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

Xiaodi Wu xiaodi.wu at gmail.com
Fri Jul 22 21:51:18 CDT 2016 

On Fri, Jul 22, 2016 at 9:46 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 9:23 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.
>

I was (that was the "=== if but not iff <=>" business above), then I
thought Matthew was saying something different and agreed with him.

What I thought that Matthew thought was actually very insightful. He didn't
actually think this, apparently, but: IEEE totalOrder does exactly what it
says on the tin. But, it is not useful for any generic comparisons or (as
far as I'm aware) any generic sorting algorithms. I cannot conceive of a
numeric algorithm or a generic algorithm that relies on two equal floating
point values being ordered based on their binary representation. We should
have some way of exposing totalOrder to a user of a BinaryFloatingPoint
type, but I don't know that it should be the basis for floating point
*identity* with respect to protocol conformance. It's explicitly *not* what
IEEE recommends for comparison anyway.


>
> --
> Dave
>
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