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

Matthew Johnson matthew at anandabits.com
Fri Jul 22 17:17:52 CDT 2016

> On Jul 22, 2016, at 4:47 PM, Dave Abrahams via swift-evolution <swift-evolution at swift.org> wrote:
> on Fri Jul 22 2016, Tony Allevato <swift-evolution at swift.org <mailto:swift-evolution at swift.org>> wrote:
>> I like a lot of this, but the changes to Equatable are where I get stuck.
>> What are the scenarios where areSame is useful *outside* the context of the
>> proposed new Comparable interface?
>> I ask because changing the requirement for Equatable to areSame instead of
>> == seems like a backwards change to me. There are plenty of unorderable
>> types where == is the obvious thing you want to implement, and this makes
>> it less obvious. It also adds a named method to a protocol to serve the
>> purpose of an operator, which I've been fighting hard against in SE-0091
>> (even though you keep the global one and delegate to it).
>> There are two concepts at play here: comparability and orderability. 99.99%
>> of the time, they are identical. 
> The concepts are “domain-specific semantics” vs “semantics that is
> useful in generic contexts.”  Yes, they are usually identical.
>> Your proposal mentions one place where they're not: IEEE floating
>> point numbers, because there exists an element in that space, NaN,
>> that doesn't satisfy an equivalence relation at all.  
> It's not limited to NaN.  The +0/-0 distinction can be tricky as well.
>> But it's still reasonable to want a stable ordering with those
>> included.
> It's also reasonable to want to search for those in a collection or use
> them as hash keys.  I'm pointing this out because it goes to the
> definition of equality, which sorting in general does not.
>> In the proposal as it's written right now, the individual inequality
>> operators are implemented in terms of <=>. That won't work for
>> FloatingPoint, because (NaN < x) and (NaN >= x) should both be false but
>> the default implementations provided would make the latter true. So
>> FloatingPoint would still have to provide its own implementations of *all
>> of the (in)equality operators*, not just ==, in order to have the correct
>> definition w.r.t. to IEEE 754. I didn't see that called out anywhere in the
>> write-up.
> That's my error, actually. I wasn't thinking straight when I proposed a
> change to the proposal that I claimed dropped the need for the other
> operators.
>> That being said, don't get me wrong—there's still a lot about this proposal
>> that I like :)  Here's what I'm thinking (which is mostly what you have
>> written, with some tweaks):
>> 1) Don't change Equatable. I don't see a need to distinguish between
>> equivalence and equality on its own (if there is one, please let me
>> know!).
> There is, because for algorithms that require Equatable to have any kind
> of meaningful semantics the equivalence relation requirement must be
> fulfilled, and prominent types exist whose `==` operator is not an
> equivalence relation.

Have you considered moving away from `==` for these domain specific operations?  Does the IEEE standard specify the exact syntax of `==` or is that just a convention?

It feels really strange to me to have an `==` operation that is not an equivalence relation (even if it is common and is the usual way to compare floating point).  Despite common practice I think it lends itself to an intuition of equivalence.  

>> As it stands today, I think the proposal "leaks" ordering concepts into
>> Equatable when it shouldn't.
> I don't see any evidence for that, and I don't even believe you've said
> anything here to support that point of view.
>> 2) Comparable defines <=>, as proposed, but *also* defines <, >, <=, >=. A
>> protocol extension provides defaults for <, >, <=, >=, ==, and !=
>> implemented in terms of <=>. This lets most implementors of Comparable
>> implement <=> and get everything else for free, but it also lets types
>> replace individual operators with customized implementations (see #4 below)
>> easily *within* the type (SE-0091).
> Check
>> 3) Comparable should be documented to imply that the default behavior is to
>> link the behavior of <=> to the individual comparisons, but that it can be
>> changed, meaning that only <=> must define a total ordering and the
>> individual comparison operators need not.
> Yes, the doc comments are missing from the proposal.
>> 4) The very few types, like FloatingPoint, that need to provide
>> domain-specific behavior to do the obvious/intended thing for users can and
>> should override <, >, <=, >=, ==, and !=. This should be called out
>> explicitly, and it would *not* affect ordering. 
> Depends what you mean by “affect ordering.”  Clearly if you sort Floats
> using < explicitly, it will have an effect.
>> I think it's entirely reasonable to have (NaN == NaN) return false and
>> (NaN != NaN) return true but (NaN <=> NaN) return .same without
>> introducing another areSame concept, because the former is demanded by
>> IEEE 754.  5) Algorithms that rely on a total order, like sorts, must
>> be implemented in terms of <=>, not in terms of the individual
>> operators, because of the possibility that the definitions can be
>> severed above.
> But you're forgetting algorithms that require an equivalence relation,
> which is basically everything that's constrained to Equatable.
>> As mentioned below, the one thing that a three-way comparison loses is the
>> easy ability to pass > instead of < to reverse the ordering, but it's
>> trivial to write a function that does this and I think it should be
>> included as part of the proposal. Something like this (may be typos, I'm
>> writing it in Gmail):
>> public func reverse<C: Comparable>(ordering: (C, C) -> Ordering) -> (C, C)
>> -> Ordering {
>>  return { lhs, rhs in
>>    switch ordering(lhs, rhs) {
>>    case .ascending: return .descending
>>    case .descending: return .ascending
>>    case .same: return .same
>>  }
>> }
>> (Comedy alternative: Add a second operator, >=<. But that might be pushing
>> it.)
> Agreed, we should do something about this use case.
> -- 
> Dave
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