Any language which has any sort of an eval construct “cannot be parsed” statically, because “that which is to be parsed” is determined at runtime. So it really doesn't take computer science to prove that.
Furthermore, let the record show that when you input any Perl program into the Perl compiler, it will be parsed, and you'll either get results or error-messages.
Bottom line is: what's the point here? What are you saying about Perl, and about what (if anything) should be done to address this “issue?” What does this formality actually do for us as practitioners who make our daily bread from this tool?