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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: comp.theory
Subject: Re: Every D(D) simulated by H presents non-halting behavior to H ...
Date: Wed, 8 May 2024 19:11:33 +0300
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On 2024-05-08 12:57:07 +0000, olcott said:

> On 5/8/2024 3:46 AM, Mikko wrote:
>> On 2024-05-07 15:40:32 +0000, olcott said:
>> 
>>> On 5/7/2024 6:18 AM, Richard Damon wrote:
>>>> On 5/7/24 3:30 AM, Mikko wrote:
>>>>> On 2024-05-06 18:28:37 +0000, olcott said:
>>>>> 
>>>>>> On 5/6/2024 11:19 AM, Mikko wrote:
>>>>>>> On 2024-05-05 17:02:25 +0000, olcott said:
>>>>>>> 
>>>>>>>> The x86utm operating system: https://github.com/plolcott/x86utm enables
>>>>>>>> one C function to execute another C function in debug step mode.
>>>>>>>> Simulating Termination analyzer H simulates the x86 machine code of its
>>>>>>>> input (using libx86emu) in debug step mode until it correctly matches a
>>>>>>>> correct non-halting behavior pattern proving that its input will never
>>>>>>>> stop running unless aborted.
>>>>>>>> 
>>>>>>>> Can D correctly simulated by H terminate normally?
>>>>>>>> 00 int H(ptr x, ptr x)  // ptr is pointer to int function
>>>>>>>> 01 int D(ptr x)
>>>>>>>> 02 {
>>>>>>>> 03   int Halt_Status = H(x, x);
>>>>>>>> 04   if (Halt_Status)
>>>>>>>> 05     HERE: goto HERE;
>>>>>>>> 06   return Halt_Status;
>>>>>>>> 07 }
>>>>>>>> 08
>>>>>>>> 09 int main()
>>>>>>>> 10 {
>>>>>>>> 11   H(D,D);
>>>>>>>> 12 }
>>>>>>>> 
>>>>>>>> *Execution Trace*
>>>>>>>> Line 11: main() invokes H(D,D);
>>>>>>>> 
>>>>>>>> *keeps repeating* (unless aborted)
>>>>>>>> Line 03: simulated D(D) invokes simulated H(D,D) that simulates D(D)
>>>>>>>> 
>>>>>>>> *Simulation invariant*
>>>>>>>> D correctly simulated by H cannot possibly reach past its own line 03.
>>>>>>>> 
>>>>>>>> The above execution trace proves that (for every H/D pair of the
>>>>>>>> infinite set of H/D pairs) each D(D) simulated by the H that this D(D)
>>>>>>>> calls cannot possibly reach past its own line 03.
>>>>>>> 
>>>>>>> When you say "every H/D pair" you should specify which set of pairs
>>>>>>> you are talking about. As you don't, your words don't mean anything.
>>>>>>> 
>>>>>> 
>>>>>> Every H/D pair in the universe where D(D) is simulated by the
>>>>>> same H(D,D) that D(D) calls. This involves 1 to ∞ steps of D
>>>>>> and also includes zero to ∞ recursive simulations where H
>>>>>> H simulates itself simulating D(D).
>>>>> 
>>>>> "In the universe" is not a set. In typical set theories like ZFC there
>>>>> is no universal set.
>>>> 
>>> 
>>> This template defines an infinite set of finite string H/D pairs where 
>>> each D(D) that is simulated by H(D,D) also calls this same H(D,D).
>> 
>> No, it does not. D does not know which H simulates it or even whther is
>> simulated at all. D calls the one whose name is H. The association of D
>> with the H of the same pair, if desired, must be done outside of D.
>> 
> 
> The template specifies that D(D) is calling the same H(D,D)
> that invokes it. All instances conform to the template.

No, it does not. The "H" in the template is a fixed "H" that does
not chage to "main" when

  int main(void) {
    D(D);
    return 0;
  }

is executed.

-- 
Mikko