Church numbers with TypeScript

interface Nat {
    name: 'zero' | 'succ';
    pred: Nat;
}

class Zero implements Nat {
    name: 'zero';
    pred: Zero;
    constructor() { this.pred = this; }
}

class Succ<T extends Nat> implements Nat {
    name: 'succ';
    pred: T;
    constructor(pred: T) { this.pred = pred; }
}

class Plus<A extends Nat, B extends Nat> {
    zero: {
        zero: B;
        succ: B;
    };
    succ: {
        zero: A;
        succ: Succ<Plus<A['pred'], B>[A['pred']['name']][B['name']]>;
    };
}

type One = Succ<Zero>;
type Two = Succ<One>;

type Sum = Plus<One, Two>[One['name']][Two['name']];