Proposed resolution:

This wording is relative to N5014.

[Drafting note: It should be pointed out that member function finish should be `noexcept` for other reasons as well, see LWG 4215.]

1. Modify [exec.run.loop.general], class `run_loop` synopsis, as indicated:

   namespace std::execution {
     class run_loop {
       // [exec.run.loop.types], associated types
       class run-loop-scheduler;                        // exposition only
       class run-loop-sender;                           // exposition only
       struct run-loop-opstate-base {                   // exposition only
         virtual void execute() noexcept = 0;           // exposition only
         run_loop* loop;                                // exposition only
         run-loop-opstate-base* next;                   // exposition only
       };
       template<class Rcvr>
         using run-loop-opstate = unspecified;          // exposition only
         
       // [exec.run.loop.members], member functions
       run-loop-opstate-base* pop-front() noexcept;     // exposition only
       void push-back(run-loop-opstate-base*) noexcept; // exposition only
       
     public:
       // [exec.run.loop.ctor], constructor and destructor
       run_loop() noexcept;
       run_loop(run_loop&&) = delete;
       ~run_loop();
       
       // [exec.run.loop.members] member functions
       run-loop-scheduler get_scheduler() noexcept;
       void run() noexcept;
       void finish() noexcept;
     };
   }
   

2. Modify [exec.run.loop.types] as indicated:

   class run-loop-sender;
   

   -5- run-loop-sender is an exposition-only type that satisfies sender. completion_signatures_of_t<runloop-sender> is

   completion_signatures<set_value_t(), set_error_t(exception_ptr), set_stopped_t()>
   

   […]

   -9- Let o be a non-const lvalue of type run-loop-opstate<Rcvr>, and let REC(o) be a non-const lvalue reference to an instance of type `Rcvr` that was initialized with the expression rcvr passed to the invocation of connect that returned o. Then:

   • (9.1) — […]
   • (9.2) — […]
   • (9.3) — The expression start(o) is equivalent to:

     try {
       o.loop->push-back(addressof(o));
     } catch(...) {
       set_error(std::move(REC(o)), current_exception());
     }
     

3. Modify [exec.run.loop.members] as indicated:

   run-loop-opstate-base* pop-front() noexcept;
   

   -1- Effects: Blocks ([defns.block]) until one of the following conditions is `true`: […]

   void push-back(run-loop-opstate-base* item) noexcept;
   

   -2- Effects: Adds `item` to the back of the queue and increments count by `1`.

   -3- Synchronization: This operation synchronizes with the pop-front operation that obtains `item`.

   run-loop-scheduler get_scheduler() noexcept;
   

   -4- Returns: An instance of run-loop-scheduler that can be used to schedule work onto this `run_loop` instance.

   void run() noexcept;
   

   -5- Preconditions: is either starting or finishing.

   -6- Effects: If state is starting, sets the state to running, otherwise leaves state unchanged. Then, equivalent to:

   while (auto* op = pop-front()) {
     op->execute();
   }
   

   -7- Remarks: When state changes, it does so without introducing data races.

   void finish() noexcept;
   

   -8- Preconditions: state is either starting or running.

   -9- Effects: Changes state to finishing.

   -10- Synchronization: `finish` synchronizes with the pop-front operation that returns `nullptr`.

When `run_loop` was proposed, the only implementation we had synchronized with a mutex and a condition variable. Operations on those can theoretically throw exceptions, so `run_loop` got a `set_error_t(exception_ptr)` completion signature.

Since then, a lock-free implementation of `run_loop` has been found. Atomic operations cannot fail with an exception, so an atomic `run_loop` can never complete with an error.