| 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 | experimental |
| Portability | portable |
| Safe Haskell | Trustworthy |
| Language | Haskell2010 |
Data.Monoid
Description
A type a is a Monoid if it provides an associative function (<>)
that lets you combine any two values of type a into one, and a neutral
element (mempty) such that
a <> mempty == mempty <> a == a
A Monoid is a Semigroup with the added requirement of a neutral element.
Thus any Monoid is a Semigroup, but not the other way around.
Examples
The Sum monoid is defined by the numerical addition operator and `0` as neutral element:
>>>mempty :: Sum IntSum 0>>>Sum 1 <> Sum 2 <> Sum 3 <> Sum 4 :: Sum IntSum {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 IntSum {getSum = 10}>>>mconcat [] :: Sum IntSum {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 IntProduct {getProduct = 24}>>>mconcat [1,2,3,4] :: Product IntProduct {getProduct = 24}>>>mconcat [] :: Product IntProduct {getProduct = 1}
Synopsis
- class Semigroup a => Monoid a where
- (<>) :: Semigroup a => a -> a -> a
- newtype Dual a = Dual {
- getDual :: a
- newtype Endo a = Endo {
- appEndo :: a -> a
- newtype All = All {}
- newtype Any = Any {}
- newtype Sum a = Sum {
- getSum :: a
- newtype Product a = Product {
- getProduct :: a
- newtype First a = First {}
- newtype Last a = Last {}
- newtype Alt f a = Alt {
- getAlt :: f a
- newtype Ap f a = Ap {
- getAp :: f a
Monoid typeclass
class Semigroup a => Monoid a where #
The class of monoids (types with an associative binary operation that has an identity). Instances should satisfy the following:
- Right identity
x<>mempty= x- Left identity
mempty<>x = x- Associativity
x(<>(y<>z) = (x<>y)<>zSemigrouplaw)- 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
Methods
Identity of mappend
>>>"Hello world" <> mempty"Hello world"
An associative operation
NOTE: This method is redundant and has the default
implementation since base-4.11.0.0.
Should it be implemented manually, since mappend = (<>)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 All # | Since: base-2.1 |
| Monoid Any # | Since: base-2.1 |
| Monoid Event # | Since: base-4.4.0.0 |
| Monoid Lifetime # |
Since: base-4.8.0.0 |
| Monoid Ordering # | Since: base-2.1 |
| Monoid () # | Since: base-2.1 |
| Monoid (Comparison a) # |
mempty :: Comparison a mempty = Comparison _ _ -> EQ |
Defined in Data.Functor.Contravariant Methods mempty :: Comparison a # mappend :: Comparison a -> Comparison a -> Comparison a # mconcat :: [Comparison a] -> Comparison a # | |
| Monoid (Equivalence a) # |
mempty :: Equivalence a mempty = Equivalence _ _ -> True |
Defined in Data.Functor.Contravariant Methods mempty :: Equivalence a # mappend :: Equivalence a -> Equivalence a -> Equivalence a # mconcat :: [Equivalence a] -> Equivalence a # | |
| Monoid (Predicate a) # |
mempty :: Predicate a mempty = _ -> True |
| Monoid a => Monoid (Identity a) # | Since: base-4.9.0.0 |
| Monoid (First a) # | Since: base-2.1 |
| Monoid (Last a) # | Since: base-2.1 |
| Monoid a => Monoid (Down a) # | Since: base-4.11.0.0 |
| (Ord a, Bounded a) => Monoid (Max a) # | Since: base-4.9.0.0 |
| (Ord a, Bounded a) => Monoid (Min a) # | Since: base-4.9.0.0 |
| Semigroup a => Monoid (Option a) # | Since: base-4.9.0.0 |
| Monoid m => Monoid (WrappedMonoid m) # | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods mempty :: WrappedMonoid m # mappend :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m # mconcat :: [WrappedMonoid m] -> WrappedMonoid m # | |
| Monoid a => Monoid (Dual a) # | Since: base-2.1 |
| Monoid (Endo a) # | Since: base-2.1 |
| Num a => Monoid (Product a) # | Since: base-2.1 |
| Num a => Monoid (Sum a) # | Since: base-2.1 |
| Monoid p => Monoid (Par1 p) # | Since: base-4.12.0.0 |
| Monoid a => Monoid (IO a) # | Since: base-4.9.0.0 |
| Semigroup a => Monoid (Maybe a) # | Lift a semigroup into Since 4.11.0: constraint on inner Since: base-2.1 |
| Monoid a => Monoid (a) # | Since: base-4.15 |
| Monoid [a] # | Since: base-2.1 |
| Monoid a => Monoid (Op a b) # |
mempty :: Op a b mempty = Op _ -> mempty |
| Monoid (Proxy s) # | Since: base-4.7.0.0 |
| Monoid (U1 p) # | Since: base-4.12.0.0 |
| Monoid a => Monoid (ST s a) # | Since: base-4.11.0.0 |
| Monoid b => Monoid (a -> b) # | Since: base-2.1 |
| (Monoid a, Monoid b) => Monoid (a, b) # | Since: base-2.1 |
| Monoid a => Monoid (Const a b) # | Since: base-4.9.0.0 |
| (Applicative f, Monoid a) => Monoid (Ap f a) # | Since: base-4.12.0.0 |
| Alternative f => Monoid (Alt f a) # | Since: base-4.8.0.0 |
| Monoid (f p) => Monoid (Rec1 f p) # | Since: base-4.12.0.0 |
| (Monoid a, Monoid b, Monoid c) => Monoid (a, b, c) # | Since: base-2.1 |
| (Monoid (f p), Monoid (g p)) => Monoid ((f :*: g) p) # | Since: base-4.12.0.0 |
| Monoid c => Monoid (K1 i c p) # | Since: base-4.12.0.0 |
| (Monoid a, Monoid b, Monoid c, Monoid d) => Monoid (a, b, c, d) # | Since: base-2.1 |
| Monoid (f (g p)) => Monoid ((f :.: g) p) # | Since: base-4.12.0.0 |
| Monoid (f p) => Monoid (M1 i c f p) # | Since: base-4.12.0.0 |
| (Monoid a, Monoid b, Monoid c, Monoid d, Monoid e) => Monoid (a, b, c, d, e) # | Since: base-2.1 |
(<>) :: Semigroup a => a -> a -> a infixr 6 #
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 # | Since: base-4.8.0.0 |
Defined in Control.Monad.Fix | |
| MonadZip Dual # | Since: base-4.8.0.0 |
| Foldable Dual # | Since: base-4.8.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Dual m -> m # foldMap :: Monoid m => (a -> m) -> Dual a -> m # foldMap' :: Monoid m => (a -> m) -> Dual a -> m # foldr :: (a -> b -> b) -> b -> Dual a -> b # foldr' :: (a -> b -> b) -> b -> Dual a -> b # foldl :: (b -> a -> b) -> b -> Dual a -> b # foldl' :: (b -> a -> b) -> b -> Dual a -> b # foldr1 :: (a -> a -> a) -> Dual a -> a # foldl1 :: (a -> a -> a) -> Dual a -> a # elem :: Eq a => a -> Dual a -> Bool # maximum :: Ord a => Dual a -> a # | |
| Traversable Dual # | Since: base-4.8.0.0 |
| Applicative Dual # | Since: base-4.8.0.0 |
| Functor Dual # | Since: base-4.8.0.0 |
| Monad Dual # | Since: base-4.8.0.0 |
| Data a => Data (Dual a) # | Since: base-4.8.0.0 |
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) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Dual a) # toConstr :: Dual a -> Constr # dataTypeOf :: Dual a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Dual a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Dual a)) # gmapT :: (forall b. Data b => b -> b) -> Dual a -> Dual a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Dual a -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Dual a -> r # gmapQ :: (forall d. Data d => d -> u) -> Dual a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Dual a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Dual a -> m (Dual a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Dual a -> m (Dual a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Dual a -> m (Dual a) # | |
| Monoid a => Monoid (Dual a) # | Since: base-2.1 |
| Semigroup a => Semigroup (Dual a) # | Since: base-4.9.0.0 |
| Bounded a => Bounded (Dual a) # | Since: base-2.1 |
| Generic (Dual a) # | |
| Read a => Read (Dual a) # | Since: base-2.1 |
| Show a => Show (Dual a) # | Since: base-2.1 |
| Eq a => Eq (Dual a) # | Since: base-2.1 |
| Ord a => Ord (Dual a) # | Since: base-2.1 |
| Generic1 Dual # | |
| type Rep (Dual a) # | Since: base-4.7.0.0 |
Defined in Data.Semigroup.Internal | |
| type Rep1 Dual # | 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!"
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 # | Since: base-4.8.0.0 |
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 # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c All # dataTypeOf :: All -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c All) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c All) # gmapT :: (forall b. Data b => b -> b) -> All -> All # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> All -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> All -> r # gmapQ :: (forall d. Data d => d -> u) -> All -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> All -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> All -> m All # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> All -> m All # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> All -> m All # | |
| Monoid All # | Since: base-2.1 |
| Semigroup All # | Since: base-4.9.0.0 |
| Bounded All # | Since: base-2.1 |
| Generic All # | |
| Read All # | Since: base-2.1 |
| Show All # | Since: base-2.1 |
| Eq All # | Since: base-2.1 |
| Ord All # | Since: base-2.1 |
| type Rep All # | 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 # | Since: base-4.8.0.0 |
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 # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Any # dataTypeOf :: Any -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Any) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Any) # gmapT :: (forall b. Data b => b -> b) -> Any -> Any # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Any -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Any -> r # gmapQ :: (forall d. Data d => d -> u) -> Any -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Any -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Any -> m Any # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Any -> m Any # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Any -> m Any # | |
| Monoid Any # | Since: base-2.1 |
| Semigroup Any # | Since: base-4.9.0.0 |
| Bounded Any # | Since: base-2.1 |
| Generic Any # | |
| Read Any # | Since: base-2.1 |
| Show Any # | Since: base-2.1 |
| Eq Any # | Since: base-2.1 |
| Ord Any # | Since: base-2.1 |
| type Rep Any # | 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 # | Since: base-4.8.0.0 |
Defined in Control.Monad.Fix | |
| MonadZip Sum # | Since: base-4.8.0.0 |
| Foldable Sum # | Since: base-4.8.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Sum m -> m # foldMap :: Monoid m => (a -> m) -> Sum a -> m # foldMap' :: Monoid m => (a -> m) -> Sum a -> m # foldr :: (a -> b -> b) -> b -> Sum a -> b # foldr' :: (a -> b -> b) -> b -> Sum a -> b # foldl :: (b -> a -> b) -> b -> Sum a -> b # foldl' :: (b -> a -> b) -> b -> Sum a -> b # foldr1 :: (a -> a -> a) -> Sum a -> a # foldl1 :: (a -> a -> a) -> Sum a -> a # elem :: Eq a => a -> Sum a -> Bool # maximum :: Ord a => Sum a -> a # | |
| Traversable Sum # | Since: base-4.8.0.0 |
| Applicative Sum # | Since: base-4.8.0.0 |
| Functor Sum # | Since: base-4.8.0.0 |
| Monad Sum # | Since: base-4.8.0.0 |
| Data a => Data (Sum a) # | Since: base-4.8.0.0 |
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) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Sum a) # dataTypeOf :: Sum a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Sum a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Sum a)) # gmapT :: (forall b. Data b => b -> b) -> Sum a -> Sum a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Sum a -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Sum a -> r # gmapQ :: (forall d. Data d => d -> u) -> Sum a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Sum a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Sum a -> m (Sum a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Sum a -> m (Sum a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Sum a -> m (Sum a) # | |
| Num a => Monoid (Sum a) # | Since: base-2.1 |
| Num a => Semigroup (Sum a) # | Since: base-4.9.0.0 |
| Bounded a => Bounded (Sum a) # | Since: base-2.1 |
| Generic (Sum a) # | |
| Num a => Num (Sum a) # | Since: base-4.7.0.0 |
| Read a => Read (Sum a) # | Since: base-2.1 |
| Show a => Show (Sum a) # | Since: base-2.1 |
| Eq a => Eq (Sum a) # | Since: base-2.1 |
| Ord a => Ord (Sum a) # | Since: base-2.1 |
Defined in Data.Semigroup.Internal | |
| Generic1 Sum # | |
| type Rep (Sum a) # | Since: base-4.7.0.0 |
Defined in Data.Semigroup.Internal | |
| type Rep1 Sum # | 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 # | Since: base-4.8.0.0 |
Defined in Control.Monad.Fix | |
| MonadZip Product # | Since: base-4.8.0.0 |
| Foldable Product # | Since: base-4.8.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Product m -> m # foldMap :: Monoid m => (a -> m) -> Product a -> m # foldMap' :: Monoid m => (a -> m) -> Product a -> m # foldr :: (a -> b -> b) -> b -> Product a -> b # foldr' :: (a -> b -> b) -> b -> Product a -> b # foldl :: (b -> a -> b) -> b -> Product a -> b # foldl' :: (b -> a -> b) -> b -> Product a -> b # foldr1 :: (a -> a -> a) -> Product a -> a # foldl1 :: (a -> a -> a) -> Product a -> a # elem :: Eq a => a -> Product a -> Bool # maximum :: Ord a => Product a -> a # minimum :: Ord a => Product a -> a # | |
| Traversable Product # | Since: base-4.8.0.0 |
| Applicative Product # | Since: base-4.8.0.0 |
| Functor Product # | Since: base-4.8.0.0 |
| Monad Product # | Since: base-4.8.0.0 |
| Data a => Data (Product a) # | Since: base-4.8.0.0 |
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) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Product a) # toConstr :: Product a -> Constr # dataTypeOf :: Product a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Product a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Product a)) # gmapT :: (forall b. Data b => b -> b) -> Product a -> Product a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Product a -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Product a -> r # gmapQ :: (forall d. Data d => d -> u) -> Product a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Product a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Product a -> m (Product a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Product a -> m (Product a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Product a -> m (Product a) # | |
| Num a => Monoid (Product a) # | Since: base-2.1 |
| Num a => Semigroup (Product a) # | Since: base-4.9.0.0 |
| Bounded a => Bounded (Product a) # | Since: base-2.1 |
| Generic (Product a) # | |
| Num a => Num (Product a) # | Since: base-4.7.0.0 |
Defined in Data.Semigroup.Internal | |
| Read a => Read (Product a) # | Since: base-2.1 |
| Show a => Show (Product a) # | Since: base-2.1 |
| Eq a => Eq (Product a) # | Since: base-2.1 |
| Ord a => Ord (Product a) # | Since: base-2.1 |
Defined in Data.Semigroup.Internal | |
| Generic1 Product # | |
| type Rep (Product a) # | Since: base-4.7.0.0 |
Defined in Data.Semigroup.Internal | |
| type Rep1 Product # | 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 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.FunctorinsertLookupWithKey :: 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.
is isomorphic to First a, but precedes it
historically.Alt Maybe a
>>>getFirst (First (Just "hello") <> First Nothing <> First (Just "world"))Just "hello"
Instances
| MonadFix First # | Since: base-4.8.0.0 |
Defined in Control.Monad.Fix | |
| MonadZip First # | Since: base-4.8.0.0 |
| Foldable First # | Since: base-4.8.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => First m -> m # foldMap :: Monoid m => (a -> m) -> First a -> m # foldMap' :: Monoid m => (a -> m) -> First a -> m # foldr :: (a -> b -> b) -> b -> First a -> b # foldr' :: (a -> b -> b) -> b -> First a -> b # foldl :: (b -> a -> b) -> b -> First a -> b # foldl' :: (b -> a -> b) -> b -> First a -> b # foldr1 :: (a -> a -> a) -> First a -> a # foldl1 :: (a -> a -> a) -> First a -> a # elem :: Eq a => a -> First a -> Bool # maximum :: Ord a => First a -> a # minimum :: Ord a => First a -> a # | |
| Traversable First # | Since: base-4.8.0.0 |
| Applicative First # | Since: base-4.8.0.0 |
| Functor First # | Since: base-4.8.0.0 |
| Monad First # | Since: base-4.8.0.0 |
| Data a => Data (First a) # | Since: base-4.8.0.0 |
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) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (First a) # toConstr :: First a -> Constr # dataTypeOf :: First a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (First a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (First a)) # gmapT :: (forall b. Data b => b -> b) -> First a -> First a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> First a -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> First a -> r # gmapQ :: (forall d. Data d => d -> u) -> First a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> First a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> First a -> m (First a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> First a -> m (First a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> First a -> m (First a) # | |
| Monoid (First a) # | Since: base-2.1 |
| Semigroup (First a) # | Since: base-4.9.0.0 |
| Generic (First a) # | |
| Read a => Read (First a) # | Since: base-2.1 |
| Show a => Show (First a) # | Since: base-2.1 |
| Eq a => Eq (First a) # | Since: base-2.1 |
| Ord a => Ord (First a) # | Since: base-2.1 |
| Generic1 First # | |
| type Rep (First a) # | Since: base-4.7.0.0 |
Defined in Data.Monoid | |
| type Rep1 First # | Since: base-4.7.0.0 |
Defined in Data.Monoid | |
Maybe monoid returning the rightmost non-Nothing value.
is isomorphic to Last a, and thus to
Dual (First a)Dual (Alt Maybe a)
>>>getLast (Last (Just "hello") <> Last Nothing <> Last (Just "world"))Just "world"
Instances
| MonadFix Last # | Since: base-4.8.0.0 |
Defined in Control.Monad.Fix | |
| MonadZip Last # | Since: base-4.8.0.0 |
| Foldable Last # | Since: base-4.8.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Last m -> m # foldMap :: Monoid m => (a -> m) -> Last a -> m # foldMap' :: Monoid m => (a -> m) -> Last a -> m # foldr :: (a -> b -> b) -> b -> Last a -> b # foldr' :: (a -> b -> b) -> b -> Last a -> b # foldl :: (b -> a -> b) -> b -> Last a -> b # foldl' :: (b -> a -> b) -> b -> Last a -> b # foldr1 :: (a -> a -> a) -> Last a -> a # foldl1 :: (a -> a -> a) -> Last a -> a # elem :: Eq a => a -> Last a -> Bool # maximum :: Ord a => Last a -> a # | |
| Traversable Last # | Since: base-4.8.0.0 |
| Applicative Last # | Since: base-4.8.0.0 |
| Functor Last # | Since: base-4.8.0.0 |
| Monad Last # | Since: base-4.8.0.0 |
| Data a => Data (Last a) # | Since: base-4.8.0.0 |
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) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Last a) # toConstr :: Last a -> Constr # dataTypeOf :: Last a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Last a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Last a)) # gmapT :: (forall b. Data b => b -> b) -> Last a -> Last a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Last a -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Last a -> r # gmapQ :: (forall d. Data d => d -> u) -> Last a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Last a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Last a -> m (Last a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Last a -> m (Last a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Last a -> m (Last a) # | |
| Monoid (Last a) # | Since: base-2.1 |
| Semigroup (Last a) # | Since: base-4.9.0.0 |
| Generic (Last a) # | |
| Read a => Read (Last a) # | Since: base-2.1 |
| Show a => Show (Last a) # | Since: base-2.1 |
| Eq a => Eq (Last a) # | Since: base-2.1 |
| Ord a => Ord (Last a) # | Since: base-2.1 |
| Generic1 Last # | |
| type Rep (Last a) # | Since: base-4.7.0.0 |
Defined in Data.Monoid | |
| type Rep1 Last # | 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) # | |
| MonadFix f => MonadFix (Alt f) # | Since: base-4.8.0.0 |
Defined in Control.Monad.Fix | |
| MonadZip f => MonadZip (Alt f) # | Since: base-4.8.0.0 |
| Foldable f => Foldable (Alt f) # | Since: base-4.12.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Alt f m -> m # foldMap :: Monoid m => (a -> m) -> Alt f a -> m # foldMap' :: Monoid m => (a -> m) -> Alt f a -> m # foldr :: (a -> b -> b) -> b -> Alt f a -> b # foldr' :: (a -> b -> b) -> b -> Alt f a -> b # foldl :: (b -> a -> b) -> b -> Alt f a -> b # foldl' :: (b -> a -> b) -> b -> Alt f a -> b # foldr1 :: (a -> a -> a) -> Alt f a -> a # foldl1 :: (a -> a -> a) -> Alt f a -> a # elem :: Eq a => a -> Alt f a -> Bool # maximum :: Ord a => Alt f a -> a # minimum :: Ord a => Alt f a -> a # | |
| Contravariant f => Contravariant (Alt f) # | |
| Traversable f => Traversable (Alt f) # | Since: base-4.12.0.0 |
| Alternative f => Alternative (Alt f) # | Since: base-4.8.0.0 |
| Applicative f => Applicative (Alt f) # | Since: base-4.8.0.0 |
| Functor f => Functor (Alt f) # | Since: base-4.8.0.0 |
| Monad f => Monad (Alt f) # | Since: base-4.8.0.0 |
| MonadPlus f => MonadPlus (Alt f) # | Since: base-4.8.0.0 |
| (Data (f a), Data a, Typeable f) => Data (Alt f a) # | Since: base-4.8.0.0 |
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) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Alt f a) # toConstr :: Alt f a -> Constr # dataTypeOf :: Alt f a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Alt f a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Alt f a)) # gmapT :: (forall b. Data b => b -> b) -> Alt f a -> Alt f a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Alt f a -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Alt f a -> r # gmapQ :: (forall d. Data d => d -> u) -> Alt f a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Alt f a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Alt f a -> m (Alt f a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Alt f a -> m (Alt f a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Alt f a -> m (Alt f a) # | |
| Alternative f => Monoid (Alt f a) # | Since: base-4.8.0.0 |
| Alternative f => Semigroup (Alt f a) # | Since: base-4.9.0.0 |
| Enum (f a) => Enum (Alt f a) # | Since: base-4.8.0.0 |
| Generic (Alt f a) # | |
| Num (f a) => Num (Alt f a) # | Since: base-4.8.0.0 |
| Read (f a) => Read (Alt f a) # | Since: base-4.8.0.0 |
| Show (f a) => Show (Alt f a) # | Since: base-4.8.0.0 |
| Eq (f a) => Eq (Alt f a) # | Since: base-4.8.0.0 |
| Ord (f a) => Ord (Alt f a) # | Since: base-4.8.0.0 |
Defined in Data.Semigroup.Internal | |
| type Rep1 (Alt f :: k -> Type) # | Since: base-4.8.0.0 |
Defined in Data.Semigroup.Internal | |
| type Rep (Alt f a) # | 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) # | |
| MonadFail f => MonadFail (Ap f) # | Since: base-4.12.0.0 |
Defined in Data.Monoid | |
| MonadFix f => MonadFix (Ap f) # | Since: base-4.12.0.0 |
Defined in Control.Monad.Fix | |
| Foldable f => Foldable (Ap f) # | Since: base-4.12.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Ap f m -> m # foldMap :: Monoid m => (a -> m) -> Ap f a -> m # foldMap' :: Monoid m => (a -> m) -> Ap f a -> m # foldr :: (a -> b -> b) -> b -> Ap f a -> b # foldr' :: (a -> b -> b) -> b -> Ap f a -> b # foldl :: (b -> a -> b) -> b -> Ap f a -> b # foldl' :: (b -> a -> b) -> b -> Ap f a -> b # foldr1 :: (a -> a -> a) -> Ap f a -> a # foldl1 :: (a -> a -> a) -> Ap f a -> a # elem :: Eq a => a -> Ap f a -> Bool # maximum :: Ord a => Ap f a -> a # | |
| Traversable f => Traversable (Ap f) # | Since: base-4.12.0.0 |
| Alternative f => Alternative (Ap f) # | Since: base-4.12.0.0 |
| Applicative f => Applicative (Ap f) # | Since: base-4.12.0.0 |
| Functor f => Functor (Ap f) # | Since: base-4.12.0.0 |
| Monad f => Monad (Ap f) # | Since: base-4.12.0.0 |
| MonadPlus f => MonadPlus (Ap f) # | Since: base-4.12.0.0 |
| (Data (f a), Data a, Typeable f) => Data (Ap f a) # | Since: base-4.12.0.0 |
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) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Ap f a) # toConstr :: Ap f a -> Constr # dataTypeOf :: Ap f a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Ap f a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Ap f a)) # gmapT :: (forall b. Data b => b -> b) -> Ap f a -> Ap f a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Ap f a -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Ap f a -> r # gmapQ :: (forall d. Data d => d -> u) -> Ap f a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Ap f a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Ap f a -> m (Ap f a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Ap f a -> m (Ap f a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Ap f a -> m (Ap f a) # | |
| (Applicative f, Monoid a) => Monoid (Ap f a) # | Since: base-4.12.0.0 |
| (Applicative f, Semigroup a) => Semigroup (Ap f a) # | Since: base-4.12.0.0 |
| (Applicative f, Bounded a) => Bounded (Ap f a) # | Since: base-4.12.0.0 |
| Enum (f a) => Enum (Ap f a) # | Since: base-4.12.0.0 |
Defined in Data.Monoid | |
| Generic (Ap f a) # | |
| (Applicative f, Num a) => Num (Ap f a) # | Note that even if the underlying Commutativity:
Additive inverse:
Distributivity:
Since: base-4.12.0.0 |
| Read (f a) => Read (Ap f a) # | Since: base-4.12.0.0 |
| Show (f a) => Show (Ap f a) # | Since: base-4.12.0.0 |
| Eq (f a) => Eq (Ap f a) # | Since: base-4.12.0.0 |
| Ord (f a) => Ord (Ap f a) # | Since: base-4.12.0.0 |
| type Rep1 (Ap f :: k -> Type) # | Since: base-4.12.0.0 |
Defined in Data.Monoid | |
| type Rep (Ap f a) # | Since: base-4.12.0.0 |
Defined in Data.Monoid | |