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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 14:03:47 -0600
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On 2/22/2025 1:40 PM, dbush wrote:
> On 2/22/2025 2:33 PM, olcott wrote:
>> On 2/22/2025 1:17 PM, dbush wrote:
>>> On 2/22/2025 1:54 PM, olcott wrote:
>>>> On 2/22/2025 12:21 PM, dbush wrote:
>>>>> On 2/22/2025 1:02 PM, olcott wrote:
>>
>>>>>>>
>>>>>> 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.
>>>>
>>>
>>> Let's make a small change so that wraparound is well defined:
>>>
>>> int F(uintptr_t i)
>>> {
>>>       if (i<10) {
>>>           return 0;
>>>       } else {
>>>           return F(i+1);
>>>       }
>>> }
>>>
>>> This ensures that F((uintptr_t)no_numbers_greater_than_10) returns 0.
>>>
>>> This doesn't change the 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?
>>
>> i starts out as the address of
>> no_numbers_greater_than_10
>> Then causes the emulation to crash.
>>
> 
> If that address is greater than 10 then F returns 0 right away, 
> otherwise it makes at most 10 recursive calls before returning 0, so 
> there would be no crash.
> 

You may be correct yet it does not see like that to me.
Please give me the line number by line number execution
trace that you are assuming.

> So you agree that no_numbers_greater_than_10 correctly
> simulated by F (i.e. if the body of the function F is replaced by an 
> unconditional simulator as you said is correct) cannot possibly return?


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