Is there a total order on JavaScript objects?

Question

The title pretty much says it all. Does JavaScript guarantee a total order on objects when using the < , > , <= and >= operators?

I wrote some code just to check total ordering on some objects. The result is consistent with total ordering, but that doesn't prove anything:

function thereIsTotalOrder(items){

    var one, other, theThird;

    // warning: n^3 complexity follows

    // If a <= b and b <= a then a = b (antisymmetry);
    for(var i=0; i<items.length; i++){
        for(var j=0; j<items.length; j++){
            one = items[i];
            other = items[j];
            if((one <= other) && (other <= one) && (one != other)){
                return false;
            }
        }
    }

    // If a <= b and b <= c then a <= c (transitivity)
    for(var i=0; i<items.length; i++){
        for(var j=0; j<items.length; j++){
            for(var k=0; k<items.length; k++){
                one = items[i];
                other = items[j];
                theThird = items[k];
                if((one <= other) && (other <= theThird) && !(one <= theThird)) {
                    return false;
                }
            }
        }
    }

    // a <= b or b <= a (totality). 
    for(var i=0; i<items.length; i++){
        for(var j=0; j<items.length; j++){
            one = items[i];
            other = items[j];
            if(!((one <= other) || (other <= one))) {
                return false;
            }
        }
    }

    return true;
}

function a(){};
function b(){};
var c = "foo";
var d = "bar";
var e = "bar";
var f = function(){};
var g = {name : "bananas"};

console.log(thereIsTotalOrder([a, b, c, d, e, f, g])); // prints "true"

Answer 1

Depends on what objects we're considering. If we confine our attention to the class of numbers , then yes, the order will be total. As your example demonstrates, the same can be said of (at least some) strings . But totality doesn't seem to hold generally.

For instance, if you add var h = 5; to your declarations and then add h to your thereIsTotalOrder call, you will get a false . That's because in a state where h = 5 and c = 'foo' , ( h ≤ c ∨ c ≤ h ) is false (which means that totality is not satisfied).

As you rightly noted, while the absence of a false value returned by thereIsTotalOrder doesn't prove that all objects are totally ordered, the presence of a false value does prove that the order (if defined) between all objects is not total.