Implementing natural numbers with Peano arithmetic in Java 😎

MainProgram.java

public class MainProgram {
	public static void main(String[] args) {
		Nat n1 = Nat.int2Nat(10);
		Nat n2 = Nat.int2Nat(20);
		
		Nat n3 = n1.add(n2);
		
		int x = Nat.nat2Int(n3);
		
		System.out.println(x);
	}
}

abstract class Nat {
	public abstract Nat add(Nat n);
	
	public static Nat int2Nat(int n) {
		if (n == 0) {
			return new Zero();
		} else {
			return new Succ(int2Nat(n - 1));
		}
	}
	
	public static int nat2Int(Nat n) {
		if (n instanceof Succ s) {
			return 1 + nat2Int(s.x);
		} else {
			return 0;
		}
	}
}

class Zero extends Nat {
	@Override
	public Nat add(Nat n) {
		return n;
	}
}

class Succ extends Nat {
	public Nat x;
	
	public Succ(Nat x) {
		this.x = x;
	}
	
	@Override
	public Nat add(Nat n) {
		return new Succ(x.add(n));
	}
}

This is equivalent to the following Haskell code:

data Nat = Zero | Succ Nat

add :: Nat -> Nat -> Nat
add Zero     y = y
add (Succ x) y = Succ (add x y)