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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory,sci.logic
Subject: Re: Every D(D) simulated by H presents non-halting behavior to H ###
Date: Mon, 27 May 2024 10:58:40 -0400
Organization: i2pn2 (i2pn.org)
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On 5/27/24 10:39 AM, olcott wrote:
> On 5/27/2024 9:10 AM, Richard Damon wrote:
>> On 5/27/24 9:52 AM, olcott wrote:
>>> On 5/27/2024 3:11 AM, Mikko wrote:
>>>> On 2024-05-26 16:50:21 +0000, olcott said:
>>>>
>>>
>>> <snip>
>>> So that: *Usenet Article Lookup*
>>> http://al.howardknight.net/
>>> can see the whole message now that
>>> *the Thai spammer killed Google Groups*
>>>
>>> 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       }
>>>
>>>>> When we see that D correctly simulated by pure simulator H would 
>>>>> remain
>>>>> stuck in 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.
>>>>
>>>> Which means that H never terminates. You said that by your definition
>>>> a function that never terminates is not a pure function. Therefore
>>>> H, if it exists, is not a pure function, and the phrase "pure function
>>>> H" does not denote.
>>>>
>>>
>>> *I should have said that more clearly*
>>> *That is why I need reviewers*
>>> *Here it is more clearly*
>>>
>>> When we hypothesize that H is a pure simulator we see that D correctly
>>> simulated by pure simulator H remains stuck in recursive simulation thus
>>> never reaches its own simulated final state at its line 06 and halts. In
>>> this case H does not halt, thus is neither a pure function nor a
>>> decider.
>>
>> But when you hypothesize that H is actually a "pure simulator" 
>> (presumably one that never aborts) then you are creating a D that uses 
>> that pure simulator, and are ONLY deriving conclusions for such a D.
>>
> 
> When D correctly simulated by pure simulator H cannot possibly reach
> its own simulated final state at line 06 and halt in an infinite number
> of simulated steps we can conclude that less than an infinite number of
> steps is also not enough steps for D to halt.
> 

But ONLY for THAT D, the one built on the pure simulator that never aborts.

That is your flaw.

The problem is that if you try to define your input "D" as being your 
template, and not an actual "program", then you first need to go through 
and define what you actually mean by all these terms, and the result 
will not be directly applicable to the problem talking about actual 
programs.

You implicitly agreed to that by not refuting the implications I gave.

So, until you actually DEFINE what all those terms mean for a 
'non-program" input, i.e, your template, you can't actually say anything.

What does it mean to "Simulate" a template, especially when you reach 
the point the templates diverge (the call H instruction)

You logic just unsoundly mixes the different programs.