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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: DD specifies non-terminating behavior to HHH --- RECURSIVE CHAIN
 --- Saving Democracy
Date: Sat, 22 Feb 2025 12:54:48 -0600
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On 2/22/2025 12:21 PM, dbush wrote:
> On 2/22/2025 1:02 PM, olcott wrote:
>> On 2/22/2025 11:10 AM, dbush wrote:
>>> 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.
>>>
>>
>> Wow finally someone that totally gets it.
>>
>>> Let's test that on another case.
>>>
>> 01 int F(int i)
>> 02 {
>> 03      if (i<10) {
>> 04          return 0;
>> 05      } else {
>> 06          return F(i+1);
>> 07      }
>> 08 }
>> 09
>> 10 int no_numbers_greater_than_10()
>> 11 {
>> 12      return F(0);
>> 13 }
>> 14
>> 15 int main()
>> 16 {
>> 17   no_numbers_greater_than_10();
>> 18   return 0;
>> 19 }
> 
> Actually, let's update main:
> 
> int main()
> {
>     F((int)no_numbers_greater_than_10);
>     return 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.
>>>
>>
>> Your code is incomplete. I added main() with line numbers.
>>
>>> 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?
>>
>> Here the execution trace that I see:
>> 15, 16, 17, 10, 11, 12, 01, 02, 03, 04, 12, 18, 19
>>
> 
> Just as you say we're not talking about the direct execution of DD, 
> we're also not talking about the direct execution of 
> no_numbers_greater_than_10.  We're talking about 
> no_numbers_greater_than_10 correctly simulated by F.
> 
> It's a verified fact that no_numbers_greater_than_10 correctly simulated 
> by F cannot possibly return so F(no_numbers_greater_than_10) is correct 
> to report non-halting, which means that there is no natural number 
> greater than 10.
> 
> Agreed?
> 

Leaving out main() made this difficult.
We can assume that the address of no_numbers_greater_than_10 > 10.
This will emulate no_numbers_greater_than_10 at incorrect byte offsets
causing it to crash. This may or may not make F crash depending
on how robust its emulator is.

-- 
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer