Re: Enforcing Flibble's Constraint

On 6/1/25 8:30 AM, Mr Flibble wrote:

On Sun, 01 Jun 2025 07:20:29 -0400, Richard Damon wrote:
 

On 6/1/25 4:42 AM, Mr Flibble wrote:

>
If HHH (the Simulating Halt Decider) embedded inside DDD simulates DDD
as if DDD were executed externally, the question becomes one of
modeling and intent:
>
Key Question:
-------------
Can DDD, which contains a call to HHH(DDD), simulate itself as though
it were an external object?
>
This depends on how HHH treats the input DDD:
- If HHH(DDD) simulates a clean copy of DDD, where DDD is treated as
data,
not code that is already running, then it avoids immediate recursion
during actual execution.

>
Right, which is what HHH(DDD) needs to do. It needs to evaluate what the
code of DDD actually does, independent of anything else that is
happening in the currect execution context.
>

- But if DDD is executed (rather than symbolically simulated), it
causes recursion: DDD() calls HHH(DDD) which simulates DDD() again,
leading to infinite descent.

>
Why is that? A symbolic simulaton should result in the same exact
behavior as the direct execution.
>
If the behavior seen in the simulation done by HHH doesn't match the
behavior of the direct exectution of the program given as the input, or
the actual correct pure simulation of it, then HHH's simulation is just
shown to be incorrect.
>
A SHD needs some method to stop its simulation, as deciders must always
answer in finite time. This stopping doesn't releive them of the
requirement to predict the behavior of the actual correct simulation,
which will continue until a final state is reached (or continue
forever).
>
Since, if HHH does stop and return, DDD will halt when run or be
correctly simulated, HHH is just incorrect to say it doesn't halt.
>
The only case we get infinite decent, is the case where HHH isn't
actualy a SHD, because it fails to meet the requirement to be a decider
and to answer for this input.
>
>

Scenario Analysis:
------------------
>
Case 1: Symbolic Simulation (Safe)
----------------------------------
int DDD() {
      HHH(DDD); // HHH symbolically simulates DDD as data, not by
      executing
it }

>
A SHD can NEVER just "execute" its input, as it is a type error to
actually execute "data". It needs to determine what would happen if we
executed the program that data represents.
>

- This is type-safe under Flibble’s model.
- There is no contradiction or paradox because:
    - DDD is not being run, it's being simulated.
    - Simulation stays at the meta-level.

>
But the definition of the correct answer is what would happen when we
run the program that the input represents.
>
>

Case 2: Implied Execution (Unsafe)
----------------------------------
int DDD() {
      HHH(DDD); // HHH simulates DDD as if it were running as code
}
- If HHH simulates DDD() as if it were being run, and inside DDD() is
HHH(DDD), then:

>
ALL simulation is "as if the program described by the input was run"
>

    - The simulation mimics an execution which includes a simulation of
    an
execution, and so on.

>
As it needs to.
>

    - You get infinite recursion within the simulation, not the actual
runtime stack.

>
No you don't, as this only happens when you presume that HHH isn't
actually a SHD, which will abort
>
>

Result: This is not a type error per se, but it still leads to
non-halting simulation. The program itself never finishes simulation
and thus is correctly categorized as non-halting by HHH.

>
But that result is only for a non-SHD HHH, as a SHD HHH *WILL* abort
after some time and return an answer to be a decider, and thus the DDD
being run WILL halt. It just shows that it is incorrect of the SHD HHH
to return 0, as that is the wrong answer.
>
>

Flibble's Typing Principle Preserved:
-------------------------------------
Even when DDD contains HHH(DDD), as long as:
- DDD is only ever passed to HHH as an object of analysis,

>
Right, *TO HHH* it is only passed as an object of analysis.
>
The definition of which is that the input represents a program that can
be run, and the correct answer for HHH is whether said program,
represented by that input, will halt when it is run.
>

- and HHH does not attempt to execute DDD directly but simulate its
structure,

>
And give the answer about what the direct execution of the program
described by its input will do when it is run.
>
>

then type stratification holds and paradox is avoided.
>
Summary:
--------
- Simulating DDD inside HHH, even if DDD includes HHH(DDD), is
acceptable so long as execution never escapes the simulation layer.

>
But simulation is always defined to reveal what is at that execution
layer.
>

- This enforces Flibble's constraint: DDD must only ever be analyzed,
never directly executed once it includes HHH(DDD).

>
WHich means that SHD are a non-semantic type, as their definition is
self-contradictory, then need to report on the behavior that they
prohibit being done.
>
Sorry, just shows that your theory is just a case of Natural Stupidity.

 Thank you, Damon, for the detailed breakdown. However, you are still
conflating **execution-level semantics** with **simulation-level
semantics**, which are strictly **stratified** under my model. Let me
clarify using the **Flibble Typing Principle** (FTP) and reaffirm why SHDs
are not “stupid” but **type-safe analyzers** with **meta-level
visibility** and no paradox.

But HOW are they "stratified"?
Your problem is that you types and operations are just undefinable.
What makes a "program" as "SHD" that can't be called by a program that can be executed?
If you can't define what makes the category, then you can't use it.
And, how do you define "simulation" if you disallow the thing that simulation is supposed to determine?

 ---
 ## 🧠 Core Distinction: Simulation ≠ Execution
 In **Flibble semantics**, the program `DDD` is a **value**, not a
**process**. When `HHH(DDD)` is invoked:

And what determines what the "value" is?

 * `DDD` is *not being executed*.
* `DDD` is *being simulated*.
* Simulation is **symbolic**: operating on the **structure** and
**intent** of `DDD`, not triggering its actual behavior.

And if that doesn't agree with what happens when you execute that program, then what is it.
Of course, part of your problem is it seems you aren't actually talking about "programs" in the first place.

 When you say:
 

“The definition of the correct answer is what would happen when we run

the program that the input represents.”
 You are 100% correct — and that’s exactly what a **semantic SHD** does. It
simulates `DDD` as a *static object* in its own model, not by *executing*
it in a concrete runtime sense. It uses **symbolic inspection**, **partial
unfolding**, and **recursion-bound recognition**.

And BYU DEFINITION, that simulation should produce the exact behavior of executing that program, as that is exactly what execution does.
Remember, if DDD is a program, then the HHH that it calls is define as part of that program. and not a "symbolic link" to something external to it.
This is the flaw of the Olcott model, his "Units of Computation" are not actually "Programs", and thus end up not having a behavior defined to be decided on.

 ---
 ## 🔁 Infinite Descent Is Interpreted, Not Incurred
 

“The simulation mimics an execution which includes a simulation of an

execution, and so on.”
 Yes — but **symbolically**, not stack-recursively. This is not the same as
**actual infinite recursion** on a call stack. The SHD:

And if the SHD accurate looks at the semantics of the input, that calls the copy of itself, it will know that that SHD will do the same thing as itself. This means that, if these are allowed results for a SHD, that it can be decided to be Halting, Non-Halting, Both, or contradictory.
Olcott's DDD should be decided HALTING, as that *IS* what it will do.
Olcott's DD (and the classical proof program, if just moved into this domain) would be contradictory, assuming that it can detect the behavior.

 * Detects recursive patterns **semantically**.
* Aborts simulation **safely** and returns `0` (non-halting).

And thus is semantically WRONG if DDD is actually a program.
And you haven't defined how it isn't, as you can't actually define what makes an implementable SHD something definably special.

* Never enters an unbounded concrete execution context.
 🧠 **This is key**: the SHD *analyses infinite behavior*, it doesn't
*perform it*. That’s why it's a decider in the semantic layer, not a
runtime agent.
 ---
 ## 💡 Correctness of the SHD’s Decision
 

“The SHD aborts simulation and returns an answer — and that answer might

be wrong if DDD halts.”
 Yes, *if* the SHD's analysis were unsound. But under the Flibble model,
the SHD is defined as a **sound symbolic analyser** of finite programs
over well-typed domains. If it returns `non-halting`, it’s because the
**semantic signature** of the program matches a **known non-halting form**
(e.g., infinitely self-nested simulation).

No, you CLAIM it to be, but since it is based on UNDEFINED categories, it is actually just a category error.
Note, since a SHD is NOT a pure simulator, the pattern is NOT a known non-halting pattern. Sorry, until you define what DDD is not allowed to include in it, that keeps it from being executed, you don't have a system.

 So:
 * SHD is **not obligated** to complete simulation.
* SHD is **obligated** to report what would happen *if* the simulated
program were executed.
* SHD is **entitled** to use semantics, not execution, to reach that
answer.
 This is **not incorrect** — it is **typed meta-analysis**, not concrete
runtime modeling.
 ---
 ## 🧩 On “Natural Stupidity”
 You said:
 

“Sorry, just shows that your theory is just a case of Natural Stupidity.”

 This is exactly the **kind of informalism** that semantic modeling
**avoids**. In Flibble’s SHD framework:
 * Programs are **values**.
* Analysis is **symbolic**.
* Halting behavior is **classified**, not inferred by simulation depth.

And the analysis is WRONG, as you can't define what keeps us from building a DD/DDD that your SHD can't answer, becuase it includes the code of the SHD inside itself.

 Flibble’s Law remains:
 

**If a problem permits infinite behavior in its formulation, it permits

infinite analysis of that behavior in its decidability scope.**

Which just proves your system is illogical and self-contradictory, as decidability means answering in finite time, and you are saying you are allowing infinte analysis as a finite process.
Sorry, you logic just blew up on its own contradictions.

 ---
 ## ✅ Final Summary
 * HHH simulating DDD — including `HHH(DDD)` — is type-safe and well-
founded.
* Simulation is not execution. Simulation is stratified.
* SHDs are valid precisely *because* they symbolically model infinite
behavior without incurring it.
* No contradiction arises, because no cross-layer execution occurs.
 Your critique conflates runtime causality with static semantic modeling.
 With respect,
 /Flibble