ECMAScript - turning a binary function into a variadic one

In my previous post, I mentioned that it's easy to take a binary JavaScript function and turn it into a variadic one. Here's the helper function to do that:

function variadic(fun, val0f, val1f) {
  return function() {
    var len = arguments.length;
    if (len == 0) {
       return val0f();
    } else if (len == 1) {
       if (val1f != undefined) {
         return val1f(arguments[0]);
       }
       else {
         return arguments[0];
       }
    } else {
      var tmp = fun(arguments[0], arguments[1]);
      for (index = 2; index < len; index++) {
        tmp = fun(tmp, arguments[index]);
      }
      return tmp;
    }
  };
}

The 'variadic' function takes three parameters:

1. the binary function;
2. a function that returns the value for the variadic version when called with zero arguments
3. a function that returns the value for the variadic version when called on a single. If not specified, the first argument to the variadic function is returned as is when called on a single argument.

For example, the summation operator is defined as

var sum = variadic(function(x,y) {return x+y;},
                   function() { return 0;},
                   function(x) { return x;});

while the equivalent of Scheme's / function is defined as

var div = variadic(function(x,y) {return x/y; },
                   function() { throw "not enough arguments to div"; },
                   function(x) { return 1/x;});

It is now possible to call

div.apply(this, [1,2,3,4,5])

to get 0.008333333333333333.