Re: And those are the facts

On 6/13/25 2:47 PM, Mr Flibble wrote:

On Fri, 13 Jun 2025 12:59:47 -0400, Richard Damon wrote:
 

On 6/13/25 11:02 AM, Mr Flibble wrote:

A simulating halt decider (SHD) must always halt (i.e. provide a
halting decision about its input) irregardless of whether or not its
input halts.
>
And those are the facts.
>
/Flibble

>
And to BE a CORRECT decider, its answer must match the criteria defined
for the input, which for a Halt Decider, is does the program represented
by the input halt.
>
Thus, an input that a SHD that returns the code for non-halting, must
never halt when actually run.
>
Since for the H/D pair that has been the focus here for years, if H(D)
returns 0, D will halt, H(D) returning 0 can not be a correct answer.
>
PERIOD. THAT IS THE FACTS.
>
The point is that a SHD can not correctly simulate a non-halting input,
and return 0 as required, and thus if the defining condition of the SHD
is that it is based on its own correct simulation, it can NEVER return
0, as that is just proven to be a contradiction to its requirements.
>
Since non-halting inputs exist, that says that a SHD based on just its
own correct simulation of its input is just a self-contradiction, and
thus the criteria is incorrect.

 ---
 ## 🧠 Core Claim (Restated)
 **Flibble’s SHD** (Simulating Halt Decider) is:
 

A **partial decider** that always halts and **refuses to analyze**

inputs that contain pathological self-reference (like `DDD()` that calls
`HHH(DDD)`).

And, how do you detect that?
Remember, DDD, if properly formed, contains a COPY of HHH, not just a direct reference to it, and that copy can be syntactially altered to disguise it, while still maintatin the exact smae computation.

 It does **not** attempt to simulate those inputs completely. Instead, it
performs **static analysis**, detects recursion patterns (e.g. mutual self-
reference), and classifies them as **non-halting** or rejects them
outright.

And, how does it do that?
Remember the condition described above,

 ---
 ## ✅ What This *Does* Achieve
 * **Avoids infinite recursion** in simulation by terminating analysis
early.

Again, How? given the option descrived above.

* Enforces a **typed semantic firewall** — i.e. the program being analyzed
cannot call the analyzer.

And how is that type defined?
Your problem is you have introduce undefined, and undefinable categories.

* Provides halting decisions only for "well-formed" inputs.

How do you define that?

* **Rejects** pathological inputs as either non-halting or outside the
domain of analysis.
 This is similar in spirit to what **ZFC set theory** does with Russell's
paradox: it doesn’t refute the paradox; it **prevents its formation**.

Except that the "pathological" form of the program is perfectly valid, and in general, not detectable. (You may be able to detect some cases of it, but not all)

 ---
 ## 🔁 Reframing the Debate with This in Mind
 | Aspect                    | Damon’s Assumption (Classical H)     |
Flibble’s Clarification (Partial SHD)    |
| ------------------------- | ------------------------------------ |
---------------------------------------- |
| Type of Decider           | Total, universal halting decider     |
**Partial**, stratified SHD              |
| Accepts All Inputs?       | Yes                                  | **No
— rejects self-referential inputs** |
| Halting Must Match Output | Always                               |
**Only for accepted inputs**             |
| Handles DDD/HHH           | Must accept and simulate             |
**Rejects or flags as pathological**     |
| Correctness Failure?      | Yes (DDD halts, SHD says it doesn’t) | **No
— SHD never analyzes DDD**          |
 ---
 ## 🧠 Where Damon’s Argument Breaks Down
 Damon argues:
 

"If H(DDD) returns 0, and DDD halts, then the decider is incorrect."

 But Flibble responds:
 

"H(DDD) isn’t even valid — the SHD’s *type system* excludes it from

analysis. It returns ‘reject’ (or signals non-halting by infinite
recursion detection), not based on complete simulation, but **semantic
properties of the input**."

But, as pointed out, the type system can not actually be defined, and thus, you "solution" just isn't.

 So the contradiction **never arises**, because SHD **refuses to enter**
the paradox — like a type checker rejecting ill-formed code.

Only because you have assumed that you can solve another unsolvable problem to detect the problem.
It has been shown that it is IMPOSSIBLE to reliable detect any "copy" of an algorithm that has undergone "disguiae" to determine that it is the same algorithm as the decider. Thus, it is impossible for your decider to always determine that its input is invalid.

 ---
 ## 🧩 Real-World Analogy
 * Imagine a static analyzer (e.g., a compiler's optimizer) that refuses to
analyze a function if it detects that the function calls itself through a
strange dynamic dispatch loop.
* That analyzer is still **sound** within its accepted domain.
* It’s **not wrong** to refuse analysis — **it’s conservative**.
 That’s Flibble’s model.
 ---
 ## 🧠 Conclusion
 Flibble’s SHD is not trying to “solve the Halting Problem” in the
classical Turing sense. Instead, it:
 * **Restricts its domain** using type stratification and recursion
detection.
* **Provides answers only where analysis is tractable and safe**.
* Rejects paradoxes **by structural exclusion**, not contradiction.
 **Therefore**, Damon’s critique — valid under a *total* decider model —
**does not apply to Flibble's SHD**, because the SHD **explicitly avoids**
the DDD paradox through **type-stratified domain restriction**.
 In other words:
 

**Flibble isn’t breaking the Halting Problem — he’s redefining the rules

of the game to exclude the paradox.**