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

Fri Jul 22 21:04:26 CDT 2016

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.

>
>
> 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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>> --
>> Dave
>>
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>> --
>> Dave
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