Is the JavaScript operator === provably transitive?

Question

JavaScript's quirky weakly-typed == operator can easily be shown to be non-transitive as follows:

var a = "16";
var b = 16;
var c = "0x10";
alert(a == b && b == c && a != c); // alerts true

I wonder if there are any similar tricks one can play with roundoff error, Infinity, or NaN that could should show === to be non-transitive, or if it can be proved to indeed be transitive.

Answer 1

The === operator in Javascript seems to be as transitive as it can get.

NaN is reliably different from NaN:

>>> 0/0 === 0/0
false
>>> 0/0 !== 0/0
true

Infinity is reliably equal to Infinity:

>>> 1/0 === 1/0
true
>>> 1/0 !== 1/0
false

Objects (hashes) are always different:

>>> var a = {}, b = {};
>>> a === b
false
>>> a !== b
true

And since the === operator does not perform any type coercion, no value conversion can occur, so the equality / inequality semantics of primitive types will remain consistent (i.e. won't contradict one another), interpreter bugs notwithstanding.

Answer 2

If you look at the spec (http://bclary.com/2004/11/07/#a-11.9.6) you will see that no type coercion is being made. Also, everything else is pretty straightforward, so maybe only implementation bugs will make it non-transitive.

Answer 3

Assuming you have variable a,b, and c you can't be 100% certain as shown here. If someone is doing something as hackish as above in production, well then you probably have bigger problems ;)

var a = 1;
var b = 1;
Object.defineProperty(window,"c",{get:function(){return b++;}});

alert(a === b && b === c && a !== c); // alerts true