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. > > -- > Dave >
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