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

Xiaodi Wu xiaodi.wu at gmail.com
Fri Jul 22 21:44:38 CDT 2016 

On Fri, Jul 22, 2016 at 9:38 PM, <jaden.geller at gmail.com> wrote:

> This seems reasonable to me. I don't see why `===` has to do a total order
> comparison when we already have another operator, `<=>`, that does that.
>

I take it back. It wouldn't solve the issue that generic `<` would still
behave in surprising ways, where two equal floating point values
represented differently might be less than each other or greater than each
other. I think what we really want is all identity and comparison divorced
from IEEE totalOrder.


> On Jul 22, 2016, at 7:35 PM, Xiaodi Wu <xiaodi.wu at gmail.com> wrote:
>
> On Fri, Jul 22, 2016 at 9:28 PM, Dave Abrahams <dabrahams at apple.com>
> wrote:
>
>>
>> on Fri Jul 22 2016, Xiaodi Wu <xiaodi.wu-AT-gmail.com> wrote:
>>
>> > 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.
>>
>> How would that work?  Can you spell out the implications, show how <=>
>> and === would be implemented, and describe what it would mean for
>> algorithms?
>>
>
> Right. I'm not married to this solution anymore, but I do think it could
> work. There would still be a relationship required between `===` and `<=>`.
> Namely:
>
> `a === b` if `(a <=> b) == .same`
>
> But for some values a and b, it is permitted that `a === b && (a <=> b) !=
> .same`. That is, two identical values may be ordered in a total ordering
> based on *inessential* qualities.
> Generic algorithms that need to produce a stable ordering of elements will
> use `<=>`. Those such as `index(of:)` will use `===` to test for identity.
> Wouldn't that work?
>
> >
>> > 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>
>> >>>>> <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>
>> >>>>>
>> >>>>>
>> >>>>>
>> >>>>> _______________________________________________
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>> >>>>> https://lists.swift.org/mailman/listinfo/swift-evolution
>> >>>>> <https://lists.swift.org/mailman/listinfo/swift-evolution>
>> >>>>>
>> >>>>> _______________________________________________
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>> >>>>> <https://lists.swift.org/mailman/listinfo/swift-evolution>
>> >>>>>
>> >>>>>
>> >>>>> --
>> >>>>> Dave
>> >>>>>
>> >>>>> _______________________________________________
>> >>>>> swift-evolution mailing list
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>> >>>>> <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>>>
>> >>>>>
>> >>>>> _______________________________________________
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>> >>>>> <mailto:swift-evolution at swift.org <swift-evolution at swift.org>
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>> >>>>> 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
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>> >>>>> <mailto:swift-evolution at swift.org <swift-evolution at swift.org>>
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>> >>>>> <https://lists.swift.org/mailman/listinfo/swift-evolution>
>> >>>>>
>> >>>>> _______________________________________________
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>> >>>>> <https://lists.swift.org/mailman/listinfo/swift-evolution>
>> >>>>>
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>> >>>>>
>> >>>>>
>> >>>>> --
>> >>>>> Dave
>> >>>>>
>> >>>>> _______________________________________________
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>> >>>>>
>> >>>>>
>> >>>>>
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>> >>>>>
>> >>>>>
>> >>>> _______________________________________________
>> >>>> swift-evolution mailing list
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>> >>>>
>> >>>>
>> >>>
>> >>
>> >>
>>
>> --
>> Dave
>>
>
>
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