[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
>>>>>>>>>>>>> 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
>>>>>>>>>>>> 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>>
>>>>>>>>>>>> 
>>>>>>>>>>> 
>>>>>>>>>>> --
>>>>>>>>>>> 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>>
>>>>>>>>>>> <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>>>>
>>>>>>>>>> _______________________________________________
>>>>>>>>>> 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>>>
>>>>>>>>>> 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>>>
>>>>>>>>> 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>>
>>>>>>> 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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>>>>>>> <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>
>>>>> https://lists.swift.org/mailman/listinfo/swift-evolution <https://lists.swift.org/mailman/listinfo/swift-evolution>
>>>> 
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>>>> 
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