peano.rs

use std::fmt;
use std::ops;

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

impl ops::Add for Nat {
    type Output = Nat;

    fn add(self, other: Nat) -> Nat {
        fn sum(a: Nat, b: Nat) -> Nat {
            match a {
                Nat::Zero => b,
                Nat::Succ(nat) => Nat::Succ(Box::new(sum(*nat, b))),
            }
        }
        sum(self, other)
    }
}

impl fmt::Display for Nat {
    fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
        fn count(nat: &Nat) -> i32 {
            match nat {
                &Nat::Zero => 0,
                &Nat::Succ(ref nat) => 1 + count(nat),
            }
        }
        write!(f, "Nat({})", count(self))
    }
}


fn main() {
    let a = Nat::Succ(Box::new(Nat::Succ(Box::new(Nat::Zero))));
    let b = Nat::Succ(Box::new(Nat::Succ(Box::new(Nat::Zero))));
    println!("Result: {}", a + b);
}