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

Dave Abrahams dabrahams at apple.com
Fri Jul 22 21:53:07 CDT 2016 

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
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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>
>>> >>>>>
>>> >>>>> _______________________________________________
>>> >>>>> 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
>>> >>>>>
>>> >>>>>
>>> >>>>>
>>> >>>>> _______________________________________________
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>>> >>>>> 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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