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From: olcott <polcott333@gmail.com>
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 12:01:25 -0500
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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.

-- 
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer