[swift-evolution] [Draft][Proposal] Formalized Ordering
jaden.geller at gmail.com
jaden.geller at gmail.com
Sat Jul 23 01:47:35 CDT 2016
What if you wanted to filter such that you keep values less than some element that happens to be positive zero; might that keep around any negative zeros? Seems problematic.
> On Jul 22, 2016, at 7:53 PM, Dave Abrahams <dabrahams at apple.com> wrote:
>
>
>> on Fri Jul 22 2016, Xiaodi Wu <xiaodi.wu-AT-gmail.com> wrote:
>>
>>> On Fri, Jul 22, 2016 at 9:38 PM, <jaden.geller at gmail.com> wrote:
>>>
>>> This seems reasonable to me. I don't see why `===` has to do a total order
>>> comparison when we already have another operator, `<=>`, that does that.
>>
>> I take it back. It wouldn't solve the issue that generic `<` would
>> still behave in surprising ways, where two equal floating point values
>> represented differently might be less than each other or greater than
>> each other.
>
> I wonder if that's really a problem. What generic algorithm are you
> going to run on a collection of floats where it *would* be problematic?
> Hmm, stableSort would not necessarily preserve the order of zeros in the
> original collection if it contained both positive and negative zeros.
>
>> I think what we really want is all identity and comparison divorced
>> from IEEE totalOrder.
>
> That might work. Thanks for thinking this problem through; keep it up!
>
>>> On Jul 22, 2016, at 7:35 PM, Xiaodi Wu <xiaodi.wu at gmail.com> wrote:
>>>
>>> On Fri, Jul 22, 2016 at 9:28 PM, Dave Abrahams <dabrahams at apple.com>
>>> wrote:
>>>
>>>>
>>>>> on Fri Jul 22 2016, Xiaodi Wu <xiaodi.wu-AT-gmail.com> wrote:
>>>>>
>>>>> On Fri, Jul 22, 2016 at 9:13 PM, Matthew Johnson <
>>>> matthew at anandabits.com>
>>>>> wrote:
>>>>>
>>>>>>
>>>>>> 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>
>>>>>> wrote:
>>>>>>
>>>>>>>
>>>>>>> On Jul 22, 2016, at 9:04 PM, Xiaodi Wu <xiaodi.wu at gmail.com> wrote:
>>>>>>>
>>>>>>> On Fri, Jul 22, 2016 at 8:57 PM, Matthew Johnson <
>>>> matthew at anandabits.com>
>>>>>>> wrote:
>>>>>>>
>>>>>>>>
>>>>>>>> On Jul 22, 2016, at 8:54 PM, Xiaodi Wu via swift-evolution <
>>>>>>>> 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> 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.
>>>>
>>>> How would that work? Can you spell out the implications, show how <=>
>>>> and === would be implemented, and describe what it would mean for
>>>> algorithms?
>>>
>>> Right. I'm not married to this solution anymore, but I do think it could
>>> work. There would still be a relationship required between `===` and `<=>`.
>>> Namely:
>>>
>>> `a === b` if `(a <=> b) == .same`
>>>
>>> But for some values a and b, it is permitted that `a === b && (a <=> b) !=
>>> .same`. That is, two identical values may be ordered in a total ordering
>>> based on *inessential* qualities.
>>> Generic algorithms that need to produce a stable ordering of elements will
>>> use `<=>`. Those such as `index(of:)` will use `===` to test for identity.
>>> Wouldn't that work?
>>>
>>>>
>>>>> On Jul 22, 2016, at 6:48 PM, Dave Abrahams via swift-evolution <
>>>>>>>>> swift-evolution at swift.org> wrote:
>>>>>>>>>
>>>>>>>>>
>>>>>>>>> on Fri Jul 22 2016, Jaden Geller <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> 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 <swift-evolution at swift.org>>>
>>>>>>>>> wrote:
>>>>>>>>>
>>>>>>>>> on Fri Jul 22 2016, Daniel Duan <daniel-AT-duan.org
>>>> <http://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 <swift-evolution at swift.org>>>
>>>>>>>>> wrote:
>>>>>>>>>
>>>>>>>>>
>>>>>>>>> on Fri Jul 22 2016, Daniel Duan
>>>>>>>>> <swift-evolution at swift.org
>>>>>>>>> <mailto:swift-evolution at swift.org <swift-evolution at swift.org>>
>>>>>>>>> <mailto:swift-evolution at swift.org <swift-evolution at swift.org>
>>>>>>>>> <mailto:swift-evolution at swift.org <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 <swift-evolution at swift.org>>
>>>>>>>>> <mailto:swift-evolution at swift.org <swift-evolution at swift.org>
>>>>>>>>> <mailto:swift-evolution at swift.org <swift-evolution at swift.org>>>>
>>>>>>>>> wrote:
>>>>>>>>>
>>>>>>>>>
>>>>>>>>> on Thu Jul 21 2016, Duan
>>>>>>>>>
>>>>>>>>>
>>>>>>>>> <swift-evolution at swift.org
>>>>>>>>> <mailto:swift-evolution at swift.org <swift-evolution at swift.org>>
>>>>>>>>> <mailto:swift-evolution at swift.org <swift-evolution at swift.org>
>>>>>>>>> <mailto:swift-evolution at swift.org <swift-evolution at swift.org>>>
>>>>>>>>> <mailto:swift-evolution at swift.org <swift-evolution at swift.org>
>>>>>>>>> <mailto:swift-evolution at swift.org <swift-evolution at swift.org>>
>>>>>>>>> <mailto:swift-evolution at swift.org <swift-evolution at swift.org>
>>>>>>>>> <mailto:swift-evolution at swift.org <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 <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 <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 <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 <swift-evolution at swift.org>>
>>>>>>>>> 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 <swift-evolution at swift.org>>
>>>>>>>>> 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 <swift-evolution at 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 at swift.org
>>>>>>>>> <mailto:swift-evolution at swift.org <swift-evolution at swift.org>>
>>>>>>>>> <mailto:swift-evolution at swift.org <swift-evolution at swift.org>
>>>>>>>>> <mailto:swift-evolution at swift.org <swift-evolution at swift.org>>
>>>>>>>>> <mailto:swift-evolution at swift.org <swift-evolution at swift.org>
>>>>>>>>> <mailto:swift-evolution at swift.org <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>>>
>>>>>>>>>
>>>>>>>>> _______________________________________________
>>>>>>>>> swift-evolution mailing list
>>>>>>>>> swift-evolution at swift.org
>>>>>>>>> <mailto:swift-evolution at swift.org <swift-evolution at swift.org>>
>>>>>>>>> <mailto:swift-evolution at swift.org <swift-evolution at swift.org>
>>>>>>>>> <mailto:swift-evolution at swift.org <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 <swift-evolution at swift.org>>
>>>>>>>>> <mailto:swift-evolution at swift.org <swift-evolution at swift.org>
>>>>>>>>> <mailto:swift-evolution at swift.org <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 <swift-evolution at swift.org>>
>>>>>>>>> https://lists.swift.org/mailman/listinfo/swift-evolution
>>>>>>>>> <https://lists.swift.org/mailman/listinfo/swift-evolution>
>>>>>>>>>
>>>>>>>>> _______________________________________________
>>>>>>>>> swift-evolution mailing list
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>>>>>>>>> <mailto:swift-evolution at swift.org <swift-evolution at swift.org>>
>>>>>>>>> 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
>>>>>>>>> https://lists.swift.org/mailman/listinfo/swift-evolution
>>>>>>>>>
>>>>>>>>>
>>>>>>>>> --
>>>>>>>>> Dave
>>>>>>>>>
>>>>>>>>> _______________________________________________
>>>>>>>>> swift-evolution mailing list
>>>>>>>>> swift-evolution at swift.org
>>>>>>>>> https://lists.swift.org/mailman/listinfo/swift-evolution
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>> _______________________________________________
>>>>>>>>> swift-evolution mailing list
>>>>>>>>> swift-evolution at swift.org
>>>>>>>>> https://lists.swift.org/mailman/listinfo/swift-evolution
>>>>>>>> _______________________________________________
>>>>>>>> swift-evolution mailing list
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>>>>>>>> https://lists.swift.org/mailman/listinfo/swift-evolution
>>>>
>>>> --
>>>> Dave
>
> --
> Dave
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