Concerning your update:
So therefore, Fallacious Conclusion: We can determine, for arbitrary Perl code, whether any Perl function has a nullary prototype or not.
It's not clear what that means. Are you talking about a function declaration in the source, a function instance produced by a given parser instance, or the function instances produced by every parser instance.
First, let me concede that the Fallacious Conclusion does follow from Observations 1-4.
You can't concede the validity of an argument. You are making an assertion.
And your assertion is false. The conclusion doesn't follow from the premises (anymore?).
Perl's compile phase does have Turing machine power,
You can't use that premise. That's the conclusion of the argument you're trying to verify.
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