enum Nat {
  Zero,
  Succ(Box<Nat>)
}

impl Nat {
  fn new(u: u32) -> Nat
  {
    if u == 0 {
      Nat::Zero
    } else {
      Nat::Succ(Box::new(Nat::new(u - 1)))
    }
  }

  fn dup(&self) -> Nat {
    if let Nat::Succ(prev) = self {
      Nat::Succ(Box::new(prev.dup()))
    } else {
      Nat::Zero
    }
  }

  fn add(&self, n: &Nat) -> Nat {
    if let Nat::Succ(prev) = n {
      Nat::Succ(Box::new(self.add(&prev)))
    } else {
      self.dup()
    }
  }

  fn to_u32(n: &Nat) -> u32
  {
    if let Nat::Succ(prev) = n {
      1 + Nat::to_u32(prev)
    } else {
      0
    }
  }
}

fn main()
{
  let z = Nat::Zero;
  let u = Nat::new(1);
  let q = Nat::new(4);
  let c = Nat::new(100);
  let hundredfour = c.add(&q);

  println!("{}", Nat::to_u32(&z));
  println!("{}", Nat::to_u32(&u));
  println!("{}", Nat::to_u32(&q));
  println!("{}", Nat::to_u32(&c));
  println!("{}", Nat::to_u32(&hundredfour));
}