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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory
Subject: Re: DD specifies non-terminating behavior to HHH --- RECURSIVE CHAIN
 --- Saving Democracy
Date: Sat, 22 Feb 2025 22:38:51 -0500
Organization: i2pn2 (i2pn.org)
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On 2/22/25 7:33 PM, olcott wrote:
> On 2/22/2025 4:59 PM, dbush wrote:
>> On 2/22/2025 5:53 PM, olcott wrote:
>>> On 2/22/2025 2:59 PM, dbush wrote:
>>>> On 2/22/2025 3:53 PM, olcott wrote:
>>>>> On 2/22/2025 2:09 PM, dbush wrote:
>>>>>> On 2/22/2025 3:03 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 int no_numbers_greater_than_10()
>>>>> 10 {
>>>>> 11   return F(0);
>>>>> 12 }
>>>>> 13
>>>>> 14 int main()
>>>>> 15 {
>>>>> 16   F((int)no_numbers_greater_than_10);
>>>>> 17   return 0;
>>>>> 18 }
>>>>>
>>>>>>
>>>>>> So if the address of no_numbers_greater_than_10 is greater than 10 
>>>>>> then 0 is returned right away, otherwise as most 10 recursive 
>>>>>> calls will be made before the condition is matched and 0 is returned.
>>>>>>
>>>>>> 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 think that you will find more bugs when you try to
>>>>> provide the line number by line number execution trace.
>>>>>
>>>>> #1 bug F never simulates anything.
>>>>>
>>>>
>>>> It is a verified fact that 
>>>
>>> F never simulates anything when i > 10.
>>>
>>
>> Remember, you agreed that the behavior of X simulated by Y is defined 
>> by replacing the code of Y with an unconditional simulator and running 
>> Y(X):
>>
>> 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:
>>  >>> 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.
>>
>>
>> So the behavior of no_numbers_greater_than_10 simulated by F is 
>> defined by replacing the code of F with an unconditional simulated and 
>> running F(no_numbers_greater_than_10).
>>
>> The finite string input to F proves that there are no instructions in 
>> no_numbers_greater_than_10 that can break the recursive simulation.
>>
>> Try to show how no_numbers_greater_than_10 correctly simulated by F 
>> can possibly halt.
> 
> Then is ceases to be analogous to HHH(DD) because
> no_numbers_greater_than_10() always terminates normally
> by reaching its own "return" instruction.
> 
> Unlike HHH(DD) F((int)no_numbers_greater_than_10);
> does not need to abort the emulation of its input
> to prevent its own non-termination.
> 


But DD also reaches its own return instruction (when run) since the 
HHH(DD) that it calls will return 0.

Your problem is you confuse the fact that HHH needs to be designed to 
abort the simulation or it creates a DIFFERENT DD (based on that 
DIFFERENT HHH that didn't abort).

Once HHH is defined to do the abort, as your HHH is, then the abort 
turns out to be an error, because it NEVER was based on correct logic.