Re: Every HHH(DDD) is correct to reject its input

On Sat, 31 May 2025 15:40:15 -0500, olcott wrote:
 

On 5/31/2025 3:30 PM, Mr Flibble wrote:

On Sat, 31 May 2025 15:10:39 -0500, olcott wrote:
>

On 5/31/2025 2:44 PM, Mr Flibble wrote:

Flibble's Argument: Execution vs Simulation in SHDs
====================================================
>
In the context of Simulating Halt Deciders (SHDs), the distinction
between execution and simulation is fundamental.
>
Correct: External Simulation ----------------------------
int main() {
       HHH(DDD); // SHD simulates/analyzes DDD from the outside.
}
>
- In this model, DDD is not being executed — it's being passed as
data to HHH, which is analyzing it.
- Even if DDD() (the function definition) contains a recursive call
to HHH(DDD), this is just part of the code being simulated, not
something that is actively executing.
- Thus, the simulation can detect infinite recursion structurally,
without running DDD.
>
Incorrect: Active Execution ---------------------------
int main() {
       DDD(); // Directly executes DDD, which calls HHH(DDD) during
       runtime.
}
>
>

We can't simply reject this as incorrect since it is the basis of
every rebuttal of my work.
>
It *is* incorrect to assume that the HHH that DDD calls is supposed to
report on the behavior of its caller.
>

- In this scenario, you’re actually running DDD, not simulating it.
- If DDD() calls HHH(DDD) at runtime, you're now mixing execution and
analysis in the same layer, violating the stratified model.
- This results in self-referential execution that undermines
decidability — a category error akin to the original halting paradox.
>
Key Insight -----------
As long as DDD is not executing and is only being simulated by HHH,
it doesn’t matter that DDD would call HHH(DDD) — because that call is
never actually made. It exists in the simulated model, not in the
runtime environment. Thus, structural recursion can be detected
safely and treated as non-halting without triggering a paradox.
>
This stratification (meta → base) is what keeps the model coherent.

>
A PhD computer scientist Eric Hehner has this same view. He explains
this view as the analyzer and the analyzed are in different
programming languages where the input cannot directly call its
analyzer.
>
I only very recently discovered that it is 100% impossible to actually
define *an input* that does the opposite of whatever value its
analyzer returns.
>
In every conventional proof of the halting problem it has always been
that the decider cannot correctly report on the behavior of its
caller.
>
You will find thousands of messages posted in this forum where
everyone says that I am wrong because HHH does not report on the
behavior of the direct execution of DDD() (AKA its caller).

>
You cannot both execute and simulate DDD as part of the same analysis,
if you do that then you are WRONG.
>
/Flibble

>
int main()
{
    DDD(); // calls HHH(DDD) that simulates its own separate
}        // instance of DDD. The analysis does not begin
           // until after HHH(DDD) is called.

 That is a type violation (category error), i.e. WRONG.  Simulation
analysis of DDD should involve no DIRECT execution of DDD WHATSOEVER.
 /Flibble