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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory,sci.logic
Subject: Re: D correctly simulated by pure function H cannot possibly reach
 its, own line 06 ---
Date: Sun, 26 May 2024 13:16:14 -0400
Organization: i2pn2 (i2pn.org)
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On 5/26/24 1:01 PM, olcott wrote:
> On 5/26/2024 11:31 AM, Richard Damon wrote:
>> On 5/26/24 10:13 AM, olcott wrote:
>>> On 5/26/2024 6:43 AM, Richard Damon wrote:
>>>
>>> typedef int (*ptr)();  // ptr is pointer to int function in C
>>> 00       int H(ptr p, ptr i);
>>> 01       int D(ptr p)
>>> 02       {
>>> 03         int Halt_Status = H(p, p);
>>> 04         if (Halt_Status)
>>> 05           HERE: goto HERE;
>>> 06         return Halt_Status;
>>> 07       }
>>> 08
>>> 09       int main()
>>> 10       {
>>> 11         H(D,D);
>>> 12         return 0;
>>> 13       }
>>>
>>>
>>>> Because, as I have said, the answer and reasoning changes depending 
>>>> on what you acknowledged are the implications of your stipulations. 
>>>> For instance, if your actual understanding of being a "Pure 
>>>> Function" is that the program is the equivalent of a Turing Machine, 
>>>> then we need to add a strictness to the definition that isn't 
>>>> normally used for just "Pure Functions", like accessing value of 
>>>> registers like the program counter or stack pointer might not be 
>>>> allowed in some cases. (which breaks you H).
>>>>
>>>
>>> Since we can see (and you already agreed) that D correctly simulated
>>> by pure simulator H remains stuck in infinite recursive simulation then
>>> we also know that D never reaches its own line 06 and halts in less
>>> than an infinite number of correctly simulated steps.
>>
>> But it depends on what H actually does, which you refuse to agree to.
>>
> 
> When I specify that D is correctly simulated by pure function H, that
> means that H is a pure simulator that stops simulating D after some
> finite number of correctly simulated steps. There is absolutely nothing
> else that needs to be known about H besides this.
> 

And, do you accept that this exact description means that H is NOT the 
computational equivalent of a Turing Machine, and that this simulation 
doesn't prove that its input is not a non-halting program?

Failure to acknowledge this means that you don't understand the meaning 
of the terms you used, and that you accept the implications.