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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: Sun, 23 Feb 2025 19:13:07 -0600
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On 2/23/2025 6:15 PM, dbush wrote:
> 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:
> 
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