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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory,sci.logic
Subject: Re: Can you see that D correctly simulated by H remains stuck in
 recursive simulation?
Date: Sun, 26 May 2024 08:38:34 -0500
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On 5/26/2024 5:47 AM, Fred. Zwarts wrote:
> Op 25.mei.2024 om 19:56 schreef olcott:
>> On 5/25/2024 7:52 AM, Richard Damon wrote:
>>> On 5/25/24 12:28 AM, olcott wrote:
>>
>>
>>
>>>>> That you H, by just needing to be a "Pure Funtion" is not 
>>>>> necessarily the computatinal eqivalent of a Turing Machine.
>>>>>
>>>>
>>>> Totally moot for the subject line.
>>>
>>> Nope, ESSENTINTIAL. I am not asking you to change your definition, 
>>> just accept its consequences.
>>>
>>
>> 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       }
>>
>> The above template refers to an infinite set of H/D pairs where D is
>> correctly simulated by pure function H. This was done because many
>> reviewers used the shell game ploy to endlessly switch which H/D pair
>> was being referred to.
>>
>> *Correct Simulation Defined*
>>     This is provided because many reviewers had a different notion of
>>     correct simulation that diverges from this notion.
>>
>>     A simulator is an x86 emulator that correctly emulates at least one
>>     of the x86 instructions of D in the order specified by the x86
>>     instructions of D.
>>
>>     This may include correctly emulating the x86 instructions of H in the
>>     order specified by the x86 instructions of H thus calling H(D,D) in
>>     recursive simulation.
>>
>> *Execution Trace*
>> Line 11: main() invokes H(D,D); H(D,D) simulates lines 01, 02, and 03 of
>> D. This invokes H(D,D) again to repeat the process in endless recursive
>> simulation.
>>
>> *This is only talking about the H/D c function pairs*
>> *This is only talking about the H/D c function pairs*
>> *This is only talking about the H/D c function pairs*
>> *This is only talking about the H/D c function pairs*
>> *This is only talking about the H/D c function pairs*
>>
>> *This is only talking about the H/D c function pairs*
>> *This is only talking about the H/D c function pairs*
>> *This is only talking about the H/D c function pairs*
>> *This is only talking about the H/D c function pairs*
>> *This is only talking about the H/D c function pairs*
>>
> 
> The claim is that the simulation of D does not halt, because it call to 
> H does not halt. The simulation does not even reach line 04, so the 
> simulation does not even see that D contradicts H. The claim, therefore 
> does not change if lines 04 and 05 are removed. What remains is that D 
> is a parameter duplicator, so that H can simulate itself. The result is 
> that each H in the infinite set of H finds that H is not halting. A 
> clear indication that a simulating decider is not a good idea.


Your transformation would have been acceptable if you retained the
fact that H is a pure function that always halts and returns some value.

In retrospect I should not have assumed that people here knew what a
pure function is.

In computer programming, a pure function is a function that has the 
following properties:

(1) the function return values are identical for identical arguments
(no variation with local static variables, non-local variables, mutable
reference arguments or input streams), and

(2) the function has no side effects (no mutation of local static
variables, non-local variables, mutable reference arguments or
input/output streams). https://en.wikipedia.org/wiki/Pure_function

Because we can see that D correctly simulated by pure function
H cannot possibly reach its final state at line 06 and halt even
when an infinite number of steps are simulated we can know that
D specifies non-halting behavior.

That H is a pure function means that H eventually halts and returns
some value. We can say H returns the meaningless value of 56.

*Thanks for your review*

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