Sure, the generation of a parse tree is unambiguous, but the traversal order of that tree is not statically determinable. I'm not even saying there is anything

Sure, the generation of a parse tree is unambiguous, but the traversal order of that tree is not statically determinable. I'm not even saying there is anything wrong with this, I'm just arguing that the way you have described the "compilation" process in Perl is basically a textbook description of an interpreter that relies on some runtime information in order to execute the program.