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

[Dave Abrahams]

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.

>
>> > 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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>> >>
>>
>> --
>> Dave
>>
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-- 
Dave