On 15 July 2013 15:49, Jeremy Martin <jmar777 at gmail.com> wrote:
>>  (a === b) >= (new Symbol(a) === new Symbol(b))
>
> Not sure I follow... so, I either I don't agree or I don't understand :).
> I'm having to dig deep to remember my math vocab here, but I think it may be
> most correct to say that the Symbol constructor, when passed an argument,
> should be injective [1].  That is,
>
> 1. let F = new Symbol
> 2. if a = b, then F(a) = F(b)
> 3. if a != b, then F(a) != F(b)

I agree, but the problem is that JavaScript's === is not an
equivalence relation, due to the dreaded NaN !== NaN that IEEE
invented in some delirium. So you cannot define injectivity based on
it. You merely get an implication for the above, which is what the >=
was supposed to encode. Object.is OTOH implements a proper equivalence
relation, i.e. a "=" in the mathematical sense. It only differs from
=== by having a sane semantics for NaN.

But as I said, I was merely picking a nit.

/Andreas

On 15 July 2013 15:49, Jeremy Martin <jmar777 at gmail.com> wrote:
> Not sure I follow... so, I either I don't agree or I don't understand :).
> I'm having to dig deep to remember my math vocab here, but I think it may be
> most correct to say that the Symbol constructor, when passed an argument,
> should be injective [1].

I agree, but the problem is that JavaScript's `===` is not an
equivalence relation, due to the dreaded `NaN !== NaN` that IEEE
invented in some delirium. So you cannot define injectivity based on
it. You merely get an implication for the above, which is what the `>=` was supposed to encode. `Object.is` OTOH implements a proper equivalence relation, i.e. a "=" in the mathematical sense. It only differs from `===` by having a sane semantics for `NaN`.

But as I said, I was merely picking a nit.