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From: "Fred. Zwarts" <F.Zwarts@HetNet.nl>
Newsgroups: comp.theory,sci.logic
Subject: Re: Two dozen people were simply wrong --- Try to prove otherwise ---
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Date: Sun, 2 Jun 2024 11:19:50 +0200
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Op 02.jun.2024 om 01:12 schreef olcott:
> On 6/1/2024 6:02 PM, Richard Damon wrote:
>> On 6/1/24 6:40 PM, olcott wrote:
>>>
>>> Show me where I said anything in the above spec about an aborted 
>>> simulation.
>>
>> So, why did HH stop simulating after some n steps?
>>
>> Did it reach a final state in the simulation? if not, it ABORTED its 
>> simulation.
>>
>>>
>>> When every possible which way DD correctly simulated by HH never reaches
>>> past its own simulated line 03 then
>>
>> And a simulation either goes until it reaches a final state of the 
>> machine it is simulating, or it aborted its simulation.
>>
> 
> typedef int (*ptr)();  // ptr is pointer to int function in C
> 00       int HH(ptr p, ptr i);
> 01       int DD(ptr p)
> 02       {
> 03         int Halt_Status = HH(p, p);
> 04         if (Halt_Status)
> 05           HERE: goto HERE;
> 06         return Halt_Status;
> 07       }
> 08
> 09       int main()
> 10       {
> 11         HH(DD,DD);
> 12         return 0;
> 13       }
> 
> When every DD correctly simulated by any HH cannot possibly reach
> past its own simulated line 03 in 1 to ∞ steps of correct simulation
> of DD by HH then we have exhaustively examined every possible HH/DD
> pair and each element has of this infinite set has the same property.

Similarly:
When every HH correctly simulated by itself cannot possibly reach its 
own simulated return in 1 to ∞ steps of correct simulation
of HH by HH then we have exhaustively examined every possible HH/DD
pair and each element has of this infinite set has the same property.

> 
> *THIS PROVES THAT THE INPUT TO H(DD,DD) DOES NOT HALT*
> *THIS PROVES THAT THE INPUT TO H(DD,DD) DOES NOT HALT*
> *THIS PROVES THAT THE INPUT TO H(DD,DD) DOES NOT HALT*
> 

And since HH is part of that input, it proves that none of these HH halt.