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

[Dave Abrahams]

on Fri Jul 22 2016, Matthew Johnson <swift-evolution at swift.org> wrote:

>> 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?  

Yes, but I think it would be a nonstarter for people who write numeric
code.

> Does the IEEE standard specify the exact syntax of `==` or is that
> just a convention?

I'm not sure.  It seems unlikely that it's an exact syntax requirement.
Steve?

> 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).  

Don't I know it!

> 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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-- 
Dave