfix :: (a -> Ap f a) -> Ap f a Source
Foldable f => Foldable (Ap f) Source	Since: base-4.12.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => Ap f m -> m Source foldMap :: Monoid m => (a -> m) -> Ap f a -> m Source foldMap' :: Monoid m => (a -> m) -> Ap f a -> m Source foldr :: (a -> b -> b) -> b -> Ap f a -> b Source foldr' :: (a -> b -> b) -> b -> Ap f a -> b Source foldl :: (b -> a -> b) -> b -> Ap f a -> b Source foldl' :: (b -> a -> b) -> b -> Ap f a -> b Source foldr1 :: (a -> a -> a) -> Ap f a -> a Source foldl1 :: (a -> a -> a) -> Ap f a -> a Source toList :: Ap f a -> [a] Source null :: Ap f a -> Bool Source length :: Ap f a -> Int Source elem :: Eq a => a -> Ap f a -> Bool Source maximum :: Ord a => Ap f a -> a Source minimum :: Ord a => Ap f a -> a Source sum :: Num a => Ap f a -> a Source product :: Num a => Ap f a -> a Source
Traversable f => Traversable (Ap f) Source	Since: base-4.12.0.0
Instance details Defined in 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
Alternative f => Alternative (Ap f) Source	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods empty :: Ap f a Source (<\|>) :: Ap f a -> Ap f a -> Ap f a Source some :: Ap f a -> Ap f [a] Source many :: Ap f a -> Ap f [a] Source
Applicative f => Applicative (Ap f) Source	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods pure :: a -> Ap f a Source (<>) :: Ap f (a -> b) -> Ap f a -> Ap f b Source liftA2 :: (a -> b -> c) -> Ap f a -> Ap f b -> Ap f c Source (>) :: Ap f a -> Ap f b -> Ap f b Source (<*) :: Ap f a -> Ap f b -> Ap f a Source
Functor f => Functor (Ap f) Source	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods fmap :: (a -> b) -> Ap f a -> Ap f b Source (<$) :: a -> Ap f b -> Ap f a Source
Monad f => Monad (Ap f) Source	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods (>>=) :: Ap f a -> (a -> Ap f b) -> Ap f b Source (>>) :: Ap f a -> Ap f b -> Ap f b Source return :: a -> Ap f a Source
MonadPlus f => MonadPlus (Ap f) Source	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods mzero :: Ap f a Source mplus :: Ap f a -> Ap f a -> Ap f a Source
(Data (f a), Data a, Typeable f) => Data (Ap f a) Source	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, Monoid a) => Monoid (Ap f a) Source	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods mempty :: Ap f a Source mappend :: Ap f a -> Ap f a -> Ap f a Source mconcat :: [Ap f a] -> Ap f a Source
(Applicative f, Semigroup a) => Semigroup (Ap f a) Source	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods (<>) :: Ap f a -> Ap f a -> Ap f a Source sconcat :: NonEmpty (Ap f a) -> Ap f a Source stimes :: Integral b => b -> Ap f a -> Ap f a Source
(Applicative f, Bounded a) => Bounded (Ap f a) Source	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) Source	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
Generic (Ap f a) Source
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, Num a) => Num (Ap f a) Source	Note that even if the underlying `Num` and `Applicative` instances are lawful, for most `Applicative`s, 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
Read (f a) => Read (Ap f a) Source	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods readsPrec :: Int -> ReadS (Ap f a) Source readList :: ReadS [Ap f a] Source readPrec :: ReadPrec (Ap f a) Source readListPrec :: ReadPrec [Ap f a] Source
Show (f a) => Show (Ap f a) Source	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods showsPrec :: Int -> Ap f a -> ShowS Source show :: Ap f a -> String Source showList :: [Ap f a] -> ShowS Source
Eq (f a) => Eq (Ap f a) Source	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods (==) :: Ap f a -> Ap f a -> Bool Source (/=) :: Ap f a -> Ap f a -> Bool Source
Ord (f a) => Ord (Ap f a) Source	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods compare :: Ap f a -> Ap f a -> Ordering Source (<) :: Ap f a -> Ap f a -> Bool Source (<=) :: Ap f a -> Ap f a -> Bool Source (>) :: Ap f a -> Ap f a -> Bool Source (>=) :: Ap f a -> Ap f a -> Bool Source max :: Ap f a -> Ap f a -> Ap f a Source min :: Ap f a -> Ap f a -> Ap f a Source
type Rep1 (Ap f :: k -> Type) Source	Since: base-4.12.0.0
Instance details Defined in 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) Source	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))))

© The University of Glasgow and others
Licensed under a BSD-style license (see top of the page).
https://downloads.haskell.org/~ghc/9.4.2/docs/libraries/base-4.17.0.0/Data-Monoid.html

Data.Monoid

Contents

Description

Examples

Monoid typeclass

Minimal complete definition

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Methods

Methods

Methods

Methods

Methods

Methods

Methods

Methods

Methods

Methods

Methods

Methods

Methods

Methods

Methods

Methods

Methods

Methods

Methods

Methods

Methods

Methods

Constructors

Fields

Instances

Methods

Methods

Methods

Methods

Methods

Methods

Methods

Associated Types

Methods

Methods

Methods

Methods

Methods

Associated Types

Methods

Methods

Methods

Methods