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. -- Dave _______________________________________________ swift-evolution mailing list swift-evolution@swift.org https://lists.swift.org/mailman/listinfo/swift-evolution
