Re: This function proves that only the outermost HHH examines the execution trace

Op 26.jul.2024 om 22:14 schreef olcott:

On 7/26/2024 2:46 PM, Mike Terry wrote:

On 26/07/2024 16:56, olcott wrote:

This is meant for Mike, Joes and Fred don't have the technical competence to understand it.
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Richard might be able to understand it yet the fact that he is
stuck in rebuttal mode makes any understanding that he may have
utterly useless.
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Mike: It seems that HHH has been a pure function of its inputs
and never has provided data downward to its slaves that corrupts
their halt status decision. They don't even make a halt status
decision thus cannot make a corrupted one.

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Well, the first two claims are literally untrue - outer HHH effectively uses the static mutable data to pass flags to the inner HHH that modify its behaviour.  The Root flag below is derived from the actual static data and causes inner HHH to totally skip its own abort logic!
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You seem to acknowledge this, but claim it does not matter for various reasons, because whatever mistakes you are making, what finally gets printed out is saying the right thing!
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 If HHH gets the correct answer in an impure way then it only
counts that it gets it in an impure way if it is impossible
to get in a pure way.

But the problem is that it gets the incorrect answer.
     if (!Root)
would be better, because then the simulator would indeed simulate an aborting and halting HHH and we would see that it gets the correct answer: halting.
But better is still wrong, because HHH s passing information to its simulated HHH, therefore, effectively it is simulating another HHH than *itself*.
You only prove that HHH cannot possibly simulate *itself* correctly.
In your example HHH is simulating another HHH.
You never proved that it is possible to get it in a pure way.
If it would be possible to do this in a pure way, then it would also possible to make an HHH that runs five cycles as Root and two cycles when not root, which would also get the correct answer.
In fact when such a construction is possible, it would be valid not only to skip a few lines when not Root, but also do completely different thing depending on root.
This al shows that you are completely off the road.