[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 10:04 PM, Matthew Johnson <matthew at anandabits.com>
> wrote:
>
>>
>> On Jul 22, 2016, at 9:57 PM, Dave Abrahams <dabrahams at apple.com> wrote:
>>
>>
>> on Fri Jul 22 2016, Xiaodi Wu <xiaodi.wu-AT-gmail.com
>> <http://xiaodi.wu-at-gmail.com/>> wrote:
>>
>> 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
>> <http://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> <
>> 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> <
>> 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> <
>> swift-evolution at swift.org>>
>> <mailto:swift-evolution at swift.org <swift-evolution at swift.org> <
>> swift-evolution at swift.org>
>> <mailto:swift-evolution at swift.org <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> <
>> swift-evolution at swift.org>>
>> <mailto:swift-evolution at swift.org <swift-evolution at swift.org> <
>> swift-evolution at swift.org>
>> <mailto:swift-evolution at swift.org <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> <
>> swift-evolution at swift.org>>
>> <mailto:swift-evolution at swift.org <swift-evolution at swift.org> <
>> swift-evolution at swift.org>
>> <mailto:swift-evolution at swift.org <swift-evolution at swift.org> <
>> swift-evolution at swift.org>>>
>> <mailto:swift-evolution at swift.org <swift-evolution at swift.org> <
>> swift-evolution at swift.org>
>> <mailto:swift-evolution at swift.org <swift-evolution at swift.org> <
>> swift-evolution at swift.org>>
>> <mailto:swift-evolution at swift.org <swift-evolution at swift.org> <
>> swift-evolution at swift.org>
>> <mailto:swift-evolution at swift.org <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.
>>
>>
>> That makes sense.  Perhaps IEEE hasn't actually made a principled
>> decision about which aspects of floating point numbers are essential,
>> and we have to do it for them.
>>
>>
>> Xiaodi is swaying me on this point as well.  I am no numerics expert so I
>> don’t know of cases where the difference between -0 and +0 matter and
>> whether the reasons they matter in these cases are applicable to generic
>> code or not.
>>
>
> Please don't let me sway you guys too much. I'm dealing with floating point
> values up to my eyeballs but I'm not even close to being an expert. We
> really need Steve to do a sanity check.

Indeed.

>> But maybe it is the case that they actually don’t.  (Or maybe they are just
>> an artifact of the implementation in which case the difference really
>> shouldn’t matter at all)
>>
>>
>> --
>> Dave
>>
>>
>>

-- 
Dave