Church Encoding in TypeScript

church-encoding.ts

type Some<T> = (x: T) => T;
var add = function <T>(m: Some<Some<T>>, n: Some<Some<T>>) {
    return function (f: Some<T>) {
        return function (x: T) {
            return m(f)(n(f)(x));
        };
    };
}, mul = function <T>(m: Some<Some<T>>, n: Some<Some<T>>) {
    return function (f: Some<T>) {
        return m(n(f));
    };
}, pow = function <T>(m: Some<Some<T>>, n: Some<Some<Some<T>>>) {
    return n(m);
}, pred = function (n) {
    return function (f) {
        return function (x) {
            return n(function (g) {
                return function (h) {
                    return h(g(f));
                }
            })(function (u) {
                return x;
            })(function (u) {
                return u;
            });
        };
    };
}, sub = function <T>(m: Some<Some<T>>, n: Some<typeof pred>): Some<Some<T>> {
    return n(pred)(m);
};

var one = function (f) {
    return function (x) {
        return f(x);
    }
};

var two = add(one, one), three = add(one, two);

var result = sub<number>(pow<number>(pow(two, three), three), three)(function (x) {
    return x + 1;
})(0);

alert(result);