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

Xiaodi Wu xiaodi.wu at gmail.com
Fri Jul 22 21:56:28 CDT 2016


On Fri, Jul 22, 2016 at 9:53 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?
>

I don't think they exist currently in stdlib, but any algorithm where
you're taking a subsequence prefix from a sorted collection up to a given
value might return a chunk of values that equal the value but compare
less-than ("ascending").


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