Numeric.Monoid.Additive

Additive Monoids

class (LeftModule Natural m, RightModule Natural m) => AdditiveMonoid m where

An additive monoid

 zero + a = a = a + zero

Methods

zero :: m

replicate :: Whole n => n -> m -> m

sumWith :: Foldable f => (a -> m) -> f a -> m

Instances

AdditiveMonoid Bool

AdditiveMonoid Int

AdditiveMonoid Int8

AdditiveMonoid Int16

AdditiveMonoid Int32

AdditiveMonoid Int64

AdditiveMonoid Integer

AdditiveMonoid Word

AdditiveMonoid Word8

AdditiveMonoid Word16

AdditiveMonoid Word32

AdditiveMonoid Word64

AdditiveMonoid ()

AdditiveMonoid Natural

Unital r => AdditiveMonoid (Log r)

AdditiveMonoid r => AdditiveMonoid (End r)

AdditiveMonoid r => AdditiveMonoid (ZeroRng r)

AdditiveMonoid r => AdditiveMonoid (Opposite r)

(Abelian r, AdditiveMonoid r) => AdditiveMonoid (RngRing r)

AdditiveMonoid r => AdditiveMonoid (e -> r)

(AdditiveMonoid a, AdditiveMonoid b) => AdditiveMonoid (a, b)

AdditiveMonoid s => AdditiveMonoid (Linear s a)

AdditiveMonoid s => AdditiveMonoid (Antilinear s a)

(AdditiveMonoid a, AdditiveMonoid b, AdditiveMonoid c) => AdditiveMonoid (a, b, c)

AdditiveMonoid s => AdditiveMonoid (Map s b a)

(AdditiveMonoid a, AdditiveMonoid b, AdditiveMonoid c, AdditiveMonoid d) => AdditiveMonoid (a, b, c, d)

(AdditiveMonoid a, AdditiveMonoid b, AdditiveMonoid c, AdditiveMonoid d, AdditiveMonoid e) => AdditiveMonoid (a, b, c, d, e)

sum :: (Foldable f, AdditiveMonoid m) => f m -> m