var A = new Class({
    initialize: $empty,
    a: function() {
        return "Hi, I'm " + arguments.callee.caller._name + ", and " + arguments.callee.caller.caller.caller._name + " called me.";
    },
    b: function() {
        alert(this.a()); //knows 'b' called it
    }
});

window.addEvent('domready', function() {
    var ex = new A();
    ex.b();
});