Re: Can Moving the Paradox Code into the SHD Layer Reintroduce the Halting Problem?

On Sun, 2025-05-25 at 09:33 +0000, Mr Flibble wrote:

Can Moving the Paradox Code into the SHD Layer Reintroduce the Halting
Problem?
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Question:
---------
In the neos solution (Flibble's typed SHD model), programs are split into
two layers:
- The SHD layer (meta-level) that analyzes programs.
- The program layer that cannot reference the SHD.
 
What happens if you move the paradoxical construction (e.g., D() = if H(D)
then loop) into the SHD layer itself?
 
Analysis:
---------
 
1. Stratification Prevents Self-Reference (If Enforced)
--------------------------------------------------------
- Typed SHD systems (like Coq, Agda, or neos with layered semantics) can
prevent self-reference by using type stratification.
- In this setup, the SHD layer cannot analyze itself.
- The construction of `D'` within the SHD layer, which calls `H(D')`,
would be semantically ill-typed and rejected.
 
2. If SHDs Can Analyze Themselves, the Paradox Returns
-------------------------------------------------------
- If SHDs are allowed to analyze other SHDs or themselves, you can
reintroduce the diagonal construction:
    D': if H(D') then loop forever; else halt;
- This results in the same contradiction as in the classical halting
problem proof.
 
Conclusion:
-----------
- Moving the paradox into the SHD layer only prevents the contradiction if
the SHD layer is **itself** stratified and prevents self-analysis.
- The paradox is not avoided merely by code relocation—it is avoided by
**semantic restriction**.
- The issue is not *where* the paradox is written, but *what is allowed*
in the system.
 
Final Verdict:
--------------
You can't escape the Halting Problem paradox simply by shifting the code
to a different layer. You must redefine your system's rules to prevent any
form of self-reference in all layers, including the SHD meta-level.

CSCall++ already solved the 'self-reference' problem >20 years ago from the very
beginning of the project: Self-reference is inenevitable.

"... This guideline (of CSCall++ library) has no strong opinion on how this self-ops
 should be handled, yet (it is like divided by zero error). Implement may check the
 self-ops (not generally doable) and return ELOOP. Working around might be needed 
 since the intent mostly assumes the argument is passed by value, nonetheless a
 theoretical bug might be thus hidden..."

Whatever you "SHD" is (assuming you are one genius who can hit the target no one can see),
it suffers the same basic problem as POOH: No one can reproduce what you say, even yourself.