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

[Xiaodi Wu]

On Fri, Jul 22, 2016 at 5:48 PM, Dave Abrahams via swift-evolution <
swift-evolution at swift.org> wrote:

>
> on Fri Jul 22 2016, Xiaodi Wu <swift-evolution at swift.org> wrote:
>
> > 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?
>
> Not if you want algorithms requiring Equatable to make sense.  There's
> just no use for anything weaker than an equivalence relation.
>

I'm assuming you mean:
s/equivalence relation/identity/

In that case, I'd think collapsing `areSame(_:)` into `===` and furnishing
some other way of comparing memory addresses for class types is the most
sensible way to go.


> >
> >> > 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
> >> >>
> >> >> _______________________________________________
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> >> >> swift-evolution at swift.org
> >> >> https://lists.swift.org/mailman/listinfo/swift-evolution
> >> >>
> >>
> >> --
> >> Dave
> >>
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> > https://lists.swift.org/mailman/listinfo/swift-evolution
> >
>
> --
> Dave
>
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