Numeric.Semigroup.Additive

Additive Semigroups

class Additive r where

 (a + b) + c = a + (b + c)
 replicate 1 a = a
 replicate (2 * n) a = replicate n a + replicate n a
 replicate (2 * n + 1) a = replicate n a + replicate n a + a

Methods

(+) :: r -> r -> r

replicate1p :: Whole n => n -> r -> r

replicate1p n r = replicate (1 + n) r

sumWith1 :: Foldable1 f => (a -> r) -> f a -> r

Instances

Additive Bool

Additive Int

Additive Int8

Additive Int16

Additive Int32

Additive Int64

Additive Integer

Additive Word

Additive Word8

Additive Word16

Additive Word32

Additive Word64

Additive ()

Additive Natural

Multiplicative r => Additive (Log r)

Additive r => Additive (End r)

Additive r => Additive (ZeroRng r)

Additive r => Additive (Opposite r)

Abelian r => Additive (RngRing r)

Additive r => Additive (b -> r)

(Additive a, Additive b) => Additive (a, b)

Additive r => Additive (Linear r a)

Additive s => Additive (Antilinear s a)

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

Additive r => Additive (Map r b a)

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

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

sum1 :: (Foldable1 f, Additive r) => f r -> r