Struct Groupoid 

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

A set equipped with an associative binary operation.

Groupoid is a representation of the abstract algebraic groupoid. Associativity is all that is required of its binary operation: its construction involves a set (specifically an AlgaeSet) and an associative BinaryOperation.

Examples

use algae_rs::algaeset::AlgaeSet;
use algae_rs::mapping::{BinaryOperation, AssociativeOperation};
use algae_rs::magma::{Magmoid, Groupoid};

let mut add = AssociativeOperation::new(&|a, b| a + b);
let mut groupoid = Groupoid::new(
    AlgaeSet::<i32>::all(),
    &mut add
);

let groupoid_sum = groupoid.with(1, 2);
assert!(groupoid_sum.is_ok());
assert!(groupoid_sum.unwrap() == 3);

let mut div = AssociativeOperation::new(&|a, b| a / b);
let mut bad_groupoid = Groupoid::new(
    AlgaeSet::<f32>::all(),
    &mut div,
);

let ok_dividend = bad_groupoid.with(1.0, 2.0);
assert!(ok_dividend.is_ok());
assert!(ok_dividend.unwrap() == 0.5);
let err_dividend = bad_groupoid.with(3.0, 6.0);
assert!(err_dividend.is_err());

Implementations

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

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

Trait Implementations

impl<'a, T> From<Groupoid<'a, T>> for Magma<'a, T>

fn from(groupoid: Groupoid<'a, T>) -> Magma<'a, T>

Converts to this type from the input type.

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> Magmoid<T> for Groupoid<'a, T>

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

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