[swift-evolution] [Draft][Proposal] Formalized Ordering
Matthew Johnson
matthew at anandabits.com
Fri Jul 22 21:13:44 CDT 2016
> On Jul 22, 2016, at 9:10 PM, Xiaodi Wu <xiaodi.wu at gmail.com> wrote:
>
> On Fri, Jul 22, 2016 at 9:08 PM, Matthew Johnson <matthew at anandabits.com <mailto:matthew at anandabits.com>> wrote:
>
>> On Jul 22, 2016, at 9:04 PM, Xiaodi Wu <xiaodi.wu at gmail.com <mailto:xiaodi.wu at gmail.com>> wrote:
>>
>> On Fri, Jul 22, 2016 at 8:57 PM, Matthew Johnson <matthew at anandabits.com <mailto:matthew at anandabits.com>> wrote:
>>
>>> On Jul 22, 2016, at 8:54 PM, Xiaodi Wu via swift-evolution <swift-evolution at swift.org <mailto:swift-evolution at swift.org>> wrote:
>>>
>>> On Fri, Jul 22, 2016 at 8:52 PM, Jaden Geller via swift-evolution <swift-evolution at swift.org <mailto:swift-evolution at swift.org>> wrote:
>>> "The totalOrder predicate will order these cases, and it also distinguishes between different representations of NaNs and between the same decimal floating point number encoded in different ways."
>>> - [Wikipedia](https://en.wikipedia.org/wiki/IEEE_floating_point#Total-ordering_predicate <https://en.wikipedia.org/wiki/IEEE_floating_point#Total-ordering_predicate>)
>>>
>>> Sounds like `===` should not return `true` for zeros of different signs, then.
>>>
>>> Fair enough; the result of that will be, as Pyry noted above, that:
>>>
>>> ```
>>> [-0.0, 1.0, .nan, 0.0].firstIndex(of: 0.0) //=> 3, not 0
>>> ```
>>
>> Maybe we need floating point specific implementations of some algorithms to resolve this problem?
>>
>> It doesn’t seem like there is a way to provide the semantics required by generic algorithms and still provide the expected behavior for floating point values.
>>
>> Well, what I'm trying to say is that generic algorithms such as `index(of:)` require only an equivalence relation. For floating point types, there are three ways to slice it:
>>
>> 1. NaN != NaN and +0 == -0 [what the traditional comparison operators are constrained to do]
>> 2. NaN == NaN, +0 == -0, and the same number encoded different ways compare equal
>> 3. NaN == NaN, +0 != -0, and the same number encoded different ways compare not equal
>>
>> Both #2 and #3 can fall out of valid equivalence relations; if `===` behaved like #2 for FloatingPoint types, then generic algorithms work just fine. If we insist on using a total ordering defined by `<=>` all the time, then we've got problems.
>
> And if we don’t then we’re back to 3 different concepts of equality. There is definitely a tradeoff no matter what we choose.
>
> If some types have three concepts of equality, each with their particular use, why must we eliminate one of them?
This isn’t about eliminating concepts of equality for a type. They can have 42 if they want.
This is about the right way to define the semantics of specific protocols. It says nothing about additional notions of equality a type may have available.
The difficulty is finding a design for the protocols that makes sense with floating point types because we want them to be able to conform to the protocols.
>
>>>> On Jul 22, 2016, at 6:48 PM, Dave Abrahams via swift-evolution <swift-evolution at swift.org <mailto:swift-evolution at swift.org>> wrote:
>>>>
>>>>
>>>> on Fri Jul 22 2016, Jaden Geller <swift-evolution at swift.org <mailto:swift-evolution at swift.org>> wrote:
>>>>
>>>>>> For floating point, I'd hope that `a === b` if `(a <=> b) == .same`
>>>>>> *but not iff*. This is to satisfy IEEE 754: "Comparisons shall
>>>>>> ignore the sign of zero (so +0 = −0)".
>>>>>
>>>>> I don't see why both `(+0) === (-0)` and `(+0) <=> (-0)` can't return
>>>>> `true` and `.same`, respectively. This doesn't break the total
>>>>> ordering of values. `===` doesn't do raw memory comparison. They're
>>>>> "identical", so it ought to return `true`.
>>>>
>>>> It ought to do whatever IEEE-754 specifies that its total ordering test
>>>> does. That is, IEEE-754 gets to decide whether the difference between
>>>> +0 and -0 is “essential” to IEEE-754 floating point types, or not.
>>>>
>>>>>
>>>>>> On Jul 22, 2016, at 6:37 PM, Xiaodi Wu via swift-evolution
>>>>>> <swift-evolution at swift.org <mailto:swift-evolution at swift.org>> wrote:
>>>>>>
>>>>>> On Fri, Jul 22, 2016 at 8:20 PM, Dave Abrahams via swift-evolution
>>>>>> <swift-evolution at swift.org <mailto:swift-evolution at swift.org>
>>>>>> <mailto:swift-evolution at swift.org <mailto:swift-evolution at swift.org>>>
>>>>>> wrote:
>>>>>>
>>>>>> on Fri Jul 22 2016, Daniel Duan <daniel-AT-duan.org <http://daniel-at-duan.org/>> wrote:
>>>>>>
>>>>>>>> On Jul 22, 2016, at 3:00 PM, Dave Abrahams via swift-evolution
>>>>>>>> <swift-evolution at swift.org <mailto:swift-evolution at swift.org>
>>>>>>>> <mailto:swift-evolution at swift.org <mailto:swift-evolution at swift.org>>>
>>>>>>>> wrote:
>>>>>>>>
>>>>>>>>
>>>>>>>> on Fri Jul 22 2016, Daniel Duan
>>>>>>>> <swift-evolution at swift.org <mailto:swift-evolution at swift.org>
>>>>>>>> <mailto:swift-evolution at swift.org <mailto:swift-evolution at swift.org>>
>>>>>>>> <mailto:swift-evolution at swift.org <mailto:swift-evolution at swift.org>
>>>>>>>> <mailto:swift-evolution at swift.org <mailto:swift-evolution at swift.org>>>>
>>>>>>>> wrote:
>>>>>>>>
>>>>>>>
>>>>>>>>>> On Jul 22, 2016, at 11:05 AM, Dave Abrahams via swift-evolution
>>>>>>>>>> <swift-evolution at swift.org <mailto:swift-evolution at swift.org>
>>>>>>>>>> <mailto:swift-evolution at swift.org <mailto:swift-evolution at swift.org>>
>>>>>>>>>> <mailto:swift-evolution at swift.org <mailto:swift-evolution at swift.org>
>>>>>>>>>> <mailto:swift-evolution at swift.org <mailto:swift-evolution at swift.org>>>>
>>>>>>>>>> wrote:
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> on Thu Jul 21 2016, Duan
>>>>>>>>>
>>>>>>>>>> <swift-evolution at swift.org <mailto:swift-evolution at swift.org>
>>>>>>>>>> <mailto:swift-evolution at swift.org <mailto:swift-evolution at swift.org>>
>>>>>>>>>> <mailto:swift-evolution at swift.org <mailto:swift-evolution at swift.org>
>>>>>>>>>> <mailto:swift-evolution at swift.org <mailto:swift-evolution at swift.org>>>
>>>>>>>>>> <mailto:swift-evolution at swift.org <mailto:swift-evolution at swift.org>
>>>>>>>>>> <mailto:swift-evolution at swift.org <mailto:swift-evolution at swift.org>>
>>>>>>>>>> <mailto:swift-evolution at swift.org <mailto:swift-evolution at swift.org>
>>>>>>>>>> <mailto:swift-evolution at swift.org <mailto:swift-evolution at swift.org>>>>>
>>>>>>>>>> wrote:
>>>>>>>>>>
>>>>>>>>>>> Great proposal. I want to second that areSame may mislead user to
>>>>>>>>>>> think this is about identity.
>>>>>>>>>>>
>>>>>>>>>>> I like areEquivalent() but there may be better names.
>>>>>>>>>>
>>>>>>>>>> It really *is* about identity as I posted in a previous message. But
>>>>>>>>>> that doesn't change the fact that areEquivalent might be a better name.
>>>>>>>>>> It's one of the things we considered; it just seemed long for no real
>>>>>>>>>> benefit.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> If the addresses of the arguments aren’t being used, then we don’t consider
>>>>>>>>> them part of their *identity*. I can follow this logic. My fear is most users
>>>>>>>>> won’t make this leap on their own and get the same initial impression as I did.
>>>>>>>>> It's entirely possible this fear is unfounded. Some educated bikesheding
>>>>>>>>> wouldn't hurt here IMO :)
>>>>>>>>
>>>>>>>> Well, it's still a very real question whether we ought to have the
>>>>>>>> additional API surface implied by areSame, or wether we should collapse
>>>>>>>> it with ===.
>>>>>>>>
>>>>>>>
>>>>>>> To spell this out (because I had to think about it for a second): === will be derived from
>>>>>>> <=>,
>>>>>>> but also becomes default implementation for ==, which remains open for
>>>>>>> customization.
>>>>>>
>>>>>> I was imagining roughly this (untested):
>>>>>>
>>>>>> /// Two references are identical if they refer to the same
>>>>>> /// instance.
>>>>>> ///
>>>>>> /// - Note: Classes with a more-refined notion of “identical”
>>>>>> /// should conform to `Identifiable` and implement `===`.
>>>>>> func ===(lhs: AnyObject, rhs: AnyObject) -> Bool {
>>>>>> ObjectIdentifier(lhs) == ObjectIdentifier(rhs)
>>>>>> }
>>>>>>
>>>>>> /// Supports testing that two values of `Self` are identical
>>>>>> ///
>>>>>> /// If `a` and `b` are of type `Self`, `a === b` means that
>>>>>> /// `a` and `b` are interchangeable in most code. A conforming
>>>>>> /// type can document that specific observable characteristics
>>>>>> /// (such as the `capacity` of an `Array`) are inessential and
>>>>>> /// thus not to be considered as part of the interchangeability
>>>>>> /// guarantee.
>>>>>> ///
>>>>>> /// - Requires: `===` induces an equivalence relation over
>>>>>> /// instances.
>>>>>> /// - Note: conforming types will gain an `==` operator that
>>>>>> /// forwards to `===`.
>>>>>> /// - Note: Types that require domain-specific `==`
>>>>>> /// implementations with different semantics (e.g. floating
>>>>>> /// point) should define a more-specific overload of `==`,
>>>>>> /// which will be used in contexts where the static type is
>>>>>> /// known to the compiler.
>>>>>> /// - Note: Generic code should usually use `==` to compare
>>>>>> /// conforming instances; that will always dispatch to `===`
>>>>>> /// and will be unaffected by more specific overloads of
>>>>>> /// `==`.
>>>>>> protocol Identifiable { // née Equatable name is negotiable
>>>>>> func ===(_: Self, _: aSelf) -> Bool
>>>>>> }
>>>>>>
>>>>>> /// Default definition of `==` for Identifiable types.
>>>>>> func ==<T: Identifiable>(lhs: T, rhs: T) -> Bool {
>>>>>> return lhs === rhs
>>>>>> }
>>>>>>
>>>>>> /// Conforming types have a default total ordering.
>>>>>> ///
>>>>>> /// If `a` and `b` are of type `Self`, `a <=> b` means that
>>>>>> /// `a` and `b` are interchangeable in most code. A conforming
>>>>>> /// type can document that specific observable characteristics
>>>>>> /// (such as the `capacity` of an `Array`) are inessential and
>>>>>> /// thus not to be considered as part of the interchangeability
>>>>>> /// guarantee.
>>>>>> ///
>>>>>> /// - Requires: `<=>` induces a total ordering over
>>>>>> /// instances.
>>>>>> /// - Requires: the semantics of `<=>` are consistent with
>>>>>> /// those of `===`. That is, `(a <=> b) == .equivalent`
>>>>>> /// iff `a === b`.
>>>>>>
>>>>>> For floating point, I'd hope that `a === b` if `(a <=> b) == .same` *but not iff*. This is to satisfy IEEE 754: "Comparisons shall ignore the sign of zero (so +0 = −0)".
>>>>>>
>>>>>> /// - Note: conforming types will gain `<`, `<=`, `>`, and `>=`
>>>>>> /// operators defined in terms of `<=>`.
>>>>>> /// - Note: Types that require domain-specific `<`, etc.
>>>>>> /// implementations with different semantics (e.g. floating
>>>>>> /// point) should define more-specific overloads of those
>>>>>> /// operators, which will be used in contexts where the
>>>>>> /// static type is known to the compiler.
>>>>>> /// - Note: Generic code can freely use `<=>` or the traditional
>>>>>> /// comparison operators to compare conforming instances;
>>>>>> /// the result will always be supplied by `<=>`
>>>>>> /// and will be unaffected by more specific overloads of
>>>>>> /// the other operators.
>>>>>> protocol Comparable : Identifiable {
>>>>>> func <=> (lhs: Self, rhs: Self) -> Ordering
>>>>>> }
>>>>>>
>>>>>> /// Default implementations of `<`, `<=`, `>`, and `>=`.
>>>>>> extension Comparable {
>>>>>> static func <(lhs: Self, rhs: Self) -> Bool {
>>>>>> return (lhs <=> rhs) == .ascending
>>>>>> }
>>>>>> static func <=(lhs: Self, rhs: Self) -> Bool {
>>>>>> return (rhs <=> lhs) != .ascending
>>>>>> }
>>>>>> static func >(lhs: Self, rhs: Self) -> Bool {
>>>>>> return (lhs <=> rhs) == .descending
>>>>>> }
>>>>>> static func >=(lhs: Self, rhs: Self) -> Bool {
>>>>>> return (rhs <=> lhs) != .descending
>>>>>> }
>>>>>> }
>>>>>>
>>>>>>> I like this idea. If we keep === as a separate thing, now users have 3 “opportunities” to define
>>>>>>> equality. The must be few, if any, use cases for this.
>>>>>>>
>>>>>>> Would love to see if anyone on the list can give us an example. Otherwise we should make
>>>>>>> areSame === again™!
>>>>>>>
>>>>>>>>>
>>>>>>>>>>> Daniel Duan
>>>>>>>>>>> Sent from my iPhone
>>>>>>>>>>>
>>>>>>>>>>>> On Jul 21, 2016, at 6:32 PM, Robert Widmann via swift-evolution
>>>>>>>>>>>> <swift-evolution at swift.org <mailto:swift-evolution at swift.org>
>>>>>>>>>>>> <mailto:swift-evolution at swift.org <mailto:swift-evolution at swift.org>>>
>>>>>>>>>>>> wrote:
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>> On Jul 21, 2016, at 6:19 PM, Xiaodi Wu
>>>>>>>>>>>>> <xiaodi.wu at gmail.com <mailto:xiaodi.wu at gmail.com>
>>>>>>>>>>>>> <mailto:xiaodi.wu at gmail.com <mailto:xiaodi.wu at gmail.com>>>
>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>
>>>>>>>>>>>>> This is nice. Is `areSame()` being proposed because static `==` is
>>>>>>>>>>>>> the status quo and you're trying to make the point that `==` in the
>>>>>>>>>>>>> future need not guarantee the same semantics?
>>>>>>>>>>>>
>>>>>>>>>>>> Yep! Equivalence and equality are strictly very different things.
>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> Nit: I think the more common term in stdlib would be
>>>>>>>>>>>>> `areEquivalent()`. Do you think `same` in that context (independent
>>>>>>>>>>>>> of the word "ordering") might erroneously suggest identity?
>>>>>>>>>>>>
>>>>>>>>>>>> There is room for improvement here. Keep ‘em coming.
>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>>> On Thu, Jul 21, 2016 at 8:11 PM, Robert Widmann via
>>>>>>>>>>>>>> swift-evolution
>>>>>>>>>>>>>> <swift-evolution at swift.org <mailto:swift-evolution at swift.org>
>>>>>>>>>>>>>> <mailto:swift-evolution at swift.org <mailto:swift-evolution at swift.org>>>
>>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>> Hello Swift Community,
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Harlan Haskins, Jaden Geller, and I have been working on a
>>>>>>>>>>>>>> proposal to clean up the semantics of ordering relations in the
>>>>>>>>>>>>>> standard library. We have a draft that you can get as a gist.
>>>>>>>>>>>>>> Any feedback you might have about this proposal helps - though
>>>>>>>>>>>>>> please keeps your comments on Swift-Evolution and not on the gist.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Cheers,
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> ~Robert Widmann
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> _______________________________________________
>>>>>>>>>>>>>> swift-evolution mailing list
>>>>>>>>>>>>>> swift-evolution at swift.org <mailto:swift-evolution at swift.org>
>>>>>>>>>>>>>> <mailto:swift-evolution at swift.org <mailto:swift-evolution at swift.org>>
>>>>>>>>>>>>>> https://lists.swift.org/mailman/listinfo/swift-evolution <https://lists.swift.org/mailman/listinfo/swift-evolution>
>>>>>>>>>>>>>> <https://lists.swift.org/mailman/listinfo/swift-evolution <https://lists.swift.org/mailman/listinfo/swift-evolution>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> _______________________________________________
>>>>>>>>>>>> swift-evolution mailing list
>>>>>>>>>>>> swift-evolution at swift.org <mailto:swift-evolution at swift.org>
>>>>>>>>>>>> <mailto:swift-evolution at swift.org <mailto:swift-evolution at swift.org>>
>>>>>>>>>>>> https://lists.swift.org/mailman/listinfo/swift-evolution <https://lists.swift.org/mailman/listinfo/swift-evolution>
>>>>>>>>>>>> <https://lists.swift.org/mailman/listinfo/swift-evolution <https://lists.swift.org/mailman/listinfo/swift-evolution>>
>>>>>>>>>>> _______________________________________________
>>>>>>>>>>> swift-evolution mailing list
>>>>>>>>>>> swift-evolution at swift.org <mailto:swift-evolution at swift.org>
>>>>>>>>>>> <mailto:swift-evolution at swift.org <mailto:swift-evolution at swift.org>>
>>>>>>>>>>> https://lists.swift.org/mailman/listinfo/swift-evolution <https://lists.swift.org/mailman/listinfo/swift-evolution>
>>>>>>>>>>> <https://lists.swift.org/mailman/listinfo/swift-evolution <https://lists.swift.org/mailman/listinfo/swift-evolution>>
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> --
>>>>>>>>>> Dave
>>>>>>>>>>
>>>>>>>>>> _______________________________________________
>>>>>>>>>> swift-evolution mailing list
>>>>>>>>>> swift-evolution at swift.org <mailto:swift-evolution at swift.org>
>>>>>>>>>> <mailto:swift-evolution at swift.org <mailto:swift-evolution at swift.org>>
>>>>>>>>>> <mailto:swift-evolution at swift.org <mailto:swift-evolution at swift.org>
>>>>>>>>>> <mailto:swift-evolution at swift.org <mailto:swift-evolution at swift.org>>
>>>>>>>>>> <mailto:swift-evolution at swift.org <mailto:swift-evolution at swift.org>
>>>>>>>>>> <mailto:swift-evolution at swift.org <mailto:swift-evolution at swift.org>>>>
>>>>>>>>>> https://lists.swift.org/mailman/listinfo/swift-evolution <https://lists.swift.org/mailman/listinfo/swift-evolution>
>>>>>>>>>> <https://lists.swift.org/mailman/listinfo/swift-evolution <https://lists.swift.org/mailman/listinfo/swift-evolution>>
>>>>>>>>>> <https://lists.swift.org/mailman/listinfo/swift-evolution <https://lists.swift.org/mailman/listinfo/swift-evolution>
>>>>>>>>>> <https://lists.swift.org/mailman/listinfo/swift-evolution <https://lists.swift.org/mailman/listinfo/swift-evolution>>>
>>>>>>>>>> <https://lists.swift.org/mailman/listinfo/swift-evolution <https://lists.swift.org/mailman/listinfo/swift-evolution>
>>>>>>>>>> <https://lists.swift.org/mailman/listinfo/swift-evolution <https://lists.swift.org/mailman/listinfo/swift-evolution>>
>>>>>>>>>> <https://lists.swift.org/mailman/listinfo/swift-evolution <https://lists.swift.org/mailman/listinfo/swift-evolution>
>>>>>>>>>> <https://lists.swift.org/mailman/listinfo/swift-evolution <https://lists.swift.org/mailman/listinfo/swift-evolution>>>>
>>>>>>>>> _______________________________________________
>>>>>>>>> swift-evolution mailing list
>>>>>>>>> swift-evolution at swift.org <mailto:swift-evolution at swift.org>
>>>>>>>>> <mailto:swift-evolution at swift.org <mailto:swift-evolution at swift.org>>
>>>>>>>>> <mailto:swift-evolution at swift.org <mailto:swift-evolution at swift.org>
>>>>>>>>> <mailto:swift-evolution at swift.org <mailto:swift-evolution at swift.org>>>
>>>>>>>>> https://lists.swift.org/mailman/listinfo/swift-evolution <https://lists.swift.org/mailman/listinfo/swift-evolution>
>>>>>>>>> <https://lists.swift.org/mailman/listinfo/swift-evolution <https://lists.swift.org/mailman/listinfo/swift-evolution>>
>>>>>>>>> <https://lists.swift.org/mailman/listinfo/swift-evolution <https://lists.swift.org/mailman/listinfo/swift-evolution>
>>>>>>>>> <https://lists.swift.org/mailman/listinfo/swift-evolution <https://lists.swift.org/mailman/listinfo/swift-evolution>>>
>>>>>>>>>
>>>>>>>>
>>>>>>>> --
>>>>>>>> Dave
>>>>>>>>
>>>>>>>> _______________________________________________
>>>>>>>> swift-evolution mailing list
>>>>>>>> swift-evolution at swift.org <mailto:swift-evolution at swift.org>
>>>>>>>> <mailto:swift-evolution at swift.org <mailto:swift-evolution at swift.org>>
>>>>>>>> <mailto:swift-evolution at swift.org <mailto:swift-evolution at swift.org>
>>>>>>>> <mailto:swift-evolution at swift.org <mailto:swift-evolution at swift.org>>>
>>>>>>>> https://lists.swift.org/mailman/listinfo/swift-evolution <https://lists.swift.org/mailman/listinfo/swift-evolution>
>>>>>>>> <https://lists.swift.org/mailman/listinfo/swift-evolution <https://lists.swift.org/mailman/listinfo/swift-evolution>>
>>>>>>>> <https://lists.swift.org/mailman/listinfo/swift-evolution <https://lists.swift.org/mailman/listinfo/swift-evolution>
>>>>>>>> <https://lists.swift.org/mailman/listinfo/swift-evolution <https://lists.swift.org/mailman/listinfo/swift-evolution>>>
>>>>>>
>>>>>> --
>>>>>> Dave
>>>>>> _______________________________________________
>>>>>> swift-evolution mailing list
>>>>>> swift-evolution at swift.org <mailto:swift-evolution at swift.org>
>>>>>> <mailto:swift-evolution at swift.org <mailto:swift-evolution at swift.org>>
>>>>>> https://lists.swift.org/mailman/listinfo/swift-evolution <https://lists.swift.org/mailman/listinfo/swift-evolution>
>>>>>> <https://lists.swift.org/mailman/listinfo/swift-evolution <https://lists.swift.org/mailman/listinfo/swift-evolution>>
>>>>>>
>>>>>> _______________________________________________
>>>>>> swift-evolution mailing list
>>>>>> swift-evolution at swift.org <mailto:swift-evolution at swift.org>
>>>>>> <mailto:swift-evolution at swift.org <mailto:swift-evolution at swift.org>>
>>>>>> https://lists.swift.org/mailman/listinfo/swift-evolution <https://lists.swift.org/mailman/listinfo/swift-evolution>
>>>>>> <https://lists.swift.org/mailman/listinfo/swift-evolution <https://lists.swift.org/mailman/listinfo/swift-evolution>>
>>>>> _______________________________________________
>>>>> swift-evolution mailing list
>>>>> swift-evolution at swift.org <mailto:swift-evolution at swift.org>
>>>>> 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>
>>>> 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>
>>> 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>
>>> https://lists.swift.org/mailman/listinfo/swift-evolution <https://lists.swift.org/mailman/listinfo/swift-evolution>
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <https://lists.swift.org/pipermail/swift-evolution/attachments/20160722/619075b5/attachment.html>
More information about the swift-evolution
mailing list