Numeric.Sum

Documentation

newtype Sum a

Monoid under addition.

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

Constructors

Sum

Fields

• getSum :: a

Instances

Monad Sum

Since: base-4.8.0.0

Defined in Data.Semigroup.Internal

Methods

(>>=) :: Sum a -> (a -> Sum b) -> Sum b

(>>) :: Sum a -> Sum b -> Sum b

return :: a -> Sum a

fail :: String -> Sum a

Functor Sum

Since: base-4.8.0.0

Defined in Data.Semigroup.Internal

Methods

fmap :: (a -> b) -> Sum a -> Sum b

(<$) :: a -> Sum b -> Sum a

MonadFix Sum

Since: base-4.8.0.0

Defined in Control.Monad.Fix

Methods

mfix :: (a -> Sum a) -> Sum a

Applicative Sum

Since: base-4.8.0.0

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

Foldable Sum

Since: base-4.8.0.0

Defined in Data.Foldable

Methods

fold :: Monoid m => Sum m -> m

foldMap :: Monoid m => (a -> m) -> Sum a -> m

foldr :: (a -> b -> b) -> b -> Sum a -> b

foldr' :: (a -> b -> b) -> b -> Sum a -> b

foldl :: (b -> a -> b) -> b -> Sum a -> b

foldl' :: (b -> a -> b) -> b -> Sum a -> b

foldr1 :: (a -> a -> a) -> Sum a -> a

foldl1 :: (a -> a -> a) -> Sum a -> a

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

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)

Distributive Sum

Defined in Data.Distributive

Methods

distribute :: Functor f => f (Sum a) -> Sum (f a)

collect :: Functor f => (a -> Sum b) -> f a -> Sum (f b)

distributeM :: Monad m => m (Sum a) -> Sum (m a)

collectM :: Monad m => (a -> Sum b) -> m a -> Sum (m b)

Representable Sum

Defined in Data.Functor.Rep

Associated Types

type Rep Sum :: *

Methods

tabulate :: (Rep Sum -> a) -> Sum a

index :: Sum a -> Rep Sum -> a

MonadZip Sum

Since: base-4.8.0.0

Defined in Control.Monad.Zip

Methods

mzip :: Sum a -> Sum b -> Sum (a, b)

mzipWith :: (a -> b -> c) -> Sum a -> Sum b -> Sum c

munzip :: Sum (a, b) -> (Sum a, Sum b)

NFData1 Sum

Since: deepseq-1.4.3.0

Defined in Control.DeepSeq

Methods

liftRnf :: (a -> ()) -> Sum a -> ()

Apply Sum

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: Sum (a -> b) -> Sum a -> Sum b

(.>) :: Sum a -> Sum b -> Sum b

(<.) :: Sum a -> Sum b -> Sum a

liftF2 :: (a -> b -> c) -> Sum a -> Sum b -> Sum c

Traversable1 Sum

Defined in Data.Semigroup.Traversable.Class

Methods

traverse1 :: Apply f => (a -> f b) -> Sum a -> f (Sum b)

sequence1 :: Apply f => Sum (f b) -> f (Sum b)

Pointed Sum

Defined in Data.Pointed

Methods

point :: a -> Sum a

Copointed Sum

Defined in Data.Copointed

Methods

copoint :: Sum a -> a

Foldable1 Sum

Defined in Data.Semigroup.Foldable.Class

Methods

fold1 :: Semigroup m => Sum m -> m

foldMap1 :: Semigroup m => (a -> m) -> Sum a -> m

toNonEmpty :: Sum a -> NonEmpty a

Bind Sum

Defined in Data.Functor.Bind.Class

Methods

(>>-) :: Sum a -> (a -> Sum b) -> Sum b

join :: Sum (Sum a) -> Sum a

Extend Sum

Defined in Data.Functor.Extend

Methods

duplicated :: Sum a -> Sum (Sum a)

extended :: (Sum a -> b) -> Sum a -> Sum b

Bounded a => Bounded (Sum a)

Defined in Data.Semigroup.Internal

Methods

minBound :: Sum a

maxBound :: Sum a

Eq a => Eq (Sum a)

Defined in Data.Semigroup.Internal

Methods

(==) :: Sum a -> Sum a -> Bool

(/=) :: Sum a -> Sum a -> Bool

Data a => Data (Sum a)

Since: base-4.8.0.0

Defined in Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Sum a -> c (Sum a)

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Sum a)

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 :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Sum a -> r

gmapQ :: (forall d. Data d => d -> u) -> Sum a -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> Sum a -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Sum a -> m (Sum a)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Sum a -> m (Sum a)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Sum a -> m (Sum a)

Num a => Num (Sum a)

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

Ord a => Ord (Sum a)

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

Read a => Read (Sum a)

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)

Defined in Data.Semigroup.Internal

Methods

showsPrec :: Int -> Sum a -> ShowS

show :: Sum a -> String

showList :: [Sum a] -> ShowS

Generic (Sum a)

Defined in Data.Semigroup.Internal

Associated Types

type Rep (Sum a) :: * -> *

Methods

from :: Sum a -> Rep (Sum a) x

to :: Rep (Sum a) x -> Sum a

Num a => Semigroup (Sum a)

Since: base-4.9.0.0

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

Num a => Monoid (Sum a)

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

mempty :: Sum a

mappend :: Sum a -> Sum a -> Sum a

mconcat :: [Sum a] -> Sum a

NFData a => NFData (Sum a)

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: Sum a -> ()

Wrapped (Sum a)

Defined in Control.Lens.Wrapped

Associated Types

type Unwrapped (Sum a) :: *

Methods

_Wrapped' :: Iso' (Sum a) (Unwrapped (Sum a))

(Eq a, Num a) => AsEmpty (Sum a)

Defined in Control.Lens.Empty

Methods

_Empty :: Prism' (Sum a) ()

Upper a => Upper (Sum a)

Defined in Data.Semilattice.Upper

Methods

upperBound :: Sum a

Lower a => Lower (Sum a)

Defined in Data.Semilattice.Lower

Methods

lowerBound :: Sum a

Serialise a => Serialise (Sum a)

Since: serialise-0.2.0.0

Defined in Codec.Serialise.Class

Methods

encode :: Sum a -> Encoding

decode :: Decoder s (Sum a)

encodeList :: [Sum a] -> Encoding

decodeList :: Decoder s [Sum a]

Generic1 Sum

Defined in Data.Semigroup.Internal

Associated Types

type Rep1 Sum :: k -> *

Methods

from1 :: Sum a -> Rep1 Sum a

to1 :: Rep1 Sum a -> Sum a

t ~ Sum b => Rewrapped (Sum a) t

Defined in Control.Lens.Wrapped

type Rep Sum

Defined in Data.Functor.Rep

type Rep Sum = ()

type Rep (Sum a)

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 Unwrapped (Sum a)

Defined in Control.Lens.Wrapped

type Unwrapped (Sum a) = a

type Rep1 Sum

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))