Monoid trait and implementations in Rust

Monoid.rs

trait Semigroup {
  fn mappend(&self, b: Self) -> Self;
}

trait Monoid: Semigroup {
  fn mempty() -> Self;
}

impl Semigroup for int {
  fn mappend(&self, b: int) -> int { *self + b }
}

impl Monoid for int {
  fn mempty() -> int { 0 }
}

impl Semigroup for ~str {
  fn mappend(&self, b: ~str) -> ~str { *self + b }
}

impl Monoid for ~str {
  fn mempty() -> ~str { ~"" }
}

fn main() {
   println((~"Hello").mappend(~"World").to_str());
   println(1.mappend(2).to_str());

   // `as` didn't work as ascription.
   let str_zero: ~str = Monoid::mempty();
   let int_zero: int = Monoid::mempty();
   println(str_zero);
   println(int_zero.to_str());
}

"Monoid" trait seems to be equvivalent to Default trait. I can't find something like this for "Semigroup" although.

Update: found the difference: Monoid: Semigroup.

@vi Monoid is not equivalent to Default.

Monoid must satisfy specific laws:

1. a.mappend(mempty()) == a
2. mempty.mappend(a) == a

Default mustn't.

Default may make sense without Semigroup, Monoid doesn't.