Safe Haskell | Safe |
---|---|
Language | Haskell2010 |
This module reexports functions to work with monoids plus adds extra useful functions.
Synopsis
- newtype Any = Any {}
- newtype Sum a = Sum {
- getSum :: a
- newtype Product a = Product {
- getProduct :: a
- newtype Last a = Last {}
- newtype First a = First {}
- class Semigroup a => Monoid a where
- newtype Alt (f :: k -> Type) (a :: k) = Alt {
- getAlt :: f a
- newtype All = All {}
- newtype Endo a = Endo {
- appEndo :: a -> a
- newtype Dual a = Dual {
- getDual :: a
- class Semigroup a where
- data WrappedMonoid m
- stimesIdempotent :: Integral b => b -> a -> a
- stimesIdempotentMonoid :: (Integral b, Monoid a) => b -> a -> a
- stimesMonoid :: (Integral b, Monoid a) => b -> a -> a
- cycle1 :: Semigroup m => m -> m
- mtimesDefault :: (Integral b, Monoid a) => b -> a -> a
- maybeToMonoid :: Monoid m => Maybe m -> m
Documentation
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 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 |
NFData Any | Since: deepseq-1.4.0.0 |
Defined in Control.DeepSeq | |
Eq Any | Since: base-2.1 |
Ord Any | Since: base-2.1 |
Unbox Any | |
Defined in Data.Vector.Unboxed.Base | |
Vector Vector Any | |
Defined in Data.Vector.Unboxed.Base basicUnsafeFreeze :: Mutable Vector s Any -> ST s (Vector Any) # basicUnsafeThaw :: Vector Any -> ST s (Mutable Vector s Any) # basicLength :: Vector Any -> Int # basicUnsafeSlice :: Int -> Int -> Vector Any -> Vector Any # basicUnsafeIndexM :: Vector Any -> Int -> Box Any # basicUnsafeCopy :: Mutable Vector s Any -> Vector Any -> ST s () # | |
MVector MVector Any | |
Defined in Data.Vector.Unboxed.Base basicLength :: MVector s Any -> Int # basicUnsafeSlice :: Int -> Int -> MVector s Any -> MVector s Any # basicOverlaps :: MVector s Any -> MVector s Any -> Bool # basicUnsafeNew :: Int -> ST s (MVector s Any) # basicInitialize :: MVector s Any -> ST s () # basicUnsafeReplicate :: Int -> Any -> ST s (MVector s Any) # basicUnsafeRead :: MVector s Any -> Int -> ST s Any # basicUnsafeWrite :: MVector s Any -> Int -> Any -> ST s () # basicClear :: MVector s Any -> ST s () # basicSet :: MVector s Any -> Any -> ST s () # basicUnsafeCopy :: MVector s Any -> MVector s Any -> ST s () # basicUnsafeMove :: MVector s Any -> MVector s Any -> ST s () # basicUnsafeGrow :: MVector s Any -> Int -> ST s (MVector s Any) # | |
type Rep Any | Since: base-4.7.0.0 |
Defined in Data.Semigroup.Internal | |
newtype Vector Any | |
newtype MVector s Any | |
Monoid under addition.
>>>
getSum (Sum 1 <> Sum 2 <> mempty)
3
Instances
Foldable Sum | Since: base-4.8.0.0 |
Defined in Data.Foldable 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 |
NFData1 Sum | Since: deepseq-1.4.3.0 |
Defined in Control.DeepSeq | |
Generic1 Sum | |
Unbox a => Vector Vector (Sum a) | |
Defined in Data.Vector.Unboxed.Base basicUnsafeFreeze :: Mutable Vector s (Sum a) -> ST s (Vector (Sum a)) # basicUnsafeThaw :: Vector (Sum a) -> ST s (Mutable Vector s (Sum a)) # basicLength :: Vector (Sum a) -> Int # basicUnsafeSlice :: Int -> Int -> Vector (Sum a) -> Vector (Sum a) # basicUnsafeIndexM :: Vector (Sum a) -> Int -> Box (Sum a) # basicUnsafeCopy :: Mutable Vector s (Sum a) -> Vector (Sum a) -> ST s () # | |
Unbox a => MVector MVector (Sum a) | |
Defined in Data.Vector.Unboxed.Base basicLength :: MVector s (Sum a) -> Int # basicUnsafeSlice :: Int -> Int -> MVector s (Sum a) -> MVector s (Sum a) # basicOverlaps :: MVector s (Sum a) -> MVector s (Sum a) -> Bool # basicUnsafeNew :: Int -> ST s (MVector s (Sum a)) # basicInitialize :: MVector s (Sum a) -> ST s () # basicUnsafeReplicate :: Int -> Sum a -> ST s (MVector s (Sum a)) # basicUnsafeRead :: MVector s (Sum a) -> Int -> ST s (Sum a) # basicUnsafeWrite :: MVector s (Sum a) -> Int -> Sum a -> ST s () # basicClear :: MVector s (Sum a) -> ST s () # basicSet :: MVector s (Sum a) -> Sum a -> ST s () # basicUnsafeCopy :: MVector s (Sum a) -> MVector s (Sum a) -> ST s () # basicUnsafeMove :: MVector s (Sum a) -> MVector s (Sum a) -> ST s () # basicUnsafeGrow :: MVector s (Sum a) -> Int -> ST s (MVector s (Sum a)) # | |
Data a => Data (Sum a) | Since: base-4.8.0.0 |
Defined in Data.Data 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 |
NFData a => NFData (Sum a) | Since: deepseq-1.4.0.0 |
Defined in Control.DeepSeq | |
Eq a => Eq (Sum a) | Since: base-2.1 |
Ord a => Ord (Sum a) | Since: base-2.1 |
Prim a => Prim (Sum a) | Since: primitive-0.6.5.0 |
Defined in Data.Primitive.Types sizeOfType# :: Proxy (Sum a) -> Int# # alignmentOfType# :: Proxy (Sum a) -> Int# # alignment# :: Sum a -> Int# # indexByteArray# :: ByteArray# -> Int# -> Sum a # readByteArray# :: MutableByteArray# s -> Int# -> State# s -> (# State# s, Sum a #) # writeByteArray# :: MutableByteArray# s -> Int# -> Sum a -> State# s -> State# s # setByteArray# :: MutableByteArray# s -> Int# -> Int# -> Sum a -> State# s -> State# s # indexOffAddr# :: Addr# -> Int# -> Sum a # readOffAddr# :: Addr# -> Int# -> State# s -> (# State# s, Sum a #) # writeOffAddr# :: Addr# -> Int# -> Sum a -> State# s -> State# s # setOffAddr# :: Addr# -> Int# -> Int# -> Sum a -> State# s -> State# s # | |
Container (Sum a) Source # | |
Defined in Universum.Container.Class toList :: Sum a -> [Element (Sum a)] Source # null :: Sum a -> Bool Source # foldr :: (Element (Sum a) -> b -> b) -> b -> Sum a -> b Source # foldl :: (b -> Element (Sum a) -> b) -> b -> Sum a -> b Source # foldl' :: (b -> Element (Sum a) -> b) -> b -> Sum a -> b Source # length :: Sum a -> Int Source # elem :: Element (Sum a) -> Sum a -> Bool Source # foldMap :: Monoid m => (Element (Sum a) -> m) -> Sum a -> m Source # fold :: Sum a -> Element (Sum a) Source # foldr' :: (Element (Sum a) -> b -> b) -> b -> Sum a -> b Source # notElem :: Element (Sum a) -> Sum a -> Bool Source # all :: (Element (Sum a) -> Bool) -> Sum a -> Bool Source # any :: (Element (Sum a) -> Bool) -> Sum a -> Bool Source # find :: (Element (Sum a) -> Bool) -> Sum a -> Maybe (Element (Sum a)) Source # safeHead :: Sum a -> Maybe (Element (Sum a)) Source # safeMaximum :: Sum a -> Maybe (Element (Sum a)) Source # safeMinimum :: Sum a -> Maybe (Element (Sum a)) Source # safeFoldr1 :: (Element (Sum a) -> Element (Sum a) -> Element (Sum a)) -> Sum a -> Maybe (Element (Sum a)) Source # safeFoldl1 :: (Element (Sum a) -> Element (Sum a) -> Element (Sum a)) -> Sum a -> Maybe (Element (Sum a)) Source # | |
Unbox a => Unbox (Sum a) | |
Defined in Data.Vector.Unboxed.Base | |
type Rep1 Sum | Since: base-4.7.0.0 |
Defined in Data.Semigroup.Internal | |
newtype MVector s (Sum a) | |
Defined in Data.Vector.Unboxed.Base | |
type Rep (Sum a) | Since: base-4.7.0.0 |
Defined in Data.Semigroup.Internal | |
type Element (Sum a) Source # | |
Defined in Universum.Container.Class | |
newtype Vector (Sum a) | |
Defined in Data.Vector.Unboxed.Base |
Monoid under multiplication.
>>>
getProduct (Product 3 <> Product 4 <> mempty)
12
Product | |
|
Instances
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"
Beware that Data.Monoid.
Last
is different from
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
.
Instances
Foldable Last | Since: base-4.8.0.0 |
Defined in Data.Foldable 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 |
NFData1 Last | Since: deepseq-1.4.3.0 |
Defined in Control.DeepSeq | |
Generic1 Last | |
Data a => Data (Last a) | Since: base-4.8.0.0 |
Defined in Data.Data 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 |
NFData a => NFData (Last a) | Since: deepseq-1.4.0.0 |
Defined in Control.DeepSeq | |
Eq a => Eq (Last a) | Since: base-2.1 |
Ord a => Ord (Last a) | Since: base-2.1 |
Container (Last a) Source # | |
Defined in Universum.Container.Class toList :: Last a -> [Element (Last a)] Source # null :: Last a -> Bool Source # foldr :: (Element (Last a) -> b -> b) -> b -> Last a -> b Source # foldl :: (b -> Element (Last a) -> b) -> b -> Last a -> b Source # foldl' :: (b -> Element (Last a) -> b) -> b -> Last a -> b Source # length :: Last a -> Int Source # elem :: Element (Last a) -> Last a -> Bool Source # foldMap :: Monoid m => (Element (Last a) -> m) -> Last a -> m Source # fold :: Last a -> Element (Last a) Source # foldr' :: (Element (Last a) -> b -> b) -> b -> Last a -> b Source # notElem :: Element (Last a) -> Last a -> Bool Source # all :: (Element (Last a) -> Bool) -> Last a -> Bool Source # any :: (Element (Last a) -> Bool) -> Last a -> Bool Source # and :: Last a -> Bool Source # find :: (Element (Last a) -> Bool) -> Last a -> Maybe (Element (Last a)) Source # safeHead :: Last a -> Maybe (Element (Last a)) Source # safeMaximum :: Last a -> Maybe (Element (Last a)) Source # safeMinimum :: Last a -> Maybe (Element (Last a)) Source # safeFoldr1 :: (Element (Last a) -> Element (Last a) -> Element (Last a)) -> Last a -> Maybe (Element (Last a)) Source # safeFoldl1 :: (Element (Last a) -> Element (Last a) -> Element (Last a)) -> Last a -> Maybe (Element (Last a)) Source # | |
type Rep1 Last | Since: base-4.7.0.0 |
Defined in Data.Monoid | |
type Rep (Last a) | Since: base-4.7.0.0 |
Defined in Data.Monoid | |
type Element (Last a) Source # | |
Defined in Universum.Container.Class |
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"
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
.
Instances
Foldable First | Since: base-4.8.0.0 |
Defined in Data.Foldable 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 |
NFData1 First | Since: deepseq-1.4.3.0 |
Defined in Control.DeepSeq | |
Generic1 First | |
Data a => Data (First a) | Since: base-4.8.0.0 |
Defined in Data.Data 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 |
NFData a => NFData (First a) | Since: deepseq-1.4.0.0 |
Defined in Control.DeepSeq | |
Eq a => Eq (First a) | Since: base-2.1 |
Ord a => Ord (First a) | Since: base-2.1 |
Container (First a) Source # | |
Defined in Universum.Container.Class toList :: First a -> [Element (First a)] Source # null :: First a -> Bool Source # foldr :: (Element (First a) -> b -> b) -> b -> First a -> b Source # foldl :: (b -> Element (First a) -> b) -> b -> First a -> b Source # foldl' :: (b -> Element (First a) -> b) -> b -> First a -> b Source # length :: First a -> Int Source # elem :: Element (First a) -> First a -> Bool Source # foldMap :: Monoid m => (Element (First a) -> m) -> First a -> m Source # fold :: First a -> Element (First a) Source # foldr' :: (Element (First a) -> b -> b) -> b -> First a -> b Source # notElem :: Element (First a) -> First a -> Bool Source # all :: (Element (First a) -> Bool) -> First a -> Bool Source # any :: (Element (First a) -> Bool) -> First a -> Bool Source # and :: First a -> Bool Source # or :: First a -> Bool Source # find :: (Element (First a) -> Bool) -> First a -> Maybe (Element (First a)) Source # safeHead :: First a -> Maybe (Element (First a)) Source # safeMaximum :: First a -> Maybe (Element (First a)) Source # safeMinimum :: First a -> Maybe (Element (First a)) Source # safeFoldr1 :: (Element (First a) -> Element (First a) -> Element (First a)) -> First a -> Maybe (Element (First a)) Source # safeFoldl1 :: (Element (First a) -> Element (First a) -> Element (First a)) -> First a -> Maybe (Element (First a)) Source # | |
type Rep1 First | Since: base-4.7.0.0 |
Defined in Data.Monoid | |
type Rep (First a) | Since: base-4.7.0.0 |
Defined in Data.Monoid | |
type Element (First a) Source # | |
Defined in Universum.Container.Class |
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)<>
zSemigroup
law)- Concatenation
mconcat
=foldr
(<>
)mempty
You can alternatively define mconcat
instead of mempty
, in which case the
laws are:
- Unit
mconcat
(pure
x) = x- Multiplication
mconcat
(join
xss) =mconcat
(fmap
mconcat
xss)- Subclass
mconcat
(toList
xs) =sconcat
xs
The method names refer to the monoid of lists under concatenation, but there are many other instances.
Some types can be viewed as a monoid in more than one way,
e.g. both addition and multiplication on numbers.
In such cases we often define newtype
s and make those instances
of Monoid
, e.g. Sum
and Product
.
NOTE: Semigroup
is a superclass of Monoid
since base-4.11.0.0.
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 ByteArray | Since: base-4.17.0.0 |
Monoid All | Since: base-2.1 |
Monoid Any | Since: base-2.1 |
Monoid Builder | |
Monoid ByteString | |
Defined in Data.ByteString.Internal.Type mempty :: ByteString # mappend :: ByteString -> ByteString -> ByteString # mconcat :: [ByteString] -> ByteString # | |
Monoid ByteString | |
Defined in Data.ByteString.Lazy.Internal mempty :: ByteString # mappend :: ByteString -> ByteString -> ByteString # mconcat :: [ByteString] -> ByteString # | |
Monoid ShortByteString | |
Defined in Data.ByteString.Short.Internal mappend :: ShortByteString -> ShortByteString -> ShortByteString # mconcat :: [ShortByteString] -> ShortByteString # | |
Monoid IntSet | |
Monoid OsString | "String-Concatenation" for |
Monoid PosixString | |
Defined in System.OsString.Internal.Types.Hidden mempty :: PosixString # mappend :: PosixString -> PosixString -> PosixString # mconcat :: [PosixString] -> PosixString # | |
Monoid WindowsString | |
Defined in System.OsString.Internal.Types.Hidden mempty :: WindowsString # mappend :: WindowsString -> WindowsString -> WindowsString # mconcat :: [WindowsString] -> WindowsString # | |
Monoid Ordering | Since: base-2.1 |
Monoid Doc | |
Monoid () | Since: base-2.1 |
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 |
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 |
Monoid m => Monoid (WrappedMonoid m) | Since: base-4.9.0.0 |
Defined in Data.Semigroup 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 a => Monoid (STM a) | Since: base-4.17.0.0 |
(Generic a, Monoid (Rep a ())) => Monoid (Generically a) | Since: base-4.17.0.0 |
Defined in GHC.Generics mempty :: Generically a # mappend :: Generically a -> Generically a -> Generically a # mconcat :: [Generically a] -> Generically a # | |
Monoid p => Monoid (Par1 p) | Since: base-4.12.0.0 |
Monoid (IntMap a) | |
Monoid (Seq a) | |
Monoid (MergeSet a) | |
Ord a => Monoid (Set a) | |
Monoid a => Monoid (IO a) | Since: base-4.9.0.0 |
Monoid a => Monoid (May a) | |
Monoid (Doc a) | |
Monoid (Array a) | |
Monoid (PrimArray a) | Since: primitive-0.6.4.0 |
Monoid (SmallArray a) | |
Defined in Data.Primitive.SmallArray mempty :: SmallArray a # mappend :: SmallArray a -> SmallArray a -> SmallArray a # mconcat :: [SmallArray a] -> SmallArray a # | |
Monoid a => Monoid (Q a) | Since: template-haskell-2.17.0.0 |
(Hashable a, Eq a) => Monoid (HashSet a) | \(O(n+m)\) To obtain good performance, the smaller set must be presented as the first argument. Examples
|
Monoid (Vector a) | |
Prim a => Monoid (Vector a) | |
Storable a => Monoid (Vector a) | |
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 (Proxy s) | Since: base-4.7.0.0 |
Monoid (U1 p) | Since: base-4.12.0.0 |
Ord k => Monoid (Map k v) | |
Applicative f => Monoid (Traversed a f) | |
Monoid a => Monoid (Err e a) | |
(Eq k, Hashable k) => Monoid (HashMap k v) | If a key occurs in both maps, the mapping from the first will be the mapping in the result. Examples
|
(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 |
(Monad m, Monoid r) => Monoid (Effect m r a) | |
(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) | 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) | 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 |
newtype Alt (f :: k -> Type) (a :: k) #
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) | |
Unbox (f a) => Vector Vector (Alt f a) | |
Defined in Data.Vector.Unboxed.Base basicUnsafeFreeze :: Mutable Vector s (Alt f a) -> ST s (Vector (Alt f a)) # basicUnsafeThaw :: Vector (Alt f a) -> ST s (Mutable Vector s (Alt f a)) # basicLength :: Vector (Alt f a) -> Int # basicUnsafeSlice :: Int -> Int -> Vector (Alt f a) -> Vector (Alt f a) # basicUnsafeIndexM :: Vector (Alt f a) -> Int -> Box (Alt f a) # basicUnsafeCopy :: Mutable Vector s (Alt f a) -> Vector (Alt f a) -> ST s () # | |
Unbox (f a) => MVector MVector (Alt f a) | |
Defined in Data.Vector.Unboxed.Base basicLength :: MVector s (Alt f a) -> Int # basicUnsafeSlice :: Int -> Int -> MVector s (Alt f a) -> MVector s (Alt f a) # basicOverlaps :: MVector s (Alt f a) -> MVector s (Alt f a) -> Bool # basicUnsafeNew :: Int -> ST s (MVector s (Alt f a)) # basicInitialize :: MVector s (Alt f a) -> ST s () # basicUnsafeReplicate :: Int -> Alt f a -> ST s (MVector s (Alt f a)) # basicUnsafeRead :: MVector s (Alt f a) -> Int -> ST s (Alt f a) # basicUnsafeWrite :: MVector s (Alt f a) -> Int -> Alt f a -> ST s () # basicClear :: MVector s (Alt f a) -> ST s () # basicSet :: MVector s (Alt f a) -> Alt f a -> ST s () # basicUnsafeCopy :: MVector s (Alt f a) -> MVector s (Alt f a) -> ST s () # basicUnsafeMove :: MVector s (Alt f a) -> MVector s (Alt f a) -> ST s () # basicUnsafeGrow :: MVector s (Alt f a) -> Int -> ST s (MVector s (Alt f a)) # | |
Foldable f => Foldable (Alt f) | Since: base-4.12.0.0 |
Defined in Data.Foldable 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 # | |
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 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 |
Unbox (f a) => Unbox (Alt f a) | |
Defined in Data.Vector.Unboxed.Base | |
type Rep1 (Alt f :: k -> Type) | Since: base-4.8.0.0 |
Defined in Data.Semigroup.Internal | |
newtype MVector s (Alt f a) | |
Defined in Data.Vector.Unboxed.Base | |
type Rep (Alt f a) | Since: base-4.8.0.0 |
Defined in Data.Semigroup.Internal | |
newtype Vector (Alt f a) | |
Defined in Data.Vector.Unboxed.Base |
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 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 |
NFData All | Since: deepseq-1.4.0.0 |
Defined in Control.DeepSeq | |
Eq All | Since: base-2.1 |
Ord All | Since: base-2.1 |
Unbox All | |
Defined in Data.Vector.Unboxed.Base | |
Vector Vector All | |
Defined in Data.Vector.Unboxed.Base basicUnsafeFreeze :: Mutable Vector s All -> ST s (Vector All) # basicUnsafeThaw :: Vector All -> ST s (Mutable Vector s All) # basicLength :: Vector All -> Int # basicUnsafeSlice :: Int -> Int -> Vector All -> Vector All # basicUnsafeIndexM :: Vector All -> Int -> Box All # basicUnsafeCopy :: Mutable Vector s All -> Vector All -> ST s () # | |
MVector MVector All | |
Defined in Data.Vector.Unboxed.Base basicLength :: MVector s All -> Int # basicUnsafeSlice :: Int -> Int -> MVector s All -> MVector s All # basicOverlaps :: MVector s All -> MVector s All -> Bool # basicUnsafeNew :: Int -> ST s (MVector s All) # basicInitialize :: MVector s All -> ST s () # basicUnsafeReplicate :: Int -> All -> ST s (MVector s All) # basicUnsafeRead :: MVector s All -> Int -> ST s All # basicUnsafeWrite :: MVector s All -> Int -> All -> ST s () # basicClear :: MVector s All -> ST s () # basicSet :: MVector s All -> All -> ST s () # basicUnsafeCopy :: MVector s All -> MVector s All -> ST s () # basicUnsafeMove :: MVector s All -> MVector s All -> ST s () # basicUnsafeGrow :: MVector s All -> Int -> ST s (MVector s All) # | |
type Rep All | Since: base-4.7.0.0 |
Defined in Data.Semigroup.Internal | |
newtype Vector All | |
newtype MVector s All | |
The monoid of endomorphisms under composition.
>>>
let computation = Endo ("Hello, " ++) <> Endo (++ "!")
>>>
appEndo computation "Haskell"
"Hello, Haskell!"
The dual of a Monoid
, obtained by swapping the arguments of mappend
.
>>>
getDual (mappend (Dual "Hello") (Dual "World"))
"WorldHello"
Instances
Foldable Dual | Since: base-4.8.0.0 |
Defined in Data.Foldable 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 |
NFData1 Dual | Since: deepseq-1.4.3.0 |
Defined in Control.DeepSeq | |
Generic1 Dual | |
Unbox a => Vector Vector (Dual a) | |
Defined in Data.Vector.Unboxed.Base basicUnsafeFreeze :: Mutable Vector s (Dual a) -> ST s (Vector (Dual a)) # basicUnsafeThaw :: Vector (Dual a) -> ST s (Mutable Vector s (Dual a)) # basicLength :: Vector (Dual a) -> Int # basicUnsafeSlice :: Int -> Int -> Vector (Dual a) -> Vector (Dual a) # basicUnsafeIndexM :: Vector (Dual a) -> Int -> Box (Dual a) # basicUnsafeCopy :: Mutable Vector s (Dual a) -> Vector (Dual a) -> ST s () # | |
Unbox a => MVector MVector (Dual a) | |
Defined in Data.Vector.Unboxed.Base basicLength :: MVector s (Dual a) -> Int # basicUnsafeSlice :: Int -> Int -> MVector s (Dual a) -> MVector s (Dual a) # basicOverlaps :: MVector s (Dual a) -> MVector s (Dual a) -> Bool # basicUnsafeNew :: Int -> ST s (MVector s (Dual a)) # basicInitialize :: MVector s (Dual a) -> ST s () # basicUnsafeReplicate :: Int -> Dual a -> ST s (MVector s (Dual a)) # basicUnsafeRead :: MVector s (Dual a) -> Int -> ST s (Dual a) # basicUnsafeWrite :: MVector s (Dual a) -> Int -> Dual a -> ST s () # basicClear :: MVector s (Dual a) -> ST s () # basicSet :: MVector s (Dual a) -> Dual a -> ST s () # basicUnsafeCopy :: MVector s (Dual a) -> MVector s (Dual a) -> ST s () # basicUnsafeMove :: MVector s (Dual a) -> MVector s (Dual a) -> ST s () # basicUnsafeGrow :: MVector s (Dual a) -> Int -> ST s (MVector s (Dual a)) # | |
Data a => Data (Dual a) | Since: base-4.8.0.0 |
Defined in Data.Data 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 |
NFData a => NFData (Dual a) | Since: deepseq-1.4.0.0 |
Defined in Control.DeepSeq | |
Eq a => Eq (Dual a) | Since: base-2.1 |
Ord a => Ord (Dual a) | Since: base-2.1 |
Prim a => Prim (Dual a) | Since: primitive-0.6.5.0 |
Defined in Data.Primitive.Types sizeOfType# :: Proxy (Dual a) -> Int# # alignmentOfType# :: Proxy (Dual a) -> Int# # alignment# :: Dual a -> Int# # indexByteArray# :: ByteArray# -> Int# -> Dual a # readByteArray# :: MutableByteArray# s -> Int# -> State# s -> (# State# s, Dual a #) # writeByteArray# :: MutableByteArray# s -> Int# -> Dual a -> State# s -> State# s # setByteArray# :: MutableByteArray# s -> Int# -> Int# -> Dual a -> State# s -> State# s # indexOffAddr# :: Addr# -> Int# -> Dual a # readOffAddr# :: Addr# -> Int# -> State# s -> (# State# s, Dual a #) # writeOffAddr# :: Addr# -> Int# -> Dual a -> State# s -> State# s # setOffAddr# :: Addr# -> Int# -> Int# -> Dual a -> State# s -> State# s # | |
Container (Dual a) Source # | |
Defined in Universum.Container.Class toList :: Dual a -> [Element (Dual a)] Source # null :: Dual a -> Bool Source # foldr :: (Element (Dual a) -> b -> b) -> b -> Dual a -> b Source # foldl :: (b -> Element (Dual a) -> b) -> b -> Dual a -> b Source # foldl' :: (b -> Element (Dual a) -> b) -> b -> Dual a -> b Source # length :: Dual a -> Int Source # elem :: Element (Dual a) -> Dual a -> Bool Source # foldMap :: Monoid m => (Element (Dual a) -> m) -> Dual a -> m Source # fold :: Dual a -> Element (Dual a) Source # foldr' :: (Element (Dual a) -> b -> b) -> b -> Dual a -> b Source # notElem :: Element (Dual a) -> Dual a -> Bool Source # all :: (Element (Dual a) -> Bool) -> Dual a -> Bool Source # any :: (Element (Dual a) -> Bool) -> Dual a -> Bool Source # and :: Dual a -> Bool Source # find :: (Element (Dual a) -> Bool) -> Dual a -> Maybe (Element (Dual a)) Source # safeHead :: Dual a -> Maybe (Element (Dual a)) Source # safeMaximum :: Dual a -> Maybe (Element (Dual a)) Source # safeMinimum :: Dual a -> Maybe (Element (Dual a)) Source # safeFoldr1 :: (Element (Dual a) -> Element (Dual a) -> Element (Dual a)) -> Dual a -> Maybe (Element (Dual a)) Source # safeFoldl1 :: (Element (Dual a) -> Element (Dual a) -> Element (Dual a)) -> Dual a -> Maybe (Element (Dual a)) Source # | |
Unbox a => Unbox (Dual a) | |
Defined in Data.Vector.Unboxed.Base | |
type Rep1 Dual | Since: base-4.7.0.0 |
Defined in Data.Semigroup.Internal | |
newtype MVector s (Dual a) | |
Defined in Data.Vector.Unboxed.Base | |
type Rep (Dual a) | Since: base-4.7.0.0 |
Defined in Data.Semigroup.Internal | |
type Element (Dual a) Source # | |
Defined in Universum.Container.Class | |
newtype Vector (Dual a) | |
Defined in Data.Vector.Unboxed.Base |
The class of semigroups (types with an associative binary operation).
Instances should satisfy the following:
You can alternatively define sconcat
instead of (<>
), in which case the
laws are:
Since: base-4.9.0.0
(<>) :: a -> a -> a infixr 6 #
An associative operation.
>>>
[1,2,3] <> [4,5,6]
[1,2,3,4,5,6]
Reduce a non-empty list with <>
The default definition should be sufficient, but this can be overridden for efficiency.
>>>
import Data.List.NonEmpty (NonEmpty (..))
>>>
sconcat $ "Hello" :| [" ", "Haskell", "!"]
"Hello Haskell!"
stimes :: Integral b => b -> a -> a #
Repeat a value n
times.
Given that this works on a Semigroup
it is allowed to fail if
you request 0 or fewer repetitions, and the default definition
will do so.
By making this a member of the class, idempotent semigroups
and monoids can upgrade this to execute in \(\mathcal{O}(1)\) by
picking stimes =
or stimesIdempotent
stimes =
respectively.stimesIdempotentMonoid
>>>
stimes 4 [1]
[1,1,1,1]
Instances
Semigroup ByteArray | Since: base-4.17.0.0 |
Semigroup All | Since: base-4.9.0.0 |
Semigroup Any | Since: base-4.9.0.0 |
Semigroup Void | Since: base-4.9.0.0 |
Semigroup Builder | |
Semigroup ByteString | |
Defined in Data.ByteString.Internal.Type (<>) :: ByteString -> ByteString -> ByteString # sconcat :: NonEmpty ByteString -> ByteString # stimes :: Integral b => b -> ByteString -> ByteString # | |
Semigroup ByteString | |
Defined in Data.ByteString.Lazy.Internal (<>) :: ByteString -> ByteString -> ByteString # sconcat :: NonEmpty ByteString -> ByteString # stimes :: Integral b => b -> ByteString -> ByteString # | |
Semigroup ShortByteString | |
Defined in Data.ByteString.Short.Internal (<>) :: ShortByteString -> ShortByteString -> ShortByteString # sconcat :: NonEmpty ShortByteString -> ShortByteString # stimes :: Integral b => b -> ShortByteString -> ShortByteString # | |
Semigroup IntSet | Since: containers-0.5.7 |
Semigroup OsString | |
Semigroup PosixString | |
Defined in System.OsString.Internal.Types.Hidden (<>) :: PosixString -> PosixString -> PosixString # sconcat :: NonEmpty PosixString -> PosixString # stimes :: Integral b => b -> PosixString -> PosixString # | |
Semigroup WindowsString | |
Defined in System.OsString.Internal.Types.Hidden (<>) :: WindowsString -> WindowsString -> WindowsString # sconcat :: NonEmpty WindowsString -> WindowsString # stimes :: Integral b => b -> WindowsString -> WindowsString # | |
Semigroup Ordering | Since: base-4.9.0.0 |
Semigroup Doc | |
Semigroup () | Since: base-4.9.0.0 |
Bits a => Semigroup (And a) | Since: base-4.16 |
FiniteBits a => Semigroup (Iff a) | This constraint is arguably
too strong. However, as some types (such as Since: base-4.16 |
Bits a => Semigroup (Ior a) | Since: base-4.16 |
Bits a => Semigroup (Xor a) | Since: base-4.16 |
Semigroup a => Semigroup (Identity a) | Since: base-4.9.0.0 |
Semigroup (First a) | Since: base-4.9.0.0 |
Semigroup (Last a) | Since: base-4.9.0.0 |
Semigroup a => Semigroup (Down a) | Since: base-4.11.0.0 |
Semigroup (First a) | Since: base-4.9.0.0 |
Semigroup (Last a) | Since: base-4.9.0.0 |
Ord a => Semigroup (Max a) | Since: base-4.9.0.0 |
Ord a => Semigroup (Min a) | Since: base-4.9.0.0 |
Monoid m => Semigroup (WrappedMonoid m) | Since: base-4.9.0.0 |
Defined in Data.Semigroup (<>) :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m # sconcat :: NonEmpty (WrappedMonoid m) -> WrappedMonoid m # stimes :: Integral b => b -> WrappedMonoid m -> WrappedMonoid m # | |
Semigroup a => Semigroup (Dual a) | Since: base-4.9.0.0 |
Semigroup (Endo a) | Since: base-4.9.0.0 |
Num a => Semigroup (Product a) | Since: base-4.9.0.0 |
Num a => Semigroup (Sum a) | Since: base-4.9.0.0 |
Semigroup (NonEmpty a) | Since: base-4.9.0.0 |
Semigroup a => Semigroup (STM a) | Since: base-4.17.0.0 |
(Generic a, Semigroup (Rep a ())) => Semigroup (Generically a) | Since: base-4.17.0.0 |
Defined in GHC.Generics (<>) :: Generically a -> Generically a -> Generically a # sconcat :: NonEmpty (Generically a) -> Generically a # stimes :: Integral b => b -> Generically a -> Generically a # | |
Semigroup p => Semigroup (Par1 p) | Since: base-4.12.0.0 |
Semigroup (IntMap a) | Since: containers-0.5.7 |
Semigroup (Seq a) | Since: containers-0.5.7 |
Ord a => Semigroup (Intersection a) | |
Defined in Data.Set.Internal (<>) :: Intersection a -> Intersection a -> Intersection a # sconcat :: NonEmpty (Intersection a) -> Intersection a # stimes :: Integral b => b -> Intersection a -> Intersection a # | |
Semigroup (MergeSet a) | |
Ord a => Semigroup (Set a) | Since: containers-0.5.7 |
Semigroup a => Semigroup (IO a) | Since: base-4.10.0.0 |
Semigroup a => Semigroup (May a) | |
Semigroup (Doc a) | |
Semigroup (Array a) | Since: primitive-0.6.3.0 |
Semigroup (PrimArray a) | Since: primitive-0.6.4.0 |
Semigroup (SmallArray a) | Since: primitive-0.6.3.0 |
Defined in Data.Primitive.SmallArray (<>) :: SmallArray a -> SmallArray a -> SmallArray a # sconcat :: NonEmpty (SmallArray a) -> SmallArray a # stimes :: Integral b => b -> SmallArray a -> SmallArray a # | |
Semigroup a => Semigroup (Q a) | Since: template-haskell-2.17.0.0 |
(Hashable a, Eq a) => Semigroup (HashSet a) | \(O(n+m)\) To obtain good performance, the smaller set must be presented as the first argument. Examples
|
Semigroup (Vector a) | |
Prim a => Semigroup (Vector a) | |
Storable a => Semigroup (Vector a) | |
Semigroup a => Semigroup (Maybe a) | Since: base-4.9.0.0 |
Semigroup a => Semigroup (a) | Since: base-4.15 |
Semigroup [a] | Since: base-4.9.0.0 |
Semigroup (Either a b) | Since: base-4.9.0.0 |
Semigroup (Proxy s) | Since: base-4.9.0.0 |
Semigroup (U1 p) | Since: base-4.12.0.0 |
Semigroup (V1 p) | Since: base-4.12.0.0 |
Ord k => Semigroup (Map k v) | |
Applicative f => Semigroup (Traversed a f) | |
Semigroup a => Semigroup (Err e a) | |
(Eq k, Hashable k) => Semigroup (HashMap k v) | If a key occurs in both maps, the mapping from the first will be the mapping in the result. Examples
|
(Semigroup a, Semigroup b) => Semigroup (a, b) | Since: base-4.9.0.0 |
Semigroup b => Semigroup (a -> b) | Since: base-4.9.0.0 |
Semigroup a => Semigroup (Const a b) | Since: base-4.9.0.0 |
(Applicative f, Semigroup a) => Semigroup (Ap f a) | Since: base-4.12.0.0 |
Alternative f => Semigroup (Alt f a) | Since: base-4.9.0.0 |
Semigroup (f p) => Semigroup (Rec1 f p) | Since: base-4.12.0.0 |
(Monad m, Semigroup r) => Semigroup (Effect m r a) | |
(Semigroup a, Semigroup b, Semigroup c) => Semigroup (a, b, c) | Since: base-4.9.0.0 |
(Semigroup (f a), Semigroup (g a)) => Semigroup (Product f g a) | Since: base-4.16.0.0 |
(Semigroup (f p), Semigroup (g p)) => Semigroup ((f :*: g) p) | Since: base-4.12.0.0 |
Semigroup c => Semigroup (K1 i c p) | Since: base-4.12.0.0 |
(Semigroup a, Semigroup b, Semigroup c, Semigroup d) => Semigroup (a, b, c, d) | Since: base-4.9.0.0 |
Semigroup (f (g a)) => Semigroup (Compose f g a) | Since: base-4.16.0.0 |
Semigroup (f (g p)) => Semigroup ((f :.: g) p) | Since: base-4.12.0.0 |
Semigroup (f p) => Semigroup (M1 i c f p) | Since: base-4.12.0.0 |
(Semigroup a, Semigroup b, Semigroup c, Semigroup d, Semigroup e) => Semigroup (a, b, c, d, e) | Since: base-4.9.0.0 |
data WrappedMonoid m #
Provide a Semigroup for an arbitrary Monoid.
NOTE: This is not needed anymore since Semigroup
became a superclass of
Monoid
in base-4.11 and this newtype be deprecated at some point in the future.
Instances
stimesIdempotent :: Integral b => b -> a -> a #
stimesIdempotentMonoid :: (Integral b, Monoid a) => b -> a -> a #
stimesMonoid :: (Integral b, Monoid a) => b -> a -> a #
mtimesDefault :: (Integral b, Monoid a) => b -> a -> a #
Repeat a value n
times.
mtimesDefault n a = a <> a <> ... <> a -- using <> (n-1) times
In many cases, `stimes 0 a` for a Monoid
will produce mempty
.
However, there are situations when it cannot do so. In particular,
the following situation is fairly common:
data T a = ... class Constraint1 a class Constraint1 a => Constraint2 a
instance Constraint1 a => Semigroup
(T a)
instance Constraint2 a => Monoid
(T a)
@
Since Constraint1
is insufficient to implement mempty
,
stimes
for T a
cannot do so.
When working with such a type, or when working polymorphically with
Semigroup
instances, mtimesDefault
should be used when the
multiplier might be zero. It is implemented using stimes
when
the multiplier is nonzero and mempty
when it is zero.