On Fri, Jul 22, 2016 at 9:13 PM, Matthew Johnson <matt...@anandabits.com> wrote:
> > On Jul 22, 2016, at 9:10 PM, Xiaodi Wu <xiaodi...@gmail.com> wrote: > > On Fri, Jul 22, 2016 at 9:08 PM, Matthew Johnson <matt...@anandabits.com> > wrote: > >> >> On Jul 22, 2016, at 9:04 PM, Xiaodi Wu <xiaodi...@gmail.com> wrote: >> >> On Fri, Jul 22, 2016 at 8:57 PM, Matthew Johnson <matt...@anandabits.com> >> wrote: >> >>> >>> On Jul 22, 2016, at 8:54 PM, Xiaodi Wu via swift-evolution < >>> swift-evolution@swift.org> wrote: >>> >>> On Fri, Jul 22, 2016 at 8:52 PM, Jaden Geller via swift-evolution < >>> swift-evolution@swift.org> wrote: >>> >>>> "The totalOrder predicate will order these cases, and it also >>>> distinguishes between different representations of NaNs and between the >>>> same decimal floating point number encoded in different ways." >>>> - [Wikipedia]( >>>> https://en.wikipedia.org/wiki/IEEE_floating_point#Total-ordering_predicate >>>> ) >>>> >>>> Sounds like `===` should not return `true` for zeros of different >>>> signs, then. >>>> >>> >>> Fair enough; the result of that will be, as Pyry noted above, that: >>> >>> ``` >>> [-0.0, 1.0, .nan, 0.0].firstIndex(of: 0.0) //=> 3, not 0 >>> ``` >>> >>> >>> Maybe we need floating point specific implementations of some algorithms >>> to resolve this problem? >>> >>> It doesn’t seem like there is a way to provide the semantics required by >>> generic algorithms and still provide the expected behavior for floating >>> point values. >>> >> >> Well, what I'm trying to say is that generic algorithms such as >> `index(of:)` require only an equivalence relation. For floating point >> types, there are three ways to slice it: >> >> 1. NaN != NaN and +0 == -0 [what the traditional comparison operators are >> constrained to do] >> 2. NaN == NaN, +0 == -0, and the same number encoded different ways >> compare equal >> 3. NaN == NaN, +0 != -0, and the same number encoded different ways >> compare not equal >> >> Both #2 and #3 can fall out of valid equivalence relations; if `===` >> behaved like #2 for FloatingPoint types, then generic algorithms work just >> fine. If we insist on using a total ordering defined by `<=>` all the time, >> then we've got problems. >> >> >> And if we don’t then we’re back to 3 different concepts of equality. >> There is definitely a tradeoff no matter what we choose. >> > > If some types have three concepts of equality, each with their particular > use, why must we eliminate one of them? > > > This isn’t about eliminating concepts of equality for a type. They can > have 42 if they want. > > This is about the right way to define the semantics of specific > protocols. It says nothing about additional notions of equality a type may > have available. > > The difficulty is finding a design for the protocols that makes sense with > floating point types because we want them to be able to conform to the > protocols. > Agreed. My argument is that if a Comparable can define its own `===`, still supplying a valid equivalence relation but not being constrained by a contract that `(a <=> b) == .same` iff `a === b`, then we are good to go with floating point types. On Jul 22, 2016, at 6:48 PM, Dave Abrahams via swift-evolution < >>>> swift-evolution@swift.org> wrote: >>>> >>>> >>>> on Fri Jul 22 2016, Jaden Geller <swift-evolution@swift.org> wrote: >>>> >>>> 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)". >>>> >>>> >>>> I don't see why both `(+0) === (-0)` and `(+0) <=> (-0)` can't return >>>> `true` and `.same`, respectively. This doesn't break the total >>>> ordering of values. `===` doesn't do raw memory comparison. They're >>>> "identical", so it ought to return `true`. >>>> >>>> >>>> It ought to do whatever IEEE-754 specifies that its total ordering test >>>> does. That is, IEEE-754 gets to decide whether the difference between >>>> +0 and -0 is “essential” to IEEE-754 floating point types, or not. >>>> >>>> >>>> On Jul 22, 2016, at 6:37 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)". >>>> >>>> /// - 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@swift.org >>>> <mailto:swift-evolution@swift.org <swift-evolution@swift.org>>> >>>> wrote: >>>> >>>> >>>> On Jul 21, 2016, at 6:19 PM, Xiaodi Wu >>>> <xiaodi...@gmail.com >>>> <mailto:xiaodi...@gmail.com <xiaodi...@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@swift.org >>>> <mailto:swift-evolution@swift.org <swift-evolution@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@swift.org >>>> <mailto:swift-evolution@swift.org <swift-evolution@swift.org>> >>>> https://lists.swift.org/mailman/listinfo/swift-evolution >>>> <https://lists.swift.org/mailman/listinfo/swift-evolution> >>>> >>>> >>>> >>>> _______________________________________________ >>>> swift-evolution mailing list >>>> swift-evolution@swift.org >>>> <mailto:swift-evolution@swift.org <swift-evolution@swift.org>> >>>> https://lists.swift.org/mailman/listinfo/swift-evolution >>>> <https://lists.swift.org/mailman/listinfo/swift-evolution> >>>> >>>> _______________________________________________ >>>> swift-evolution mailing list >>>> swift-evolution@swift.org >>>> <mailto:swift-evolution@swift.org <swift-evolution@swift.org>> >>>> https://lists.swift.org/mailman/listinfo/swift-evolution >>>> <https://lists.swift.org/mailman/listinfo/swift-evolution> >>>> >>>> >>>> -- >>>> Dave >>>> >>>> _______________________________________________ >>>> swift-evolution mailing list >>>> 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>>>> >>>> https://lists.swift.org/mailman/listinfo/swift-evolution >>>> <https://lists.swift.org/mailman/listinfo/swift-evolution> >>>> <https://lists.swift.org/mailman/listinfo/swift-evolution >>>> <https://lists.swift.org/mailman/listinfo/swift-evolution>> >>>> <https://lists.swift.org/mailman/listinfo/swift-evolution >>>> <https://lists.swift.org/mailman/listinfo/swift-evolution> >>>> <https://lists.swift.org/mailman/listinfo/swift-evolution >>>> <https://lists.swift.org/mailman/listinfo/swift-evolution>>> >>>> >>>> _______________________________________________ >>>> swift-evolution mailing list >>>> 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>>> >>>> https://lists.swift.org/mailman/listinfo/swift-evolution >>>> <https://lists.swift.org/mailman/listinfo/swift-evolution> >>>> <https://lists.swift.org/mailman/listinfo/swift-evolution >>>> <https://lists.swift.org/mailman/listinfo/swift-evolution>> >>>> >>>> >>>> -- >>>> Dave >>>> >>>> _______________________________________________ >>>> swift-evolution mailing list >>>> 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>>> >>>> https://lists.swift.org/mailman/listinfo/swift-evolution >>>> <https://lists.swift.org/mailman/listinfo/swift-evolution> >>>> <https://lists.swift.org/mailman/listinfo/swift-evolution >>>> <https://lists.swift.org/mailman/listinfo/swift-evolution>> >>>> >>>> >>>> -- >>>> Dave >>>> _______________________________________________ >>>> swift-evolution mailing list >>>> swift-evolution@swift.org >>>> <mailto:swift-evolution@swift.org <swift-evolution@swift.org>> >>>> https://lists.swift.org/mailman/listinfo/swift-evolution >>>> <https://lists.swift.org/mailman/listinfo/swift-evolution> >>>> >>>> _______________________________________________ >>>> swift-evolution mailing list >>>> swift-evolution@swift.org >>>> <mailto:swift-evolution@swift.org <swift-evolution@swift.org>> >>>> https://lists.swift.org/mailman/listinfo/swift-evolution >>>> <https://lists.swift.org/mailman/listinfo/swift-evolution> >>>> >>>> _______________________________________________ >>>> swift-evolution mailing list >>>> swift-evolution@swift.org >>>> https://lists.swift.org/mailman/listinfo/swift-evolution >>>> >>>> >>>> -- >>>> Dave >>>> >>>> _______________________________________________ >>>> swift-evolution mailing list >>>> swift-evolution@swift.org >>>> https://lists.swift.org/mailman/listinfo/swift-evolution >>>> >>>> >>>> >>>> _______________________________________________ >>>> swift-evolution mailing list >>>> swift-evolution@swift.org >>>> https://lists.swift.org/mailman/listinfo/swift-evolution >>>> >>>> >>> _______________________________________________ >>> swift-evolution mailing list >>> swift-evolution@swift.org >>> https://lists.swift.org/mailman/listinfo/swift-evolution >>> >>> >> > >
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