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

Xiaodi Wu xiaodi.wu at gmail.com
Fri Jul 22 21:10:13 CDT 2016

```On Fri, Jul 22, 2016 at 9:08 PM, Matthew Johnson <matthew at anandabits.com>
wrote:

>
> On Jul 22, 2016, at 9:04 PM, Xiaodi Wu <xiaodi.wu at gmail.com> wrote:
>
> On Fri, Jul 22, 2016 at 8:57 PM, Matthew Johnson <matthew at anandabits.com>
> wrote:
>
>>
>> On Jul 22, 2016, at 8:54 PM, Xiaodi Wu via swift-evolution <
>> swift-evolution at swift.org> wrote:
>>
>> 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
>> ```
>>
>>
>> Maybe we need floating point specific implementations of some algorithms
>> to resolve this problem?
>>
>> It doesn’t seem like there is a way to provide the semantics required by
>> generic algorithms and still provide the expected behavior for floating
>> point values.
>>
>
> Well, what I'm trying to say is that generic algorithms such as
> `index(of:)` require only an equivalence relation. For floating point
> types, there are three ways to slice it:
>
> 1. NaN != NaN and +0 == -0 [what the traditional comparison operators are
> constrained to do]
> 2. NaN == NaN, +0 == -0, and the same number encoded different ways
> compare equal
> 3. NaN == NaN, +0 != -0, and the same number encoded different ways
> compare not equal
>
> Both #2 and #3 can fall out of valid equivalence relations; if `===`
> behaved like #2 for FloatingPoint types, then generic algorithms work just
> fine. If we insist on using a total ordering defined by `<=>` all the time,
> then we've got problems.
>
>
> And if we don’t then we’re back to 3 different concepts of equality.
> There is definitely a tradeoff no matter what we choose.
>

If some types have three concepts of equality, each with their particular
use, why must we eliminate one of them?

> 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.
>>>
>>> Cheers,
>>>
>>> ~Robert Widmann
>>>
>>>
>>>
>>>
>>>
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>>>
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>>>
>>> --
>>> Dave
>>>
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>>> --
>>> Dave
>>>
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>>> --
>>> Dave
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>>>
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