Trait un_algebra::monoid::add_monoid::AddMonoid

pub trait AddMonoid: AddSemigroup {
    fn zero() -> Self;

    fn is_zero(&self) -> bool { ... }
    fn axiom_left_add_identity(x: &Self) -> bool { ... }
    fn axiom_right_add_identity(&self) -> bool { ... }
}

An algebraic additive monoid.

Required Methods

fn zero() -> Self

Unique zero (additive identity) element. Zero is ideally a const value, but the const rules make it too difficult to create const instances for many third party types.

Provided Methods

fn is_zero(&self) -> bool

Test for the zero (additive identity) element.

fn axiom_left_add_identity(x: &Self) -> bool

Test the left additive identity axiom.

fn axiom_right_add_identity(&self) -> bool

Test the right additive identity axiom.

Implementations on Foreign Types

impl AddMonoid for u8

fn zero() -> Self

Zero is just integer zero.

fn is_zero(&self) -> bool

fn axiom_left_add_identity(x: &Self) -> bool

fn axiom_right_add_identity(&self) -> bool

impl AddMonoid for u16

fn zero() -> Self

Zero is just integer zero.

fn is_zero(&self) -> bool

fn axiom_left_add_identity(x: &Self) -> bool

fn axiom_right_add_identity(&self) -> bool

impl AddMonoid for u32

fn zero() -> Self

Zero is just integer zero.

fn is_zero(&self) -> bool

fn axiom_left_add_identity(x: &Self) -> bool

fn axiom_right_add_identity(&self) -> bool

impl AddMonoid for u64

fn zero() -> Self

Zero is just integer zero.

fn is_zero(&self) -> bool

fn axiom_left_add_identity(x: &Self) -> bool

fn axiom_right_add_identity(&self) -> bool

impl AddMonoid for u128

fn zero() -> Self

Zero is just integer zero.

fn is_zero(&self) -> bool

fn axiom_left_add_identity(x: &Self) -> bool

fn axiom_right_add_identity(&self) -> bool

impl AddMonoid for usize

fn zero() -> Self

Zero is just integer zero.

fn is_zero(&self) -> bool

fn axiom_left_add_identity(x: &Self) -> bool

fn axiom_right_add_identity(&self) -> bool

impl AddMonoid for i8

fn zero() -> Self

Zero is just integer zero.

fn is_zero(&self) -> bool

fn axiom_left_add_identity(x: &Self) -> bool

fn axiom_right_add_identity(&self) -> bool

impl AddMonoid for i16

fn zero() -> Self

Zero is just integer zero.

fn is_zero(&self) -> bool

fn axiom_left_add_identity(x: &Self) -> bool

fn axiom_right_add_identity(&self) -> bool

impl AddMonoid for i32

fn zero() -> Self

Zero is just integer zero.

fn is_zero(&self) -> bool

fn axiom_left_add_identity(x: &Self) -> bool

fn axiom_right_add_identity(&self) -> bool

impl AddMonoid for i64

fn zero() -> Self

Zero is just integer zero.

fn is_zero(&self) -> bool

fn axiom_left_add_identity(x: &Self) -> bool

fn axiom_right_add_identity(&self) -> bool

impl AddMonoid for i128

fn zero() -> Self

Zero is just integer zero.

fn is_zero(&self) -> bool

fn axiom_left_add_identity(x: &Self) -> bool

fn axiom_right_add_identity(&self) -> bool

impl AddMonoid for isize

fn zero() -> Self

Zero is just integer zero.

fn is_zero(&self) -> bool

fn axiom_left_add_identity(x: &Self) -> bool

fn axiom_right_add_identity(&self) -> bool

impl AddMonoid for BigRational

Rational numbers form an additive monoid.

fn zero() -> Self

Zero is rational zero.

fn is_zero(&self) -> bool

fn axiom_left_add_identity(x: &Self) -> bool

fn axiom_right_add_identity(&self) -> bool

Implementors