Proposed resolution:

This wording is relative to N4820.

1. Change [concept.swappable] as indicated:

   -1- Let t1 and t2 be equality-preserving expressions that denote distinct equal objects of type T, and let u1 and u2 similarly denote distinct equal objects of type U. [Note: t1 and u1 can denote distinct objects, or the same object. — end note] An operation exchanges the values denoted by t1 and u1 if and only if the operation modifies neither t2 nor u2 and:

   1. (1.1) — If T and U are the same type, the result of the operation is that t1 equals u2 and u1 equals t2.

   2. (1.2) — If T and U are different types that model CommonReference<const T&, const U&>and CommonReference<decltype((t1)), decltype((u1))> is modeled, the result of the operation is that C(t1) equals C(u2) and C(u1) equals C(t2) where C is common_reference_t<const T&, const U&decltype((t1)), decltype((u1))>.

   -2- […]

   -3- […]

   template<class T>
     concept Swappable = requires(T& a, T& b) { ranges::swap(a, b); };
     
   template<class T, class U>
     concept SwappableWith =
     CommonReference<T, Uconst remove_reference_t<T>&, const remove_reference_t<U>&> &&
     requires(T&& t, U&& u) {
       ranges::swap(std::forward<T>(t), std::forward<T>(t));
       ranges::swap(std::forward<U>(u), std::forward<U>(u));
       ranges::swap(std::forward<T>(t), std::forward<U>(u));
       ranges::swap(std::forward<U>(u), std::forward<T>(t));
     };
   

   -4- […]

   -5- [Example: User code can ensure that the evaluation of swap calls is performed in an appropriate context under the various conditions as follows:

   #include <cassert>
   #include <concepts>
   #include <utility>
   
   namespace ranges = std::ranges;
   
   template<class T, std::SwappableWith<T> U>
   void value_swap(T&& t, U&& u) {
     ranges::swap(std::forward<T>(t), std::forward<U>(u));
   }
   
   template<std::Swappable T>
   void lv_swap(T& t1, T& t2) {
     ranges::swap(t1, t2);
   }
   
   namespace N {
     struct A { int m; };
     struct Proxy { 
       A* a;
       Proxy(A& a) : a{&a} {}
       friend void swap(Proxy x, Proxy y) {
         ranges::swap(*x.a, *y.a);
       }
     };
     Proxy proxy(A& a) { return Proxy{ &a }; }
     void swap(A& x, Proxy p) {
       ranges::swap(x.m, p.a->m);
     }
     void swap(Proxy p, A& x) { swap(x, p); } // satisfy symmetry requirement
   }
   
   int main() {
     int i = 1, j = 2;
     lv_swap(i, j);
     assert(i == 2 && j == 1);
     N::A a1 = { 5 }, a2 = { -5 };
     value_swap(a1, proxy(a2));
     assert(a1.m == -5 && a2.m == 5);
   }
   

[ 2020-02-10 Move to Immediate Monday afternoon in Prague ]

[ 2020-01-16 Priority set to 1 after discussion on the reflector. ]

[ 2019-06-20; Casey Carter comments and provides improved wording ]

The purpose of the CommonReference requirements in the cross-type concepts is to provide a sanity check. The fact that two types satisfy a single-type concept, have a common reference type that satisfies that concept, and implement cross-type operations required by the cross-type flavor of that concept very strongly suggests the programmer intends them to model the cross-type concept. It's an opt-in that requires some actual work, so it's unlikely to be inadvertent.

The CommonReference<const T&, const U&> pattern makes sense for the comparison concepts which require that all variations of const and value category be comparable: we use const lvalues to trigger the "implicit expression variation" wording in [concepts.equality]. SwappableWith, however, doesn't care about implicit expression variations: it only needs to witness that we can exchange the values denoted by two reference-y expressions E1 and E2. This suggests that CommonReference<decltype((E1)), decltype((E2))> is a more appropriate requirement than the current CommonReference<const remove_reference_t<…> mess that was blindly copied from the comparison concepts.

We must change the definition of "exchange the values" in [concept.swappable] — which refers to the common reference type — consistently.

This wording is relative to N4791.

1. Change [concept.swappable] as indicated:

   -3- […]

   template<class T>
     concept Swappable = requires(T& a, T& b) { ranges::swap(a, b); };
     
   template<class T, class U>
     concept SwappableWith =
     CommonReference<T, Uconst remove_reference_t<T>&, const remove_reference_t<U>&> &&
     requires(T&& t, U&& u) {
       ranges::swap(std::forward<T>(t), std::forward<T>(t));
       ranges::swap(std::forward<U>(u), std::forward<U>(u));
       ranges::swap(std::forward<T>(t), std::forward<U>(u));
       ranges::swap(std::forward<U>(u), std::forward<T>(t));
     };
   

   -4- […]

   -5- [Example: User code can ensure that the evaluation of swap calls is performed in an appropriate context under the various conditions as follows:

   #include <cassert>
   #include <concepts>
   #include <utility>
   
   namespace ranges = std::ranges;
   
   template<class T, std::SwappableWith<T> U>
   void value_swap(T&& t, U&& u) {
     ranges::swap(std::forward<T>(t), std::forward<U>(u));
   }
   
   template<std::Swappable T>
   void lv_swap(T& t1, T& t2) {
     ranges::swap(t1, t2);
   }
   
   namespace N {
     struct A { int m; };
     struct Proxy { 
       A* a;
       Proxy(A& a) : a{&a} {}
       friend void swap(Proxy&& x, Proxy&& y) {
         ranges::swap(x.a, y.a);
       }
     };
     Proxy proxy(A& a) { return Proxy{ &a }; }
     void swap(A& x, Proxy p) {
       ranges::swap(x.m, p.a->m);
     }
     void swap(Proxy p, A& x) { swap(x, p); } // satisfy symmetry requirement
   }
   
   int main() {
     int i = 1, j = 2;
     lv_swap(i, j);
     assert(i == 2 && j == 1);
     N::A a1 = { 5 }, a2 = { -5 };
     value_swap(a1, proxy(a2));
     assert(a1.m == -5 && a2.m == 5);
   }
   

The defect stems from the example found in sub-clause [concept.swappable] p5:

[…]

template<class T, std::SwappableWith<T> U>
void value_swap(T&& t, U&& u) {
  ranges::swap(std::forward<T>(t), std::forward<U>(u));
}

[…]
namespace N {
  struct A { int m; };
  struct Proxy { A* a; };
  Proxy proxy(A& a) { return Proxy{ &a }; }
  
  void swap(A& x, Proxy p) {
    ranges::swap(x.m, p.a->m);
  }
  void swap(Proxy p, A& x) { swap(x, p); } // satisfy symmetry requirement
}

int main() {
  […]
  N::A a1 = { 5 }, a2 = { -5 };
  value_swap(a1, proxy(a2)); // diagnostic manifests here(#1)
  assert(a1.m == -5 && a2.m == 5);
}

The call to value_swap(a1, proxy(a2)) resolves to [T = N::A&, U = N::Proxy] The compiler will issue a diagnostic for #1 because:

1. rvalue proxy(a2) is not swappable

2. concept SwappableWith<T, U> requires N::A and Proxy to model CommonReference<const remove_reference_t<T>&, const remove_reference_t<U>&> It follows from the example that there is no common reference for [T = N::A&, U = N::Proxy]