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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
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 newtype
s 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
Methods
Identity of mappend
>>> "Hello world" <> mempty
"Hello world"
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
.
Fold a list using the monoid.
For most types, the default definition for mconcat
will be used, but the function is included in the class definition so that an optimized version can be provided for specific types.
>>> mconcat ["Hello", " ", "Haskell", "!"]
"Hello Haskell!"
Instances
Monoid ByteArray Source | Since: base-4.17.0.0 |
Monoid All Source | Since: base-2.1 |
Monoid Any Source | Since: base-2.1 |
Monoid Event Source | Since: base-4.4.0.0 |
Monoid Lifetime Source |
Since: base-4.8.0.0 |
Monoid Ordering Source | Since: base-2.1 |
Monoid () Source | Since: base-2.1 |
FiniteBits a => Monoid (And a) Source | This constraint is arguably too strong. However, as some types (such as Since: base-4.16 |
FiniteBits a => Monoid (Iff a) Source | This constraint is arguably too strong. However, as some types (such as Since: base-4.16 |
Bits a => Monoid (Ior a) Source | Since: base-4.16 |
Bits a => Monoid (Xor a) Source | Since: base-4.16 |
Monoid (Comparison a) Source |
|
Defined in Data.Functor.Contravariant Methodsmempty :: Comparison a Source mappend :: Comparison a -> Comparison a -> Comparison a Source mconcat :: [Comparison a] -> Comparison a Source |
|
Monoid (Equivalence a) Source |
|
Defined in Data.Functor.Contravariant Methodsmempty :: Equivalence a Source mappend :: Equivalence a -> Equivalence a -> Equivalence a Source mconcat :: [Equivalence a] -> Equivalence a Source |
|
Monoid (Predicate a) Source |
|
Monoid a => Monoid (Identity a) Source | Since: base-4.9.0.0 |
Monoid (First a) Source | Since: base-2.1 |
Monoid (Last a) Source | Since: base-2.1 |
Monoid a => Monoid (Down a) Source | Since: base-4.11.0.0 |
(Ord a, Bounded a) => Monoid (Max a) Source | Since: base-4.9.0.0 |
(Ord a, Bounded a) => Monoid (Min a) Source | Since: base-4.9.0.0 |
Monoid m => Monoid (WrappedMonoid m) Source | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methodsmempty :: 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 |
Monoid (Endo a) Source | Since: base-2.1 |
Num a => Monoid (Product a) Source | Since: base-2.1 |
Num a => Monoid (Sum a) Source | Since: base-2.1 |
Monoid a => Monoid (STM a) Source | Since: base-4.17.0.0 |
(Generic a, Monoid (Rep a ())) => Monoid (Generically a) Source | Since: base-4.17.0.0 |
Defined in GHC.Generics Methodsmempty :: 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 |
Monoid a => Monoid (IO a) Source | Since: base-4.9.0.0 |
Semigroup a => Monoid (Maybe a) Source | Lift a semigroup into Since 4.11.0: constraint on inner Since: base-2.1 |
Monoid a => Monoid (a) Source | Since: base-4.15 |
Monoid [a] Source | Since: base-2.1 |
Monoid a => Monoid (Op a b) Source |
|
Monoid (Proxy s) Source | Since: base-4.7.0.0 |
Monoid (U1 p) Source | Since: base-4.12.0.0 |
Monoid a => Monoid (ST s a) Source | Since: base-4.11.0.0 |
Monoid b => Monoid (a -> b) Source | Since: base-2.1 |
(Monoid a, Monoid b) => Monoid (a, b) Source | Since: base-2.1 |
Monoid a => Monoid (Const a b) Source | Since: base-4.9.0.0 |
(Applicative f, Monoid a) => Monoid (Ap f a) Source | Since: base-4.12.0.0 |
Alternative f => Monoid (Alt f a) Source | Since: base-4.8.0.0 |
Monoid (f p) => Monoid (Rec1 f p) Source | Since: base-4.12.0.0 |
(Monoid a, Monoid b, Monoid c) => Monoid (a, b, c) Source | Since: base-2.1 |
(Monoid (f a), Monoid (g a)) => Monoid (Product f g a) Source | Since: base-4.16.0.0 |
(Monoid (f p), Monoid (g p)) => Monoid ((f :*: g) p) Source | Since: base-4.12.0.0 |
Monoid c => Monoid (K1 i c p) Source | Since: base-4.12.0.0 |
(Monoid a, Monoid b, Monoid c, Monoid d) => Monoid (a, b, c, d) Source | Since: base-2.1 |
Monoid (f (g a)) => Monoid (Compose f g a) Source | Since: base-4.16.0.0 |
Monoid (f (g p)) => Monoid ((f :.: g) p) Source | Since: base-4.12.0.0 |
Monoid (f p) => Monoid (M1 i c f p) Source | Since: base-4.12.0.0 |
(Monoid a, Monoid b, Monoid c, Monoid d, Monoid e) => Monoid (a, b, c, d, e) Source | Since: base-2.1 |
(<>) :: Semigroup a => a -> a -> a infixr 6 Source
An associative operation.
>>> [1,2,3] <> [4,5,6]
[1,2,3,4,5,6]
The dual of a Monoid
, obtained by swapping the arguments of mappend
.
>>> getDual (mappend (Dual "Hello") (Dual "World"))
"WorldHello"
Instances
MonadFix Dual Source | Since: base-4.8.0.0 |
Defined in Control.Monad.Fix |
|
MonadZip Dual Source | Since: base-4.8.0.0 |
Foldable Dual Source | Since: base-4.8.0.0 |
Defined in Data.Foldable Methodsfold :: 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 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 |
|
Traversable Dual Source | Since: base-4.8.0.0 |
Applicative Dual Source | Since: base-4.8.0.0 |
Functor Dual Source | Since: base-4.8.0.0 |
Monad Dual Source | Since: base-4.8.0.0 |
Generic1 Dual Source | |
Data a => Data (Dual a) Source | Since: base-4.8.0.0 |
Defined in Data.Data Methodsgfoldl :: (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 |
Semigroup a => Semigroup (Dual a) Source | Since: base-4.9.0.0 |
Bounded a => Bounded (Dual a) Source | Since: base-2.1 |
Generic (Dual a) Source | |
Read a => Read (Dual a) Source | Since: base-2.1 |
Show a => Show (Dual a) Source | Since: base-2.1 |
Eq a => Eq (Dual a) Source | Since: base-2.1 |
Ord a => Ord (Dual a) Source | Since: base-2.1 |
Defined in Data.Semigroup.Internal |
|
type Rep1 Dual Source | Since: base-4.7.0.0 |
Defined in Data.Semigroup.Internal |
|
type Rep (Dual a) Source | Since: base-4.7.0.0 |
Defined in Data.Semigroup.Internal |
The monoid of endomorphisms under composition.
>>> let computation = Endo ("Hello, " ++) <> Endo (++ "!")
>>> appEndo computation "Haskell"
"Hello, Haskell!"
Instances
Bool wrappers
Boolean monoid under conjunction (&&
).
>>> getAll (All True <> mempty <> All False)
False
>>> getAll (mconcat (map (\x -> All (even x)) [2,4,6,7,8]))
False
Instances
Data All Source | Since: base-4.8.0.0 |
Defined in Data.Data Methodsgfoldl :: (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 |
Semigroup All Source | Since: base-4.9.0.0 |
Bounded All Source | Since: base-2.1 |
Generic All Source | |
Read All Source | Since: base-2.1 |
Show All Source | Since: base-2.1 |
Eq All Source | Since: base-2.1 |
Ord All Source | Since: base-2.1 |
type Rep All Source | Since: base-4.7.0.0 |
Defined in Data.Semigroup.Internal |
Boolean monoid under disjunction (||
).
>>> getAny (Any True <> mempty <> Any False)
True
>>> getAny (mconcat (map (\x -> Any (even x)) [2,4,6,7,8]))
True
Instances
Data Any Source | Since: base-4.8.0.0 |
Defined in Data.Data Methodsgfoldl :: (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 |
Semigroup Any Source | Since: base-4.9.0.0 |
Bounded Any Source | Since: base-2.1 |
Generic Any Source | |
Read Any Source | Since: base-2.1 |
Show Any Source | Since: base-2.1 |
Eq Any Source | Since: base-2.1 |
Ord Any Source | Since: base-2.1 |
type Rep Any Source | Since: base-4.7.0.0 |
Defined in Data.Semigroup.Internal |
Num wrappers
Monoid under addition.
>>> getSum (Sum 1 <> Sum 2 <> mempty)
3
Instances
MonadFix Sum Source | Since: base-4.8.0.0 |
Defined in Control.Monad.Fix |
|
MonadZip Sum Source | Since: base-4.8.0.0 |
Foldable Sum Source | Since: base-4.8.0.0 |
Defined in Data.Foldable Methodsfold :: 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 elem :: Eq a => a -> Sum a -> Bool Source maximum :: Ord a => Sum a -> a Source minimum :: Ord a => Sum a -> a Source |
|
Traversable Sum Source | Since: base-4.8.0.0 |
Applicative Sum Source | Since: base-4.8.0.0 |
Functor Sum Source | Since: base-4.8.0.0 |
Monad Sum Source | Since: base-4.8.0.0 |
Generic1 Sum Source | |
Data a => Data (Sum a) Source | Since: base-4.8.0.0 |
Defined in Data.Data Methodsgfoldl :: (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 |
Num a => Semigroup (Sum a) Source | Since: base-4.9.0.0 |
Bounded a => Bounded (Sum a) Source | Since: base-2.1 |
Generic (Sum a) Source | |
Num a => Num (Sum a) Source | Since: base-4.7.0.0 |
Read a => Read (Sum a) Source | Since: base-2.1 |
Show a => Show (Sum a) Source | Since: base-2.1 |
Eq a => Eq (Sum a) Source | Since: base-2.1 |
Ord a => Ord (Sum a) Source | Since: base-2.1 |
Defined in Data.Semigroup.Internal |
|
type Rep1 Sum Source | Since: base-4.7.0.0 |
Defined in Data.Semigroup.Internal |
|
type Rep (Sum a) Source | Since: base-4.7.0.0 |
Defined in Data.Semigroup.Internal |
Monoid under multiplication.
>>> getProduct (Product 3 <> Product 4 <> mempty)
12
Constructors
Product | |
Fields
|
Instances
MonadFix Product Source | Since: base-4.8.0.0 |
Defined in Control.Monad.Fix |
|
MonadZip Product Source | Since: base-4.8.0.0 |
Foldable Product Source | Since: base-4.8.0.0 |
Defined in Data.Foldable Methodsfold :: 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 |
|
Traversable Product Source | Since: base-4.8.0.0 |
Defined in Data.Traversable |
|
Applicative Product Source | Since: base-4.8.0.0 |
Defined in Data.Semigroup.Internal |
|
Functor Product Source | Since: base-4.8.0.0 |
Monad Product Source | Since: base-4.8.0.0 |
Generic1 Product Source | |
Data a => Data (Product a) Source | Since: base-4.8.0.0 |
Defined in Data.Data Methodsgfoldl :: (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 |
Num a => Semigroup (Product a) Source | Since: base-4.9.0.0 |
Bounded a => Bounded (Product a) Source | Since: base-2.1 |
Generic (Product a) Source | |
Num a => Num (Product a) Source | Since: base-4.7.0.0 |
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 |
Show a => Show (Product a) Source | Since: base-2.1 |
Eq a => Eq (Product a) Source | Since: base-2.1 |
Ord a => Ord (Product a) Source | Since: base-2.1 |
Defined in Data.Semigroup.Internal |
|
type Rep1 Product Source | Since: base-4.7.0.0 |
Defined in Data.Semigroup.Internal |
|
type Rep (Product a) Source | Since: base-4.7.0.0 |
Defined in Data.Semigroup.Internal |
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 Map
s 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))
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"
Instances
MonadFix First Source | Since: base-4.8.0.0 |
Defined in Control.Monad.Fix |
|
MonadZip First Source | Since: base-4.8.0.0 |
Foldable First Source | Since: base-4.8.0.0 |
Defined in Data.Foldable Methodsfold :: 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 |
|
Traversable First Source | Since: base-4.8.0.0 |
Applicative First Source | Since: base-4.8.0.0 |
Functor First Source | Since: base-4.8.0.0 |
Monad First Source | Since: base-4.8.0.0 |
Generic1 First Source | |
Data a => Data (First a) Source | Since: base-4.8.0.0 |
Defined in Data.Data Methodsgfoldl :: (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 |
Semigroup (First a) Source | Since: base-4.9.0.0 |
Generic (First a) Source | |
Read a => Read (First a) Source | Since: base-2.1 |
Show a => Show (First a) Source | Since: base-2.1 |
Eq a => Eq (First a) Source | Since: base-2.1 |
Ord a => Ord (First a) Source | Since: base-2.1 |
type Rep1 First Source | Since: base-4.7.0.0 |
Defined in Data.Monoid |
|
type Rep (First a) Source | Since: base-4.7.0.0 |
Defined in Data.Monoid |
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"
Instances
MonadFix Last Source | Since: base-4.8.0.0 |
Defined in Control.Monad.Fix |
|
MonadZip Last Source | Since: base-4.8.0.0 |
Foldable Last Source | Since: base-4.8.0.0 |
Defined in Data.Foldable Methodsfold :: 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 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 |
|
Traversable Last Source | Since: base-4.8.0.0 |
Applicative Last Source | Since: base-4.8.0.0 |
Functor Last Source | Since: base-4.8.0.0 |
Monad Last Source | Since: base-4.8.0.0 |
Generic1 Last Source | |
Data a => Data (Last a) Source | Since: base-4.8.0.0 |
Defined in Data.Data Methodsgfoldl :: (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 |
Semigroup (Last a) Source | Since: base-4.9.0.0 |
Generic (Last a) Source | |
Read a => Read (Last a) Source | Since: base-2.1 |
Show a => Show (Last a) Source | Since: base-2.1 |
Eq a => Eq (Last a) Source | Since: base-2.1 |
Ord a => Ord (Last a) Source | Since: base-2.1 |
Defined in Data.Monoid |
|
type Rep1 Last Source | Since: base-4.7.0.0 |
Defined in Data.Monoid |
|
type Rep (Last a) Source | Since: base-4.7.0.0 |
Defined in Data.Monoid |
Alternative wrapper
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
Instances
Generic1 (Alt f :: k -> Type) Source | |
MonadFix f => MonadFix (Alt f) Source | Since: base-4.8.0.0 |
Defined in Control.Monad.Fix |
|
MonadZip f => MonadZip (Alt f) Source | Since: base-4.8.0.0 |
Foldable f => Foldable (Alt f) Source | Since: base-4.12.0.0 |
Defined in Data.Foldable Methodsfold :: 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 |
|
Contravariant f => Contravariant (Alt f) Source | |
Traversable f => Traversable (Alt f) Source | Since: base-4.12.0.0 |
Alternative f => Alternative (Alt f) Source | Since: base-4.8.0.0 |
Applicative f => Applicative (Alt f) Source | Since: base-4.8.0.0 |
Functor f => Functor (Alt f) Source | Since: base-4.8.0.0 |
Monad f => Monad (Alt f) Source | Since: base-4.8.0.0 |
MonadPlus f => MonadPlus (Alt f) Source | Since: base-4.8.0.0 |
(Data (f a), Data a, Typeable f) => Data (Alt f a) Source | Since: base-4.8.0.0 |
Defined in Data.Data Methodsgfoldl :: (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 |
Alternative f => Semigroup (Alt f a) Source | Since: base-4.9.0.0 |
Enum (f a) => Enum (Alt f a) Source | Since: base-4.8.0.0 |
Defined in Data.Semigroup.Internal Methodssucc :: 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 | |
Num (f a) => Num (Alt f a) Source | Since: base-4.8.0.0 |
Defined in Data.Semigroup.Internal |
|
Read (f a) => Read (Alt f a) Source | Since: base-4.8.0.0 |
Show (f a) => Show (Alt f a) Source | Since: base-4.8.0.0 |
Eq (f a) => Eq (Alt f a) Source | Since: base-4.8.0.0 |
Ord (f a) => Ord (Alt f a) Source | Since: base-4.8.0.0 |
Defined in Data.Semigroup.Internal |
|
type Rep1 (Alt f :: k -> Type) Source | Since: base-4.8.0.0 |
Defined in Data.Semigroup.Internal |
|
type Rep (Alt f a) Source | Since: base-4.8.0.0 |
Defined in Data.Semigroup.Internal |
Applicative wrapper
This data type witnesses the lifting of a Monoid
into an Applicative
pointwise.
Since: base-4.12.0.0
Instances
Generic1 (Ap f :: k -> Type) Source | |
MonadFail f => MonadFail (Ap f) Source | Since: base-4.12.0.0 |
Defined in Data.Monoid |
|
MonadFix f => MonadFix (Ap f) Source | Since: base-4.12.0.0 |
Defined in Control.Monad.Fix |
|
Foldable f => Foldable (Ap f) Source | Since: base-4.12.0.0 |
Defined in Data.Foldable Methodsfold :: 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 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 |
|
Traversable f => Traversable (Ap f) Source | Since: base-4.12.0.0 |
Alternative f => Alternative (Ap f) Source | Since: base-4.12.0.0 |
Applicative f => Applicative (Ap f) Source | Since: base-4.12.0.0 |
Functor f => Functor (Ap f) Source | Since: base-4.12.0.0 |
Monad f => Monad (Ap f) Source | Since: base-4.12.0.0 |
MonadPlus f => MonadPlus (Ap f) Source | Since: base-4.12.0.0 |
(Data (f a), Data a, Typeable f) => Data (Ap f a) Source | Since: base-4.12.0.0 |
Defined in Data.Data Methodsgfoldl :: (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 |
(Applicative f, Semigroup a) => Semigroup (Ap f a) Source | Since: base-4.12.0.0 |
(Applicative f, Bounded a) => Bounded (Ap f a) Source | Since: base-4.12.0.0 |
Enum (f a) => Enum (Ap f a) Source | Since: base-4.12.0.0 |
Defined in Data.Monoid Methodssucc :: 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 | |
(Applicative f, Num a) => Num (Ap f a) Source | Note that even if the underlying Commutativity: Additive inverse: Distributivity: Since: base-4.12.0.0 |
Read (f a) => Read (Ap f a) Source | Since: base-4.12.0.0 |
Show (f a) => Show (Ap f a) Source | Since: base-4.12.0.0 |
Eq (f a) => Eq (Ap f a) Source | Since: base-4.12.0.0 |
Ord (f a) => Ord (Ap f a) Source | Since: base-4.12.0.0 |
Defined in Data.Monoid |
|
type Rep1 (Ap f :: k -> Type) Source | Since: base-4.12.0.0 |
Defined in Data.Monoid |
|
type Rep (Ap f a) Source | Since: base-4.12.0.0 |
Defined in Data.Monoid |
© 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