Said knobunc:

That would work if there was a reference to the function involved. The original case had a simple subroutine definition.

OK, you're wrong, and you obviously didn't try it, or even look in the manual.

Says perlfunc:defined:

You may also use defined(&func) to check whether subroutine &func has ever been defined.

With all that code you wrote to show off, I would have thought you could also write the following three-line test to avoid embarassing yourself:

    sub a1 {} 
    print "a1 is defined\n" if defined &a1;
    print "a2 is defined\n" if defined &a2;
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