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From: dbush <dbush.mobile@gmail.com>
Newsgroups: comp.theory
Subject: Re: DD specifies non-terminating behavior to HHH --- COMPLETE PROOF
Date: Tue, 25 Feb 2025 21:52:30 -0500
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On 2/25/2025 6:14 PM, olcott wrote:
> On 2/25/2025 2:46 PM, olcott wrote:
>> On 2/25/2025 12:49 PM, dbush wrote:
>>> On 2/25/2025 1:01 PM, olcott wrote:
>>>> On 2/25/2025 10:13 AM, Mikko wrote:
>>>>> Althogh the subject line has the words "COMPLETE PROOF" there is no
>>>>> proof or pointer to proof below.
>>>>>
>>>>
>>>>
>>>> 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 above does specify that DD simulated by HHH
>>>> cannot possibly terminate normally by reaching its
>>>> own "return" instruction.
>>>>
>>>> That this may be beyond your technical skill level.
>>>> is less than no rebuttal at all.
>>>>
>>>> Ignoring the code in main() seemed dishonest.
>>>>
>>>
>>> int no_numbers_greater_than_10();
>>>
>>> int F(uintptr_t p);
>>>
>>> int no_numbers_greater_than_10()
>>> {
>>>    return F((uintptr_t)no_numbers_greater_than_10);
>>> }
>>>
>>> int main()
>>> {
>>>    F((uintptr_t)no_numbers_greater_than_10);
>>>    return 0;
>>> }
>>>
>>>
>>> The above does specify that no_numbers_greater_than_10 simulated by F
>>> cannot possibly terminate normally by reaching its
>>> own "return" instruction.
>>>
>>> That this may be beyond your technical skill level
>>> is less than no rebuttal at all.
>>
>> Finally you made something that was not wrong in several different ways.
>> So what is your point?
>>
> 
> Yes.
> 

Good.  So now looking again at the code, this time showing the 
implementation of F:

int no_numbers_greater_than_10();

int F(uintptr_t p)
{
   uintptr_t ptr = (uintptr_t)no_numbers_greater_than_10;
   uintptr_t i = p ^ ptr;
   if (i > 10)
     return 0;
   else
     return F((i+1) ^ ptr);
}

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

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

no_numbers_greater_than_10 determines whether there exists a number 
greater than 10 by testing all numbers.  If if finds one, it aborts and 
halts returning 0.  If it does not, it gets stuck in infinite recursion 
and does not halt.

Since it was correctly determined, and you agreed, that 
no_numbers_greater_than_10 does not halt, we can conclude that there are 
no natural numbers greater than 10.

Agreed?