I'm not very literate in functional programming ... so excuse such a dumb question. But I'm curious why you write the recursing function duplicated? eg. isn't this version of your code equivalent?

    function Y(X) {
      var fn = function(procedure) {
        return X(function(arg) {
          return procedure(procedure)(arg);
        });
      };
      return fn(fn);
    }

Or am I missing something vital here about how it is all working? The shorter version seems clearer to me (not that any of this is clear to me), and functionally equivalent.