Overloading methods in TypeScript

At yesterday's presentation at Desert Code Camp I felt that I gave an inadequate explanation on how you would implement an overloaded method in TypeScript. Hopefully this code snippet will address that:

interface Thing {
    a: number;
    b: string;
    foo(x: string): string;
    foo(n: number): number;
}

function myfunction(myParam: Thing) {
    var stringResult: string = myParam.foo(myParam.b);
    var numberResult: number = myParam.foo(myParam.a);

    console.log(stringResult);
    console.log(numberResult);
}


var myObj = {
    a: 16,
    b: "My String",
    foo: (x: any) => {
        if (x && typeof x === 'string') {
            return x.length.toString();
        } else if (x && typeof x === 'number') {
            return x * x;
        } else {
            if (x) {
                throw { message: "null parameter is unsupported" };
            } else {
                throw { message: "unsupported type: " + typeof x };
            }
        }
    }
}

myfunction(myObj);

Note that in myfunction() you would not be able to call myParam.foo() with any other type of parameter than string or number because the compiler will complain about that. So even though the implementation checks for another type in the final else you cannot pass in another type (e.g. object) because TypeScript won't let you.