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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 --- Dishonest?
Date: Sun, 26 May 2024 12:31:45 -0400
Organization: i2pn2 (i2pn.org)
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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.

Yes, you have shown that a blindly simulating H that never aborts will 
get into an infinite simulation loop with D and thus NEITHER of them 
return a result.

THAT IS ALL THAT HAS BEEN AGREED TO. That an H that never aborts, and 
the D that calls that particular H form a non-halting pair.

But that H doesn't answer, so can't be the decider you claim.

The meaning and results of your more complicated statement (and if such 
an H can be written) has yet to be determined.

> 
> This is what I had in mind all along. Because I am a relatively
> terrible communicator it takes me a very long time to translate
> my intuitions into simple words.
> 

And that is why I am asking you to agree to the consequences of your 
statements, as that helps confirm that you are saying what you think you 
are saying.

If your implications don't match what you think, then you don't have 
your terms properly defined.

This is where if you would have taken the time to learn the language of 
the field you are talking about would have been a big help.

Since you don't actually know it, we don't know if you mean what you are 
saying, as has been found to have been the problem in the past.