Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable

On 07/05/2025 22:59, olcott wrote:

On 5/7/2025 4:52 PM, Richard Heathfield wrote:

On 07/05/2025 22:46, olcott wrote:

On 5/7/2025 4:30 PM, Richard Heathfield wrote:

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<snip>
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If the simulation can't reach code that the directly executed program reaches, then it's not a faithful simulation.
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If is was true that it is not a faithful simulation
then you would be able to show exactly what sequence
of instructions would be a faithful simulation.

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If it were false, you'd be able to chop out the unreachable code without any adverse effects. Can you?
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<snip>
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 I already know the answer.

Then you already know why your simulation code fails to simulate correctly... but of course you /don't/ know, so I'll explain.
Let us postulate a program that contains a function as follows:
void invisible(void)
{
   secret();
}
When directly executed, the program calls invisible(), but when simulated, the invisible() call is unreachable.
secret() could do nothing, or it might launch a for(;;); or it could catch SIGABRT with a returning handler and call abort(). The simulator has no way of knowing which is which.
Therefore a termination analyser that attempts to analyse this program but cannot reach all the code is doomed to be unable to run a correct simulation and is necessarily reduced to guesswork.
--
Richard Heathfield
Email: rjh at cpax dot org dot uk
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