[swift-evolution] [Draft][Proposal] Formalized Ordering
Dave Abrahams
dabrahams at apple.com
Sat Jul 23 13:42:30 CDT 2016
on Fri Jul 22 2016, jaden.geller-AT-gmail.com wrote:
> 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.
I agree.
>> 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
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>>>>>>>>>> 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
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>>>>>>>>>> <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>
>>>>>>>>>>
>>>>>>>>>> _______________________________________________
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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
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>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> --
>>>>>>>>>> Dave
>>>>>>>>>>
>>>>>>>>>> _______________________________________________
>>>>>>>>>> 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
>>>>>>>>> _______________________________________________
>>>>>>>>> swift-evolution mailing list
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>>>>>>>>> https://lists.swift.org/mailman/listinfo/swift-evolution
>>>>>
>>>>> --
>>>>> Dave
>>
>> --
>> Dave
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