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From: dbush <dbush.mobile@gmail.com>
Newsgroups: comp.theory
Subject: Re: DD specifies non-terminating behavior to HHH --- RECURSIVE CHAIN
 --- Saving Democracy
Date: Sat, 22 Feb 2025 12:10:31 -0500
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On 2/22/2025 11:43 AM, olcott wrote:
> On 2/22/2025 5:01 AM, joes wrote:
>> Am Fri, 21 Feb 2025 21:55:32 -0600 schrieb olcott:
>>> On 2/20/2025 4:00 AM, joes wrote:
> 
> 
>>>> Not even the variable Root in line 502 of Halt7.c?
>>> https://github.com/plolcott/x86utm/blob/master/Halt7.c You are not even
>>> in the correct function.
>> 1059
>>
> 
> Unless we go through a 100% precise sequence of steps
> my reviewers will always consistently dodge the point
> as they have done for several years.
> 
> typedef void (*ptr)();
> int HHH(ptr P);
> 
> int DD()
> {
>    int Halt_Status = HHH(DD);
>    if (Halt_Status)
>      HERE: goto HERE;
>    return Halt_Status;
> }
> 
> int main()
> {
>    HHH(DD);
> }
> 
> The first point is DD correctly simulated by HHH cannot
> possibly terminate normally by reaching its own "return"
> instruction.

In other words, if the code of HHH is replaced with an unconditional 
simulator then it can be shown that DD is non-halting and therefore 
HHH(DD)==0 is correct.

Let's test that on another case.

int F(int i)
{
     if (i<10) {
         return 0;
     } else {
         return F(i+1);
     }
}

int no_numbers_greater_than_10()
{
     return F(0);
}


The function no_numbers_greater_than_10() checks if any natural number 
exists that is greater than 10.  It does this by checking all natural 
numbers one at a time.  If one such number exists it halts and return 0. 
  If no such number exists, it will run forever as no such number will 
satisfy the condition.

We can see that no_numbers_greater_than_10 correctly simulated by F 
cannot possibly terminate normal by reaching its own "return" 
instruction.  This means that F correctly reports that 
no_numbers_greater_than_10 is non-halting.  It further means, since 
no_numbers_greater_than_10  doesn't halt that there is no natural number 
greater than 10.

Agreed?