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From: "Fred. Zwarts" <F.Zwarts@HetNet.nl>
Newsgroups: comp.theory,sci.logic
Subject: Re: Can you see that D correctly simulated by H remains stuck in
 recursive simulation?
Date: Sun, 26 May 2024 12:47:58 +0200
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Op 25.mei.2024 om 19:56 schreef olcott:
> On 5/25/2024 7:52 AM, Richard Damon wrote:
>> On 5/25/24 12:28 AM, olcott wrote:
> 
> 
> 
>>>> That you H, by just needing to be a "Pure Funtion" is not 
>>>> necessarily the computatinal eqivalent of a Turing Machine.
>>>>
>>>
>>> Totally moot for the subject line.
>>
>> Nope, ESSENTINTIAL. I am not asking you to change your definition, 
>> just accept its consequences.
>>
> 
> 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 many reviewers 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.
> 
> *This is only talking about the H/D c function pairs*
> *This is only talking about the H/D c function pairs*
> *This is only talking about the H/D c function pairs*
> *This is only talking about the H/D c function pairs*
> *This is only talking about the H/D c function pairs*
> 
> *This is only talking about the H/D c function pairs*
> *This is only talking about the H/D c function pairs*
> *This is only talking about the H/D c function pairs*
> *This is only talking about the H/D c function pairs*
> *This is only talking about the H/D c function pairs*
> 

The claim is that the simulation of D does not halt, because it call to 
H does not halt. The simulation does not even reach line 04, so the 
simulation does not even see that D contradicts H. The claim, therefore 
does not change if lines 04 and 05 are removed. What remains is that D 
is a parameter duplicator, so that H can simulate itself. The result is 
that each H in the infinite set of H finds that H is not halting. A 
clear indication that a simulating decider is not a good idea.