On Fri, Jul 22, 2016 at 9:57 PM, Dave Abrahams <dabrah...@apple.com> wrote:
> > on Fri Jul 22 2016, Xiaodi Wu <xiaodi.wu-AT-gmail.com> wrote: > > > On Fri, Jul 22, 2016 at 9:46 PM, Dave Abrahams <dabrah...@apple.com> > wrote: > > > >> > >> on Fri Jul 22 2016, Xiaodi Wu <xiaodi.wu-AT-gmail.com> wrote: > >> > >> > On Fri, Jul 22, 2016 at 9:23 PM, Matthew Johnson < > matt...@anandabits.com > >> > > >> > wrote: > >> > > >> >> > >> >> On Jul 22, 2016, at 9:17 PM, Xiaodi Wu <xiaodi...@gmail.com> wrote: > >> >> > >> >> On Fri, Jul 22, 2016 at 9:15 PM, Matthew Johnson via swift-evolution > < > >> >> swift-evolution@swift.org> wrote: > >> >> > >> >>> > >> >>> On Jul 22, 2016, at 9:04 PM, Dave Abrahams via swift-evolution < > >> >>> swift-evolution@swift.org> wrote: > >> >>> > >> >>> > >> >>> on Fri Jul 22 2016, Matthew Johnson <swift-evolution@swift.org> > wrote: > >> >>> > >> >>> On Jul 22, 2016, at 8:37 PM, Xiaodi Wu via swift-evolution > >> >>> <swift-evolution@swift.org> wrote: > >> >>> > >> >>> On Fri, Jul 22, 2016 at 8:20 PM, Dave Abrahams via swift-evolution > >> >>> <swift-evolution@swift.org > >> >>> > >> >>> > >> >>> <mailto:swift-evolution@swift.org <swift-evolution@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@swift.org > >> >>> <mailto:swift-evolution@swift.org <swift-evolution@swift.org>>> > >> >>> wrote: > >> >>> > >> >>> > >> >>> on Fri Jul 22 2016, Daniel Duan > >> >>> <swift-evolution@swift.org > >> >>> <mailto:swift-evolution@swift.org <swift-evolution@swift.org>> > >> >>> <mailto:swift-evolution@swift.org <swift-evolution@swift.org> > >> >>> <mailto:swift-evolution@swift.org <swift-evolution@swift.org>>>> > >> >>> wrote: > >> >>> > >> >>> > >> >>> On Jul 22, 2016, at 11:05 AM, Dave Abrahams via swift-evolution > >> >>> <swift-evolution@swift.org > >> >>> <mailto:swift-evolution@swift.org <swift-evolution@swift.org>> > >> >>> <mailto:swift-evolution@swift.org <swift-evolution@swift.org> > >> >>> <mailto:swift-evolution@swift.org <swift-evolution@swift.org>>>> > >> >>> wrote: > >> >>> > >> >>> > >> >>> on Thu Jul 21 2016, Duan > >> >>> > >> >>> > >> >>> <swift-evolution@swift.org > >> >>> <mailto:swift-evolution@swift.org <swift-evolution@swift.org>> > >> >>> <mailto:swift-evolution@swift.org <swift-evolution@swift.org> > >> >>> <mailto:swift-evolution@swift.org <swift-evolution@swift.org>>> > >> >>> <mailto:swift-evolution@swift.org <swift-evolution@swift.org> > >> >>> <mailto:swift-evolution@swift.org <swift-evolution@swift.org>> > >> >>> <mailto:swift-evolution@swift.org <swift-evolution@swift.org> > >> >>> <mailto:swift-evolution@swift.org <swift-evolution@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 > >> >>> :-) > >> >>> > >> >>> > >> >>> 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. > >> >> > >> > > >> > Actually, here I doubt it. The total ordering isn't exposed as part of > >> any > >> > comparison operator defined in the IEEE spec. In fact, the total > ordering > >> > wasn't introduced until a (fairly) recent IEEE revision, IIUC. > Breaking > >> > `==` would definitely cause people to jump, but `<=>` needn't be the > IEEE > >> > totalOrder predicate IMO. > >> > >> Wait, I thought we were saying that `<=>` could be IEEE totalOrder, and > >> `===` could be like `==` but with well-behaved NaNs, so it's still an > >> equivalence relation, thus declaring the signedness of 0 to be > >> inessential. > >> > > > > I was (that was the "=== if but not iff <=>" business above), then I > > thought Matthew was saying something different and agreed with him. > > > > What I thought that Matthew thought was actually very insightful. He > didn't > > actually think this, apparently, but: IEEE totalOrder does exactly what > it > > says on the tin. But, it is not useful for any generic comparisons or (as > > far as I'm aware) any generic sorting algorithms. I cannot conceive of a > > numeric algorithm or a generic algorithm that relies on two equal > floating > > point values being ordered based on their binary representation. We > should > > have some way of exposing totalOrder to a user of a BinaryFloatingPoint > > type, but I don't know that it should be the basis for floating point > > *identity* with respect to protocol conformance. It's explicitly *not* > what > > IEEE recommends for comparison anyway. > > That makes sense. Perhaps IEEE hasn't actually made a principled > decision about which aspects of floating point numbers are essential, > and we have to do it for them. > I may have to walk back some comments. IEEE totalOrder rules should work fine for <=> if we relax "a === b iff (a <=> b) == .same", as it explicitly states: a) If x < y, totalOrder(x, y) is true. [i.e. compares ascending] b) If x > y, totalOrder(x, y) is false. [i.e. does not compare ascending] This is where Steve's expertise comes in. In either case, I think we might have a solution for `===` behaving weirdly in generic algorithms.
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