| 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
Contents
Description
A class for monoids (types with an associative binary operation that has an identity) with various general-purpose instances.
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 laws:
x
<>mempty= xmempty<>x = xx(<>(y<>z) = (x<>y)<>zSemigrouplaw)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
An associative operation
NOTE: This method is redundant and has the default
implementation since base-4.11.0.0.mappend = '(<>)'
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.
Instances
| Monoid Ordering # | Since: base-2.1 |
| Monoid () # | Since: base-2.1 |
| Monoid Any # | Since: base-2.1 |
| Monoid All # | Since: base-2.1 |
| Monoid Lifetime # |
Since: base-4.8.0.0 |
| Monoid Event # | Since: base-4.4.0.0 |
| Monoid [a] # | Since: base-2.1 |
| Semigroup a => Monoid (Maybe a) # | Lift a semigroup into Since 4.11.0: constraint on inner Since: base-2.1 |
| Monoid a => Monoid (IO a) # | Since: base-4.9.0.0 |
| Monoid p => Monoid (Par1 p) # | Since: base-4.12.0.0 |
| Monoid a => Monoid (Down a) # | Since: base-4.11.0.0 |
| Num a => Monoid (Product a) # | Since: base-2.1 |
| Num a => Monoid (Sum a) # | Since: base-2.1 |
| Monoid (Endo a) # | Since: base-2.1 |
| Monoid a => Monoid (Dual a) # | Since: base-2.1 |
| Monoid (Last a) # | Since: base-2.1 |
| Monoid (First a) # | Since: base-2.1 |
| Monoid a => Monoid (Identity 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 # | |
| (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 |
| Monoid (Equivalence a) # | |
Defined in Data.Functor.Contravariant Methods mempty :: Equivalence a # mappend :: Equivalence a -> Equivalence a -> Equivalence a # mconcat :: [Equivalence a] -> Equivalence a # | |
| Monoid (Comparison a) # | |
Defined in Data.Functor.Contravariant Methods mempty :: Comparison a # mappend :: Comparison a -> Comparison a -> Comparison a # mconcat :: [Comparison a] -> Comparison a # | |
| Monoid (Predicate a) # | |
| Monoid b => Monoid (a -> b) # | Since: base-2.1 |
| Monoid (U1 p) # | Since: base-4.12.0.0 |
| (Monoid a, Monoid b) => Monoid (a, b) # | Since: base-2.1 |
| Monoid a => Monoid (ST s a) # | Since: base-4.11.0.0 |
| Monoid (Proxy s) # | Since: base-4.7.0.0 |
| Monoid a => Monoid (Op a b) # | |
| 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 |
| Alternative f => Monoid (Alt f a) # | Since: base-4.8.0.0 |
| (Applicative f, Monoid a) => Monoid (Ap f a) # | Since: base-4.12.0.0 |
| Monoid a => Monoid (Const a b) # | Since: base-4.9.0.0 |
| Monoid c => Monoid (K1 i c p) # | Since: base-4.12.0.0 |
| (Monoid (f p), Monoid (g p)) => Monoid ((f :*: g) 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 p) => Monoid (M1 i c f p) # | Since: base-4.12.0.0 |
| Monoid (f (g p)) => Monoid ((f :.: g) 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 |
The dual of a Monoid, obtained by swapping the arguments of mappend.
>>>getDual (mappend (Dual "Hello") (Dual "World"))"WorldHello"
Instances
| Monad Dual # | Since: base-4.8.0.0 |
| Functor Dual # | Since: base-4.8.0.0 |
| MonadFix Dual # | Since: base-4.8.0.0 |
Defined in Control.Monad.Fix | |
| Applicative 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 # 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 |
| MonadZip Dual # | Since: base-4.8.0.0 |
| Bounded a => Bounded (Dual a) # | Since: base-2.1 |
| Eq a => Eq (Dual a) # | Since: base-2.1 |
| 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 :: (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) # | |
| Ord a => Ord (Dual a) # | Since: base-2.1 |
| Read a => Read (Dual a) # | Since: base-2.1 |
| Show a => Show (Dual a) # | Since: base-2.1 |
| Generic (Dual a) # | |
| Semigroup a => Semigroup (Dual a) # | Since: base-4.9.0.0 |
| Monoid a => Monoid (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
| Bounded All # | Since: base-2.1 |
| Eq All # | Since: base-2.1 |
| 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 :: (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 # | |
| Ord All # | Since: base-2.1 |
| Read All # | Since: base-2.1 |
| Show All # | Since: base-2.1 |
| Generic All # | |
| Semigroup All # | Since: base-4.9.0.0 |
| Monoid 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
| Bounded Any # | Since: base-2.1 |
| Eq Any # | Since: base-2.1 |
| 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 :: (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 # | |
| Ord Any # | Since: base-2.1 |
| Read Any # | Since: base-2.1 |
| Show Any # | Since: base-2.1 |
| Generic Any # | |
| Semigroup Any # | Since: base-4.9.0.0 |
| Monoid 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
| Monad Sum # | Since: base-4.8.0.0 |
| Functor Sum # | Since: base-4.8.0.0 |
| MonadFix Sum # | Since: base-4.8.0.0 |
Defined in Control.Monad.Fix | |
| Applicative 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 # 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 |
| MonadZip Sum # | Since: base-4.8.0.0 |
| Bounded a => Bounded (Sum a) # | Since: base-2.1 |
| Eq a => Eq (Sum a) # | Since: base-2.1 |
| 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 :: (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 => Num (Sum a) # | Since: base-4.7.0.0 |
| Ord a => Ord (Sum a) # | Since: base-2.1 |
Defined in Data.Semigroup.Internal | |
| Read a => Read (Sum a) # | Since: base-2.1 |
| Show a => Show (Sum a) # | Since: base-2.1 |
| Generic (Sum a) # | |
| Num a => Semigroup (Sum a) # | Since: base-4.9.0.0 |
| Num a => Monoid (Sum a) # | Since: base-2.1 |
| 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
| Monad Product # | Since: base-4.8.0.0 |
| Functor Product # | Since: base-4.8.0.0 |
| MonadFix Product # | Since: base-4.8.0.0 |
Defined in Control.Monad.Fix | |
| Applicative 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 # 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 |
| MonadZip Product # | Since: base-4.8.0.0 |
| Bounded a => Bounded (Product a) # | Since: base-2.1 |
| Eq a => Eq (Product a) # | Since: base-2.1 |
| 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 :: (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 => Num (Product a) # | Since: base-4.7.0.0 |
Defined in Data.Semigroup.Internal | |
| Ord a => Ord (Product a) # | Since: base-2.1 |
Defined in Data.Semigroup.Internal | |
| Read a => Read (Product a) # | Since: base-2.1 |
| Show a => Show (Product a) # | Since: base-2.1 |
| Generic (Product a) # | |
| Num a => Semigroup (Product a) # | Since: base-4.9.0.0 |
| Num a => Monoid (Product a) # | Since: base-2.1 |
| 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 Data.Map's interface can be implemented with
Data.Map.alter. Some of the rest can be implemented with a new
alterA function and either First or Last:
alterA :: (Applicative f, Ord k) =>
(Maybe a -> f (Maybe a)) -> k -> Map k a -> f (Map k a)
instance Monoid a => Applicative ((,) a) -- from Control.ApplicativeinsertLookupWithKey :: Ord k => (k -> v -> v -> v) -> k -> v
-> Map k v -> (Maybe v, Map k v)
insertLookupWithKey combine key value =
Arrow.first getFirst . alterA 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"
Use of this type is discouraged. Note the following equivalence:
Data.Monoid.First x === Maybe (Data.Semigroup.First x)
In addition to being equivalent in the structural sense, the two
also have Monoid instances that behave the same. This type will
be marked deprecated in GHC 8.8, and removed in GHC 8.10.
Users are advised to use the variant from Data.Semigroup and wrap
it in Maybe.
Instances
| Monad First # | Since: base-4.8.0.0 |
| Functor First # | Since: base-4.8.0.0 |
| MonadFix First # | Since: base-4.8.0.0 |
Defined in Control.Monad.Fix | |
| Applicative 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 # 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 |
| MonadZip First # | Since: base-4.8.0.0 |
| Eq a => Eq (First a) # | Since: base-2.1 |
| 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 :: (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) # | |
| Ord a => Ord (First a) # | Since: base-2.1 |
| Read a => Read (First a) # | Since: base-2.1 |
| Show a => Show (First a) # | Since: base-2.1 |
| Generic (First a) # | |
| Semigroup (First a) # | Since: base-4.9.0.0 |
| Monoid (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"
Use of this type is discouraged. Note the following equivalence:
Data.Monoid.Last x === Maybe (Data.Semigroup.Last x)
In addition to being equivalent in the structural sense, the two
also have Monoid instances that behave the same. This type will
be marked deprecated in GHC 8.8, and removed in GHC 8.10.
Users are advised to use the variant from Data.Semigroup and wrap
it in Maybe.
Instances
| Monad Last # | Since: base-4.8.0.0 |
| Functor Last # | Since: base-4.8.0.0 |
| MonadFix Last # | Since: base-4.8.0.0 |
Defined in Control.Monad.Fix | |
| Applicative 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 # 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 |
| MonadZip Last # | Since: base-4.8.0.0 |
| Eq a => Eq (Last a) # | Since: base-2.1 |
| 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 :: (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) # | |
| Ord a => Ord (Last a) # | Since: base-2.1 |
| Read a => Read (Last a) # | Since: base-2.1 |
| Show a => Show (Last a) # | Since: base-2.1 |
| Generic (Last a) # | |
| Semigroup (Last a) # | Since: base-4.9.0.0 |
| Monoid (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 <|>.
Since: base-4.8.0.0
Instances
| Generic1 (Alt f :: k -> Type) # | |
| Monad f => Monad (Alt f) # | Since: base-4.8.0.0 |
| Functor f => Functor (Alt f) # | Since: base-4.8.0.0 |
| MonadFix f => MonadFix (Alt f) # | Since: base-4.8.0.0 |
Defined in Control.Monad.Fix | |
| Applicative f => Applicative (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 # 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 # | |
| Traversable f => Traversable (Alt f) # | Since: base-4.12.0.0 |
| MonadPlus f => MonadPlus (Alt f) # | Since: base-4.8.0.0 |
| Alternative f => Alternative (Alt f) # | Since: base-4.8.0.0 |
| MonadZip f => MonadZip (Alt f) # | Since: base-4.8.0.0 |
| Contravariant f => Contravariant (Alt f) # | |
| Enum (f a) => Enum (Alt f a) # | Since: base-4.8.0.0 |
| Eq (f a) => Eq (Alt f a) # | 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 :: (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) # | |
| Num (f a) => Num (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 | |
| 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 |
| Generic (Alt f a) # | |
| Alternative f => Semigroup (Alt f a) # | Since: base-4.9.0.0 |
| Alternative f => Monoid (Alt f a) # | Since: base-4.8.0.0 |
| 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) # | |
| Monad f => Monad (Ap f) # | Since: base-4.12.0.0 |
| Functor f => Functor (Ap f) # | Since: base-4.12.0.0 |
| MonadFix f => MonadFix (Ap f) # | Since: base-4.12.0.0 |
Defined in Control.Monad.Fix | |
| MonadFail f => MonadFail (Ap f) # | Since: base-4.12.0.0 |
Defined in Data.Monoid | |
| Applicative f => Applicative (Ap f) # | Since: base-4.12.0.0 |
| 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 # 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 |
| MonadPlus f => MonadPlus (Ap f) # | Since: base-4.12.0.0 |
| Alternative f => Alternative (Ap f) # | 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 | |
| Eq (f a) => Eq (Ap f a) # | 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 :: (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, Num a) => Num (Ap f a) # | Since: base-4.12.0.0 |
| Ord (f a) => Ord (Ap f a) # | 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 |
| Generic (Ap f a) # | |
| (Applicative f, Semigroup a) => Semigroup (Ap f a) # | Since: base-4.12.0.0 |
| (Applicative f, Monoid a) => Monoid (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 | |