Re: Every D(D) simulated by H presents non-halting behavior to H ###

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.
The results do NOT apply for a D built on a different H, that happens to abort its simulation,

  From this we correctly conclude that D correctly simulated by pure
function H never reaches its simulated final state at its own line 06
and halts in Less than an infinite (AKA finite) number of simulated
steps. Here is a concrete example of that:

Right, but ONLY for a D built on such a pure simulator. It says nothing if you build a

 https://en.wikipedia.org/wiki/Googolplex
When pure function H correctly simulates a Googolplex ^ Googolplex
number of steps of D, then D never reaches its simulated final state
at its own line 06 and halts. Pure function H halts after this finite
number of steps of correct simulation.

But then H is NOT that "Pure Simulator" you were imagining above, and thus you can't use that result.

 In other words when the *INPUT* to H(D,D) is correctly simulated by
either pure simulator H or pure function H this correctly simulated
*INPUT* never halts no matter what, thus the INPUT to H(D,D) is
definitely non halting.

Nope. You might be able to claim that your H can't reach the final step in its simulation, but you can't claim that the input doesn't halt when simulated by a Pure Simulator. You have admited that if H(D,D) returns 0 then D(D) will halt.
You then try to claim, without being able to prove the false statement, that somehow it is ok for H to give the wrong answer, but of course that is just an admission that you logic system is broken and inconsistent.

 *This is STEP ONE of my four step proof*
STEP TWO applies these same ideas to the Peter Linz HP proof.
STEP THREE shows how the Linz Ĥ.H sees the behavior of its recursive
      simulations.
STEP FOUR shows why the behavior of the INPUT is the correct basis.
 

And it seems ALL You steps have similar error, because you just don't understand what you are talking about. This is the problem of trying to work in a system you haven't actually studied.