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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 17:59:20 -0500
Organization: A noiseless patient Spider
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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.