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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: Sun, 23 Feb 2025 19:15:37 -0500
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On 2/23/2025 7:10 PM, olcott wrote:
> On 2/23/2025 11:57 AM, dbush wrote:
>> On 2/23/2025 12:30 PM, olcott wrote:
>>> On 2/22/2025 8:34 PM, dbush wrote:
>>>> On 2/22/2025 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.
>>>>
>>>> In other words, when we actually run no_numbers_greater_than_10() it 
>>>> reaches its own "return" instruction.
>>>>
>>>> That means we've now established that the direct execution of a 
>>>> program (which includes all the functions it calls UNMODIFIED) 
>>>> defines whether or not it halts.
>>>>
>>>> Likewise, when we actually run DD() unmodified it also reaches its 
>>>> own "return" instruction.
>>>>
>>>> Therefore HHH(DD)==0 is wrong.
>>>>
>>>>
>>>
>>> _DD()
>>> [00002133] 55         push ebp      ; housekeeping
>>> [00002134] 8bec       mov ebp,esp   ; housekeeping
>>> [00002136] 51         push ecx      ; make space for local
>>> [00002137] 6833210000 push 00002133 ; push DD
>>> [0000213c] e882f4ffff call 000015c3 ; call HHH(DD)
>>> [00002141] 83c404     add esp,+04
>>> [00002144] 8945fc     mov [ebp-04],eax
>>> [00002147] 837dfc00   cmp dword [ebp-04],+00
>>> [0000214b] 7402       jz 0000214f
>>> [0000214d] ebfe       jmp 0000214d
>>> [0000214f] 8b45fc     mov eax,[ebp-04]
>>> [00002152] 8be5       mov esp,ebp
>>> [00002154] 5d         pop ebp
>>> [00002155] c3         ret
>>> Size in bytes:(0035) [00002155]
>>>
>>> When DD is correctly simulated by HHH according to the behavior
>>> that the above machine code specifies then the call from DD
>>> to HHH(DD) cannot possibly return and this correctly simulated
>>> DD cannot possibly terminate  normally by reaching its own machine
>>> address 00002155.
>>>
>>
>> Similarly:
>>
>> 0000000000400534 <no_numbers_greater_than_10>:
>>    400534:    55                       push   %rbp
>>    400535:    48 89 e5                 mov    %rsp,%rbp
>>    400538:    b8 34 05 40 00           mov    $0x400534,%eax
>>    40053d:    48 89 c7                 mov    %rax,%rdi
>>    400540:    e8 a8 ff ff ff           callq  4004ed <F>
>>    400545:    5d                       pop    %rbp
>>    400546:    c3                       retq
>>
>>
>> When no_numbers_greater_than_10 is correctly simulated by F according 
>> to the behavior that the above machine code specifies then the call 
>> from no_numbers_greater_than_10  to F(no_numbers_greater_than_10) 
>> cannot possibly terminate normally by reaching its own machine address 
>> 400545
>>
>> So F(no_numbers_greater_than_10)==0 is correct, and therefore no 
>> natural number exists that is greater than 10
>>
>> Agreed?
> 
> I Only understand Intel format assembly language.
> 

It corresponds to the following C code:

int no_numbers_greater_than_10()
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