[swift-evolution] [Draft][Proposal] Formalized Ordering
Xiaodi Wu
xiaodi.wu at gmail.com
Fri Jul 22 21:35:58 CDT 2016
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/>> 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>
> >>>>>
> >>>>> _______________________________________________
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> >>>>> <https://lists.swift.org/mailman/listinfo/swift-evolution>
> >>>>>
> >>>>>
> >>>>> --
> >>>>> Dave
> >>>>>
> >>>>> _______________________________________________
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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>>>>
> >>>>> 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>>
> >>>>> <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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> >>>>> <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>>>
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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>>
> >>>>>
> >>>>>
> >>>>> --
> >>>>> Dave
> >>>>> _______________________________________________
> >>>>> swift-evolution mailing list
> >>>>> 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
> >>>>>
> >>>>> _______________________________________________
> >>>>> swift-evolution mailing list
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> >>>>>
> >>>>>
> >>>>>
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> >>>>>
> >>>>>
> >>>> _______________________________________________
> >>>> swift-evolution mailing list
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> >>>>
> >>>>
> >>>
> >>
> >>
>
> --
> Dave
>
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