[swift-evolution] [Draft][Proposal] Formalized Ordering

Matthew Johnson matthew at anandabits.com
Fri Jul 22 21:13:44 CDT 2016


> On Jul 22, 2016, at 9:10 PM, Xiaodi Wu <xiaodi.wu at gmail.com> wrote:
> 
> On Fri, Jul 22, 2016 at 9:08 PM, Matthew Johnson <matthew at anandabits.com <mailto:matthew at anandabits.com>> wrote:
> 
>> On Jul 22, 2016, at 9:04 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.
> 
> 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.

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