Trait MonoidHom 

pub trait MonoidHom: SemigroupHom { }

A monoid homomorphism: a structure-preserving map between monoids that preserves both combine and identity.

A homomorphism f: M → N preserves both the monoid operation and identity:

Laws (not enforced by type system):

• Preserve combine: f(x.combine(y)) == f(x).combine(f(y))
• Preserve identity: f(M::empty()) == N::empty()

Example

use algebra::Max;
use algebra::Monoid;
use algebra::MonoidHom;
use algebra::Semigroup;
use algebra::SemigroupHom;

// A monoid homomorphism that widens Max<u32> to Max<u64>.
// This preserves identity because bottom for both is 0.
struct Widen;

impl SemigroupHom for Widen {
    type Source = Max<u32>;
    type Target = Max<u64>;

    fn apply(&self, x: &Max<u32>) -> Max<u64> {
        Max(x.0 as u64)
    }
}

impl MonoidHom for Widen {}

// Verify identity preservation: f(⊥) = ⊥
let widen = Widen;
assert_eq!(widen.apply(&Max::<u32>::empty()), Max::<u64>::empty());

// Verify combine preservation
let a = Max(10u32);
let b = Max(20u32);
assert_eq!(
    widen.apply(&a.combine(&b)),
    widen.apply(&a).combine(&widen.apply(&b))
);

Implementors