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

Xiaodi Wu xiaodi.wu at gmail.com
Fri Jul 22 21:15:25 CDT 2016 

On Fri, Jul 22, 2016 at 9:13 PM, Matthew Johnson <matthew at anandabits.com>
wrote:

>
> On Jul 22, 2016, at 9:10 PM, Xiaodi Wu <xiaodi.wu at gmail.com> wrote:
>
> 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?
>
>
> This isn’t about eliminating concepts of equality for a type.  They can
> have 42 if they want.
>
> This is about the right way to define the semantics of specific
> protocols.  It says nothing about additional notions of equality a type may
> have available.
>
> The difficulty is finding a design for the protocols that makes sense with
> floating point types because we want them to be able to conform to the
> protocols.
>


Agreed. My argument is that if a Comparable can define its own `===`, still
supplying a valid equivalence relation but not being constrained by a
contract that `(a <=> b) == .same` iff `a === b`, then we are good to go
with floating point types.

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
>>>>
>>>>
>>>>
>>>>
>>>>
>>>> _______________________________________________
>>>> swift-evolution mailing list
>>>> swift-evolution at swift.org
>>>> <mailto:swift-evolution at swift.org <swift-evolution at swift.org>>
>>>> https://lists.swift.org/mailman/listinfo/swift-evolution
>>>> <https://lists.swift.org/mailman/listinfo/swift-evolution>
>>>>
>>>>
>>>>
>>>> _______________________________________________
>>>> swift-evolution mailing list
>>>> swift-evolution at swift.org
>>>> <mailto:swift-evolution at swift.org <swift-evolution at swift.org>>
>>>> https://lists.swift.org/mailman/listinfo/swift-evolution
>>>> <https://lists.swift.org/mailman/listinfo/swift-evolution>
>>>>
>>>> _______________________________________________
>>>> swift-evolution mailing list
>>>> swift-evolution at swift.org
>>>> <mailto:swift-evolution at swift.org <swift-evolution at swift.org>>
>>>> https://lists.swift.org/mailman/listinfo/swift-evolution
>>>> <https://lists.swift.org/mailman/listinfo/swift-evolution>
>>>>
>>>>
>>>> --
>>>> Dave
>>>>
>>>> _______________________________________________
>>>> swift-evolution mailing list
>>>> 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>>>>
>>>> https://lists.swift.org/mailman/listinfo/swift-evolution
>>>> <https://lists.swift.org/mailman/listinfo/swift-evolution>
>>>> <https://lists.swift.org/mailman/listinfo/swift-evolution
>>>> <https://lists.swift.org/mailman/listinfo/swift-evolution>>
>>>> <https://lists.swift.org/mailman/listinfo/swift-evolution
>>>> <https://lists.swift.org/mailman/listinfo/swift-evolution>
>>>> <https://lists.swift.org/mailman/listinfo/swift-evolution
>>>> <https://lists.swift.org/mailman/listinfo/swift-evolution>>>
>>>>
>>>> _______________________________________________
>>>> swift-evolution mailing list
>>>> 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>>>
>>>> https://lists.swift.org/mailman/listinfo/swift-evolution
>>>> <https://lists.swift.org/mailman/listinfo/swift-evolution>
>>>> <https://lists.swift.org/mailman/listinfo/swift-evolution
>>>> <https://lists.swift.org/mailman/listinfo/swift-evolution>>
>>>>
>>>>
>>>> --
>>>> Dave
>>>>
>>>> _______________________________________________
>>>> swift-evolution mailing list
>>>> 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>>>
>>>> https://lists.swift.org/mailman/listinfo/swift-evolution
>>>> <https://lists.swift.org/mailman/listinfo/swift-evolution>
>>>> <https://lists.swift.org/mailman/listinfo/swift-evolution
>>>> <https://lists.swift.org/mailman/listinfo/swift-evolution>>
>>>>
>>>>
>>>> --
>>>> Dave
>>>> _______________________________________________
>>>> swift-evolution mailing list
>>>> swift-evolution at swift.org
>>>> <mailto:swift-evolution at swift.org <swift-evolution at swift.org>>
>>>> https://lists.swift.org/mailman/listinfo/swift-evolution
>>>> <https://lists.swift.org/mailman/listinfo/swift-evolution>
>>>>
>>>> _______________________________________________
>>>> swift-evolution mailing list
>>>> swift-evolution at swift.org
>>>> <mailto:swift-evolution at swift.org <swift-evolution at swift.org>>
>>>> https://lists.swift.org/mailman/listinfo/swift-evolution
>>>> <https://lists.swift.org/mailman/listinfo/swift-evolution>
>>>>
>>>> _______________________________________________
>>>> swift-evolution mailing list
>>>> swift-evolution at swift.org
>>>> https://lists.swift.org/mailman/listinfo/swift-evolution
>>>>
>>>>
>>>> --
>>>> Dave
>>>>
>>>> _______________________________________________
>>>> swift-evolution mailing list
>>>> swift-evolution at swift.org
>>>> https://lists.swift.org/mailman/listinfo/swift-evolution
>>>>
>>>>
>>>>
>>>> _______________________________________________
>>>> swift-evolution mailing list
>>>> swift-evolution at swift.org
>>>> https://lists.swift.org/mailman/listinfo/swift-evolution
>>>>
>>>>
>>> _______________________________________________
>>> swift-evolution mailing list
>>> swift-evolution at swift.org
>>> https://lists.swift.org/mailman/listinfo/swift-evolution
>>>
>>>
>>
>
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <https://lists.swift.org/pipermail/swift-evolution/attachments/20160722/a9dd93d1/attachment.html>

More information about the swift-evolution mailing list