<=>
?Document #:  P1186R3 
Date:  20190716 
Project:  Programming Language C++ CWG 
Replyto: 
Barry Revzin <barry.revzin@gmail.com> 
[P1186R0] was approved by both EWG and LEWG. Under Core review, the issue of unintentional comparison category strengthening was brought up as a reason to strongly oppose the design.
[P1186R1] proposed a new design to solve the issues from R0 and was presented to EWG in Kona. It was approved with a modification that synthesis of weak_ordering
is only done by using both ==
and <
. The previous versions of this proposal would try to fallback to invoking <
twice.
This paper instead of considering wellformedness of expressions or validity of expressions instead uses the notion of “shallowly wellformed” as described in [P1630R0] and is based on a new term usable function. Some examples have changed meaning as a result.
The library portion of R0 was moved into [P1188R0]. This paper is solely a proposal for language change.
[P0515R3] introduced operator<=>
as a way of generating all six comparison operators from a single function. As a result of [P1185R2], that has become two functions, but importantly you still only need to declare one operator function to generate each of the four relational comparison operators.
In a future world, where all types have adopted <=>
, this will work great. It will be very easy to implement <=>
for a type like optional<T>
(writing as a nonmember function for clarity):
template <typename T>
compare_3way_type_t<T> // see P1188
operator<=>(optional<T> const& lhs, optional<T> const& rhs)
{
if (lhs.has_value() && rhs.has_value()) {
return *lhs <=> *rhs;
} else {
return lhs.has_value() <=> rhs.has_value();
}
}
This is a clean and elegant way of implementing this functionality, and gives us <
, >
, <=
, and >=
that all do the right thing. What about vector<T>
?
template <typename T>
compare_3way_type_t<T>
operator<=>(vector<T> const& lhs, vector<T> const& rhs)
{
return lexicographical_compare_3way(
lhs.begin(), lhs.end(),
rhs.begin(), rhs.end());
}
Even better.
What about a simple aggregate type, where all we want is to do normal memberbymember lexicographical comparison? No problem:
Beautiful.
The problem is that we’re not in this future world quite yet. No programdefined types have <=>
, the only standard library type that has <=>
so far is nullptr_t
. Which means we can’t just replace the existing relational operators from optional<T>
and vector<T>
with <=>
and probably won’t be able to just default Aggr
’s <=>
. We need to do something more involved.
How do we implement <=>
for a type that looks like this:
// not in our immedate control
struct Legacy {
bool operator==(Legacy const&) const;
bool operator<(Legacy const&) const;
};
// trying to write/update this type
struct Aggr {
int i;
char c;
Legacy q;
// ok, easy, thanks to P1185
bool operator==(Aggr const&) const = default;
// ... but not this
auto operator<=>(Aggr const&) const = default;
};
The implementation of <=>
won’t work for Aggr
. Legacy
doesn’t have a <=>
, so our spaceship operator ends up being defined as deleted. We don’t get the “free” memberwise comparison from just defaulting. Right now, we have to write it by hand:
strong_ordering operator<=>(Aggr const& rhs) const
{
if (auto cmp = i <=> rhs.i; cmp != 0) return cmp;
if (auto cmp = c <=> rhs.c; cmp != 0) return cmp;
if (q == rhs.q) return strong_ordering::equal;
if (q < rhs.q) return strong_ordering::less;
return strong_ordering::greater;
}
Such an implementation would always give us a correct answer, but it’s not actually a good implementation. At some point, Legacy
is going to adopt <=>
and we really need to plan in advance for that scenario; we definitely want to use <=>
whenever it’s available.
It would be better to write:
strong_ordering operator<=>(Aggr const& rhs) const
{
if (auto cmp = i <=> rhs.i; cmp != 0) return cmp;
if (auto cmp = c <=> rhs.c; cmp != 0) return cmp;
return compare_3way(q, rhs.q);
}
It’s at this point that R0 went onto suggest that because compare_3way()
is transparent to <=>
, you may as well just always use compare_3way()
and then you may as well just define <=>
to be that exact logic. That language change would allow us to just = default
the spaceship operator for types like Aggr
.
// P1186R0, this involves just synthesizing an <=> for Legacy
auto operator<=>(Aggr const&) const = default;
Consider the following legacy type:
struct Q {
float f;
bool operator==(Q rhs) const { return f == rhs.f; }
bool operator<(Q rhs) const { return f < rhs.f; }
bool operator>(Q rhs) const { return f > rhs.f; }
};
Using float
just makes for a short example, but the salient point here is that Q
’s ordering is partial, not total. The significance of partial orders is that these can all be false
:
However, the proposed synthesis rules in P1186R0 would have led (with no source code changes!) to the following:
This is because the proposed rules assumed a total order, wherein !(a == b) && !(a < b)
imply a > b
.
Now, you might ask… why don’t we just synthesize a partial ordering instead of a total ordering? Wouldn’t we get it correct in that situation? Yes, we would. But synthesizing a partial order requires an extra comparison:
friend partial_ordering operator<=>(Q const& a, Q const& b)
{
if (a == b) return partial_ordering::equivalent;
if (a < b) return partial_ordering::less;
if (b < a) return partial_ordering::greater;
return partial_ordering::unordered;
}
Many types which do not provide <=>
do still implement a total order. While assuming a partial order is completely safe and correct (we might say equivalent
when it really should be equal
, but at least we won’t ever say greater
when it really should be unordered
!), for many types that’s a performance burden. For totally ordered types, that last comparison is unnecessary  since by definition there is no case where we return unordered
. It would be unfortunate to adopt a language feature as purely a convenience feature to ease adoption of <=>
, but end up with a feature that many will eschew and handwrite their own comparisons  possibly incorrectly.
The goal of this proposal is to try to have our cake an eat it too:
Aggr
which just want the simple, default, memberwise comparisons to express that with as little typing as possibleThe first bullet implies the need for some language change. The second bullet kills P1186R0, the third bullet kills a variant of P1186R0 that would synthesize partial_ordering
instead of strong_ordering
, and the two taken together basically ensure that we cannot have a language feature that synthesis <=>
for a type with optin.
Taking a step to the side to talk about an adoption story for class templates. How would vector<T>
and optional<T>
and similar containers and templates adopt operator<=>
?
R0 of this paper argued against the claim that “[a]ny compound type should have <=>
only if all of its constituents have <=>
.” At the time, my understanding of what “conditional spaceship” meant was this:
// to handle legacy types. This is called Cpp17LessThanComparable in the
// working draft
template <typename T>
concept HasLess = requires (remove_reference_t<T> const& t) {
{ t < t } > bool
};
template <HasLess T>
bool operator<(vector<T> const&, vector<T> const&);
template <ThreeWayComparable T> // see P1188
compare_3way_type_t operator<=>(vector<T> const&, vector<T> const&);
This is, indeed, a bad implementation strategy because v1 < v2
would invoke operator<
even if operator<=>
was a viable option, so we lose the potential performance benefit. It’s quite important to ensure that we use <=>
if that’s at all an option. It’s this problem that partially led to my writing P1186R0.
But since I wrote this paper, I’ve come up with a much better way of conditionally adopting spaceship [Revzin]:
template <HasLess T>
bool operator<(vector<T> const&, vector<T> const&);
template <ThreeWayComparable T> requires HasLess<T>
compare_3way_type_t operator<=>(vector<T> const&, vector<T> const&);
It’s a small, seemingly redundant change (after all, if ThreeWayComparable<T>
then surely HasLess<T>
for all types other than pathologically absurd ones that provide <=>
but explicitly delete <
), but it ensures that v1 < v2
invokes operator<=>
where possible.
Conditionally adopting spaceship between C++17 and C++20 is actually even easier:
template <typename T>
enable_if_t<supports_lt<T>::value, bool> // normal C++17 SFINAE machinery
operator<(vector<T> const&, vector<T> const&);
// use the featuretest macro for operator<=>
#if __cpp_impl_three_way_comparison
template <ThreeWayComparable T>
compare_3way_type_t<T> operator<=>(vector<T> const&, vector<T> const&);
#endif
In short, conditionally adopting <=>
has a good user story, once you know how to do it. This is very doable, and is no longer, if of itself, a motivation for making a language change. It is, however, a motivation for not synthesizing <=>
in a way that leads to incorrect answers or poor performance  as this would have farreaching effects.
The above is solely about the case where we want to adopt <=>
conditionally. If we want to adopt <=>
unconditionally, we’ll need to do the same kind of things in the template case as we want to do in the nontemplate case. We need some way of invoking <=>
where possible, but falling back to a synthesized threeway comparison from the twoway comparison operators.
To be perfectly clear, the current rule for defaulting operator<=>
for a class C
is roughly as follows:
x
and y
of type const C
, we compare their corresponding subobjects x_{i}
and y_{i}
until the first i where given auto v_{i} = x_{i} <=> y_{i}
, v_{i} != 0
. If such an i exists, we return v_{i}
. Else, we return strong_ordering::equal
.operator<=>
is auto
, we determine the return type by taking the common comparison category of all of the x_{i} <=> y_{i}
expressions. If the return type is provided, we ensure that it is valid. If any of the pairwise comparisons is illformed, or are not compatible with the provided return type, the defaulted operator<=>
is defined as deleted.In other words, for the Aggr
example, the declaration strong_ordering operator<=>(Aggr const&) const = default;
expands into something like
struct Aggr {
int i;
char c;
Legacy q;
strong_ordering operator<=>(Aggr const& rhs) const {
if (auto cmp = i <=> rhs.i; cmp != 0) return cmp;
if (auto cmp = c <=> rhs.c; cmp != 0) return cmp;
if (auto cmp = q <=> rhs.q; cmp != 0) return cmp; // (*)
return strong_ordering::equal
}
};
Or it would, if the marked line were valid. Legacy
has no <=>
, so that pairwise comparison is illformed, so the operator function would be defined as deleted.
This paper proposes a new direction for a stopgap adoption measure for operator<=>
: we will synthesize an operator<=>
for a type, but only under very specific conditions, and only when the user provides the comparison category that the comparison needs to use. All we need is a very narrow ability to help with <=>
adoption. This is that narrow ability.
Currently, the pairwise comparison of the subobjects is always x_{i}
<=>
y_{i}
. Always operator<=>
.
This paper proposes defining a new say of synthesizing a threeway comparison, which only has meaning in the context of defining what a defaulted operator<=>
does. The function definition is very wordy, but it’s not actually complicated: we will use the provided return type to synthesize an appropriate ordering. The key points are:
auto
.<=>
is always preferred to any kind of synthetic fallback.strong_ordering
requires both ==
and <
.weak_ordering
requires both ==
and <
.partial_ordering
requires both ==
and <
and will do up to three comparisons. Those three comparisons are necessary for correctness. Any fewer comparisons would not be sound.strong_equality
or weak_equality
requires ==
.We then change the meaning of defaulted operator<=>
to be defined in terms of this new synthesis instead of in terms of x_{i}
<=>
y_{i}
.
It would be sound to synthesize strong_ordering
from just performing <
both ways, but equality is the salient difference between weak_ordering
and strong_ordering
and it doesn’t seem right to synthesize a strong_ordering
from a type that doesn’t even provide an ==
.
There is no other sound way to synthesize partial_ordering
from ==
and <
. If we just do <
both ways, we’d have to decide between equivalent
and unordered
in the case where !(a < b) && !(b < a)
 the former gets the unordered cases wrong and the latter means our order isn’t reflexive.
In the above description, I said that a synthesis might require both ==
and <
. What does that actually mean? How much do we want to require? At the very extreme end, we might require both a == b
and a < b
be wellformed expressions whose types are bool
. But we cannot require that the expression is wellformed, the most we can do is say that overload resolution succeeds and finds a candidate that isn’t deleted or inaccessible. Do we want to require contextually convertible to bool
? Exactly bool
?
Ultimately, the questions are all about: what do we want to happen in the error cases? Do we want to end up with a deleted spaceship or an illformed spaceship?
Consider these two cases:
struct Eq {
friend bool operator==(Eq, Eq);
};
struct Weak {
friend weak_ordering operator<=>(Weak, Weak);
};
struct SomeDsl {
struct NotBool { };
NotBool operator==(SomeDsl) const;
NotBool operator<(SomeDsl) const;
};
struct Nothing { };
template <typename T>
struct C {
T t;
strong_ordering operator<=>(C const&) const = default;
};
Clearly none of C<Eq>
, C<Weak>
, C<SomeDsl>
, and C<Nothing>
can have a valid operator<=>
, but should they be deleted or illformed? Erring on the side of illformed helps programmers catch bugs earlier. Erring on the side of deleted lets you actually check programmaticaly if a type has a function or not. A defaulted copy constructor, for instance, is defined as deleted if some member isn’t copyable  it isn’t illformed. Arguably comparison is a very nearly a special member function.
To that end, I propose we split the difference here. This particular proposal is entirely about being a stopgap for types that don’t have spaceship  it really shouldn’t be broadly used in templates. The line I’m going to draw is that we check that the functions we need exist and are usable but we don’t check that their return types meet our requirements. In other words:
C<Eq>
’s <=>
is deleted because we need to have both ==
and <
and we only have one.C<Weak>
’s <=>
is illformed because we just check that we have <=>
. But using that <=>
won’t work because weak_ordering
isn’t convertible to strong_ordering
, but that’s a “late” failure rather than an “early” one.C<SomeDsl>
’s <=>
is illformed because we just check that we have ==
and <
, and we do. We don’t check that those operators return something that we can actually build comparisons out of.C<Nothing>
’s <=>
is deleted because we just don’t have anything.I think that’s the right line.
This might make more sense with examples.
Consider the highlighted lines in the following example:
struct Q {
bool operator==(Q const&) const;
bool operator<(Q const&) const;
};
Q{} <=> Q{}; // #1
struct X {
Q q;
auto operator<=>(X const&) const = default; // #2
};
struct Y {
Q q;
strong_ordering operator<=>(Y const&) const = default; // #3
};
In the working draft, #1
is illformed and #2
and #3
are both defined as deleted because Q
has no <=>
.
With P1186R0, #1
is a valid expression of type std::strong_ordering
, and #2
and #3
are both defined as defaulted. In all cases, synthesizing a strong comparison.
With this proposal, #1
is still illformed. #2
is defined as deleted, because Q
still has no <=>
. The only change is that in the case of #3
, because we know the user wants strong_ordering
, we provide one.
The proposal here only applies to the specific case where we are defaulting operator<=>
and provide the comparison category that we want to default to. That might seem inherently limiting, but we can build up quite a lot from there.
Consider std::pair<T, U>
. Today, its operator<=
is defined in terms of its operator<
, which assumes a weak ordering. One thing we could do (which this paper is not proposing, this is just a thought experiment) is to synthesize <=>
with weak ordering as a fallback.
We do that with just a simple helper trait (which this paper is also not proposing):
// use whatever <=> does, or pick weak_ordering
template <typename T, typename C>
using fallback_to = conditional_t<ThreeWayComparable<T>, compare_3way_type_t<T>, C>;
// and then we can just...
template <typename T, typename U>
struct pair {
T first;
U second;
common_comparison_category_t<
fallback_to<T, weak_ordering>,
fallback_to<U, weak_ordering>>
operator<=>(pair const&) const = default;
};
pair<T,U>
is a simple type, we just want the default comparisons. Being able to default spaceship is precisely what we want. This proposal gets us there, with minimal acrobatics. Note that as a result of P1185R0, this would also give us a defaulted ==
, and hence we get all six comparison functions in one go.
Building on this idea, we can create a wrapper type which defaults <=>
using these language rules for a single type, and wrap that into more complex function objects:
// a type that defaults a 3way comparison for T for the given category
template <typename T, typename Cat>
struct cmp_with_fallback {
T const& t;
fallback_to<T,Cat> operator<=>(cmp_with_fallback const&) const = default;
};
// Check if that wrapper type has a nondeleted <=>, whether because T
// has one or because T provides the necessary operators for one to be
// synthesized per this proposal
template <typename T, typename Cat>
concept FallbackThreeWayComparable =
ThreeWayComparable<cmp_with_fallback<T, Cat>>;
// Function objects to do a threeway comparison with the specified fallback
template <typename Cat>
struct compare_3way_fallback_t {
template <FallbackThreeWayComparable<Cat> T>
constexpr auto operator()(T const& lhs, T const& rhs) {
using C = cmp_with_fallback<T, Cat>;
return C{lhs} <=> C{rhs};
}
};
template <typename Cat>
inline constexpr compare_3way_fallback_t<Cat> compare_3way_fallback{};
And now implementing <=>
for vector<T>
unconditionally is straightforward:
template <FallbackThreeWayComparable<weak_ordering> T>
constexpr auto operator<=>(vector<T> const& lhs, vector<T> const& rhs) {
// Use <=> if T has it, otherwise use a combination of either ==/<
// or just < based on what T actually has. The proposed language
// change does the right thing for us
return lexicographical_compare_3way(
lhs.begin(), lhs.end(),
rhs.begin(), rhs.end(),
compare_3way_fallback<weak_ordering>);
}
As currently specified, std::weak_order()
and std::partial_order()
from [cmp.alg] basically follow the language rules proposed here. We can implement those with a slightly different approach to the above  no fallback necessary here because we need to enforce a particular category:
template <typename T, typename Cat>
struct compare_as {
T const& t;
Cat operator<=>(compare_as const&) const = default;
};
// Check if the compare_as wrapper has nondeleted <=>, whether because T
// provides the desired comparison category or because we can synthesize one
template <typename T, typename Cat>
concept SyntheticThreeWayComparable = ThreeWayComparable<compare_as<T, Cat>, Cat>;
template <SyntheticThreeWayComparable<weak_ordering> T>
weak_ordering weak_order(T const& a, T const& b) {
using C = compare_as<T, weak_ordering>;
return C{a} <=> C{b};
}
template <SyntheticThreeWayComparable<partial_ordering> T>
partial_ordering partial_order(T const& a, T const& b) {
using C = compare_as<T, partial_ordering>;
return C{a} <=> C{b};
}
None of the above is being proposed, it’s just a demonstration that this language feature is sufficient to build up fairly complex tools in a short amount of code.
compare_3way()
?Notably absent from this paper has been a real discussion over the fate of std::compare_3way()
. R0 of this paper made this algorithm obsolete, but that’s technically no longer true. It does, however, fall out from the tools we will need to build up in code to solve other problems. In fact, we’ve already written it:
For further discussion, see [P1188R0]. This paper focuses just on the language change for operator<=>
.
XXX_equality
?This paper proposes synthesizing strong_equality
and weak_equality
orderings, simply for consistency, even if such return types from operator<=>
are somewhat questionable. As long as we have language types for which <=>
yields a comparison category of type XXX_equality
, all the rules we build on top of <=>
should respect that and be consistent.
[ Editor's note: The wording here introduces the term usable function, which is also introduced in [P1630R0] with the same wording. ]
Add a new subbullet in 6.2 [basic.def.odr], paragraph 12:
12 Given such an entity named
D
defined in more than one translation unit, then
 (12.8) if
D
is a class with a defaulted threeway comparison operator function ([class.spaceship]), it is as if the operator was implicitly defined in every translation unit where it is odrused, and the implicit definition in every translation unit shall call the same comparison operators for each subobject ofD
.
Insert a new paragraph before 11.10.3 [class.spaceship], paragraph 1:
0 The synthesized threeway comparison for comparison category type
R
([cmp.categories]) of glvaluesa
andb
of the same type is defined as follows:
(0.1) If overload resolution for
a <=> b
finds a usable function ([over.match]),static_cast<R>(a <=> b)
;(0.2) Otherwise, if overload resolution for
a <=> b
finds at least one viable candidate, the synthesized threeway comparison is not defined;(0.3) Otherwise, if
R
isstrong_ordering
, then(0.4) Otherwise, if
R
isweak_ordering
, then(0.5) Otherwise, if
R
ispartial_ordering
, then(0.6) Otherwise, if
R
isstrong_equality
, thena == b ? strong_equality::equal : strong_equality::nonequal
;(0.7) Otherwise, if
R
isweak_equality
, thena == b ? weak_equality::equivalent : weak_equality::nonequivalent
;(0.8) Otherwise, the synthesized threeway comparison is not defined.
[Note: A synthesized threeway comparison may be illformed if overload resolution finds usable functions that do not otherwise meet the requirements implied by the defined expression. end node ]
Change 11.10.3 [class.spaceship], paragraph 1:
1 Given an expanded list of subobjects for an object
x
of typeC
, the type of the expressionx_{i}
<=>
x_{i}
is denoted byR_{i}
. If overload resolution as applied tox_{i}
<=>
x_{i}
does not find a usable function, thenR_{i}
isvoid
. If the declared return type of a defaulted threeway comparison operator function isauto
, then the return type is deduced as the common comparison type (see below) ofR_{0}
,R_{1}
, …,R_{n−1}
. [Note: Otherwise, the program will be illformed if the expressionx_{i}
<=>
x_{i}
is not implicitly convertible to the declared return type for anyi
.—end note] If the return type is deduced asvoid
, the operator function is defined as deleted. If the declared return type of a defaulted threeway comparison operator function isR
and the synthesized threeway comparison for comparison category typeR
between any objectsx_{i}
andx_{i}
is not defined or would be illformed, the operator function is defined as deleted.
Change 11.10.3 [class.spaceship], paragraph 2, to use the new synthesized comparison instead of <=>
2 The return value
V
of typeR
of the defaulted threeway comparison operator function with parametersx
andy
of the same type is determined by comparing corresponding elementsx_{i}
andy_{i}
in the expanded lists of subobjects forx
andy
(in increasing index order) until the first indexi
wherethe synthesized threeway comparison for comparison category typex_{i}
<=>
y_{i}
R
betweenx_{i}
andy_{i}
yields a result valuev_{i}
wherev_{i}
!= 0
, contextually converted tobool
, yieldstrue
;V
isv_{i}
converted toR
. If no such index exists,V
isstd::strong_ordering::equal
converted toR
.
Add to the end of 12.3 [over.match], the new term usable function:
Overload resolution results in a usable function if overload resolution succeeds and the selected function is not deleted and is accessible from the context in which overload resolution was performed.
Update the featuretest macro in 15.10 [cpp.predefined] for __cpp_impl_three_way_comparison
to the date of the editor’s choosing:
Macro name  Value 

__cpp_impl_three_way_comparison

201711L ??????L

[ Editor's note: Why is it __cpp_impl_three_way_comparison
as opposed to __cpp_three_way_comparison
or even __cpp_spaceship
? ]
Thanks to Gašper Ažman, Agustín Bergé, Jens Maurer, Richard Smith, Jeff Snyder, Tim Song, Herb Sutter, and Tony van Eerd for the many discussions around these issues. Thanks to the Core Working Group for being vigilant and ensuring a better proposal.
[P0515R3] Herb Sutter, Jens Maurer, Walter E. Brown. 2017. Consistent comparison.
https://wg21.link/p0515r3
[P1185R2] Barry Revzin. 2019. <=> != ==
.
https://wg21.link/p1185r2
[P1186R0] Barry Revzin. 2019. When do you actually use <=>
?
https://wg21.link/p1186r0
[P1186R1] Barry Revzin. 2019. When do you actually use <=>
?
https://wg21.link/p1186r1
[P1188R0] Barry Revzin. 2019. Library utilities for <=>
.
https://wg21.link/p1188r0
[P1630R0] Barry Revzin. 2019. Spaceship needs a tuneup: Addressing some discovered issues with P0515 and P1185.
https://wg21.link/p1630r0
[Revzin] Barry Revzin. 2018. Conditionally implementing spaceship.
https://brevzin.github.io/c++/2018/12/21/spaceshipforvector/