[swift-evolution] [Draft][Proposal] Formalized Ordering
Matthew Johnson
matthew at anandabits.com
Fri Jul 22 21:23:55 CDT 2016
> On Jul 22, 2016, at 9:17 PM, Xiaodi Wu <xiaodi.wu at gmail.com> wrote:
>
> On Fri, Jul 22, 2016 at 9:15 PM, Matthew Johnson via swift-evolution <swift-evolution at swift.org <mailto:swift-evolution at swift.org>> wrote:
>
>> On Jul 22, 2016, at 9:04 PM, Dave Abrahams via swift-evolution <swift-evolution at swift.org <mailto:swift-evolution at swift.org>> wrote:
>>
>>
>> on Fri Jul 22 2016, Matthew Johnson <swift-evolution at swift.org <mailto:swift-evolution at swift.org>> wrote:
>>
>>>> On Jul 22, 2016, at 8:37 PM, Xiaodi Wu via swift-evolution
>>>> <swift-evolution at swift.org <mailto:swift-evolution at swift.org>> wrote:
>>>>
>>>> On Fri, Jul 22, 2016 at 8:20 PM, Dave Abrahams via swift-evolution
>>>> <swift-evolution at swift.org <mailto:swift-evolution at swift.org>
>>>
>>>> <mailto:swift-evolution at swift.org <mailto:swift-evolution at swift.org>>>
>>>> wrote:
>>>>
>>>> on Fri Jul 22 2016, Daniel Duan <daniel-AT-duan.org <http://daniel-at-duan.org/>> wrote:
>>>>
>>>>>> On Jul 22, 2016, at 3:00 PM, Dave Abrahams via swift-evolution
>>>>>> <swift-evolution at swift.org <mailto:swift-evolution at swift.org>
>>>>>> <mailto:swift-evolution at swift.org <mailto:swift-evolution at swift.org>>>
>>>>>> wrote:
>>>>>>
>>>>>>
>>>>>> on Fri Jul 22 2016, Daniel Duan
>>>>>> <swift-evolution at swift.org <mailto:swift-evolution at swift.org>
>>>>>> <mailto:swift-evolution at swift.org <mailto:swift-evolution at swift.org>>
>>>>>> <mailto:swift-evolution at swift.org <mailto:swift-evolution at swift.org>
>>>>>> <mailto:swift-evolution at swift.org <mailto:swift-evolution at swift.org>>>>
>>>>>> wrote:
>>>>>>
>>>>>
>>>>>>>> On Jul 22, 2016, at 11:05 AM, Dave Abrahams via swift-evolution
>>>>>>>> <swift-evolution at swift.org <mailto:swift-evolution at swift.org>
>>>>>>>> <mailto:swift-evolution at swift.org <mailto:swift-evolution at swift.org>>
>>>>>>>> <mailto:swift-evolution at swift.org <mailto:swift-evolution at swift.org>
>>>>>>>> <mailto:swift-evolution at swift.org <mailto:swift-evolution at swift.org>>>>
>>>>>>>> wrote:
>>>>>>>>
>>>>>>>>
>>>>>>>> on Thu Jul 21 2016, Duan
>>>>>>>
>>>>>>>> <swift-evolution at swift.org <mailto:swift-evolution at swift.org>
>>>>>>>> <mailto:swift-evolution at swift.org <mailto:swift-evolution at swift.org>>
>>>>>>>> <mailto:swift-evolution at swift.org <mailto:swift-evolution at swift.org>
>>>>>>>> <mailto:swift-evolution at swift.org <mailto:swift-evolution at swift.org>>>
>>>>>>>> <mailto:swift-evolution at swift.org <mailto:swift-evolution at swift.org>
>>>>>>>> <mailto:swift-evolution at swift.org <mailto:swift-evolution at swift.org>>
>>>>>>>> <mailto:swift-evolution at swift.org <mailto:swift-evolution at swift.org>
>>>>>>>> <mailto:swift-evolution at swift.org <mailto: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. 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.
>>>>>>>>
>>>>>>>
>>>>>>> If the addresses of the arguments aren’t being used, then we don’t consider
>>>>>>> them part of their *identity*. I can follow this logic. My fear is most users
>>>>>>> won’t make this leap on their own and get the same initial impression as I did.
>>>>>>> It's entirely possible this fear is unfounded. Some educated bikesheding
>>>>>>> wouldn't hurt here IMO :)
>>>>>>
>>>>>> Well, it's still a very real question whether we ought to have the
>>>>>> additional API surface implied by areSame, or wether we should collapse
>>>>>> it with ===.
>>>>>>
>>>>>
>>>>> To spell this out (because I had to think about it for a second): === will be derived from
>>>>> <=>,
>>>>> but also becomes default implementation for ==, which remains open for
>>>>> customization.
>>>>
>>>> I was imagining roughly this (untested):
>>>>
>>>> /// Two references are identical if they refer to the same
>>>> /// instance.
>>>> ///
>>>> /// - Note: Classes with a more-refined notion of “identical”
>>>> /// should conform to `Identifiable` and implement `===`.
>>>> func ===(lhs: AnyObject, rhs: AnyObject) -> Bool {
>>>> ObjectIdentifier(lhs) == ObjectIdentifier(rhs)
>>>> }
>>>>
>>>> /// Supports testing that two values of `Self` are identical
>>>> ///
>>>> /// If `a` and `b` are of type `Self`, `a === b` means that
>>>> /// `a` and `b` are interchangeable in most code. A conforming
>>>> /// type can document that specific observable characteristics
>>>> /// (such as the `capacity` of an `Array`) are inessential and
>>>> /// thus not to be considered as part of the interchangeability
>>>> /// guarantee.
>>>> ///
>>>> /// - Requires: `===` induces an equivalence relation over
>>>> /// instances.
>>>> /// - Note: conforming types will gain an `==` operator that
>>>> /// forwards to `===`.
>>>> /// - Note: Types that require domain-specific `==`
>>>> /// implementations with different semantics (e.g. floating
>>>> /// point) should define a more-specific overload of `==`,
>>>> /// which will be used in contexts where the static type is
>>>> /// known to the compiler.
>>>> /// - Note: Generic code should usually use `==` to compare
>>>> /// conforming instances; that will always dispatch to `===`
>>>> /// and will be unaffected by more specific overloads of
>>>> /// `==`.
>>>> protocol Identifiable { // née Equatable name is negotiable
>>>> func ===(_: Self, _: aSelf) -> Bool
>>>> }
>>>>
>>>> /// Default definition of `==` for Identifiable types.
>>>> func ==<T: Identifiable>(lhs: T, rhs: T) -> Bool {
>>>> return lhs === rhs
>>>> }
>>>>
>>>> /// Conforming types have a default total ordering.
>>>> ///
>>>> /// If `a` and `b` are of type `Self`, `a <=> b` means that
>>>> /// `a` and `b` are interchangeable in most code. A conforming
>>>> /// type can document that specific observable characteristics
>>>> /// (such as the `capacity` of an `Array`) are inessential and
>>>> /// thus not to be considered as part of the interchangeability
>>>> /// guarantee.
>>>> ///
>>>> /// - Requires: `<=>` induces a total ordering over
>>>> /// instances.
>>>> /// - Requires: the semantics of `<=>` are consistent with
>>>> /// those of `===`. That is, `(a <=> b) == .equivalent`
>>>> /// iff `a === b`.
>>>>
>>>> For floating point, I'd hope that `a === b` if `(a <=> b) == .same` *but not iff*. This is to satisfy IEEE 754: "Comparisons shall ignore the sign of zero (so +0 = −0)”.
>>>
>>> The point of this design is that `===` means identity and that `.same ` also means identity.
>>>
>>> Since this is new territory I suppose we get to decide what identity
>>> means for floating point. Should +0 and -0 have the same identity or
>>> not? I’ll leave the answer to folks more knowledgable about numerics
>>> than I.
>>
>> It's settled law
>> https://en.wikipedia.org/wiki/IEEE_floating_point#Total-ordering_predicate <https://en.wikipedia.org/wiki/IEEE_floating_point#Total-ordering_predicate>
>> :-)
>
> Yes, assuming we want to define identity in terms of the IEEE definition of total ordering.
>
> I see what you're saying here. That could work. Comparable `===` and Equatable `<=>` could do its own thing, and FloatingPoint `isTotallyOrdered(below:)` can preserve the IEEE definition of total ordering
Actually, I was hinting at your argument that `===` true iff `<=>` same shouldn’t be a semantic requirement of the protocols.
This is another option, but I don’t think it’s going to fly. It seems reasonable to assume that `<=>` will have IEEE semantics. We will trip a lot of people up if it doesn’t. That’s a big reason we can’t consider changing floating point `==` to define an equivalence relation.
> .
>
>>>> /// - Note: conforming types will gain `<`, `<=`, `>`, and `>=`
>>>> /// operators defined in terms of `<=>`.
>>>> /// - Note: Types that require domain-specific `<`, etc.
>>>> /// implementations with different semantics (e.g. floating
>>>> /// point) should define more-specific overloads of those
>>>> /// operators, which will be used in contexts where the
>>>> /// static type is known to the compiler.
>>>> /// - Note: Generic code can freely use `<=>` or the traditional
>>>> /// comparison operators to compare conforming instances;
>>>> /// the result will always be supplied by `<=>`
>>>> /// and will be unaffected by more specific overloads of
>>>> /// the other operators.
>>>> protocol Comparable : Identifiable {
>>>> func <=> (lhs: Self, rhs: Self) -> Ordering
>>>> }
>>>>
>>>> /// Default implementations of `<`, `<=`, `>`, and `>=`.
>>>> extension Comparable {
>>>> static func <(lhs: Self, rhs: Self) -> Bool {
>>>> return (lhs <=> rhs) == .ascending
>>>> }
>>>> static func <=(lhs: Self, rhs: Self) -> Bool {
>>>> return (rhs <=> lhs) != .ascending
>>>> }
>>>> static func >(lhs: Self, rhs: Self) -> Bool {
>>>> return (lhs <=> rhs) == .descending
>>>> }
>>>> static func >=(lhs: Self, rhs: Self) -> Bool {
>>>> return (rhs <=> lhs) != .descending
>>>> }
>>>> }
>>>>
>>>>> I like this idea. If we keep === as a separate thing, now users have 3 “opportunities” to define
>>>>> equality. The must be few, if any, use cases for this.
>>>>>
>>>>> Would love to see if anyone on the list can give us an example. Otherwise we should make
>>>>> areSame === again™!
>>>>>
>>>>>>>
>>>>>>>>> Daniel Duan
>>>>>>>>> Sent from my iPhone
>>>>>>>>>
>>>>>>>>>> On Jul 21, 2016, at 6:32 PM, Robert Widmann via swift-evolution
>>>>>>>>>> <swift-evolution at swift.org <mailto:swift-evolution at swift.org>
>>>>>>>>>> <mailto:swift-evolution at swift.org <mailto:swift-evolution at swift.org>>>
>>>>>>>>>> wrote:
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>> On Jul 21, 2016, at 6:19 PM, Xiaodi Wu
>>>>>>>>>>> <xiaodi.wu at gmail.com <mailto:xiaodi.wu at gmail.com>
>>>>>>>>>>> <mailto:xiaodi.wu at gmail.com <mailto: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 <mailto:swift-evolution at swift.org>
>>>>>>>>>>>> <mailto:swift-evolution at swift.org <mailto: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
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>
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>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>
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>>>>>>>>>
>>>>>>>>
>>>>>>>> --
>>>>>>>> Dave
>>>>>>>>
>>>>>>>> _______________________________________________
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>>>>>>>
>>>>>>
>>>>>> --
>>>>>> Dave
>>>>>>
>>>>>> _______________________________________________
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>>>>
>>>> --
>>>> Dave
>>>> _______________________________________________
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>>
>> --
>> Dave
>>
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