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AddMonoid

typeclass A: AddMonoid extends AddSemigroup, Zero {
    add_identity_right(a: A) {
        a + A.0 = a
    }
    add_identity_left(a: A) {
        A.0 + a = a
    }
}

An additive monoid is an additive semigroup with an identity element.

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add​

Inherited from Add.

add_associative​

Inherited from AddSemigroup.

add_identity_left​

add_identity_left(a: A) {
    A.0 + a = a
}

The identity element must satisfy the identity property on the left.

add_identity_right​

add_identity_right(a: A) {
    a + A.0 = a
}

The identity element must satisfy the identity property on the right.