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

Dave Abrahams dabrahams at apple.com
Fri Jul 22 21:05:37 CDT 2016

```on Fri Jul 22 2016, Jaden Geller <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.

Right.

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

--
Dave

```