01 int D(int (*x)())
02 {
03 int Halt_Status = H(x, x);
04 if (Halt_Status)
05 HERE: goto HERE;
06 return Halt_Status;
07 }
08
09 void main()
10 {
11 H(D,D);
12 }

Here is the sequence when H never aborts it simulation:
main() calls H(D,D) that simulates D(D) at line 11
keeps repeating: simulated D(D) calls simulated H(D,D) that simulates
D(D) at line 03 ...

When it is understood that halting requires reaching a final state and
stopping for any other reason does not count as halting then

The fact that D correctly simulated by H cannot possibly reach its own
final state at line 6 conclusively proves that this simulated D does not
halt.

*When H returns 0 it is only affirming this verified fact*

The notion of a UTM conclusively proves that D correctly simulated by H
does derive the behavior that a simulating halt decider must measure.

Because all deciders must compute the mapping from their inputs to their
own accept or reject state anyone and anything that says that H must
report on the behavior of non-inputs contradicts the definition of a
decider.

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 3/17/23 9:10 PM, olcott wrote:
> 01 int D(int (*x)())
> 02 {
> 03   int Halt_Status = H(x, x);
> 04   if (Halt_Status)
> 05     HERE: goto HERE;
> 06   return Halt_Status;
> 07 }
> 08
> 09 void main()
> 10 {
> 11   H(D,D);
> 12 }
>
> Here is the sequence when H never aborts it simulation:
>   main() calls H(D,D) that simulates D(D) at line 11
>   keeps repeating: simulated D(D) calls simulated H(D,D) that simulates
> D(D) at line 03 ...

Which only happen if H will NEVER abort it simulation.

>
> When it is understood that halting requires reaching a final state and
> stopping for any other reason does not count as halting then

Right, so the question is will main calling D(D) see D return.

THAT is the machine presented to the input of H.

And THAT return, as you have admitted.

>
> The fact that D correctly simulated by H cannot possibly reach its own
> final state at line 6 conclusively proves that this simulated D does not
> halt.

No, since this isn't the H that correct simulates its input, it isn't
reelvent.

>
> *When H returns 0 it is only affirming this verified fact*

No, it afferms that the condition assumed at the begining was a FALSEHOOD.

>
> The notion of a UTM conclusively proves that D correctly simulated by H
> does derive the behavior that a simulating halt decider must measure.

Nope, because H isn't a UTM.

>
> Because all deciders must compute the mapping from their inputs to their
> own accept or reject state anyone and anything that says that H must
> report on the behavior of non-inputs contradicts the definition of a
> decider.
>

Right, and since the input to H was the description of the machine D(D),
and you have admitted that this halts, the correct answer is Halting.

Your the one that says you H looks at something that isn't its input, in
that it presumes that the H called by D isn't the actual H that exists
in this prograam.

Thus you are admitting you H isn't a decider.

You are just proving you don't understand what you are talking about.

This is just poisoning your ideas of "Correct Reasoning" which are
looking more like "Unsound Reasoning".