Re: Can you see that D correctly simulated by H remains stuck in recursive simulation?

Op 23.mei.2024 om 19:04 schreef olcott:

typedef int (*ptr)();  // ptr is pointer to int function in C
00       int H(ptr p, ptr i);
01       int D(ptr p)
02       {
03         int Halt_Status = H(p, p);
04         if (Halt_Status)
05           HERE: goto HERE;
06         return Halt_Status;
07       }
08
09       int main()
10       {
11         H(D,D);
12         return 0;
13       }
 The above template refers to an infinite set of H/D pairs where D is
correctly simulated by pure function H. This was done because many
reviewers used the shell game ploy to endlessly switch which H/D pair
was being referred to.
 *Correct Simulation Defined*
    This is provided because every reviewer had a different notion of
    correct simulation that diverges from this notion.
     A simulator is an x86 emulator that correctly emulates at least one
    of the x86 instructions of D in the order specified by the x86
    instructions of D.
     This may include correctly emulating the x86 instructions of H in
    the order specified by the x86 instructions of H thus calling H(D,D)
    in recursive simulation.
 *Execution Trace*
    Line 11: main() invokes H(D,D); H(D,D) simulates lines 01, 02, and 03
    of D. This invokes H(D,D) again to repeat the process in endless
    recursive simulation.
 

Of course this depends very much on the exact meaning of 'correct simulation', or 'correctly emulating'. E.g., take the call to H(p, p). If H recognizes that it is a call to a H with the same algorithm as is it using itself, and it knows that itself returns a certain integer value K, than it can be argued that it is a correct emulation to substitute the call to H with this integer value K, which is assigned to Halt_Status. Then the simulation of D can proceed to line 04.
What we need is an exact definition of 'correct simulation', in this case for the call instruction. Is it allowed to make assumptions for the result of a call, or is a call only correctly emulated by simulating the instructions of the called function?