[swift-evolution] [Draft][Proposal] Formalized Ordering

Fri Jul 22 17:36:36 CDT 2016

On Fri, Jul 22, 2016 at 3:54 PM, Dave Abrahams <dabrahams at apple.com> wrote:

>
> on Fri Jul 22 2016, Xiaodi Wu <xiaodi.wu-AT-gmail.com> wrote:
>
> > On Fri, Jul 22, 2016 at 1:05 PM, Dave Abrahams via swift-evolution <
> > swift-evolution at swift.org> wrote:
> >
> >>
> >> on Thu Jul 21 2016, Duan <swift-evolution at swift.org> wrote:
> >>
> >> > Great proposal. I want to second that areSame may mislead user to
> >> > think this is about identity.
> >> >
> >> > I like areEquivalent() but there may be better names.
> >>
> >> It really *is* about identity as I posted in a previous message.
> >
> > Correct me if I'm wrong:
>
> Not to put too fine a point on it, but... ;-)
>

Please do :) This discussion has been very edifying (for me), so thank you
for taking the time.

> > Identity is an equality relation, and `==` is about just that.
> > By contrast, `areSame()` is to define an *equivalence* relation
>
> The phrase “equality relation” has no commonly-understood formal or
> informal meaning AFAIK.
>
> “Identity” is a slightly informal term IIUC, but for any
> commonly-understood meaning of that word, the “is identical to” is
> *always* an equivalence relation.
>
> > through which, by default, `==` is to be dispatched.
> > Since this design specifically
> > contemplates scenarios in which certain Equatables will override `==`
> *not*
> > to dispatch through `areSame()`,
>
> [Since `==` wouldn't be a protocol requirement (except in FloatingPoint),
> it's technically shadowing rather than overriding in the general case.
> I imagine this detail doesn't matter to your point]
>
> > the latter function evaluates only *equivalence* with respect to an
> > arbitrary equivalence relation, not identity.
>
> Saying that areSame is just any old arbitrary equivalence relation,
> would complicate the system in undesirable ways.

Ah, well, there goes my dream of using `{ return true }` as my equivalence
relation... :P

> It's
> a bit subtle but I'll try to walk you through the reasoning:
>
> 1. We had a choice about whether to document that Comparable requires
>    that <=> be a total order or a strict weak order [A strict weak order
>    is a total order over equivalence classes of elements that aren't
>    ordered with respect to other members of the same class].  Either one
>    will work for the standard algorithms.
>
> 2. Because the concept of total order is more accessible and requiring
>    <=> to be a total order doesn't seem to reduce expressivity, we
>    decided on a total order.
>
> 3. The only difference between these two orderings is that in a total
>    order the equivalence classes have only a single element, **which
>    means that the equivalence relation in play has to, in some sense,
>    tell you whether two things are identical**.  This all comes down to
>    how you measure “are a and b the same element?”
>
> The alternative is to say that <=> is just a strict weak ordering and
> areSame is just any arbitrary equivalence relation, but that really
> complicates everything (not just the definition of Comparable).  For
> example, you can't document `a.firstIndex(of: b)` as the first index where
> `b` appears in `a`; you have to say it's the first index of an element
> that satisfies `{ Element.areSame($0, b) }`.
>

I hadn't considered how closely yoked Equatable and Comparable have to be.
You can't have Comparable refine Equatable such that
`Comparable.areSame(_:)` has stricter semantic requirements than plain
Equatable?

> > Put another way, the future `Equatable` is a contract that conforming
> > types will supply a definition of equality *and* an equivalence
> > relation, where the former by default is dispatched through the
> > latter; but it is specifically envisioned that the two may be
> > separated in domain-specific scenarios.
>
> That is correct.  However, the equivalence relation in question still
> is, in some very real sense, an identity check.
>
> >> But
> >> that doesn't change the fact that areEquivalent might be a better name.
> >> It's one of the things we considered; it just seemed long for no real
> >> benefit.
> >>
> >> > Daniel Duan
> >> > Sent from my iPhone
> >> >
> >> >> On Jul 21, 2016, at 6:32 PM, Robert Widmann via swift-evolution
> >> >> <swift-evolution at swift.org> wrote:
> >> >>
> >> >>
> >> >>> On Jul 21, 2016, at 6:19 PM, Xiaodi Wu <xiaodi.wu at gmail.com> wrote:
> >> >>>
> >> >>> This is nice. Is `areSame()` being proposed because static `==` is
> >> >>> the status quo and you're trying to make the point that `==` in the
> >> >>> future need not guarantee the same semantics?
> >> >>
> >> >> Yep!  Equivalence and equality are strictly very different things.
> >> >>
> >> >>>
> >> >>> Nit: I think the more common term in stdlib would be
> >> >>> `areEquivalent()`. Do you think `same` in that context (independent
> >> >>> of the word "ordering") might erroneously suggest identity?
> >> >>
> >> >> There is room for improvement here.  Keep ‘em coming.
> >> >>
> >> >>>
> >> >>>
> >> >>>> On Thu, Jul 21, 2016 at 8:11 PM, Robert Widmann via
> >> >>>> swift-evolution
> >> >>>> <swift-evolution at swift.org> wrote:
> >> >>>> Hello Swift Community,
> >> >>>>
> >> >>>> Harlan Haskins, Jaden Geller, and I have been working on a
> >> >>>> proposal to clean up the semantics of ordering relations in the
> >> >>>> standard library.  We have a draft that you can get as a gist.
> >> >>>> Any feedback you might have about this proposal helps - though
> >> >>>> please keeps your comments on Swift-Evolution and not on the gist.
> >> >>>>
> >> >>>> Cheers,
> >> >>>>
> >> >>>> ~Robert Widmann
> >> >>>>
> >> >>>>
> >> >>>>
> >> >>>>
> >> >>>>
> >> >>>> _______________________________________________
> >> >>>> swift-evolution mailing list
> >> >>>> swift-evolution at swift.org
> >> >>>> https://lists.swift.org/mailman/listinfo/swift-evolution
> >> >>>>
> >> >>>
> >> >>
> >> >> _______________________________________________
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> >> >
> >>
> >> --
> >> Dave
> >>
> >> _______________________________________________
> >> swift-evolution mailing list
> >> swift-evolution at swift.org
> >> https://lists.swift.org/mailman/listinfo/swift-evolution
> >>
>
> --
> Dave
>
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