Safe Haskell	Safe
Language	Haskell2010

Universum.Monoid

Description

This module reexports functions to work with monoids plus adds extra useful functions.

Synopsis

newtype Any = Any {
- getAny :: Bool
}
newtype Sum a = Sum {
- getSum :: a
}
newtype Product a = Product {
- getProduct :: a
}
newtype Last a = Last {
- getLast :: Maybe a
}
newtype First a = First {
- getFirst :: Maybe a
}
class Semigroup a => Monoid a where
- mempty :: a
- mappend :: a -> a -> a
- mconcat :: [a] -> a
newtype Alt (f :: k -> Type) (a :: k) = Alt {
- getAlt :: f a
}
newtype All = All {
- getAll :: Bool
}
newtype Endo a = Endo {
- appEndo :: a -> a
}
newtype Dual a = Dual {
- getDual :: a
}
class Semigroup a where
- (<>) :: a -> a -> a
- sconcat :: NonEmpty a -> a
- stimes :: Integral b => b -> a -> a
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

newtype Any #

Boolean monoid under disjunction (||).

>>> getAny (Any True <> mempty <> Any False)
True

>>> getAny (mconcat (map (\x -> Any (even x)) [2,4,6,7,8]))
True

Constructors

Any
Fields getAny :: Bool

Instances

Instances details

Data Any	Since: base-4.8.0.0
Instance details 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 # toConstr :: Any -> Constr # 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
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Any # mappend :: Any -> Any -> Any # mconcat :: [Any] -> Any #
Semigroup Any	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Any -> Any -> Any # sconcat :: NonEmpty Any -> Any # stimes :: Integral b => b -> Any -> Any #
Bounded Any	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods minBound :: Any # maxBound :: Any #
Generic Any
Instance details Defined in Data.Semigroup.Internal Associated Types type Rep Any :: Type -> Type # Methods from :: Any -> Rep Any x # to :: Rep Any x -> Any #
Read Any	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods readsPrec :: Int -> ReadS Any # readList :: ReadS [Any] # readPrec :: ReadPrec Any # readListPrec :: ReadPrec [Any] #
Show Any	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods showsPrec :: Int -> Any -> ShowS # show :: Any -> String # showList :: [Any] -> ShowS #
NFData Any	Since: deepseq-1.4.0.0
Instance details Defined in Control.DeepSeq Methods rnf :: Any -> () #
Eq Any	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods (==) :: Any -> Any -> Bool # (/=) :: Any -> Any -> Bool #
Ord Any	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods compare :: Any -> Any -> Ordering # (<) :: Any -> Any -> Bool # (<=) :: Any -> Any -> Bool # (>) :: Any -> Any -> Bool # (>=) :: Any -> Any -> Bool # max :: Any -> Any -> Any # min :: Any -> Any -> Any #
Unbox Any
Instance details Defined in Data.Vector.Unboxed.Base
Vector Vector Any
Instance details Defined in Data.Vector.Unboxed.Base Methods 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 () # elemseq :: Vector Any -> Any -> b -> b #
MVector MVector Any
Instance details Defined in Data.Vector.Unboxed.Base Methods 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
Instance details Defined in Data.Semigroup.Internal type Rep Any = D1 ('MetaData "Any" "Data.Semigroup.Internal" "base" 'True) (C1 ('MetaCons "Any" 'PrefixI 'True) (S1 ('MetaSel ('Just "getAny") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 Bool)))
newtype Vector Any
Instance details Defined in Data.Vector.Unboxed.Base newtype Vector Any = V_Any (Vector Bool)
newtype MVector s Any
Instance details Defined in Data.Vector.Unboxed.Base newtype MVector s Any = MV_Any (MVector s Bool)

newtype Sum a #

Monoid under addition.

>>> getSum (Sum 1 <> Sum 2 <> mempty)
3

Constructors

Sum
Fields getSum :: a

Instances

Instances details

Foldable Sum	Since: base-4.8.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => Sum m -> m # foldMap :: Monoid m => (a -> m) -> Sum a -> m # foldMap' :: Monoid m => (a -> m) -> Sum a -> m # foldr :: (a -> b -> b) -> b -> Sum a -> b # foldr' :: (a -> b -> b) -> b -> Sum a -> b # foldl :: (b -> a -> b) -> b -> Sum a -> b # foldl' :: (b -> a -> b) -> b -> Sum a -> b # foldr1 :: (a -> a -> a) -> Sum a -> a # foldl1 :: (a -> a -> a) -> Sum a -> a # toList :: Sum a -> [a] # null :: Sum a -> Bool # length :: Sum a -> Int # elem :: Eq a => a -> Sum a -> Bool # maximum :: Ord a => Sum a -> a # minimum :: Ord a => Sum a -> a # sum :: Num a => Sum a -> a # product :: Num a => Sum a -> a #
Traversable Sum	Since: base-4.8.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Sum a -> f (Sum b) # sequenceA :: Applicative f => Sum (f a) -> f (Sum a) # mapM :: Monad m => (a -> m b) -> Sum a -> m (Sum b) # sequence :: Monad m => Sum (m a) -> m (Sum a) #
Applicative Sum	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods pure :: a -> Sum a # (<>) :: Sum (a -> b) -> Sum a -> Sum b # liftA2 :: (a -> b -> c) -> Sum a -> Sum b -> Sum c # (>) :: Sum a -> Sum b -> Sum b # (<*) :: Sum a -> Sum b -> Sum a #
Functor Sum	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods fmap :: (a -> b) -> Sum a -> Sum b # (<$) :: a -> Sum b -> Sum a #
Monad Sum	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods (>>=) :: Sum a -> (a -> Sum b) -> Sum b # (>>) :: Sum a -> Sum b -> Sum b # return :: a -> Sum a #
NFData1 Sum	Since: deepseq-1.4.3.0
Instance details Defined in Control.DeepSeq Methods liftRnf :: (a -> ()) -> Sum a -> () #
Generic1 Sum
Instance details Defined in Data.Semigroup.Internal Associated Types type Rep1 Sum :: k -> Type # Methods from1 :: forall (a :: k). Sum a -> Rep1 Sum a # to1 :: forall (a :: k). Rep1 Sum a -> Sum a #
Unbox a => Vector Vector (Sum a)
Instance details Defined in Data.Vector.Unboxed.Base Methods 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 () # elemseq :: Vector (Sum a) -> Sum a -> b -> b #
Unbox a => MVector MVector (Sum a)
Instance details Defined in Data.Vector.Unboxed.Base Methods 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
Instance details 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) # toConstr :: Sum a -> Constr # 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
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Sum a # mappend :: Sum a -> Sum a -> Sum a # mconcat :: [Sum a] -> Sum a #
Num a => Semigroup (Sum a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Sum a -> Sum a -> Sum a # sconcat :: NonEmpty (Sum a) -> Sum a # stimes :: Integral b => b -> Sum a -> Sum a #
Bounded a => Bounded (Sum a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods minBound :: Sum a # maxBound :: Sum a #
Generic (Sum a)
Instance details Defined in Data.Semigroup.Internal Associated Types type Rep (Sum a) :: Type -> Type # Methods from :: Sum a -> Rep (Sum a) x # to :: Rep (Sum a) x -> Sum a #
Num a => Num (Sum a)	Since: base-4.7.0.0
Instance details Defined in Data.Semigroup.Internal Methods (+) :: Sum a -> Sum a -> Sum a # (-) :: Sum a -> Sum a -> Sum a # (*) :: Sum a -> Sum a -> Sum a # negate :: Sum a -> Sum a # abs :: Sum a -> Sum a # signum :: Sum a -> Sum a # fromInteger :: Integer -> Sum a #
Read a => Read (Sum a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods readsPrec :: Int -> ReadS (Sum a) # readList :: ReadS [Sum a] # readPrec :: ReadPrec (Sum a) # readListPrec :: ReadPrec [Sum a] #
Show a => Show (Sum a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods showsPrec :: Int -> Sum a -> ShowS # show :: Sum a -> String # showList :: [Sum a] -> ShowS #
NFData a => NFData (Sum a)	Since: deepseq-1.4.0.0
Instance details Defined in Control.DeepSeq Methods rnf :: Sum a -> () #
Eq a => Eq (Sum a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods (==) :: Sum a -> Sum a -> Bool # (/=) :: Sum a -> Sum a -> Bool #
Ord a => Ord (Sum a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods compare :: Sum a -> Sum a -> Ordering # (<) :: Sum a -> Sum a -> Bool # (<=) :: Sum a -> Sum a -> Bool # (>) :: Sum a -> Sum a -> Bool # (>=) :: Sum a -> Sum a -> Bool # max :: Sum a -> Sum a -> Sum a # min :: Sum a -> Sum a -> Sum a #
Prim a => Prim (Sum a)	Since: primitive-0.6.5.0
Instance details Defined in Data.Primitive.Types Methods sizeOfType# :: Proxy (Sum a) -> Int# # sizeOf# :: 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 #
Instance details Defined in Universum.Container.Class Associated Types type Element (Sum a) Source # Methods 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 # and :: Sum a -> Bool Source # or :: 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)
Instance details Defined in Data.Vector.Unboxed.Base
type Rep1 Sum	Since: base-4.7.0.0
Instance details Defined in Data.Semigroup.Internal type Rep1 Sum = D1 ('MetaData "Sum" "Data.Semigroup.Internal" "base" 'True) (C1 ('MetaCons "Sum" 'PrefixI 'True) (S1 ('MetaSel ('Just "getSum") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))
newtype MVector s (Sum a)
Instance details Defined in Data.Vector.Unboxed.Base newtype MVector s (Sum a) = MV_Sum (MVector s a)
type Rep (Sum a)	Since: base-4.7.0.0
Instance details Defined in Data.Semigroup.Internal type Rep (Sum a) = D1 ('MetaData "Sum" "Data.Semigroup.Internal" "base" 'True) (C1 ('MetaCons "Sum" 'PrefixI 'True) (S1 ('MetaSel ('Just "getSum") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))
type Element (Sum a) Source #
Instance details Defined in Universum.Container.Class type Element (Sum a)
newtype Vector (Sum a)
Instance details Defined in Data.Vector.Unboxed.Base newtype Vector (Sum a) = V_Sum (Vector a)

newtype Product a #

Monoid under multiplication.

>>> getProduct (Product 3 <> Product 4 <> mempty)
12

Constructors

Product
Fields getProduct :: a

Instances

Instances details

Foldable Product	Since: base-4.8.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => Product m -> m # foldMap :: Monoid m => (a -> m) -> Product a -> m # foldMap' :: Monoid m => (a -> m) -> Product a -> m # foldr :: (a -> b -> b) -> b -> Product a -> b # foldr' :: (a -> b -> b) -> b -> Product a -> b # foldl :: (b -> a -> b) -> b -> Product a -> b # foldl' :: (b -> a -> b) -> b -> Product a -> b # foldr1 :: (a -> a -> a) -> Product a -> a # foldl1 :: (a -> a -> a) -> Product a -> a # toList :: Product a -> [a] # null :: Product a -> Bool # length :: Product a -> Int # elem :: Eq a => a -> Product a -> Bool # maximum :: Ord a => Product a -> a # minimum :: Ord a => Product a -> a # sum :: Num a => Product a -> a # product :: Num a => Product a -> a #
Traversable Product	Since: base-4.8.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Product a -> f (Product b) # sequenceA :: Applicative f => Product (f a) -> f (Product a) # mapM :: Monad m => (a -> m b) -> Product a -> m (Product b) # sequence :: Monad m => Product (m a) -> m (Product a) #
Applicative Product	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods pure :: a -> Product a # (<>) :: Product (a -> b) -> Product a -> Product b # liftA2 :: (a -> b -> c) -> Product a -> Product b -> Product c # (>) :: Product a -> Product b -> Product b # (<*) :: Product a -> Product b -> Product a #
Functor Product	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods fmap :: (a -> b) -> Product a -> Product b # (<$) :: a -> Product b -> Product a #
Monad Product	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods (>>=) :: Product a -> (a -> Product b) -> Product b # (>>) :: Product a -> Product b -> Product b # return :: a -> Product a #
NFData1 Product	Since: deepseq-1.4.3.0
Instance details Defined in Control.DeepSeq Methods liftRnf :: (a -> ()) -> Product a -> () #
Generic1 Product
Instance details Defined in Data.Semigroup.Internal Associated Types type Rep1 Product :: k -> Type # Methods from1 :: forall (a :: k). Product a -> Rep1 Product a # to1 :: forall (a :: k). Rep1 Product a -> Product a #
Unbox a => Vector Vector (Product a)
Instance details Defined in Data.Vector.Unboxed.Base Methods basicUnsafeFreeze :: Mutable Vector s (Product a) -> ST s (Vector (Product a)) # basicUnsafeThaw :: Vector (Product a) -> ST s (Mutable Vector s (Product a)) # basicLength :: Vector (Product a) -> Int # basicUnsafeSlice :: Int -> Int -> Vector (Product a) -> Vector (Product a) # basicUnsafeIndexM :: Vector (Product a) -> Int -> Box (Product a) # basicUnsafeCopy :: Mutable Vector s (Product a) -> Vector (Product a) -> ST s () # elemseq :: Vector (Product a) -> Product a -> b -> b #
Unbox a => MVector MVector (Product a)
Instance details Defined in Data.Vector.Unboxed.Base Methods basicLength :: MVector s (Product a) -> Int # basicUnsafeSlice :: Int -> Int -> MVector s (Product a) -> MVector s (Product a) # basicOverlaps :: MVector s (Product a) -> MVector s (Product a) -> Bool # basicUnsafeNew :: Int -> ST s (MVector s (Product a)) # basicInitialize :: MVector s (Product a) -> ST s () # basicUnsafeReplicate :: Int -> Product a -> ST s (MVector s (Product a)) # basicUnsafeRead :: MVector s (Product a) -> Int -> ST s (Product a) # basicUnsafeWrite :: MVector s (Product a) -> Int -> Product a -> ST s () # basicClear :: MVector s (Product a) -> ST s () # basicSet :: MVector s (Product a) -> Product a -> ST s () # basicUnsafeCopy :: MVector s (Product a) -> MVector s (Product a) -> ST s () # basicUnsafeMove :: MVector s (Product a) -> MVector s (Product a) -> ST s () # basicUnsafeGrow :: MVector s (Product a) -> Int -> ST s (MVector s (Product a)) #
Data a => Data (Product a)	Since: base-4.8.0.0
Instance details Defined in Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Product a -> c (Product a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Product a) # toConstr :: Product a -> Constr # dataTypeOf :: Product a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Product a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Product a)) # gmapT :: (forall b. Data b => b -> b) -> Product a -> Product a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Product a -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Product a -> r # gmapQ :: (forall d. Data d => d -> u) -> Product a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Product a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Product a -> m (Product a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Product a -> m (Product a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Product a -> m (Product a) #
Num a => Monoid (Product a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Product a # mappend :: Product a -> Product a -> Product a # mconcat :: [Product a] -> Product a #
Num a => Semigroup (Product a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Product a -> Product a -> Product a # sconcat :: NonEmpty (Product a) -> Product a # stimes :: Integral b => b -> Product a -> Product a #
Bounded a => Bounded (Product a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods minBound :: Product a # maxBound :: Product a #
Generic (Product a)
Instance details Defined in Data.Semigroup.Internal Associated Types type Rep (Product a) :: Type -> Type # Methods from :: Product a -> Rep (Product a) x # to :: Rep (Product a) x -> Product a #
Num a => Num (Product a)	Since: base-4.7.0.0
Instance details Defined in Data.Semigroup.Internal Methods (+) :: Product a -> Product a -> Product a # (-) :: Product a -> Product a -> Product a # (*) :: Product a -> Product a -> Product a # negate :: Product a -> Product a # abs :: Product a -> Product a # signum :: Product a -> Product a # fromInteger :: Integer -> Product a #
Read a => Read (Product a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods readsPrec :: Int -> ReadS (Product a) # readList :: ReadS [Product a] # readPrec :: ReadPrec (Product a) # readListPrec :: ReadPrec [Product a] #
Show a => Show (Product a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods showsPrec :: Int -> Product a -> ShowS # show :: Product a -> String # showList :: [Product a] -> ShowS #
NFData a => NFData (Product a)	Since: deepseq-1.4.0.0
Instance details Defined in Control.DeepSeq Methods rnf :: Product a -> () #
Eq a => Eq (Product a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods (==) :: Product a -> Product a -> Bool # (/=) :: Product a -> Product a -> Bool #
Ord a => Ord (Product a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods compare :: Product a -> Product a -> Ordering # (<) :: Product a -> Product a -> Bool # (<=) :: Product a -> Product a -> Bool # (>) :: Product a -> Product a -> Bool # (>=) :: Product a -> Product a -> Bool # max :: Product a -> Product a -> Product a # min :: Product a -> Product a -> Product a #
Prim a => Prim (Product a)	Since: primitive-0.6.5.0
Instance details Defined in Data.Primitive.Types Methods sizeOfType# :: Proxy (Product a) -> Int# # sizeOf# :: Product a -> Int# # alignmentOfType# :: Proxy (Product a) -> Int# # alignment# :: Product a -> Int# # indexByteArray# :: ByteArray# -> Int# -> Product a # readByteArray# :: MutableByteArray# s -> Int# -> State# s -> (# State# s, Product a #) # writeByteArray# :: MutableByteArray# s -> Int# -> Product a -> State# s -> State# s # setByteArray# :: MutableByteArray# s -> Int# -> Int# -> Product a -> State# s -> State# s # indexOffAddr# :: Addr# -> Int# -> Product a # readOffAddr# :: Addr# -> Int# -> State# s -> (# State# s, Product a #) # writeOffAddr# :: Addr# -> Int# -> Product a -> State# s -> State# s # setOffAddr# :: Addr# -> Int# -> Int# -> Product a -> State# s -> State# s #
Container (Product a) Source #
Instance details Defined in Universum.Container.Class Associated Types type Element (Product a) Source # Methods toList :: Product a -> [Element (Product a)] Source # null :: Product a -> Bool Source # foldr :: (Element (Product a) -> b -> b) -> b -> Product a -> b Source # foldl :: (b -> Element (Product a) -> b) -> b -> Product a -> b Source # foldl' :: (b -> Element (Product a) -> b) -> b -> Product a -> b Source # length :: Product a -> Int Source # elem :: Element (Product a) -> Product a -> Bool Source # foldMap :: Monoid m => (Element (Product a) -> m) -> Product a -> m Source # fold :: Product a -> Element (Product a) Source # foldr' :: (Element (Product a) -> b -> b) -> b -> Product a -> b Source # notElem :: Element (Product a) -> Product a -> Bool Source # all :: (Element (Product a) -> Bool) -> Product a -> Bool Source # any :: (Element (Product a) -> Bool) -> Product a -> Bool Source # and :: Product a -> Bool Source # or :: Product a -> Bool Source # find :: (Element (Product a) -> Bool) -> Product a -> Maybe (Element (Product a)) Source # safeHead :: Product a -> Maybe (Element (Product a)) Source # safeMaximum :: Product a -> Maybe (Element (Product a)) Source # safeMinimum :: Product a -> Maybe (Element (Product a)) Source # safeFoldr1 :: (Element (Product a) -> Element (Product a) -> Element (Product a)) -> Product a -> Maybe (Element (Product a)) Source # safeFoldl1 :: (Element (Product a) -> Element (Product a) -> Element (Product a)) -> Product a -> Maybe (Element (Product a)) Source #
Unbox a => Unbox (Product a)
Instance details Defined in Data.Vector.Unboxed.Base
type Rep1 Product	Since: base-4.7.0.0
Instance details Defined in Data.Semigroup.Internal type Rep1 Product = D1 ('MetaData "Product" "Data.Semigroup.Internal" "base" 'True) (C1 ('MetaCons "Product" 'PrefixI 'True) (S1 ('MetaSel ('Just "getProduct") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))
newtype MVector s (Product a)
Instance details Defined in Data.Vector.Unboxed.Base newtype MVector s (Product a) = MV_Product (MVector s a)
type Rep (Product a)	Since: base-4.7.0.0
Instance details Defined in Data.Semigroup.Internal type Rep (Product a) = D1 ('MetaData "Product" "Data.Semigroup.Internal" "base" 'True) (C1 ('MetaCons "Product" 'PrefixI 'True) (S1 ('MetaSel ('Just "getProduct") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))
type Element (Product a) Source #
Instance details Defined in Universum.Container.Class type Element (Product a)
newtype Vector (Product a)
Instance details Defined in Data.Vector.Unboxed.Base newtype Vector (Product a) = V_Product (Vector a)

newtype Last a #

Maybe monoid returning the rightmost non-Nothing value.

Last a is isomorphic to Dual (First a), and thus to Dual (Alt Maybe a)

>>> getLast (Last (Just "hello") <> Last Nothing <> Last (Just "world"))
Just "world"

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.

Constructors

Last
Fields getLast :: Maybe a

Instances

Instances details

Foldable Last	Since: base-4.8.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => Last m -> m # foldMap :: Monoid m => (a -> m) -> Last a -> m # foldMap' :: Monoid m => (a -> m) -> Last a -> m # foldr :: (a -> b -> b) -> b -> Last a -> b # foldr' :: (a -> b -> b) -> b -> Last a -> b # foldl :: (b -> a -> b) -> b -> Last a -> b # foldl' :: (b -> a -> b) -> b -> Last a -> b # foldr1 :: (a -> a -> a) -> Last a -> a # foldl1 :: (a -> a -> a) -> Last a -> a # toList :: Last a -> [a] # null :: Last a -> Bool # length :: Last a -> Int # elem :: Eq a => a -> Last a -> Bool # maximum :: Ord a => Last a -> a # minimum :: Ord a => Last a -> a # sum :: Num a => Last a -> a # product :: Num a => Last a -> a #
Traversable Last	Since: base-4.8.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Last a -> f (Last b) # sequenceA :: Applicative f => Last (f a) -> f (Last a) # mapM :: Monad m => (a -> m b) -> Last a -> m (Last b) # sequence :: Monad m => Last (m a) -> m (Last a) #
Applicative Last	Since: base-4.8.0.0
Instance details Defined in Data.Monoid Methods pure :: a -> Last a # (<>) :: Last (a -> b) -> Last a -> Last b # liftA2 :: (a -> b -> c) -> Last a -> Last b -> Last c # (>) :: Last a -> Last b -> Last b # (<*) :: Last a -> Last b -> Last a #
Functor Last	Since: base-4.8.0.0
Instance details Defined in Data.Monoid Methods fmap :: (a -> b) -> Last a -> Last b # (<$) :: a -> Last b -> Last a #
Monad Last	Since: base-4.8.0.0
Instance details Defined in Data.Monoid Methods (>>=) :: Last a -> (a -> Last b) -> Last b # (>>) :: Last a -> Last b -> Last b # return :: a -> Last a #
NFData1 Last	Since: deepseq-1.4.3.0
Instance details Defined in Control.DeepSeq Methods liftRnf :: (a -> ()) -> Last a -> () #
Generic1 Last
Instance details Defined in Data.Monoid Associated Types type Rep1 Last :: k -> Type # Methods from1 :: forall (a :: k). Last a -> Rep1 Last a # to1 :: forall (a :: k). Rep1 Last a -> Last a #
Data a => Data (Last a)	Since: base-4.8.0.0
Instance details Defined in Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Last a -> c (Last a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Last a) # toConstr :: Last a -> Constr # dataTypeOf :: Last a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Last a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Last a)) # gmapT :: (forall b. Data b => b -> b) -> Last a -> Last a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Last a -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Last a -> r # gmapQ :: (forall d. Data d => d -> u) -> Last a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Last a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Last a -> m (Last a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Last a -> m (Last a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Last a -> m (Last a) #
Monoid (Last a)	Since: base-2.1
Instance details Defined in Data.Monoid Methods mempty :: Last a # mappend :: Last a -> Last a -> Last a # mconcat :: [Last a] -> Last a #
Semigroup (Last a)	Since: base-4.9.0.0
Instance details Defined in Data.Monoid Methods (<>) :: Last a -> Last a -> Last a # sconcat :: NonEmpty (Last a) -> Last a # stimes :: Integral b => b -> Last a -> Last a #
Generic (Last a)
Instance details Defined in Data.Monoid Associated Types type Rep (Last a) :: Type -> Type # Methods from :: Last a -> Rep (Last a) x # to :: Rep (Last a) x -> Last a #
Read a => Read (Last a)	Since: base-2.1
Instance details Defined in Data.Monoid Methods readsPrec :: Int -> ReadS (Last a) # readList :: ReadS [Last a] # readPrec :: ReadPrec (Last a) # readListPrec :: ReadPrec [Last a] #
Show a => Show (Last a)	Since: base-2.1
Instance details Defined in Data.Monoid Methods showsPrec :: Int -> Last a -> ShowS # show :: Last a -> String # showList :: [Last a] -> ShowS #
NFData a => NFData (Last a)	Since: deepseq-1.4.0.0
Instance details Defined in Control.DeepSeq Methods rnf :: Last a -> () #
Eq a => Eq (Last a)	Since: base-2.1
Instance details Defined in Data.Monoid Methods (==) :: Last a -> Last a -> Bool # (/=) :: Last a -> Last a -> Bool #
Ord a => Ord (Last a)	Since: base-2.1
Instance details Defined in Data.Monoid Methods compare :: Last a -> Last a -> Ordering # (<) :: Last a -> Last a -> Bool # (<=) :: Last a -> Last a -> Bool # (>) :: Last a -> Last a -> Bool # (>=) :: Last a -> Last a -> Bool # max :: Last a -> Last a -> Last a # min :: Last a -> Last a -> Last a #
Container (Last a) Source #
Instance details Defined in Universum.Container.Class Associated Types type Element (Last a) Source # Methods 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 # or :: 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
Instance details Defined in Data.Monoid type Rep1 Last = D1 ('MetaData "Last" "Data.Monoid" "base" 'True) (C1 ('MetaCons "Last" 'PrefixI 'True) (S1 ('MetaSel ('Just "getLast") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 Maybe)))
type Rep (Last a)	Since: base-4.7.0.0
Instance details Defined in Data.Monoid type Rep (Last a) = D1 ('MetaData "Last" "Data.Monoid" "base" 'True) (C1 ('MetaCons "Last" 'PrefixI 'True) (S1 ('MetaSel ('Just "getLast") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (Maybe a))))
type Element (Last a) Source #
Instance details Defined in Universum.Container.Class type Element (Last a)

newtype First a #

Maybe monoid returning the leftmost non-Nothing value.

First a is isomorphic to Alt Maybe a, but precedes it historically.

>>> getFirst (First (Just "hello") <> First Nothing <> First (Just "world"))
Just "hello"

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.

Constructors

First
Fields getFirst :: Maybe a

Instances

Instances details

Foldable First	Since: base-4.8.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => First m -> m # foldMap :: Monoid m => (a -> m) -> First a -> m # foldMap' :: Monoid m => (a -> m) -> First a -> m # foldr :: (a -> b -> b) -> b -> First a -> b # foldr' :: (a -> b -> b) -> b -> First a -> b # foldl :: (b -> a -> b) -> b -> First a -> b # foldl' :: (b -> a -> b) -> b -> First a -> b # foldr1 :: (a -> a -> a) -> First a -> a # foldl1 :: (a -> a -> a) -> First a -> a # toList :: First a -> [a] # null :: First a -> Bool # length :: First a -> Int # elem :: Eq a => a -> First a -> Bool # maximum :: Ord a => First a -> a # minimum :: Ord a => First a -> a # sum :: Num a => First a -> a # product :: Num a => First a -> a #
Traversable First	Since: base-4.8.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> First a -> f (First b) # sequenceA :: Applicative f => First (f a) -> f (First a) # mapM :: Monad m => (a -> m b) -> First a -> m (First b) # sequence :: Monad m => First (m a) -> m (First a) #
Applicative First	Since: base-4.8.0.0
Instance details Defined in Data.Monoid Methods pure :: a -> First a # (<>) :: First (a -> b) -> First a -> First b # liftA2 :: (a -> b -> c) -> First a -> First b -> First c # (>) :: First a -> First b -> First b # (<*) :: First a -> First b -> First a #
Functor First	Since: base-4.8.0.0
Instance details Defined in Data.Monoid Methods fmap :: (a -> b) -> First a -> First b # (<$) :: a -> First b -> First a #
Monad First	Since: base-4.8.0.0
Instance details Defined in Data.Monoid Methods (>>=) :: First a -> (a -> First b) -> First b # (>>) :: First a -> First b -> First b # return :: a -> First a #
NFData1 First	Since: deepseq-1.4.3.0
Instance details Defined in Control.DeepSeq Methods liftRnf :: (a -> ()) -> First a -> () #
Generic1 First
Instance details Defined in Data.Monoid Associated Types type Rep1 First :: k -> Type # Methods from1 :: forall (a :: k). First a -> Rep1 First a # to1 :: forall (a :: k). Rep1 First a -> First a #
Data a => Data (First a)	Since: base-4.8.0.0
Instance details Defined in Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> First a -> c (First a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (First a) # toConstr :: First a -> Constr # dataTypeOf :: First a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (First a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (First a)) # gmapT :: (forall b. Data b => b -> b) -> First a -> First a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> First a -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> First a -> r # gmapQ :: (forall d. Data d => d -> u) -> First a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> First a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> First a -> m (First a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> First a -> m (First a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> First a -> m (First a) #
Monoid (First a)	Since: base-2.1
Instance details Defined in Data.Monoid Methods mempty :: First a # mappend :: First a -> First a -> First a # mconcat :: [First a] -> First a #
Semigroup (First a)	Since: base-4.9.0.0
Instance details Defined in Data.Monoid Methods (<>) :: First a -> First a -> First a # sconcat :: NonEmpty (First a) -> First a # stimes :: Integral b => b -> First a -> First a #
Generic (First a)
Instance details Defined in Data.Monoid Associated Types type Rep (First a) :: Type -> Type # Methods from :: First a -> Rep (First a) x # to :: Rep (First a) x -> First a #
Read a => Read (First a)	Since: base-2.1
Instance details Defined in Data.Monoid Methods readsPrec :: Int -> ReadS (First a) # readList :: ReadS [First a] # readPrec :: ReadPrec (First a) # readListPrec :: ReadPrec [First a] #
Show a => Show (First a)	Since: base-2.1
Instance details Defined in Data.Monoid Methods showsPrec :: Int -> First a -> ShowS # show :: First a -> String # showList :: [First a] -> ShowS #
NFData a => NFData (First a)	Since: deepseq-1.4.0.0
Instance details Defined in Control.DeepSeq Methods rnf :: First a -> () #
Eq a => Eq (First a)	Since: base-2.1
Instance details Defined in Data.Monoid Methods (==) :: First a -> First a -> Bool # (/=) :: First a -> First a -> Bool #
Ord a => Ord (First a)	Since: base-2.1
Instance details Defined in Data.Monoid Methods compare :: First a -> First a -> Ordering # (<) :: First a -> First a -> Bool # (<=) :: First a -> First a -> Bool # (>) :: First a -> First a -> Bool # (>=) :: First a -> First a -> Bool # max :: First a -> First a -> First a # min :: First a -> First a -> First a #
Container (First a) Source #
Instance details Defined in Universum.Container.Class Associated Types type Element (First a) Source # Methods 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
Instance details Defined in Data.Monoid type Rep1 First = D1 ('MetaData "First" "Data.Monoid" "base" 'True) (C1 ('MetaCons "First" 'PrefixI 'True) (S1 ('MetaSel ('Just "getFirst") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 Maybe)))
type Rep (First a)	Since: base-4.7.0.0
Instance details Defined in Data.Monoid type Rep (First a) = D1 ('MetaData "First" "Data.Monoid" "base" 'True) (C1 ('MetaCons "First" 'PrefixI 'True) (S1 ('MetaSel ('Just "getFirst") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (Maybe a))))
type Element (First a) Source #
Instance details Defined in Universum.Container.Class type Element (First a)

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) <> z (Semigroup 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 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

mempty | mconcat

Methods

mempty :: a #

Identity of mappend

>>> "Hello world" <> mempty
"Hello world"

mappend :: a -> a -> a #

An associative operation

NOTE: This method is redundant and has the default implementation mappend = (<>) since base-4.11.0.0. Should it be implemented manually, since mappend is a synonym for (<>), it is expected that the two functions are defined the same way. In a future GHC release mappend will be removed from Monoid.

mconcat :: [a] -> a #

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

Instances details

Monoid ByteArray	Since: base-4.17.0.0
Instance details Defined in Data.Array.Byte Methods mempty :: ByteArray # mappend :: ByteArray -> ByteArray -> ByteArray # mconcat :: [ByteArray] -> ByteArray #
Monoid All	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: All # mappend :: All -> All -> All # mconcat :: [All] -> All #
Monoid Any	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Any # mappend :: Any -> Any -> Any # mconcat :: [Any] -> Any #
Monoid Builder
Instance details Defined in Data.ByteString.Builder.Internal Methods mempty :: Builder # mappend :: Builder -> Builder -> Builder # mconcat :: [Builder] -> Builder #
Monoid ByteString
Instance details Defined in Data.ByteString.Internal.Type Methods mempty :: ByteString # mappend :: ByteString -> ByteString -> ByteString # mconcat :: [ByteString] -> ByteString #
Monoid ByteString
Instance details Defined in Data.ByteString.Lazy.Internal Methods mempty :: ByteString # mappend :: ByteString -> ByteString -> ByteString # mconcat :: [ByteString] -> ByteString #
Monoid ShortByteString
Instance details Defined in Data.ByteString.Short.Internal Methods mempty :: ShortByteString # mappend :: ShortByteString -> ShortByteString -> ShortByteString # mconcat :: [ShortByteString] -> ShortByteString #
Monoid IntSet
Instance details Defined in Data.IntSet.Internal Methods mempty :: IntSet # mappend :: IntSet -> IntSet -> IntSet # mconcat :: [IntSet] -> IntSet #
Monoid Ordering	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: Ordering # mappend :: Ordering -> Ordering -> Ordering # mconcat :: [Ordering] -> Ordering #
Monoid OsString	"String-Concatenation" for `OsString`. This is not the same as `(</>)`.
Instance details Defined in System.OsString.Internal.Types Methods mempty :: OsString # mappend :: OsString -> OsString -> OsString # mconcat :: [OsString] -> OsString #
Monoid PosixString
Instance details Defined in System.OsString.Internal.Types Methods mempty :: PosixString # mappend :: PosixString -> PosixString -> PosixString # mconcat :: [PosixString] -> PosixString #
Monoid WindowsString
Instance details Defined in System.OsString.Internal.Types Methods mempty :: WindowsString # mappend :: WindowsString -> WindowsString -> WindowsString # mconcat :: [WindowsString] -> WindowsString #
Monoid Doc
Instance details Defined in Text.PrettyPrint.HughesPJ Methods mempty :: Doc # mappend :: Doc -> Doc -> Doc # mconcat :: [Doc] -> Doc #
Monoid ()	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: () # mappend :: () -> () -> () # mconcat :: [()] -> () #
FiniteBits a => Monoid (And a)	This constraint is arguably too strong. However, as some types (such as `Natural`) have undefined `complement`, this is the only safe choice. Since: base-4.16
Instance details Defined in Data.Bits Methods mempty :: And a # mappend :: And a -> And a -> And a # mconcat :: [And a] -> And a #
FiniteBits a => Monoid (Iff a)	This constraint is arguably too strong. However, as some types (such as `Natural`) have undefined `complement`, this is the only safe choice. Since: base-4.16
Instance details Defined in Data.Bits Methods mempty :: Iff a # mappend :: Iff a -> Iff a -> Iff a # mconcat :: [Iff a] -> Iff a #
Bits a => Monoid (Ior a)	Since: base-4.16
Instance details Defined in Data.Bits Methods mempty :: Ior a # mappend :: Ior a -> Ior a -> Ior a # mconcat :: [Ior a] -> Ior a #
Bits a => Monoid (Xor a)	Since: base-4.16
Instance details Defined in Data.Bits Methods mempty :: Xor a # mappend :: Xor a -> Xor a -> Xor a # mconcat :: [Xor a] -> Xor a #
Monoid a => Monoid (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods mempty :: Identity a # mappend :: Identity a -> Identity a -> Identity a # mconcat :: [Identity a] -> Identity a #
Monoid (First a)	Since: base-2.1
Instance details Defined in Data.Monoid Methods mempty :: First a # mappend :: First a -> First a -> First a # mconcat :: [First a] -> First a #
Monoid (Last a)	Since: base-2.1
Instance details Defined in Data.Monoid Methods mempty :: Last a # mappend :: Last a -> Last a -> Last a # mconcat :: [Last a] -> Last a #
Monoid a => Monoid (Down a)	Since: base-4.11.0.0
Instance details Defined in Data.Ord Methods mempty :: Down a # mappend :: Down a -> Down a -> Down a # mconcat :: [Down a] -> Down a #
(Ord a, Bounded a) => Monoid (Max a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods mempty :: Max a # mappend :: Max a -> Max a -> Max a # mconcat :: [Max a] -> Max a #
(Ord a, Bounded a) => Monoid (Min a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods mempty :: Min a # mappend :: Min a -> Min a -> Min a # mconcat :: [Min a] -> Min a #
Monoid m => Monoid (WrappedMonoid m)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods mempty :: WrappedMonoid m # mappend :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m # mconcat :: [WrappedMonoid m] -> WrappedMonoid m #
Monoid a => Monoid (Dual a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Dual a # mappend :: Dual a -> Dual a -> Dual a # mconcat :: [Dual a] -> Dual a #
Monoid (Endo a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Endo a # mappend :: Endo a -> Endo a -> Endo a # mconcat :: [Endo a] -> Endo a #
Num a => Monoid (Product a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Product a # mappend :: Product a -> Product a -> Product a # mconcat :: [Product a] -> Product a #
Num a => Monoid (Sum a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Sum a # mappend :: Sum a -> Sum a -> Sum a # mconcat :: [Sum a] -> Sum a #
Monoid a => Monoid (STM a)	Since: base-4.17.0.0
Instance details Defined in GHC.Conc.Sync Methods mempty :: STM a # mappend :: STM a -> STM a -> STM a # mconcat :: [STM a] -> STM a #
(Generic a, Monoid (Rep a ())) => Monoid (Generically a)	Since: base-4.17.0.0
Instance details Defined in GHC.Generics Methods 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
Instance details Defined in GHC.Generics Methods mempty :: Par1 p # mappend :: Par1 p -> Par1 p -> Par1 p # mconcat :: [Par1 p] -> Par1 p #
Monoid (IntMap a)
Instance details Defined in Data.IntMap.Internal Methods mempty :: IntMap a # mappend :: IntMap a -> IntMap a -> IntMap a # mconcat :: [IntMap a] -> IntMap a #
Monoid (Seq a)
Instance details Defined in Data.Sequence.Internal Methods mempty :: Seq a # mappend :: Seq a -> Seq a -> Seq a # mconcat :: [Seq a] -> Seq a #
Monoid (MergeSet a)
Instance details Defined in Data.Set.Internal Methods mempty :: MergeSet a # mappend :: MergeSet a -> MergeSet a -> MergeSet a # mconcat :: [MergeSet a] -> MergeSet a #
Ord a => Monoid (Set a)
Instance details Defined in Data.Set.Internal Methods mempty :: Set a # mappend :: Set a -> Set a -> Set a # mconcat :: [Set a] -> Set a #
Monoid a => Monoid (IO a)	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods mempty :: IO a # mappend :: IO a -> IO a -> IO a # mconcat :: [IO a] -> IO a #
Monoid a => Monoid (May a)
Instance details Defined in Lens.Micro.Mtl.Internal Methods mempty :: May a # mappend :: May a -> May a -> May a # mconcat :: [May a] -> May a #
Monoid (Doc a)
Instance details Defined in Text.PrettyPrint.Annotated.HughesPJ Methods mempty :: Doc a # mappend :: Doc a -> Doc a -> Doc a # mconcat :: [Doc a] -> Doc a #
Monoid (Array a)
Instance details Defined in Data.Primitive.Array Methods mempty :: Array a # mappend :: Array a -> Array a -> Array a # mconcat :: [Array a] -> Array a #
Monoid (PrimArray a)	Since: primitive-0.6.4.0
Instance details Defined in Data.Primitive.PrimArray Methods mempty :: PrimArray a # mappend :: PrimArray a -> PrimArray a -> PrimArray a # mconcat :: [PrimArray a] -> PrimArray a #
Monoid (SmallArray a)
Instance details Defined in Data.Primitive.SmallArray Methods 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
Instance details Defined in Language.Haskell.TH.Syntax Methods mempty :: Q a # mappend :: Q a -> Q a -> Q a # mconcat :: [Q a] -> Q a #
(Hashable a, Eq a) => Monoid (HashSet a)	`mempty` = `empty` `mappend` = `union` $O(n+m)$ To obtain good performance, the smaller set must be presented as the first argument. Examples Expand `>>>` `mappend (fromList [1,2]) (fromList [2,3])`fromList [1,2,3]
Instance details Defined in Data.HashSet.Internal Methods mempty :: HashSet a # mappend :: HashSet a -> HashSet a -> HashSet a # mconcat :: [HashSet a] -> HashSet a #
Monoid (Vector a)
Instance details Defined in Data.Vector Methods mempty :: Vector a # mappend :: Vector a -> Vector a -> Vector a # mconcat :: [Vector a] -> Vector a #
Prim a => Monoid (Vector a)
Instance details Defined in Data.Vector.Primitive Methods mempty :: Vector a # mappend :: Vector a -> Vector a -> Vector a # mconcat :: [Vector a] -> Vector a #
Storable a => Monoid (Vector a)
Instance details Defined in Data.Vector.Storable Methods mempty :: Vector a # mappend :: Vector a -> Vector a -> Vector a # mconcat :: [Vector a] -> Vector a #
Semigroup a => Monoid (Maybe a)	Lift a semigroup into `Maybe` forming a `Monoid` according to http://en.wikipedia.org/wiki/Monoid: "Any semigroup `S` may be turned into a monoid simply by adjoining an element `e` not in `S` and defining `ee = e` and `es = s = se` for all `s ∈ S`." Since 4.11.0: constraint on inner `a` value generalised from `Monoid` to `Semigroup`. Since: base-2.1*
Instance details Defined in GHC.Base Methods mempty :: Maybe a # mappend :: Maybe a -> Maybe a -> Maybe a # mconcat :: [Maybe a] -> Maybe a #
Monoid a => Monoid (a)	Since: base-4.15
Instance details Defined in GHC.Base Methods mempty :: (a) # mappend :: (a) -> (a) -> (a) # mconcat :: [(a)] -> (a) #
Monoid [a]	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: [a] # mappend :: [a] -> [a] -> [a] # mconcat :: [[a]] -> [a] #
Monoid (Proxy s)	Since: base-4.7.0.0
Instance details Defined in Data.Proxy Methods mempty :: Proxy s # mappend :: Proxy s -> Proxy s -> Proxy s # mconcat :: [Proxy s] -> Proxy s #
Monoid (U1 p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods mempty :: U1 p # mappend :: U1 p -> U1 p -> U1 p # mconcat :: [U1 p] -> U1 p #
Ord k => Monoid (Map k v)
Instance details Defined in Data.Map.Internal Methods mempty :: Map k v # mappend :: Map k v -> Map k v -> Map k v # mconcat :: [Map k v] -> Map k v #
Applicative f => Monoid (Traversed a f)
Instance details Defined in Lens.Micro Methods mempty :: Traversed a f # mappend :: Traversed a f -> Traversed a f -> Traversed a f # mconcat :: [Traversed a f] -> Traversed a f #
Monoid a => Monoid (Err e a)
Instance details Defined in Lens.Micro.Mtl.Internal Methods mempty :: Err e a # mappend :: Err e a -> Err e a -> Err e a # mconcat :: [Err e a] -> Err e a #
(Eq k, Hashable k) => Monoid (HashMap k v)	`mempty` = `empty` `mappend` = `union` If a key occurs in both maps, the mapping from the first will be the mapping in the result. Examples Expand `>>>` `mappend (fromList [(1,'a'),(2,'b')]) (fromList [(2,'c'),(3,'d')])`fromList [(1,'a'),(2,'b'),(3,'d')]
Instance details Defined in Data.HashMap.Internal Methods mempty :: HashMap k v # mappend :: HashMap k v -> HashMap k v -> HashMap k v # mconcat :: [HashMap k v] -> HashMap k v #
(Monoid a, Monoid b) => Monoid (a, b)	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: (a, b) # mappend :: (a, b) -> (a, b) -> (a, b) # mconcat :: [(a, b)] -> (a, b) #
Monoid b => Monoid (a -> b)	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: a -> b # mappend :: (a -> b) -> (a -> b) -> a -> b # mconcat :: [a -> b] -> a -> b #
Monoid a => Monoid (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods mempty :: Const a b # mappend :: Const a b -> Const a b -> Const a b # mconcat :: [Const a b] -> Const a b #
(Applicative f, Monoid a) => Monoid (Ap f a)	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods mempty :: Ap f a # mappend :: Ap f a -> Ap f a -> Ap f a # mconcat :: [Ap f a] -> Ap f a #
Alternative f => Monoid (Alt f a)	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Alt f a # mappend :: Alt f a -> Alt f a -> Alt f a # mconcat :: [Alt f a] -> Alt f a #
Monoid (f p) => Monoid (Rec1 f p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods mempty :: Rec1 f p # mappend :: Rec1 f p -> Rec1 f p -> Rec1 f p # mconcat :: [Rec1 f p] -> Rec1 f p #
(Monad m, Monoid r) => Monoid (Effect m r a)
Instance details Defined in Lens.Micro.Mtl.Internal Methods mempty :: Effect m r a # mappend :: Effect m r a -> Effect m r a -> Effect m r a # mconcat :: [Effect m r a] -> Effect m r a #
(Monoid a, Monoid b, Monoid c) => Monoid (a, b, c)	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: (a, b, c) # mappend :: (a, b, c) -> (a, b, c) -> (a, b, c) # mconcat :: [(a, b, c)] -> (a, b, c) #
(Monoid (f a), Monoid (g a)) => Monoid (Product f g a)	Since: base-4.16.0.0
Instance details Defined in Data.Functor.Product Methods mempty :: Product f g a # mappend :: Product f g a -> Product f g a -> Product f g a # mconcat :: [Product f g a] -> Product f g a #
(Monoid (f p), Monoid (g p)) => Monoid ((f :*: g) p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods mempty :: (f :: g) p # mappend :: (f :: g) p -> (f :: g) p -> (f :: g) p # mconcat :: [(f :: g) p] -> (f :: g) p #
Monoid c => Monoid (K1 i c p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods mempty :: K1 i c p # mappend :: K1 i c p -> K1 i c p -> K1 i c p # mconcat :: [K1 i c p] -> K1 i c p #
(Monoid a, Monoid b, Monoid c, Monoid d) => Monoid (a, b, c, d)	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: (a, b, c, d) # mappend :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) # mconcat :: [(a, b, c, d)] -> (a, b, c, d) #
Monoid (f (g a)) => Monoid (Compose f g a)	Since: base-4.16.0.0
Instance details Defined in Data.Functor.Compose Methods mempty :: Compose f g a # mappend :: Compose f g a -> Compose f g a -> Compose f g a # mconcat :: [Compose f g a] -> Compose f g a #
Monoid (f (g p)) => Monoid ((f :.: g) p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods mempty :: (f :.: g) p # mappend :: (f :.: g) p -> (f :.: g) p -> (f :.: g) p # mconcat :: [(f :.: g) p] -> (f :.: g) p #
Monoid (f p) => Monoid (M1 i c f p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods mempty :: M1 i c f p # mappend :: M1 i c f p -> M1 i c f p -> M1 i c f p # mconcat :: [M1 i c f p] -> M1 i c f p #
(Monoid a, Monoid b, Monoid c, Monoid d, Monoid e) => Monoid (a, b, c, d, e)	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: (a, b, c, d, e) # mappend :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) # mconcat :: [(a, b, c, d, e)] -> (a, b, c, d, e) #

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

Constructors

Alt
Fields getAlt :: f a

Instances

Instances details

Generic1 (Alt f :: k -> Type)
Instance details Defined in Data.Semigroup.Internal Associated Types type Rep1 (Alt f) :: k -> Type # Methods from1 :: forall (a :: k0). Alt f a -> Rep1 (Alt f) a # to1 :: forall (a :: k0). Rep1 (Alt f) a -> Alt f a #
Unbox (f a) => Vector Vector (Alt f a)
Instance details Defined in Data.Vector.Unboxed.Base Methods 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 () # elemseq :: Vector (Alt f a) -> Alt f a -> b -> b #
Unbox (f a) => MVector MVector (Alt f a)
Instance details Defined in Data.Vector.Unboxed.Base Methods 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
Instance details Defined in Data.Foldable Methods fold :: Monoid m => Alt f m -> m # foldMap :: Monoid m => (a -> m) -> Alt f a -> m # foldMap' :: Monoid m => (a -> m) -> Alt f a -> m # foldr :: (a -> b -> b) -> b -> Alt f a -> b # foldr' :: (a -> b -> b) -> b -> Alt f a -> b # foldl :: (b -> a -> b) -> b -> Alt f a -> b # foldl' :: (b -> a -> b) -> b -> Alt f a -> b # foldr1 :: (a -> a -> a) -> Alt f a -> a # foldl1 :: (a -> a -> a) -> Alt f a -> a # toList :: Alt f a -> [a] # null :: Alt f a -> Bool # length :: Alt f a -> Int # elem :: Eq a => a -> Alt f a -> Bool # maximum :: Ord a => Alt f a -> a # minimum :: Ord a => Alt f a -> a # sum :: Num a => Alt f a -> a # product :: Num a => Alt f a -> a #
Traversable f => Traversable (Alt f)	Since: base-4.12.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> Alt f a -> f0 (Alt f b) # sequenceA :: Applicative f0 => Alt f (f0 a) -> f0 (Alt f a) # mapM :: Monad m => (a -> m b) -> Alt f a -> m (Alt f b) # sequence :: Monad m => Alt f (m a) -> m (Alt f a) #
Alternative f => Alternative (Alt f)	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods empty :: Alt f a # (<\|>) :: Alt f a -> Alt f a -> Alt f a # some :: Alt f a -> Alt f [a] # many :: Alt f a -> Alt f [a] #
Applicative f => Applicative (Alt f)	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods pure :: a -> Alt f a # (<>) :: Alt f (a -> b) -> Alt f a -> Alt f b # liftA2 :: (a -> b -> c) -> Alt f a -> Alt f b -> Alt f c # (>) :: Alt f a -> Alt f b -> Alt f b # (<*) :: Alt f a -> Alt f b -> Alt f a #
Functor f => Functor (Alt f)	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods fmap :: (a -> b) -> Alt f a -> Alt f b # (<$) :: a -> Alt f b -> Alt f a #
Monad f => Monad (Alt f)	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods (>>=) :: Alt f a -> (a -> Alt f b) -> Alt f b # (>>) :: Alt f a -> Alt f b -> Alt f b # return :: a -> Alt f a #
MonadPlus f => MonadPlus (Alt f)	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods mzero :: Alt f a # mplus :: Alt f a -> Alt f a -> Alt f a #
(Data (f a), Data a, Typeable f) => Data (Alt f a)	Since: base-4.8.0.0
Instance details Defined in Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Alt f a -> c (Alt f a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Alt f a) # toConstr :: Alt f a -> Constr # dataTypeOf :: Alt f a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Alt f a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Alt f a)) # gmapT :: (forall b. Data b => b -> b) -> Alt f a -> Alt f a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Alt f a -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Alt f a -> r # gmapQ :: (forall d. Data d => d -> u) -> Alt f a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Alt f a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Alt f a -> m (Alt f a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Alt f a -> m (Alt f a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Alt f a -> m (Alt f a) #
Alternative f => Monoid (Alt f a)	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Alt f a # mappend :: Alt f a -> Alt f a -> Alt f a # mconcat :: [Alt f a] -> Alt f a #
Alternative f => Semigroup (Alt f a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Alt f a -> Alt f a -> Alt f a # sconcat :: NonEmpty (Alt f a) -> Alt f a # stimes :: Integral b => b -> Alt f a -> Alt f a #
Enum (f a) => Enum (Alt f a)	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods succ :: Alt f a -> Alt f a # pred :: Alt f a -> Alt f a # toEnum :: Int -> Alt f a # fromEnum :: Alt f a -> Int # enumFrom :: Alt f a -> [Alt f a] # enumFromThen :: Alt f a -> Alt f a -> [Alt f a] # enumFromTo :: Alt f a -> Alt f a -> [Alt f a] # enumFromThenTo :: Alt f a -> Alt f a -> Alt f a -> [Alt f a] #
Generic (Alt f a)
Instance details Defined in Data.Semigroup.Internal Associated Types type Rep (Alt f a) :: Type -> Type # Methods from :: Alt f a -> Rep (Alt f a) x # to :: Rep (Alt f a) x -> Alt f a #
Num (f a) => Num (Alt f a)	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods (+) :: Alt f a -> Alt f a -> Alt f a # (-) :: Alt f a -> Alt f a -> Alt f a # (*) :: Alt f a -> Alt f a -> Alt f a # negate :: Alt f a -> Alt f a # abs :: Alt f a -> Alt f a # signum :: Alt f a -> Alt f a # fromInteger :: Integer -> Alt f a #
Read (f a) => Read (Alt f a)	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods readsPrec :: Int -> ReadS (Alt f a) # readList :: ReadS [Alt f a] # readPrec :: ReadPrec (Alt f a) # readListPrec :: ReadPrec [Alt f a] #
Show (f a) => Show (Alt f a)	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods showsPrec :: Int -> Alt f a -> ShowS # show :: Alt f a -> String # showList :: [Alt f a] -> ShowS #
Eq (f a) => Eq (Alt f a)	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods (==) :: Alt f a -> Alt f a -> Bool # (/=) :: Alt f a -> Alt f a -> Bool #
Ord (f a) => Ord (Alt f a)	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods compare :: Alt f a -> Alt f a -> Ordering # (<) :: Alt f a -> Alt f a -> Bool # (<=) :: Alt f a -> Alt f a -> Bool # (>) :: Alt f a -> Alt f a -> Bool # (>=) :: Alt f a -> Alt f a -> Bool # max :: Alt f a -> Alt f a -> Alt f a # min :: Alt f a -> Alt f a -> Alt f a #
Unbox (f a) => Unbox (Alt f a)
Instance details Defined in Data.Vector.Unboxed.Base
type Rep1 (Alt f :: k -> Type)	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal type Rep1 (Alt f :: k -> Type) = D1 ('MetaData "Alt" "Data.Semigroup.Internal" "base" 'True) (C1 ('MetaCons "Alt" 'PrefixI 'True) (S1 ('MetaSel ('Just "getAlt") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 f)))
newtype MVector s (Alt f a)
Instance details Defined in Data.Vector.Unboxed.Base newtype MVector s (Alt f a) = MV_Alt (MVector s (f a))
type Rep (Alt f a)	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal type Rep (Alt f a) = D1 ('MetaData "Alt" "Data.Semigroup.Internal" "base" 'True) (C1 ('MetaCons "Alt" 'PrefixI 'True) (S1 ('MetaSel ('Just "getAlt") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (f a))))
newtype Vector (Alt f a)
Instance details Defined in Data.Vector.Unboxed.Base newtype Vector (Alt f a) = V_Alt (Vector (f a))

newtype All #

Boolean monoid under conjunction (&&).

>>> getAll (All True <> mempty <> All False)
False

>>> getAll (mconcat (map (\x -> All (even x)) [2,4,6,7,8]))
False

Constructors

All
Fields getAll :: Bool

Instances

Instances details

Data All	Since: base-4.8.0.0
Instance details 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 # toConstr :: All -> Constr # 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
Instance details Defined in Data.Semigroup.Internal Methods mempty :: All # mappend :: All -> All -> All # mconcat :: [All] -> All #
Semigroup All	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: All -> All -> All # sconcat :: NonEmpty All -> All # stimes :: Integral b => b -> All -> All #
Bounded All	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods minBound :: All # maxBound :: All #
Generic All
Instance details Defined in Data.Semigroup.Internal Associated Types type Rep All :: Type -> Type # Methods from :: All -> Rep All x # to :: Rep All x -> All #
Read All	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods readsPrec :: Int -> ReadS All # readList :: ReadS [All] # readPrec :: ReadPrec All # readListPrec :: ReadPrec [All] #
Show All	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods showsPrec :: Int -> All -> ShowS # show :: All -> String # showList :: [All] -> ShowS #
NFData All	Since: deepseq-1.4.0.0
Instance details Defined in Control.DeepSeq Methods rnf :: All -> () #
Eq All	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods (==) :: All -> All -> Bool # (/=) :: All -> All -> Bool #
Ord All	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods compare :: All -> All -> Ordering # (<) :: All -> All -> Bool # (<=) :: All -> All -> Bool # (>) :: All -> All -> Bool # (>=) :: All -> All -> Bool # max :: All -> All -> All # min :: All -> All -> All #
Unbox All
Instance details Defined in Data.Vector.Unboxed.Base
Vector Vector All
Instance details Defined in Data.Vector.Unboxed.Base Methods 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 () # elemseq :: Vector All -> All -> b -> b #
MVector MVector All
Instance details Defined in Data.Vector.Unboxed.Base Methods 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
Instance details Defined in Data.Semigroup.Internal type Rep All = D1 ('MetaData "All" "Data.Semigroup.Internal" "base" 'True) (C1 ('MetaCons "All" 'PrefixI 'True) (S1 ('MetaSel ('Just "getAll") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 Bool)))
newtype Vector All
Instance details Defined in Data.Vector.Unboxed.Base newtype Vector All = V_All (Vector Bool)
newtype MVector s All
Instance details Defined in Data.Vector.Unboxed.Base newtype MVector s All = MV_All (MVector s Bool)

newtype Endo a #

The monoid of endomorphisms under composition.

>>> let computation = Endo ("Hello, " ++) <> Endo (++ "!")
>>> appEndo computation "Haskell"
"Hello, Haskell!"

Constructors

Endo
Fields appEndo :: a -> a

Instances

Instances details

Monoid (Endo a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Endo a # mappend :: Endo a -> Endo a -> Endo a # mconcat :: [Endo a] -> Endo a #
Semigroup (Endo a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Endo a -> Endo a -> Endo a # sconcat :: NonEmpty (Endo a) -> Endo a # stimes :: Integral b => b -> Endo a -> Endo a #
Generic (Endo a)
Instance details Defined in Data.Semigroup.Internal Associated Types type Rep (Endo a) :: Type -> Type # Methods from :: Endo a -> Rep (Endo a) x # to :: Rep (Endo a) x -> Endo a #
type Rep (Endo a)	Since: base-4.7.0.0
Instance details Defined in Data.Semigroup.Internal type Rep (Endo a) = D1 ('MetaData "Endo" "Data.Semigroup.Internal" "base" 'True) (C1 ('MetaCons "Endo" 'PrefixI 'True) (S1 ('MetaSel ('Just "appEndo") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (a -> a))))

newtype Dual a #

The dual of a Monoid, obtained by swapping the arguments of mappend.

>>> getDual (mappend (Dual "Hello") (Dual "World"))
"WorldHello"

Constructors

Dual
Fields getDual :: a

Instances

Instances details

Foldable Dual	Since: base-4.8.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => Dual m -> m # foldMap :: Monoid m => (a -> m) -> Dual a -> m # foldMap' :: Monoid m => (a -> m) -> Dual a -> m # foldr :: (a -> b -> b) -> b -> Dual a -> b # foldr' :: (a -> b -> b) -> b -> Dual a -> b # foldl :: (b -> a -> b) -> b -> Dual a -> b # foldl' :: (b -> a -> b) -> b -> Dual a -> b # foldr1 :: (a -> a -> a) -> Dual a -> a # foldl1 :: (a -> a -> a) -> Dual a -> a # toList :: Dual a -> [a] # null :: Dual a -> Bool # length :: Dual a -> Int # elem :: Eq a => a -> Dual a -> Bool # maximum :: Ord a => Dual a -> a # minimum :: Ord a => Dual a -> a # sum :: Num a => Dual a -> a # product :: Num a => Dual a -> a #
Traversable Dual	Since: base-4.8.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Dual a -> f (Dual b) # sequenceA :: Applicative f => Dual (f a) -> f (Dual a) # mapM :: Monad m => (a -> m b) -> Dual a -> m (Dual b) # sequence :: Monad m => Dual (m a) -> m (Dual a) #
Applicative Dual	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods pure :: a -> Dual a # (<>) :: Dual (a -> b) -> Dual a -> Dual b # liftA2 :: (a -> b -> c) -> Dual a -> Dual b -> Dual c # (>) :: Dual a -> Dual b -> Dual b # (<*) :: Dual a -> Dual b -> Dual a #
Functor Dual	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods fmap :: (a -> b) -> Dual a -> Dual b # (<$) :: a -> Dual b -> Dual a #
Monad Dual	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods (>>=) :: Dual a -> (a -> Dual b) -> Dual b # (>>) :: Dual a -> Dual b -> Dual b # return :: a -> Dual a #
NFData1 Dual	Since: deepseq-1.4.3.0
Instance details Defined in Control.DeepSeq Methods liftRnf :: (a -> ()) -> Dual a -> () #
Generic1 Dual
Instance details Defined in Data.Semigroup.Internal Associated Types type Rep1 Dual :: k -> Type # Methods from1 :: forall (a :: k). Dual a -> Rep1 Dual a # to1 :: forall (a :: k). Rep1 Dual a -> Dual a #
Unbox a => Vector Vector (Dual a)
Instance details Defined in Data.Vector.Unboxed.Base Methods 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 () # elemseq :: Vector (Dual a) -> Dual a -> b -> b #
Unbox a => MVector MVector (Dual a)
Instance details Defined in Data.Vector.Unboxed.Base Methods 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
Instance details Defined in Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Dual a -> c (Dual a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Dual a) # toConstr :: Dual a -> Constr # dataTypeOf :: Dual a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Dual a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Dual a)) # gmapT :: (forall b. Data b => b -> b) -> Dual a -> Dual a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Dual a -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Dual a -> r # gmapQ :: (forall d. Data d => d -> u) -> Dual a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Dual a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Dual a -> m (Dual a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Dual a -> m (Dual a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Dual a -> m (Dual a) #
Monoid a => Monoid (Dual a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Dual a # mappend :: Dual a -> Dual a -> Dual a # mconcat :: [Dual a] -> Dual a #
Semigroup a => Semigroup (Dual a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Dual a -> Dual a -> Dual a # sconcat :: NonEmpty (Dual a) -> Dual a # stimes :: Integral b => b -> Dual a -> Dual a #
Bounded a => Bounded (Dual a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods minBound :: Dual a # maxBound :: Dual a #
Generic (Dual a)
Instance details Defined in Data.Semigroup.Internal Associated Types type Rep (Dual a) :: Type -> Type # Methods from :: Dual a -> Rep (Dual a) x # to :: Rep (Dual a) x -> Dual a #
Read a => Read (Dual a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods readsPrec :: Int -> ReadS (Dual a) # readList :: ReadS [Dual a] # readPrec :: ReadPrec (Dual a) # readListPrec :: ReadPrec [Dual a] #
Show a => Show (Dual a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods showsPrec :: Int -> Dual a -> ShowS # show :: Dual a -> String # showList :: [Dual a] -> ShowS #
NFData a => NFData (Dual a)	Since: deepseq-1.4.0.0
Instance details Defined in Control.DeepSeq Methods rnf :: Dual a -> () #
Eq a => Eq (Dual a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods (==) :: Dual a -> Dual a -> Bool # (/=) :: Dual a -> Dual a -> Bool #
Ord a => Ord (Dual a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods compare :: Dual a -> Dual a -> Ordering # (<) :: Dual a -> Dual a -> Bool # (<=) :: Dual a -> Dual a -> Bool # (>) :: Dual a -> Dual a -> Bool # (>=) :: Dual a -> Dual a -> Bool # max :: Dual a -> Dual a -> Dual a # min :: Dual a -> Dual a -> Dual a #
Prim a => Prim (Dual a)	Since: primitive-0.6.5.0
Instance details Defined in Data.Primitive.Types Methods sizeOfType# :: Proxy (Dual a) -> Int# # sizeOf# :: 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 #
Instance details Defined in Universum.Container.Class Associated Types type Element (Dual a) Source # Methods 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 # or :: 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)
Instance details Defined in Data.Vector.Unboxed.Base
type Rep1 Dual	Since: base-4.7.0.0
Instance details Defined in Data.Semigroup.Internal type Rep1 Dual = D1 ('MetaData "Dual" "Data.Semigroup.Internal" "base" 'True) (C1 ('MetaCons "Dual" 'PrefixI 'True) (S1 ('MetaSel ('Just "getDual") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))
newtype MVector s (Dual a)
Instance details Defined in Data.Vector.Unboxed.Base newtype MVector s (Dual a) = MV_Dual (MVector s a)
type Rep (Dual a)	Since: base-4.7.0.0
Instance details Defined in Data.Semigroup.Internal type Rep (Dual a) = D1 ('MetaData "Dual" "Data.Semigroup.Internal" "base" 'True) (C1 ('MetaCons "Dual" 'PrefixI 'True) (S1 ('MetaSel ('Just "getDual") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))
type Element (Dual a) Source #
Instance details Defined in Universum.Container.Class type Element (Dual a)
newtype Vector (Dual a)
Instance details Defined in Data.Vector.Unboxed.Base newtype Vector (Dual a) = V_Dual (Vector a)

class Semigroup a where #

The class of semigroups (types with an associative binary operation).

Instances should satisfy the following:

Associativity: x <> (y <> z) = (x <> y) <> z

You can alternatively define sconcat instead of (<>), in which case the laws are:

Unit: sconcat (pure x) = x
Multiplication: sconcat (join xss) = sconcat (fmap sconcat xss)

Since: base-4.9.0.0

Minimal complete definition

(<>) | sconcat

Methods

(<>) :: a -> a -> a infixr 6 #

An associative operation.

>>> [1,2,3] <> [4,5,6]
[1,2,3,4,5,6]

sconcat :: NonEmpty a -> a #

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 = stimesIdempotent or stimes = stimesIdempotentMonoid respectively.

>>> stimes 4 [1]
[1,1,1,1]

Instances

Instances details

Semigroup ByteArray	Since: base-4.17.0.0
Instance details Defined in Data.Array.Byte Methods (<>) :: ByteArray -> ByteArray -> ByteArray # sconcat :: NonEmpty ByteArray -> ByteArray # stimes :: Integral b => b -> ByteArray -> ByteArray #
Semigroup All	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: All -> All -> All # sconcat :: NonEmpty All -> All # stimes :: Integral b => b -> All -> All #
Semigroup Any	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Any -> Any -> Any # sconcat :: NonEmpty Any -> Any # stimes :: Integral b => b -> Any -> Any #
Semigroup Void	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: Void -> Void -> Void # sconcat :: NonEmpty Void -> Void # stimes :: Integral b => b -> Void -> Void #
Semigroup Builder
Instance details Defined in Data.ByteString.Builder.Internal Methods (<>) :: Builder -> Builder -> Builder # sconcat :: NonEmpty Builder -> Builder # stimes :: Integral b => b -> Builder -> Builder #
Semigroup ByteString
Instance details Defined in Data.ByteString.Internal.Type Methods (<>) :: ByteString -> ByteString -> ByteString # sconcat :: NonEmpty ByteString -> ByteString # stimes :: Integral b => b -> ByteString -> ByteString #
Semigroup ByteString
Instance details Defined in Data.ByteString.Lazy.Internal Methods (<>) :: ByteString -> ByteString -> ByteString # sconcat :: NonEmpty ByteString -> ByteString # stimes :: Integral b => b -> ByteString -> ByteString #
Semigroup ShortByteString
Instance details Defined in Data.ByteString.Short.Internal Methods (<>) :: ShortByteString -> ShortByteString -> ShortByteString # sconcat :: NonEmpty ShortByteString -> ShortByteString # stimes :: Integral b => b -> ShortByteString -> ShortByteString #
Semigroup IntSet	Since: containers-0.5.7
Instance details Defined in Data.IntSet.Internal Methods (<>) :: IntSet -> IntSet -> IntSet # sconcat :: NonEmpty IntSet -> IntSet # stimes :: Integral b => b -> IntSet -> IntSet #
Semigroup Ordering	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: Ordering -> Ordering -> Ordering # sconcat :: NonEmpty Ordering -> Ordering # stimes :: Integral b => b -> Ordering -> Ordering #
Semigroup OsString
Instance details Defined in System.OsString.Internal.Types Methods (<>) :: OsString -> OsString -> OsString # sconcat :: NonEmpty OsString -> OsString # stimes :: Integral b => b -> OsString -> OsString #
Semigroup PosixString
Instance details Defined in System.OsString.Internal.Types Methods (<>) :: PosixString -> PosixString -> PosixString # sconcat :: NonEmpty PosixString -> PosixString # stimes :: Integral b => b -> PosixString -> PosixString #
Semigroup WindowsString
Instance details Defined in System.OsString.Internal.Types Methods (<>) :: WindowsString -> WindowsString -> WindowsString # sconcat :: NonEmpty WindowsString -> WindowsString # stimes :: Integral b => b -> WindowsString -> WindowsString #
Semigroup Doc
Instance details Defined in Text.PrettyPrint.HughesPJ Methods (<>) :: Doc -> Doc -> Doc # sconcat :: NonEmpty Doc -> Doc # stimes :: Integral b => b -> Doc -> Doc #
Semigroup ()	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: () -> () -> () # sconcat :: NonEmpty () -> () # stimes :: Integral b => b -> () -> () #
Bits a => Semigroup (And a)	Since: base-4.16
Instance details Defined in Data.Bits Methods (<>) :: And a -> And a -> And a # sconcat :: NonEmpty (And a) -> And a # stimes :: Integral b => b -> And a -> And a #
FiniteBits a => Semigroup (Iff a)	This constraint is arguably too strong. However, as some types (such as `Natural`) have undefined `complement`, this is the only safe choice. Since: base-4.16
Instance details Defined in Data.Bits Methods (<>) :: Iff a -> Iff a -> Iff a # sconcat :: NonEmpty (Iff a) -> Iff a # stimes :: Integral b => b -> Iff a -> Iff a #
Bits a => Semigroup (Ior a)	Since: base-4.16
Instance details Defined in Data.Bits Methods (<>) :: Ior a -> Ior a -> Ior a # sconcat :: NonEmpty (Ior a) -> Ior a # stimes :: Integral b => b -> Ior a -> Ior a #
Bits a => Semigroup (Xor a)	Since: base-4.16
Instance details Defined in Data.Bits Methods (<>) :: Xor a -> Xor a -> Xor a # sconcat :: NonEmpty (Xor a) -> Xor a # stimes :: Integral b => b -> Xor a -> Xor a #
Semigroup a => Semigroup (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods (<>) :: Identity a -> Identity a -> Identity a # sconcat :: NonEmpty (Identity a) -> Identity a # stimes :: Integral b => b -> Identity a -> Identity a #
Semigroup (First a)	Since: base-4.9.0.0
Instance details Defined in Data.Monoid Methods (<>) :: First a -> First a -> First a # sconcat :: NonEmpty (First a) -> First a # stimes :: Integral b => b -> First a -> First a #
Semigroup (Last a)	Since: base-4.9.0.0
Instance details Defined in Data.Monoid Methods (<>) :: Last a -> Last a -> Last a # sconcat :: NonEmpty (Last a) -> Last a # stimes :: Integral b => b -> Last a -> Last a #
Semigroup a => Semigroup (Down a)	Since: base-4.11.0.0
Instance details Defined in Data.Ord Methods (<>) :: Down a -> Down a -> Down a # sconcat :: NonEmpty (Down a) -> Down a # stimes :: Integral b => b -> Down a -> Down a #
Semigroup (First a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (<>) :: First a -> First a -> First a # sconcat :: NonEmpty (First a) -> First a # stimes :: Integral b => b -> First a -> First a #
Semigroup (Last a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (<>) :: Last a -> Last a -> Last a # sconcat :: NonEmpty (Last a) -> Last a # stimes :: Integral b => b -> Last a -> Last a #
Ord a => Semigroup (Max a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (<>) :: Max a -> Max a -> Max a # sconcat :: NonEmpty (Max a) -> Max a # stimes :: Integral b => b -> Max a -> Max a #
Ord a => Semigroup (Min a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (<>) :: Min a -> Min a -> Min a # sconcat :: NonEmpty (Min a) -> Min a # stimes :: Integral b => b -> Min a -> Min a #
Monoid m => Semigroup (WrappedMonoid m)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (<>) :: 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
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Dual a -> Dual a -> Dual a # sconcat :: NonEmpty (Dual a) -> Dual a # stimes :: Integral b => b -> Dual a -> Dual a #
Semigroup (Endo a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Endo a -> Endo a -> Endo a # sconcat :: NonEmpty (Endo a) -> Endo a # stimes :: Integral b => b -> Endo a -> Endo a #
Num a => Semigroup (Product a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Product a -> Product a -> Product a # sconcat :: NonEmpty (Product a) -> Product a # stimes :: Integral b => b -> Product a -> Product a #
Num a => Semigroup (Sum a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Sum a -> Sum a -> Sum a # sconcat :: NonEmpty (Sum a) -> Sum a # stimes :: Integral b => b -> Sum a -> Sum a #
Semigroup (NonEmpty a)	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: NonEmpty a -> NonEmpty a -> NonEmpty a # sconcat :: NonEmpty (NonEmpty a) -> NonEmpty a # stimes :: Integral b => b -> NonEmpty a -> NonEmpty a #
Semigroup a => Semigroup (STM a)	Since: base-4.17.0.0
Instance details Defined in GHC.Conc.Sync Methods (<>) :: STM a -> STM a -> STM a # sconcat :: NonEmpty (STM a) -> STM a # stimes :: Integral b => b -> STM a -> STM a #
(Generic a, Semigroup (Rep a ())) => Semigroup (Generically a)	Since: base-4.17.0.0
Instance details Defined in GHC.Generics Methods (<>) :: 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
Instance details Defined in GHC.Generics Methods (<>) :: Par1 p -> Par1 p -> Par1 p # sconcat :: NonEmpty (Par1 p) -> Par1 p # stimes :: Integral b => b -> Par1 p -> Par1 p #
Semigroup (IntMap a)	Since: containers-0.5.7
Instance details Defined in Data.IntMap.Internal Methods (<>) :: IntMap a -> IntMap a -> IntMap a # sconcat :: NonEmpty (IntMap a) -> IntMap a # stimes :: Integral b => b -> IntMap a -> IntMap a #
Semigroup (Seq a)	Since: containers-0.5.7
Instance details Defined in Data.Sequence.Internal Methods (<>) :: Seq a -> Seq a -> Seq a # sconcat :: NonEmpty (Seq a) -> Seq a # stimes :: Integral b => b -> Seq a -> Seq a #
Ord a => Semigroup (Intersection a)
Instance details Defined in Data.Set.Internal Methods (<>) :: Intersection a -> Intersection a -> Intersection a # sconcat :: NonEmpty (Intersection a) -> Intersection a # stimes :: Integral b => b -> Intersection a -> Intersection a #
Semigroup (MergeSet a)
Instance details Defined in Data.Set.Internal Methods (<>) :: MergeSet a -> MergeSet a -> MergeSet a # sconcat :: NonEmpty (MergeSet a) -> MergeSet a # stimes :: Integral b => b -> MergeSet a -> MergeSet a #
Ord a => Semigroup (Set a)	Since: containers-0.5.7
Instance details Defined in Data.Set.Internal Methods (<>) :: Set a -> Set a -> Set a # sconcat :: NonEmpty (Set a) -> Set a # stimes :: Integral b => b -> Set a -> Set a #
Semigroup a => Semigroup (IO a)	Since: base-4.10.0.0
Instance details Defined in GHC.Base Methods (<>) :: IO a -> IO a -> IO a # sconcat :: NonEmpty (IO a) -> IO a # stimes :: Integral b => b -> IO a -> IO a #
Semigroup a => Semigroup (May a)
Instance details Defined in Lens.Micro.Mtl.Internal Methods (<>) :: May a -> May a -> May a # sconcat :: NonEmpty (May a) -> May a # stimes :: Integral b => b -> May a -> May a #
Semigroup (Doc a)
Instance details Defined in Text.PrettyPrint.Annotated.HughesPJ Methods (<>) :: Doc a -> Doc a -> Doc a # sconcat :: NonEmpty (Doc a) -> Doc a # stimes :: Integral b => b -> Doc a -> Doc a #
Semigroup (Array a)	Since: primitive-0.6.3.0
Instance details Defined in Data.Primitive.Array Methods (<>) :: Array a -> Array a -> Array a # sconcat :: NonEmpty (Array a) -> Array a # stimes :: Integral b => b -> Array a -> Array a #
Semigroup (PrimArray a)	Since: primitive-0.6.4.0
Instance details Defined in Data.Primitive.PrimArray Methods (<>) :: PrimArray a -> PrimArray a -> PrimArray a # sconcat :: NonEmpty (PrimArray a) -> PrimArray a # stimes :: Integral b => b -> PrimArray a -> PrimArray a #
Semigroup (SmallArray a)	Since: primitive-0.6.3.0
Instance details Defined in Data.Primitive.SmallArray Methods (<>) :: 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
Instance details Defined in Language.Haskell.TH.Syntax Methods (<>) :: Q a -> Q a -> Q a # sconcat :: NonEmpty (Q a) -> Q a # stimes :: Integral b => b -> Q a -> Q a #
(Hashable a, Eq a) => Semigroup (HashSet a)	`<>` = `union` $O(n+m)$ To obtain good performance, the smaller set must be presented as the first argument. Examples Expand `>>>` `fromList [1,2] <> fromList [2,3]`fromList [1,2,3]
Instance details Defined in Data.HashSet.Internal Methods (<>) :: HashSet a -> HashSet a -> HashSet a # sconcat :: NonEmpty (HashSet a) -> HashSet a # stimes :: Integral b => b -> HashSet a -> HashSet a #
Semigroup (Vector a)
Instance details Defined in Data.Vector Methods (<>) :: Vector a -> Vector a -> Vector a # sconcat :: NonEmpty (Vector a) -> Vector a # stimes :: Integral b => b -> Vector a -> Vector a #
Prim a => Semigroup (Vector a)
Instance details Defined in Data.Vector.Primitive Methods (<>) :: Vector a -> Vector a -> Vector a # sconcat :: NonEmpty (Vector a) -> Vector a # stimes :: Integral b => b -> Vector a -> Vector a #
Storable a => Semigroup (Vector a)
Instance details Defined in Data.Vector.Storable Methods (<>) :: Vector a -> Vector a -> Vector a # sconcat :: NonEmpty (Vector a) -> Vector a # stimes :: Integral b => b -> Vector a -> Vector a #
Semigroup a => Semigroup (Maybe a)	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: Maybe a -> Maybe a -> Maybe a # sconcat :: NonEmpty (Maybe a) -> Maybe a # stimes :: Integral b => b -> Maybe a -> Maybe a #
Semigroup a => Semigroup (a)	Since: base-4.15
Instance details Defined in GHC.Base Methods (<>) :: (a) -> (a) -> (a) # sconcat :: NonEmpty (a) -> (a) # stimes :: Integral b => b -> (a) -> (a) #
Semigroup [a]	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: [a] -> [a] -> [a] # sconcat :: NonEmpty [a] -> [a] # stimes :: Integral b => b -> [a] -> [a] #
Semigroup (Either a b)	Since: base-4.9.0.0
Instance details Defined in Data.Either Methods (<>) :: Either a b -> Either a b -> Either a b # sconcat :: NonEmpty (Either a b) -> Either a b # stimes :: Integral b0 => b0 -> Either a b -> Either a b #
Semigroup (Proxy s)	Since: base-4.9.0.0
Instance details Defined in Data.Proxy Methods (<>) :: Proxy s -> Proxy s -> Proxy s # sconcat :: NonEmpty (Proxy s) -> Proxy s # stimes :: Integral b => b -> Proxy s -> Proxy s #
Semigroup (U1 p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods (<>) :: U1 p -> U1 p -> U1 p # sconcat :: NonEmpty (U1 p) -> U1 p # stimes :: Integral b => b -> U1 p -> U1 p #
Semigroup (V1 p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods (<>) :: V1 p -> V1 p -> V1 p # sconcat :: NonEmpty (V1 p) -> V1 p # stimes :: Integral b => b -> V1 p -> V1 p #
Ord k => Semigroup (Map k v)
Instance details Defined in Data.Map.Internal Methods (<>) :: Map k v -> Map k v -> Map k v # sconcat :: NonEmpty (Map k v) -> Map k v # stimes :: Integral b => b -> Map k v -> Map k v #
Applicative f => Semigroup (Traversed a f)
Instance details Defined in Lens.Micro Methods (<>) :: Traversed a f -> Traversed a f -> Traversed a f # sconcat :: NonEmpty (Traversed a f) -> Traversed a f # stimes :: Integral b => b -> Traversed a f -> Traversed a f #
Semigroup a => Semigroup (Err e a)
Instance details Defined in Lens.Micro.Mtl.Internal Methods (<>) :: Err e a -> Err e a -> Err e a # sconcat :: NonEmpty (Err e a) -> Err e a # stimes :: Integral b => b -> Err e a -> Err e a #
(Eq k, Hashable k) => Semigroup (HashMap k v)	`<>` = `union` If a key occurs in both maps, the mapping from the first will be the mapping in the result. Examples Expand `>>>` `fromList [(1,'a'),(2,'b')] <> fromList [(2,'c'),(3,'d')]`fromList [(1,'a'),(2,'b'),(3,'d')]
Instance details Defined in Data.HashMap.Internal Methods (<>) :: HashMap k v -> HashMap k v -> HashMap k v # sconcat :: NonEmpty (HashMap k v) -> HashMap k v # stimes :: Integral b => b -> HashMap k v -> HashMap k v #
(Semigroup a, Semigroup b) => Semigroup (a, b)	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: (a, b) -> (a, b) -> (a, b) # sconcat :: NonEmpty (a, b) -> (a, b) # stimes :: Integral b0 => b0 -> (a, b) -> (a, b) #
Semigroup b => Semigroup (a -> b)	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: (a -> b) -> (a -> b) -> a -> b # sconcat :: NonEmpty (a -> b) -> a -> b # stimes :: Integral b0 => b0 -> (a -> b) -> a -> b #
Semigroup a => Semigroup (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods (<>) :: Const a b -> Const a b -> Const a b # sconcat :: NonEmpty (Const a b) -> Const a b # stimes :: Integral b0 => b0 -> Const a b -> Const a b #
(Applicative f, Semigroup a) => Semigroup (Ap f a)	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods (<>) :: Ap f a -> Ap f a -> Ap f a # sconcat :: NonEmpty (Ap f a) -> Ap f a # stimes :: Integral b => b -> Ap f a -> Ap f a #
Alternative f => Semigroup (Alt f a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Alt f a -> Alt f a -> Alt f a # sconcat :: NonEmpty (Alt f a) -> Alt f a # stimes :: Integral b => b -> Alt f a -> Alt f a #
Semigroup (f p) => Semigroup (Rec1 f p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods (<>) :: Rec1 f p -> Rec1 f p -> Rec1 f p # sconcat :: NonEmpty (Rec1 f p) -> Rec1 f p # stimes :: Integral b => b -> Rec1 f p -> Rec1 f p #
(Monad m, Semigroup r) => Semigroup (Effect m r a)
Instance details Defined in Lens.Micro.Mtl.Internal Methods (<>) :: Effect m r a -> Effect m r a -> Effect m r a # sconcat :: NonEmpty (Effect m r a) -> Effect m r a # stimes :: Integral b => b -> Effect m r a -> Effect m r a #
(Semigroup a, Semigroup b, Semigroup c) => Semigroup (a, b, c)	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: (a, b, c) -> (a, b, c) -> (a, b, c) # sconcat :: NonEmpty (a, b, c) -> (a, b, c) # stimes :: Integral b0 => b0 -> (a, b, c) -> (a, b, c) #
(Semigroup (f a), Semigroup (g a)) => Semigroup (Product f g a)	Since: base-4.16.0.0
Instance details Defined in Data.Functor.Product Methods (<>) :: Product f g a -> Product f g a -> Product f g a # sconcat :: NonEmpty (Product f g a) -> Product f g a # stimes :: Integral b => b -> Product f g a -> Product f g a #
(Semigroup (f p), Semigroup (g p)) => Semigroup ((f :*: g) p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods (<>) :: (f :: g) p -> (f :: g) p -> (f :: g) p # sconcat :: NonEmpty ((f :: g) p) -> (f :: g) p # stimes :: Integral b => b -> (f :: g) p -> (f :*: g) p #
Semigroup c => Semigroup (K1 i c p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods (<>) :: K1 i c p -> K1 i c p -> K1 i c p # sconcat :: NonEmpty (K1 i c p) -> K1 i c p # stimes :: Integral b => b -> K1 i c p -> K1 i c p #
(Semigroup a, Semigroup b, Semigroup c, Semigroup d) => Semigroup (a, b, c, d)	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) # sconcat :: NonEmpty (a, b, c, d) -> (a, b, c, d) # stimes :: Integral b0 => b0 -> (a, b, c, d) -> (a, b, c, d) #
Semigroup (f (g a)) => Semigroup (Compose f g a)	Since: base-4.16.0.0
Instance details Defined in Data.Functor.Compose Methods (<>) :: Compose f g a -> Compose f g a -> Compose f g a # sconcat :: NonEmpty (Compose f g a) -> Compose f g a # stimes :: Integral b => b -> Compose f g a -> Compose f g a #
Semigroup (f (g p)) => Semigroup ((f :.: g) p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods (<>) :: (f :.: g) p -> (f :.: g) p -> (f :.: g) p # sconcat :: NonEmpty ((f :.: g) p) -> (f :.: g) p # stimes :: Integral b => b -> (f :.: g) p -> (f :.: g) p #
Semigroup (f p) => Semigroup (M1 i c f p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods (<>) :: M1 i c f p -> M1 i c f p -> M1 i c f p # sconcat :: NonEmpty (M1 i c f p) -> M1 i c f p # stimes :: Integral b => b -> M1 i c f p -> M1 i c f p #
(Semigroup a, Semigroup b, Semigroup c, Semigroup d, Semigroup e) => Semigroup (a, b, c, d, e)	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) # sconcat :: NonEmpty (a, b, c, d, e) -> (a, b, c, d, e) # stimes :: Integral b0 => b0 -> (a, b, c, d, e) -> (a, b, c, d, e) #

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

Instances details

NFData1 WrappedMonoid	Since: deepseq-1.4.3.0
Instance details Defined in Control.DeepSeq Methods liftRnf :: (a -> ()) -> WrappedMonoid a -> () #
Generic1 WrappedMonoid
Instance details Defined in Data.Semigroup Associated Types type Rep1 WrappedMonoid :: k -> Type # Methods from1 :: forall (a :: k). WrappedMonoid a -> Rep1 WrappedMonoid a # to1 :: forall (a :: k). Rep1 WrappedMonoid a -> WrappedMonoid a #
Unbox a => Vector Vector (WrappedMonoid a)
Instance details Defined in Data.Vector.Unboxed.Base Methods basicUnsafeFreeze :: Mutable Vector s (WrappedMonoid a) -> ST s (Vector (WrappedMonoid a)) # basicUnsafeThaw :: Vector (WrappedMonoid a) -> ST s (Mutable Vector s (WrappedMonoid a)) # basicLength :: Vector (WrappedMonoid a) -> Int # basicUnsafeSlice :: Int -> Int -> Vector (WrappedMonoid a) -> Vector (WrappedMonoid a) # basicUnsafeIndexM :: Vector (WrappedMonoid a) -> Int -> Box (WrappedMonoid a) # basicUnsafeCopy :: Mutable Vector s (WrappedMonoid a) -> Vector (WrappedMonoid a) -> ST s () # elemseq :: Vector (WrappedMonoid a) -> WrappedMonoid a -> b -> b #
Unbox a => MVector MVector (WrappedMonoid a)
Instance details Defined in Data.Vector.Unboxed.Base Methods basicLength :: MVector s (WrappedMonoid a) -> Int # basicUnsafeSlice :: Int -> Int -> MVector s (WrappedMonoid a) -> MVector s (WrappedMonoid a) # basicOverlaps :: MVector s (WrappedMonoid a) -> MVector s (WrappedMonoid a) -> Bool # basicUnsafeNew :: Int -> ST s (MVector s (WrappedMonoid a)) # basicInitialize :: MVector s (WrappedMonoid a) -> ST s () # basicUnsafeReplicate :: Int -> WrappedMonoid a -> ST s (MVector s (WrappedMonoid a)) # basicUnsafeRead :: MVector s (WrappedMonoid a) -> Int -> ST s (WrappedMonoid a) # basicUnsafeWrite :: MVector s (WrappedMonoid a) -> Int -> WrappedMonoid a -> ST s () # basicClear :: MVector s (WrappedMonoid a) -> ST s () # basicSet :: MVector s (WrappedMonoid a) -> WrappedMonoid a -> ST s () # basicUnsafeCopy :: MVector s (WrappedMonoid a) -> MVector s (WrappedMonoid a) -> ST s () # basicUnsafeMove :: MVector s (WrappedMonoid a) -> MVector s (WrappedMonoid a) -> ST s () # basicUnsafeGrow :: MVector s (WrappedMonoid a) -> Int -> ST s (MVector s (WrappedMonoid a)) #
Data m => Data (WrappedMonoid m)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> WrappedMonoid m -> c (WrappedMonoid m) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (WrappedMonoid m) # toConstr :: WrappedMonoid m -> Constr # dataTypeOf :: WrappedMonoid m -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (WrappedMonoid m)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (WrappedMonoid m)) # gmapT :: (forall b. Data b => b -> b) -> WrappedMonoid m -> WrappedMonoid m # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> WrappedMonoid m -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> WrappedMonoid m -> r # gmapQ :: (forall d. Data d => d -> u) -> WrappedMonoid m -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> WrappedMonoid m -> u # gmapM :: Monad m0 => (forall d. Data d => d -> m0 d) -> WrappedMonoid m -> m0 (WrappedMonoid m) # gmapMp :: MonadPlus m0 => (forall d. Data d => d -> m0 d) -> WrappedMonoid m -> m0 (WrappedMonoid m) # gmapMo :: MonadPlus m0 => (forall d. Data d => d -> m0 d) -> WrappedMonoid m -> m0 (WrappedMonoid m) #
Monoid m => Monoid (WrappedMonoid m)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods mempty :: WrappedMonoid m # mappend :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m # mconcat :: [WrappedMonoid m] -> WrappedMonoid m #
Monoid m => Semigroup (WrappedMonoid m)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (<>) :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m # sconcat :: NonEmpty (WrappedMonoid m) -> WrappedMonoid m # stimes :: Integral b => b -> WrappedMonoid m -> WrappedMonoid m #
Bounded m => Bounded (WrappedMonoid m)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods minBound :: WrappedMonoid m # maxBound :: WrappedMonoid m #
Enum a => Enum (WrappedMonoid a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods succ :: WrappedMonoid a -> WrappedMonoid a # pred :: WrappedMonoid a -> WrappedMonoid a # toEnum :: Int -> WrappedMonoid a # fromEnum :: WrappedMonoid a -> Int # enumFrom :: WrappedMonoid a -> [WrappedMonoid a] # enumFromThen :: WrappedMonoid a -> WrappedMonoid a -> [WrappedMonoid a] # enumFromTo :: WrappedMonoid a -> WrappedMonoid a -> [WrappedMonoid a] # enumFromThenTo :: WrappedMonoid a -> WrappedMonoid a -> WrappedMonoid a -> [WrappedMonoid a] #
Generic (WrappedMonoid m)
Instance details Defined in Data.Semigroup Associated Types type Rep (WrappedMonoid m) :: Type -> Type # Methods from :: WrappedMonoid m -> Rep (WrappedMonoid m) x # to :: Rep (WrappedMonoid m) x -> WrappedMonoid m #
Read m => Read (WrappedMonoid m)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods readsPrec :: Int -> ReadS (WrappedMonoid m) # readList :: ReadS [WrappedMonoid m] # readPrec :: ReadPrec (WrappedMonoid m) # readListPrec :: ReadPrec [WrappedMonoid m] #
Show m => Show (WrappedMonoid m)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods showsPrec :: Int -> WrappedMonoid m -> ShowS # show :: WrappedMonoid m -> String # showList :: [WrappedMonoid m] -> ShowS #
NFData m => NFData (WrappedMonoid m)	Since: deepseq-1.4.2.0
Instance details Defined in Control.DeepSeq Methods rnf :: WrappedMonoid m -> () #
Eq m => Eq (WrappedMonoid m)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (==) :: WrappedMonoid m -> WrappedMonoid m -> Bool # (/=) :: WrappedMonoid m -> WrappedMonoid m -> Bool #
Ord m => Ord (WrappedMonoid m)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods compare :: WrappedMonoid m -> WrappedMonoid m -> Ordering # (<) :: WrappedMonoid m -> WrappedMonoid m -> Bool # (<=) :: WrappedMonoid m -> WrappedMonoid m -> Bool # (>) :: WrappedMonoid m -> WrappedMonoid m -> Bool # (>=) :: WrappedMonoid m -> WrappedMonoid m -> Bool # max :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m # min :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m #
Hashable a => Hashable (WrappedMonoid a)
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> WrappedMonoid a -> Int # hash :: WrappedMonoid a -> Int #
Unbox a => Unbox (WrappedMonoid a)
Instance details Defined in Data.Vector.Unboxed.Base
type Rep1 WrappedMonoid	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup type Rep1 WrappedMonoid = D1 ('MetaData "WrappedMonoid" "Data.Semigroup" "base" 'True) (C1 ('MetaCons "WrapMonoid" 'PrefixI 'True) (S1 ('MetaSel ('Just "unwrapMonoid") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))
newtype MVector s (WrappedMonoid a)
Instance details Defined in Data.Vector.Unboxed.Base newtype MVector s (WrappedMonoid a) = MV_WrappedMonoid (MVector s a)
type Rep (WrappedMonoid m)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup type Rep (WrappedMonoid m) = D1 ('MetaData "WrappedMonoid" "Data.Semigroup" "base" 'True) (C1 ('MetaCons "WrapMonoid" 'PrefixI 'True) (S1 ('MetaSel ('Just "unwrapMonoid") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 m)))
newtype Vector (WrappedMonoid a)
Instance details Defined in Data.Vector.Unboxed.Base newtype Vector (WrappedMonoid a) = V_WrappedMonoid (Vector a)

stimesIdempotent :: Integral b => b -> a -> a #

This is a valid definition of stimes for an idempotent Semigroup.

When x <> x = x, this definition should be preferred, because it works in $\mathcal{O}(1)$ rather than $\mathcal{O}(\log n)$.

stimesIdempotentMonoid :: (Integral b, Monoid a) => b -> a -> a #

This is a valid definition of stimes for an idempotent Monoid.

When mappend x x = x, this definition should be preferred, because it works in $\mathcal{O}(1)$ rather than $\mathcal{O}(\log n)$

stimesMonoid :: (Integral b, Monoid a) => b -> a -> a #

This is a valid definition of stimes for a Monoid.

Unlike the default definition of stimes, it is defined for 0 and so it should be preferred where possible.

cycle1 :: Semigroup m => m -> m #

A generalization of cycle to an arbitrary Semigroup. May fail to terminate for some values in some semigroups.

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.

maybeToMonoid :: Monoid m => Maybe m -> m Source #

Extracts Monoid value from Maybe returning mempty if Nothing.

>>> maybeToMonoid (Just [1,2,3] :: Maybe [Int])
[1,2,3]
>>> maybeToMonoid (Nothing :: Maybe [Int])
[]

Documentation

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