[swift-evolution] [Draft][Proposal] Formalized Ordering
Matthew Johnson
matthew at anandabits.com
Fri Jul 22 21:24:37 CDT 2016
> On Jul 22, 2016, at 9:20 PM, Xiaodi Wu <xiaodi.wu at gmail.com> wrote:
>
> On Fri, Jul 22, 2016 at 9:19 PM, Matthew Johnson <matthew at anandabits.com <mailto:matthew at anandabits.com>> wrote:
>
>> On Jul 22, 2016, at 9:12 PM, Xiaodi Wu <xiaodi.wu at gmail.com <mailto:xiaodi.wu at gmail.com>> wrote:
>>
>> On Fri, Jul 22, 2016 at 9:09 PM, Jaden Geller <jaden.geller at gmail.com <mailto:jaden.geller at gmail.com>> wrote:
>>> 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
>>
>>
>> Though it seems super confusing that a language have THREE ways to compare values, that does almost seem necessary here. Do we actually need an operator that performs #3? I understand that that is equality under total ordering, but couldn't users just write `(a <=> b) == .same` if they want that?
>>
>> For floating point types, I think `===` shouldn't be #3. From a practical standpoint, no one ever wants that definition unless they are ordering things. Whereas you'd want #2 for things like `.index(of:)` and #1 for the traditional comparison operators.
>
> However, we have to introduce a new notion of identity for floating point types if `===` isn’t #3. Floating points are tricky enough already. Is that really a good thing?
>
> Further, it encodes three separate meanings of equality in the protocols. We should avoid that if we can.
>
> It feels like maybe the right solution is floating point specific algorithm overloads. It doesn’t seem like too big a surprise that this is the case when you really dig into the details.
>
>
> I see what you're getting at here. But I like your other alternative better, which is to define identity in a generically useful way for floating point types, and preserve IEEE semantics in its own method for floating point types.
That wasn’t actually my idea - it was yours! :)
>
>>> On Jul 22, 2016, at 7:04 PM, Xiaodi Wu <xiaodi.wu at gmail.com <mailto:xiaodi.wu at gmail.com>> wrote:
>>>
>>> On Fri, Jul 22, 2016 at 8:57 PM, Matthew Johnson <matthew at anandabits.com <mailto:matthew at anandabits.com>> wrote:
>>>
>>>> On Jul 22, 2016, at 8:54 PM, Xiaodi Wu via swift-evolution <swift-evolution at swift.org <mailto:swift-evolution at swift.org>> wrote:
>>>>
>>>> On Fri, Jul 22, 2016 at 8:52 PM, Jaden Geller via swift-evolution <swift-evolution at swift.org <mailto:swift-evolution at 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 <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.
>>>
>>>
>>>
>>>>
>>>>> On Jul 22, 2016, at 6:48 PM, Dave Abrahams via swift-evolution <swift-evolution at swift.org <mailto:swift-evolution at swift.org>> wrote:
>>>>>
>>>>>
>>>>> on Fri Jul 22 2016, Jaden Geller <swift-evolution at swift.org <mailto:swift-evolution at 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 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)".
>>>>>>>
>>>>>>> /// - 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
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> _______________________________________________
>>>>>>>>>>>>>>> swift-evolution mailing list
>>>>>>>>>>>>>>> swift-evolution at swift.org <mailto:swift-evolution at swift.org>
>>>>>>>>>>>>>>> <mailto:swift-evolution at swift.org <mailto:swift-evolution at 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>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> _______________________________________________
>>>>>>>>>>>>> swift-evolution mailing list
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>>>>>>>>>>>>> <https://lists.swift.org/mailman/listinfo/swift-evolution <https://lists.swift.org/mailman/listinfo/swift-evolution>>
>>>>>>>>>>>> _______________________________________________
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>>>>>>>>>>>> <https://lists.swift.org/mailman/listinfo/swift-evolution <https://lists.swift.org/mailman/listinfo/swift-evolution>>
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> --
>>>>>>>>>>> Dave
>>>>>>>>>>>
>>>>>>>>>>> _______________________________________________
>>>>>>>>>>> swift-evolution mailing list
>>>>>>>>>>> swift-evolution at swift.org <mailto:swift-evolution at swift.org>
>>>>>>>>>>> <mailto:swift-evolution at swift.org <mailto:swift-evolution at swift.org>>
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>>>>>>>>>>> <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>>>>
>>>>>>>>>>> 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>>>
>>>>>>>>>>> <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>>>>
>>>>>>>>>> _______________________________________________
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>>>>>>>>>> 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>>>
>>>>>>>>>> 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>>>
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> --
>>>>>>>>> Dave
>>>>>>>>>
>>>>>>>>> _______________________________________________
>>>>>>>>> swift-evolution mailing list
>>>>>>>>> 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>>>
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>>>>>>>>> <https://lists.swift.org/mailman/listinfo/swift-evolution <https://lists.swift.org/mailman/listinfo/swift-evolution>>
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>>>>>>>>> <https://lists.swift.org/mailman/listinfo/swift-evolution <https://lists.swift.org/mailman/listinfo/swift-evolution>>>
>>>>>>>
>>>>>>> --
>>>>>>> Dave
>>>>>>> _______________________________________________
>>>>>>> swift-evolution mailing list
>>>>>>> swift-evolution at swift.org <mailto:swift-evolution at swift.org>
>>>>>>> <mailto:swift-evolution at swift.org <mailto:swift-evolution at swift.org>>
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>>>>>>>
>>>>>>> _______________________________________________
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>>>>>>
>>>>>
>>>>> --
>>>>> Dave
>>>>>
>>>>> _______________________________________________
>>>>> swift-evolution mailing list
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>>>>> https://lists.swift.org/mailman/listinfo/swift-evolution <https://lists.swift.org/mailman/listinfo/swift-evolution>
>>>>
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>>>>
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