algebra-2.0.2: Constructive abstract algebra

Numeric.Additive.Class

Contents

Synopsis

Additive Semigroups

class Additive r whereSource

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

Methods

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

sinnum1p :: Whole n => n -> r -> rSource

sinnum1p n r = sinnum (1 + n) r

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

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

Additive Abelian semigroups

class Additive r => Abelian r Source

an additive abelian semigroup

a + b = b + a

Additive Monoids

class Additive r => Idempotent r Source

An additive semigroup with idempotent addition.

 a + a = a

Partitionable semigroups