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

[Dave Abrahams]

on Fri Jul 22 2016, Xiaodi Wu <xiaodi.wu-AT-gmail.com> wrote:

> On Fri, Jul 22, 2016 at 9:23 PM, Matthew Johnson <matthew at anandabits.com>
> wrote:
>
>>
>> On Jul 22, 2016, at 9:17 PM, Xiaodi Wu <xiaodi.wu at gmail.com> wrote:
>>
>> On Fri, Jul 22, 2016 at 9:15 PM, Matthew Johnson via swift-evolution <
>> swift-evolution at swift.org> wrote:
>>
>>>
>>> On Jul 22, 2016, at 9:04 PM, Dave Abrahams via swift-evolution <
>>> swift-evolution at swift.org> wrote:
>>>
>>>
>>> on Fri Jul 22 2016, Matthew Johnson <swift-evolution at swift.org> wrote:
>>>
>>> On Jul 22, 2016, at 8:37 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/>> 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)”.
>>>
>>>
>>> The point of this design is that `===` means identity and that `.same `
>>> also means identity.
>>>
>>> Since this is new territory I suppose we get to decide what identity
>>> means for floating point.  Should +0 and -0 have the same identity or
>>> not?  I’ll leave the answer to folks more knowledgable about numerics
>>> than I.
>>>
>>>
>>> It's settled law
>>> https://en.wikipedia.org/wiki/IEEE_floating_point#Total-ordering_predicate
>>> :-)
>>>
>>>
>>> Yes, assuming we want to define identity in terms of the IEEE definition
>>> of total ordering.
>>>
>>
>> I see what you're saying here. That could work. Comparable `===` and
>> Equatable `<=>` could do its own thing, and FloatingPoint
>> `isTotallyOrdered(below:)` can preserve the IEEE definition of total
>> ordering
>>
>>
>> Actually, I was hinting at your argument that `===` true iff `<=>` same
>> shouldn’t be a semantic requirement of the protocols.
>>
>> This is another option, but I don’t think it’s going to fly.  It seems
>> reasonable to assume that `<=>` will have IEEE semantics.  We will trip a
>> lot of people up if it doesn’t.  That’s a big reason we can’t consider
>> changing floating point `==` to define an equivalence relation.
>>
>
> Actually, here I doubt it. The total ordering isn't exposed as part of any
> comparison operator defined in the IEEE spec. In fact, the total ordering
> wasn't introduced until a (fairly) recent IEEE revision, IIUC. Breaking
> `==` would definitely cause people to jump, but `<=>` needn't be the IEEE
> totalOrder predicate IMO.

Wait, I thought we were saying that `<=>` could be IEEE totalOrder, and
`===` could be like `==` but with well-behaved NaNs, so it's still an
equivalence relation, thus declaring the signedness of 0 to be
inessential.

-- 
Dave