| 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 | Safe |
| 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 {getSum = 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 :: k -> Type) (a :: k) = Alt {
- getAlt :: f a
- newtype Ap (f :: k -> Type) (a :: k) = Ap {
- getAp :: f a
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)<>zSemigrouplaw)- Concatenation
mconcat=foldr(<>)mempty
You can alternatively define mconcat instead of mempty, in which case the
laws are:
- Unit
mconcat(purex) = x- Multiplication
mconcat(joinxss) =mconcat(fmapmconcatxss)- Subclass
mconcat(toListxs) =sconcatxs
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.
Methods
Identity of mappend
Examples
>>>"Hello world" <> mempty"Hello world"
>>>mempty <> [1, 2, 3][1,2,3]
mappend :: a -> a -> a Source #
An associative operation
NOTE: This method is redundant and has the default
implementation 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 ByteArray Source # | Since: base-4.17.0.0 |
| Monoid All | Since: base-2.1 |
| Monoid Any | Since: base-2.1 |
| Monoid Event | Since: base-4.4.0.0 |
| Monoid EventLifetime | Since: base-4.8.0.0 |
| Monoid Lifetime |
Since: base-4.8.0.0 |
| Monoid ExceptionContext | |
Defined in GHC.Internal.Exception.Context Methods mempty :: ExceptionContext Source # mappend :: ExceptionContext -> ExceptionContext -> ExceptionContext Source # mconcat :: [ExceptionContext] -> ExceptionContext Source # | |
| Monoid Ordering | Since: base-2.1 |
| Monoid () | Since: base-2.1 |
| Monoid (Comparison a) Source # |
mempty :: Comparison a mempty = Comparison _ _ -> EQ |
Defined in Data.Functor.Contravariant Methods mempty :: Comparison a Source # mappend :: Comparison a -> Comparison a -> Comparison a Source # mconcat :: [Comparison a] -> Comparison a Source # | |
| Monoid (Equivalence a) Source # |
mempty :: Equivalence a mempty = Equivalence _ _ -> True |
Defined in Data.Functor.Contravariant Methods mempty :: Equivalence a Source # mappend :: Equivalence a -> Equivalence a -> Equivalence a Source # mconcat :: [Equivalence a] -> Equivalence a Source # | |
| Monoid (Predicate a) Source # |
mempty :: Predicate a mempty = _ -> True |
| (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 Methods mempty :: WrappedMonoid m Source # mappend :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m Source # mconcat :: [WrappedMonoid m] -> WrappedMonoid m Source # | |
| Monoid a => Monoid (STM a) | Since: base-4.17.0.0 |
| FiniteBits a => Monoid (And a) | This constraint is arguably too strong. However,
as some types (such as Since: base-4.16 |
| FiniteBits a => Monoid (Iff a) | This constraint is arguably
too strong. However, as some types (such as Since: base-4.16 |
| Bits a => Monoid (Ior a) | Since: base-4.16 |
| Bits a => Monoid (Xor a) | Since: base-4.16 |
| Monoid a => Monoid (Identity a) | Since: base-4.9.0.0 |
| Ord a => Monoid (Max a) | Since: base-4.8.0.0 |
| Ord a => Monoid (Min a) | Since: base-4.8.0.0 |
| 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 |
| 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 |
| (Generic a, Monoid (Rep a ())) => Monoid (Generically a) | Since: base-4.17.0.0 |
Defined in GHC.Internal.Generics Methods mempty :: Generically a Source # mappend :: Generically a -> Generically a -> Generically a Source # mconcat :: [Generically a] -> Generically a Source # | |
| Monoid p => Monoid (Par1 p) | 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 (Solo a) | Since: base-4.15 |
| Monoid [a] | Since: base-2.1 |
| Monoid a => Monoid (Op a b) Source # |
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 a, Monoid b) => Monoid (a, b) | Since: base-2.1 |
| 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 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) | 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 a)) => Monoid (Compose f g a) Source # | Since: base-4.16.0.0 |
| 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 Source #
An associative operation.
Examples
>>>[1,2,3] <> [4,5,6][1,2,3,4,5,6]
>>>Just [1, 2, 3] <> Just [4, 5, 6]Just [1,2,3,4,5,6]
>>>putStr "Hello, " <> putStrLn "World!"Hello, World!
The dual of a Monoid, obtained by swapping the arguments of (<>).
Dual a <> Dual b == Dual (b <> a)
Examples
>>>Dual "Hello" <> Dual "World"Dual {getDual = "WorldHello"}
>>>Dual (Dual "Hello") <> Dual (Dual "World")Dual {getDual = Dual {getDual = "HelloWorld"}}
Instances
| MonadZip Dual Source # | Since: base-4.8.0.0 | ||||
| Foldable1 Dual Source # | Since: base-4.18.0.0 | ||||
Defined in Data.Foldable1 Methods fold1 :: Semigroup m => Dual m -> m Source # foldMap1 :: Semigroup m => (a -> m) -> Dual a -> m Source # foldMap1' :: Semigroup m => (a -> m) -> Dual a -> m Source # toNonEmpty :: Dual a -> NonEmpty a Source # maximum :: Ord a => Dual a -> a Source # minimum :: Ord a => Dual a -> a Source # foldrMap1 :: (a -> b) -> (a -> b -> b) -> Dual a -> b Source # foldlMap1' :: (a -> b) -> (b -> a -> b) -> Dual a -> b Source # foldlMap1 :: (a -> b) -> (b -> a -> b) -> Dual a -> b Source # foldrMap1' :: (a -> b) -> (a -> b -> b) -> Dual a -> b Source # | |||||
| Applicative Dual | Since: base-4.8.0.0 | ||||
| Functor Dual | Since: base-4.8.0.0 | ||||
| Monad Dual | Since: base-4.8.0.0 | ||||
| MonadFix Dual | Since: base-4.8.0.0 | ||||
| Foldable Dual | Since: base-4.8.0.0 | ||||
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => Dual m -> m Source # foldMap :: Monoid m => (a -> m) -> Dual a -> m Source # foldMap' :: Monoid m => (a -> m) -> Dual a -> m Source # foldr :: (a -> b -> b) -> b -> Dual a -> b Source # foldr' :: (a -> b -> b) -> b -> Dual a -> b Source # foldl :: (b -> a -> b) -> b -> Dual a -> b Source # foldl' :: (b -> a -> b) -> b -> Dual a -> b Source # foldr1 :: (a -> a -> a) -> Dual a -> a Source # foldl1 :: (a -> a -> a) -> Dual a -> a Source # toList :: Dual a -> [a] Source # null :: Dual a -> Bool Source # length :: Dual a -> Int Source # elem :: Eq a => a -> Dual a -> Bool Source # maximum :: Ord a => Dual a -> a Source # minimum :: Ord a => Dual a -> a Source # | |||||
| Traversable Dual | Since: base-4.8.0.0 | ||||
Defined in GHC.Internal.Data.Traversable | |||||
| Generic1 Dual | |||||
Defined in GHC.Internal.Data.Semigroup.Internal Associated Types
| |||||
| Monoid a => Monoid (Dual a) | Since: base-2.1 | ||||
| Semigroup a => Semigroup (Dual a) | Since: base-4.9.0.0 | ||||
| Data a => Data (Dual a) | Since: base-4.8.0.0 | ||||
Defined in GHC.Internal.Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Dual a -> c (Dual a) Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Dual a) Source # toConstr :: Dual a -> Constr Source # dataTypeOf :: Dual a -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Dual a)) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Dual a)) Source # gmapT :: (forall b. Data b => b -> b) -> Dual a -> Dual a Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Dual a -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Dual a -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Dual a -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Dual a -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Dual a -> m (Dual a) Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Dual a -> m (Dual a) Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Dual a -> m (Dual a) Source # | |||||
| Bounded a => Bounded (Dual a) | Since: base-2.1 | ||||
| Generic (Dual a) | |||||
Defined in GHC.Internal.Data.Semigroup.Internal Associated Types
| |||||
| 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 | ||||
Defined in GHC.Internal.Data.Semigroup.Internal | |||||
| type Rep1 Dual | Since: base-4.7.0.0 | ||||
Defined in GHC.Internal.Data.Semigroup.Internal | |||||
| type Rep (Dual a) | Since: base-4.7.0.0 | ||||
Defined in GHC.Internal.Data.Semigroup.Internal | |||||
The monoid of endomorphisms under composition.
Endo f <> Endo g == Endo (f . g)
Examples
>>>let computation = Endo ("Hello, " ++) <> Endo (++ "!")>>>appEndo computation "Haskell""Hello, Haskell!"
>>>let computation = Endo (*3) <> Endo (+1)>>>appEndo computation 16
Instances
| Monoid (Endo a) | Since: base-2.1 | ||||
| Semigroup (Endo a) | Since: base-4.9.0.0 | ||||
| Generic (Endo a) | |||||
Defined in GHC.Internal.Data.Semigroup.Internal Associated Types
| |||||
| type Rep (Endo a) | Since: base-4.7.0.0 | ||||
Defined in GHC.Internal.Data.Semigroup.Internal | |||||
Bool wrappers
Boolean monoid under conjunction (&&).
All x <> All y = All (x && y)
Examples
>>>All True <> mempty <> All False)All {getAll = False}
>>>mconcat (map (\x -> All (even x)) [2,4,6,7,8])All {getAll = False}
>>>All True <> memptyAll {getAll = True}
Instances
| Monoid All | Since: base-2.1 | ||||
| Semigroup All | Since: base-4.9.0.0 | ||||
| Data All | Since: base-4.8.0.0 | ||||
Defined in GHC.Internal.Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> All -> c All Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c All Source # toConstr :: All -> Constr Source # dataTypeOf :: All -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c All) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c All) Source # gmapT :: (forall b. Data b => b -> b) -> All -> All Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> All -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> All -> r Source # gmapQ :: (forall d. Data d => d -> u) -> All -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> All -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> All -> m All Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> All -> m All Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> All -> m All Source # | |||||
| Bounded All | Since: base-2.1 | ||||
| Generic All | |||||
Defined in GHC.Internal.Data.Semigroup.Internal Associated Types
| |||||
| Read All | Since: base-2.1 | ||||
| Show All | Since: base-2.1 | ||||
| Eq All | Since: base-2.1 | ||||
| Ord All | Since: base-2.1 | ||||
Defined in GHC.Internal.Data.Semigroup.Internal | |||||
| type Rep All | Since: base-4.7.0.0 | ||||
Defined in GHC.Internal.Data.Semigroup.Internal | |||||
Boolean monoid under disjunction (||).
Any x <> Any y = Any (x || y)
Examples
>>>Any True <> mempty <> Any FalseAny {getAny = True}
>>>mconcat (map (\x -> Any (even x)) [2,4,6,7,8])Any {getAny = True}
>>>Any False <> memptyAny {getAny = False}
Instances
| Monoid Any | Since: base-2.1 | ||||
| Semigroup Any | Since: base-4.9.0.0 | ||||
| Data Any | Since: base-4.8.0.0 | ||||
Defined in GHC.Internal.Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Any -> c Any Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Any Source # toConstr :: Any -> Constr Source # dataTypeOf :: Any -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Any) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Any) Source # gmapT :: (forall b. Data b => b -> b) -> Any -> Any Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Any -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Any -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Any -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Any -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Any -> m Any Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Any -> m Any Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Any -> m Any Source # | |||||
| Bounded Any | Since: base-2.1 | ||||
| Generic Any | |||||
Defined in GHC.Internal.Data.Semigroup.Internal Associated Types
| |||||
| Read Any | Since: base-2.1 | ||||
| Show Any | Since: base-2.1 | ||||
| Eq Any | Since: base-2.1 | ||||
| Ord Any | Since: base-2.1 | ||||
Defined in GHC.Internal.Data.Semigroup.Internal | |||||
| type Rep Any | Since: base-4.7.0.0 | ||||
Defined in GHC.Internal.Data.Semigroup.Internal | |||||
Num wrappers
Monoid under addition.
Sum a <> Sum b = Sum (a + b)
Examples
>>>Sum 1 <> Sum 2 <> memptySum {getSum = 3}
>>>mconcat [ Sum n | n <- [3 .. 9]]Sum {getSum = 42}
Instances
| MonadZip Sum Source # | Since: base-4.8.0.0 | ||||
| Foldable1 Sum Source # | Since: base-4.18.0.0 | ||||
Defined in Data.Foldable1 Methods fold1 :: Semigroup m => Sum m -> m Source # foldMap1 :: Semigroup m => (a -> m) -> Sum a -> m Source # foldMap1' :: Semigroup m => (a -> m) -> Sum a -> m Source # toNonEmpty :: Sum a -> NonEmpty a Source # maximum :: Ord a => Sum a -> a Source # minimum :: Ord a => Sum a -> a Source # foldrMap1 :: (a -> b) -> (a -> b -> b) -> Sum a -> b Source # foldlMap1' :: (a -> b) -> (b -> a -> b) -> Sum a -> b Source # foldlMap1 :: (a -> b) -> (b -> a -> b) -> Sum a -> b Source # foldrMap1' :: (a -> b) -> (a -> b -> b) -> Sum a -> b Source # | |||||
| Applicative Sum | Since: base-4.8.0.0 | ||||
| Functor Sum | Since: base-4.8.0.0 | ||||
| Monad Sum | Since: base-4.8.0.0 | ||||
| MonadFix Sum | Since: base-4.8.0.0 | ||||
| Foldable Sum | Since: base-4.8.0.0 | ||||
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => Sum m -> m Source # foldMap :: Monoid m => (a -> m) -> Sum a -> m Source # foldMap' :: Monoid m => (a -> m) -> Sum a -> m Source # foldr :: (a -> b -> b) -> b -> Sum a -> b Source # foldr' :: (a -> b -> b) -> b -> Sum a -> b Source # foldl :: (b -> a -> b) -> b -> Sum a -> b Source # foldl' :: (b -> a -> b) -> b -> Sum a -> b Source # foldr1 :: (a -> a -> a) -> Sum a -> a Source # foldl1 :: (a -> a -> a) -> Sum a -> a Source # toList :: Sum a -> [a] Source # null :: Sum a -> Bool Source # length :: Sum a -> Int Source # elem :: Eq a => a -> Sum a -> Bool Source # maximum :: Ord a => Sum a -> a Source # minimum :: Ord a => Sum a -> a Source # | |||||
| Traversable Sum | Since: base-4.8.0.0 | ||||
| Generic1 Sum | |||||
Defined in GHC.Internal.Data.Semigroup.Internal Associated Types
| |||||
| Num a => Monoid (Sum a) | Since: base-2.1 | ||||
| Num a => Semigroup (Sum a) | Since: base-4.9.0.0 | ||||
| Data a => Data (Sum a) | Since: base-4.8.0.0 | ||||
Defined in GHC.Internal.Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Sum a -> c (Sum a) Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Sum a) Source # toConstr :: Sum a -> Constr Source # dataTypeOf :: Sum a -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Sum a)) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Sum a)) Source # gmapT :: (forall b. Data b => b -> b) -> Sum a -> Sum a Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Sum a -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Sum a -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Sum a -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Sum a -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Sum a -> m (Sum a) Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Sum a -> m (Sum a) Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Sum a -> m (Sum a) Source # | |||||
| Bounded a => Bounded (Sum a) | Since: base-2.1 | ||||
| Generic (Sum a) | |||||
Defined in GHC.Internal.Data.Semigroup.Internal Associated Types
| |||||
| Num a => Num (Sum a) | Since: base-4.7.0.0 | ||||
Defined in GHC.Internal.Data.Semigroup.Internal | |||||
| 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 GHC.Internal.Data.Semigroup.Internal | |||||
| type Rep1 Sum | Since: base-4.7.0.0 | ||||
Defined in GHC.Internal.Data.Semigroup.Internal | |||||
| type Rep (Sum a) | Since: base-4.7.0.0 | ||||
Defined in GHC.Internal.Data.Semigroup.Internal | |||||
Monoid under multiplication.
Product x <> Product y == Product (x * y)
Examples
>>>Product 3 <> Product 4 <> memptyProduct {getProduct = 12}
>>>mconcat [ Product n | n <- [2 .. 10]]Product {getProduct = 3628800}
Constructors
| Product | |
Fields
| |
Instances
| MonadZip Product Source # | Since: base-4.8.0.0 | ||||
| Foldable1 Product Source # | Since: base-4.18.0.0 | ||||
Defined in Data.Foldable1 Methods fold1 :: Semigroup m => Product m -> m Source # foldMap1 :: Semigroup m => (a -> m) -> Product a -> m Source # foldMap1' :: Semigroup m => (a -> m) -> Product a -> m Source # toNonEmpty :: Product a -> NonEmpty a Source # maximum :: Ord a => Product a -> a Source # minimum :: Ord a => Product a -> a Source # head :: Product a -> a Source # last :: Product a -> a Source # foldrMap1 :: (a -> b) -> (a -> b -> b) -> Product a -> b Source # foldlMap1' :: (a -> b) -> (b -> a -> b) -> Product a -> b Source # foldlMap1 :: (a -> b) -> (b -> a -> b) -> Product a -> b Source # foldrMap1' :: (a -> b) -> (a -> b -> b) -> Product a -> b Source # | |||||
| Applicative Product | Since: base-4.8.0.0 | ||||
Defined in GHC.Internal.Data.Semigroup.Internal | |||||
| Functor Product | Since: base-4.8.0.0 | ||||
| Monad Product | Since: base-4.8.0.0 | ||||
| MonadFix Product | Since: base-4.8.0.0 | ||||
| Foldable Product | Since: base-4.8.0.0 | ||||
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => Product m -> m Source # foldMap :: Monoid m => (a -> m) -> Product a -> m Source # foldMap' :: Monoid m => (a -> m) -> Product a -> m Source # foldr :: (a -> b -> b) -> b -> Product a -> b Source # foldr' :: (a -> b -> b) -> b -> Product a -> b Source # foldl :: (b -> a -> b) -> b -> Product a -> b Source # foldl' :: (b -> a -> b) -> b -> Product a -> b Source # foldr1 :: (a -> a -> a) -> Product a -> a Source # foldl1 :: (a -> a -> a) -> Product a -> a Source # toList :: Product a -> [a] Source # null :: Product a -> Bool Source # length :: Product a -> Int Source # elem :: Eq a => a -> Product a -> Bool Source # maximum :: Ord a => Product a -> a Source # minimum :: Ord a => Product a -> a Source # | |||||
| Traversable Product | Since: base-4.8.0.0 | ||||
Defined in GHC.Internal.Data.Traversable | |||||
| Generic1 Product | |||||
Defined in GHC.Internal.Data.Semigroup.Internal Associated Types
| |||||
| Num a => Monoid (Product a) | Since: base-2.1 | ||||
| Num a => Semigroup (Product a) | Since: base-4.9.0.0 | ||||
| Data a => Data (Product a) | Since: base-4.8.0.0 | ||||
Defined in GHC.Internal.Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Product a -> c (Product a) Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Product a) Source # toConstr :: Product a -> Constr Source # dataTypeOf :: Product a -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Product a)) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Product a)) Source # gmapT :: (forall b. Data b => b -> b) -> Product a -> Product a Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Product a -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Product a -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Product a -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Product a -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Product a -> m (Product a) Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Product a -> m (Product a) Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Product a -> m (Product a) Source # | |||||
| Bounded a => Bounded (Product a) | Since: base-2.1 | ||||
| Generic (Product a) | |||||
Defined in GHC.Internal.Data.Semigroup.Internal Associated Types
| |||||
| Num a => Num (Product a) | Since: base-4.7.0.0 | ||||
Defined in GHC.Internal.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) | 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 GHC.Internal.Data.Semigroup.Internal | |||||
| type Rep1 Product | Since: base-4.7.0.0 | ||||
Defined in GHC.Internal.Data.Semigroup.Internal | |||||
| type Rep (Product a) | Since: base-4.7.0.0 | ||||
Defined in GHC.Internal.Data.Semigroup.Internal | |||||
Maybe wrappers
Maybe monoid returning the leftmost non-Nothing value.
First aAlt Maybe a
Beware that Data.Monoid.First is different from
Data.Semigroup.First. The former returns the first non-Nothing,
so Data.Monoid.First Nothing <> x = x. The latter simply returns the first value,
thus Data.Semigroup.First Nothing <> x = Data.Semigroup.First Nothing.
Examples
>>>First (Just "hello") <> First Nothing <> First (Just "world")First {getFirst = Just "hello"}
>>>First Nothing <> memptyFirst {getFirst = Nothing}
Instances
| MonadZip First Source # | 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 | ||||
| MonadFix First | Since: base-4.8.0.0 | ||||
| Foldable First | Since: base-4.8.0.0 | ||||
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => First m -> m Source # foldMap :: Monoid m => (a -> m) -> First a -> m Source # foldMap' :: Monoid m => (a -> m) -> First a -> m Source # foldr :: (a -> b -> b) -> b -> First a -> b Source # foldr' :: (a -> b -> b) -> b -> First a -> b Source # foldl :: (b -> a -> b) -> b -> First a -> b Source # foldl' :: (b -> a -> b) -> b -> First a -> b Source # foldr1 :: (a -> a -> a) -> First a -> a Source # foldl1 :: (a -> a -> a) -> First a -> a Source # toList :: First a -> [a] Source # null :: First a -> Bool Source # length :: First a -> Int Source # elem :: Eq a => a -> First a -> Bool Source # maximum :: Ord a => First a -> a Source # minimum :: Ord a => First a -> a Source # | |||||
| Traversable First | Since: base-4.8.0.0 | ||||
Defined in GHC.Internal.Data.Traversable | |||||
| Generic1 First | |||||
Defined in GHC.Internal.Data.Monoid Associated Types
| |||||
| Monoid (First a) | Since: base-2.1 | ||||
| Semigroup (First a) | Since: base-4.9.0.0 | ||||
| Data a => Data (First a) | Since: base-4.8.0.0 | ||||
Defined in GHC.Internal.Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> First a -> c (First a) Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (First a) Source # toConstr :: First a -> Constr Source # dataTypeOf :: First a -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (First a)) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (First a)) Source # gmapT :: (forall b. Data b => b -> b) -> First a -> First a Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> First a -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> First a -> r Source # gmapQ :: (forall d. Data d => d -> u) -> First a -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> First a -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> First a -> m (First a) Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> First a -> m (First a) Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> First a -> m (First a) Source # | |||||
| Generic (First a) | |||||
Defined in GHC.Internal.Data.Monoid Associated Types
| |||||
| 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 | ||||
Defined in GHC.Internal.Data.Monoid | |||||
| type Rep1 First | Since: base-4.7.0.0 | ||||
Defined in GHC.Internal.Data.Monoid | |||||
| type Rep (First a) | Since: base-4.7.0.0 | ||||
Defined in GHC.Internal.Data.Monoid | |||||
Maybe monoid returning the rightmost non-Nothing value.
Last aDual (First a)Dual (Alt Maybe a)
Data.Semigroup.Last. The former returns the last non-Nothing,
so x <> Data.Monoid.Last Nothing = x. The latter simply returns the last value,
thus x <> Data.Semigroup.Last Nothing = Data.Semigroup.Last Nothing.
Examples
>>>Last (Just "hello") <> Last Nothing <> Last (Just "world")Last {getLast = Just "world"}
>>>Last Nothing <> memptyLast {getLast = Nothing}
Instances
| MonadZip Last Source # | 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 | ||||
| MonadFix Last | Since: base-4.8.0.0 | ||||
| Foldable Last | Since: base-4.8.0.0 | ||||
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => Last m -> m Source # foldMap :: Monoid m => (a -> m) -> Last a -> m Source # foldMap' :: Monoid m => (a -> m) -> Last a -> m Source # foldr :: (a -> b -> b) -> b -> Last a -> b Source # foldr' :: (a -> b -> b) -> b -> Last a -> b Source # foldl :: (b -> a -> b) -> b -> Last a -> b Source # foldl' :: (b -> a -> b) -> b -> Last a -> b Source # foldr1 :: (a -> a -> a) -> Last a -> a Source # foldl1 :: (a -> a -> a) -> Last a -> a Source # toList :: Last a -> [a] Source # null :: Last a -> Bool Source # length :: Last a -> Int Source # elem :: Eq a => a -> Last a -> Bool Source # maximum :: Ord a => Last a -> a Source # minimum :: Ord a => Last a -> a Source # | |||||
| Traversable Last | Since: base-4.8.0.0 | ||||
Defined in GHC.Internal.Data.Traversable | |||||
| Generic1 Last | |||||
Defined in GHC.Internal.Data.Monoid Associated Types
| |||||
| Monoid (Last a) | Since: base-2.1 | ||||
| Semigroup (Last a) | Since: base-4.9.0.0 | ||||
| Data a => Data (Last a) | Since: base-4.8.0.0 | ||||
Defined in GHC.Internal.Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Last a -> c (Last a) Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Last a) Source # toConstr :: Last a -> Constr Source # dataTypeOf :: Last a -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Last a)) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Last a)) Source # gmapT :: (forall b. Data b => b -> b) -> Last a -> Last a Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Last a -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Last a -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Last a -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Last a -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Last a -> m (Last a) Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Last a -> m (Last a) Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Last a -> m (Last a) Source # | |||||
| Generic (Last a) | |||||
Defined in GHC.Internal.Data.Monoid Associated Types
| |||||
| 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 | ||||
| type Rep1 Last | Since: base-4.7.0.0 | ||||
Defined in GHC.Internal.Data.Monoid | |||||
| type Rep (Last a) | Since: base-4.7.0.0 | ||||
Defined in GHC.Internal.Data.Monoid | |||||
Alternative wrapper
newtype Alt (f :: k -> Type) (a :: k) Source #
Monoid under <|>.
Alt l <> Alt r == Alt (l <|> r)
Examples
>>>Alt (Just 12) <> Alt (Just 24)Alt {getAlt = Just 12}
>>>Alt Nothing <> Alt (Just 24)Alt {getAlt = Just 24}
Since: base-4.8.0.0
Instances
| Generic1 (Alt f :: k -> Type) | |||||
Defined in GHC.Internal.Data.Semigroup.Internal Associated Types
| |||||
| MonadZip f => MonadZip (Alt f) Source # | Since: base-4.8.0.0 | ||||
| Foldable1 f => Foldable1 (Alt f) Source # | Since: base-4.18.0.0 | ||||
Defined in Data.Foldable1 Methods fold1 :: Semigroup m => Alt f m -> m Source # foldMap1 :: Semigroup m => (a -> m) -> Alt f a -> m Source # foldMap1' :: Semigroup m => (a -> m) -> Alt f a -> m Source # toNonEmpty :: Alt f a -> NonEmpty a Source # maximum :: Ord a => Alt f a -> a Source # minimum :: Ord a => Alt f a -> a Source # foldrMap1 :: (a -> b) -> (a -> b -> b) -> Alt f a -> b Source # foldlMap1' :: (a -> b) -> (b -> a -> b) -> Alt f a -> b Source # foldlMap1 :: (a -> b) -> (b -> a -> b) -> Alt f a -> b Source # foldrMap1' :: (a -> b) -> (a -> b -> b) -> Alt f a -> b Source # | |||||
| Contravariant f => Contravariant (Alt f) Source # | |||||
| 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 | ||||
| MonadFix f => MonadFix (Alt f) | Since: base-4.8.0.0 | ||||
| Foldable f => Foldable (Alt f) | Since: base-4.12.0.0 | ||||
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => Alt f m -> m Source # foldMap :: Monoid m => (a -> m) -> Alt f a -> m Source # foldMap' :: Monoid m => (a -> m) -> Alt f a -> m Source # foldr :: (a -> b -> b) -> b -> Alt f a -> b Source # foldr' :: (a -> b -> b) -> b -> Alt f a -> b Source # foldl :: (b -> a -> b) -> b -> Alt f a -> b Source # foldl' :: (b -> a -> b) -> b -> Alt f a -> b Source # foldr1 :: (a -> a -> a) -> Alt f a -> a Source # foldl1 :: (a -> a -> a) -> Alt f a -> a Source # toList :: Alt f a -> [a] Source # null :: Alt f a -> Bool Source # length :: Alt f a -> Int Source # elem :: Eq a => a -> Alt f a -> Bool Source # maximum :: Ord a => Alt f a -> a Source # minimum :: Ord a => Alt f a -> a Source # | |||||
| Traversable f => Traversable (Alt f) | Since: base-4.12.0.0 | ||||
Defined in GHC.Internal.Data.Traversable | |||||
| Alternative f => Monoid (Alt f a) | Since: base-4.8.0.0 | ||||
| Alternative f => Semigroup (Alt f a) | Since: base-4.9.0.0 | ||||
| (Data (f a), Data a, Typeable f) => Data (Alt f a) | Since: base-4.8.0.0 | ||||
Defined in GHC.Internal.Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Alt f a -> c (Alt f a) Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Alt f a) Source # toConstr :: Alt f a -> Constr Source # dataTypeOf :: Alt f a -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Alt f a)) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Alt f a)) Source # gmapT :: (forall b. Data b => b -> b) -> Alt f a -> Alt f a Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Alt f a -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Alt f a -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Alt f a -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Alt f a -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Alt f a -> m (Alt f a) Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Alt f a -> m (Alt f a) Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Alt f a -> m (Alt f a) Source # | |||||
| Enum (f a) => Enum (Alt f a) | Since: base-4.8.0.0 | ||||
Defined in GHC.Internal.Data.Semigroup.Internal Methods succ :: Alt f a -> Alt f a Source # pred :: Alt f a -> Alt f a Source # toEnum :: Int -> Alt f a Source # fromEnum :: Alt f a -> Int Source # enumFrom :: Alt f a -> [Alt f a] Source # enumFromThen :: Alt f a -> Alt f a -> [Alt f a] Source # enumFromTo :: Alt f a -> Alt f a -> [Alt f a] Source # enumFromThenTo :: Alt f a -> Alt f a -> Alt f a -> [Alt f a] Source # | |||||
| Generic (Alt f a) | |||||
Defined in GHC.Internal.Data.Semigroup.Internal Associated Types
| |||||
| Num (f a) => Num (Alt f a) | Since: base-4.8.0.0 | ||||
Defined in GHC.Internal.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 | ||||
| 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 GHC.Internal.Data.Semigroup.Internal | |||||
| type Rep1 (Alt f :: k -> Type) | Since: base-4.8.0.0 | ||||
Defined in GHC.Internal.Data.Semigroup.Internal | |||||
| type Rep (Alt f a) | Since: base-4.8.0.0 | ||||
Defined in GHC.Internal.Data.Semigroup.Internal | |||||
Applicative wrapper
newtype Ap (f :: k -> Type) (a :: k) Source #
This data type witnesses the lifting of a Monoid into an
Applicative pointwise.
Examples
>>>Ap (Just [1, 2, 3]) <> Ap NothingAp {getAp = Nothing}
>>>Ap [Sum 10, Sum 20] <> Ap [Sum 1, Sum 2]Ap {getAp = [Sum {getSum = 11},Sum {getSum = 12},Sum {getSum = 21},Sum {getSum = 22}]}
Since: base-4.12.0.0
Instances
| Generic1 (Ap f :: k -> Type) | |||||
Defined in GHC.Internal.Data.Monoid Associated Types
| |||||
| Foldable1 f => Foldable1 (Ap f) Source # | Since: base-4.18.0.0 | ||||
Defined in Data.Foldable1 Methods fold1 :: Semigroup m => Ap f m -> m Source # foldMap1 :: Semigroup m => (a -> m) -> Ap f a -> m Source # foldMap1' :: Semigroup m => (a -> m) -> Ap f a -> m Source # toNonEmpty :: Ap f a -> NonEmpty a Source # maximum :: Ord a => Ap f a -> a Source # minimum :: Ord a => Ap f a -> a Source # foldrMap1 :: (a -> b) -> (a -> b -> b) -> Ap f a -> b Source # foldlMap1' :: (a -> b) -> (b -> a -> b) -> Ap f a -> b Source # foldlMap1 :: (a -> b) -> (b -> a -> b) -> Ap f a -> b Source # foldrMap1' :: (a -> b) -> (a -> b -> b) -> Ap f a -> b Source # | |||||
| 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 | ||||
| MonadFail f => MonadFail (Ap f) | Since: base-4.12.0.0 | ||||
| MonadFix f => MonadFix (Ap f) | Since: base-4.12.0.0 | ||||
| Foldable f => Foldable (Ap f) | Since: base-4.12.0.0 | ||||
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => Ap f m -> m Source # foldMap :: Monoid m => (a -> m) -> Ap f a -> m Source # foldMap' :: Monoid m => (a -> m) -> Ap f a -> m Source # foldr :: (a -> b -> b) -> b -> Ap f a -> b Source # foldr' :: (a -> b -> b) -> b -> Ap f a -> b Source # foldl :: (b -> a -> b) -> b -> Ap f a -> b Source # foldl' :: (b -> a -> b) -> b -> Ap f a -> b Source # foldr1 :: (a -> a -> a) -> Ap f a -> a Source # foldl1 :: (a -> a -> a) -> Ap f a -> a Source # toList :: Ap f a -> [a] Source # null :: Ap f a -> Bool Source # length :: Ap f a -> Int Source # elem :: Eq a => a -> Ap f a -> Bool Source # maximum :: Ord a => Ap f a -> a Source # minimum :: Ord a => Ap f a -> a Source # | |||||
| Traversable f => Traversable (Ap f) | Since: base-4.12.0.0 | ||||
Defined in GHC.Internal.Data.Traversable | |||||
| (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 | ||||
| (Data (f a), Data a, Typeable f) => Data (Ap f a) | Since: base-4.12.0.0 | ||||
Defined in GHC.Internal.Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Ap f a -> c (Ap f a) Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Ap f a) Source # toConstr :: Ap f a -> Constr Source # dataTypeOf :: Ap f a -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Ap f a)) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Ap f a)) Source # gmapT :: (forall b. Data b => b -> b) -> Ap f a -> Ap f a Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Ap f a -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Ap f a -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Ap f a -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Ap f a -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Ap f a -> m (Ap f a) Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Ap f a -> m (Ap f a) Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Ap f a -> m (Ap f a) Source # | |||||
| (Applicative f, 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 GHC.Internal.Data.Monoid Methods succ :: Ap f a -> Ap f a Source # pred :: Ap f a -> Ap f a Source # toEnum :: Int -> Ap f a Source # fromEnum :: Ap f a -> Int Source # enumFrom :: Ap f a -> [Ap f a] Source # enumFromThen :: Ap f a -> Ap f a -> [Ap f a] Source # enumFromTo :: Ap f a -> Ap f a -> [Ap f a] Source # enumFromThenTo :: Ap f a -> Ap f a -> Ap f a -> [Ap f a] Source # | |||||
| Generic (Ap f a) | |||||
Defined in GHC.Internal.Data.Monoid Associated Types
| |||||
| (Applicative f, Num a) => Num (Ap f a) | Note that even if the underlying Commutativity:
Additive inverse:
Distributivity:
Since: base-4.12.0.0 | ||||
Defined in GHC.Internal.Data.Monoid | |||||
| 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 GHC.Internal.Data.Monoid | |||||
| type Rep (Ap f a) | Since: base-4.12.0.0 | ||||
Defined in GHC.Internal.Data.Monoid | |||||