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

Xiaodi Wu xiaodi.wu at gmail.com
Fri Jul 22 20:54:49 CDT 2016 

On Fri, Jul 22, 2016 at 8:52 PM, Jaden Geller via swift-evolution <
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.
>

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
```

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> 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> 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)".
>
>  /// - 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 <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 <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 <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
>
>
>
>
>
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> --
> Dave
>
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