Perhaps a clearer distinction is the following:
It is easy to determine whether a defined sub has a nullary prototype.
Indeed, your runtime_nullary sub determines just that. And "defined" here is important, as we will see below. On the other hand,
It is undecidable to determine whether an arbitrary computation (say, the BEGIN phase of a perl script) results in defining a sub with nullary prototype.
This is demonstrated by your previous undecidability posts. I agree with ikegami in terms of how things are worded. Your "fallacious conclusion" is not fallacious. Its wording makes it sound like the hard part is: given a code ref, determine its prototype. But you can always determine the prototype of a Perl sub. What you can't do is determine whether an arbitrary piece of code will result in defining a nullary prototyped sub. Update: it is this "given arbitrary code" part that I think is not formally exposited in your post.

The thing about "reaching" the determining code is a red herring. It's just part of one (bad?) method of trying to determine the outcome of an arbitrary computation -- by running the computation and then (when it is done) looking for its result. Of course we know that can't work, but it's not saying much more than "you can't wait for a computation to finish, when you're not sure whether the computation will finish".

You could say that this is directly analogous to the halting problem itself. It is easy to determine whether a Turing Machine that has already halted has halted with 0 or 1 on its output tape -- just look at the tape! However, it is undecidable to determine, given a Turing machine, whether it will eventually halt with 0 or 1.

In our context, the sub's prototype is just a place to store the outcome of an arbitrary Turing Machine computation. The problem of reading or interpreting the computation's outcome (determining the sub's prototype) is not undecidable, it's the problem of determining what that outcome of an arbitrary computation will be.

I hope this helps making the distinction clearer & more precise.

blokhead

In reply to Re: Perl is not Dynamically Parseable by blokhead
in thread Perl is not Dynamically Parseable by Jeffrey Kegler

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