Struct Monoid 

pub struct Monoid<'a, T> { /* private fields */ }

A set equipped with an associative binary operation with identity.

Monoid is a representation of the abstract algebraic monoid. Associativity and identity are required of its binary operation. Its construction involves a set (specifically an AlgaeSet and a BinaryOperation with the aforementioned properties.

Examples

use algae_rs::algaeset::AlgaeSet;
use algae_rs::mapping::{BinaryOperation, MonoidOperation};
use algae_rs::magma::{Magmoid, Monoid};

let mut add = MonoidOperation::new(&|a, b| a + b, 0);
let mut monoid = Monoid::new(
    AlgaeSet::<i32>::all(),
    &mut add,
    0
);

let monoid_sum = monoid.with(1, 2);
assert!(monoid_sum.is_ok());
assert!(monoid_sum.unwrap() == 3);

let mut bad_add = MonoidOperation::new(&|a, b| a + b, 1);
let mut bad_monoid = Monoid::new(
    AlgaeSet::<i32>::all(),
    &mut bad_add,
    1
);

let bad_monoid_sum = bad_monoid.with(1, 2);
assert!(bad_monoid_sum.is_err());

Implementations

impl<'a, T: Copy + PartialEq> Monoid<'a, T>

pub fn new( aset: AlgaeSet<T>, binop: &'a mut dyn BinaryOperation<T>, identity: T, ) -> Self

Trait Implementations

impl<'a, T: Copy + PartialEq> From<Monoid<'a, T>> for Groupoid<'a, T>

fn from(monoid: Monoid<'a, T>) -> Groupoid<'a, T>

Converts to this type from the input type.

impl<'a, T: Copy + PartialEq> From<Monoid<'a, T>> for Magma<'a, T>

fn from(monoid: Monoid<'a, T>) -> Magma<'a, T>

Converts to this type from the input type.

impl<'a, T: Copy + PartialEq> From<Monoid<'a, T>> for UnitalMagma<'a, T>

fn from(monoid: Monoid<'a, T>) -> UnitalMagma<'a, T>

Converts to this type from the input type.

impl<'a, T: Copy + PartialEq> Magmoid<T> for Monoid<'a, T>

fn binop(&mut self) -> &mut dyn BinaryOperation<T>

fn with(&mut self, left: T, right: T) -> Result<T, PropertyError>