I've been using several Python libraries for working with PDFs. At least one of them allows you to walk the AST. (will look up in a bit and edit this comment)
I've been using pypdf for working with PDFs in Python. My uses are pretty humble. I create Jupyter notebooks for managing sheet music that I receive in PDF format, allowing me to do things like break up a book of tunes into individual files, and so forth. This in turns makes it easier to pull up individual tunes on my tablet during a performance. But it looks like you can treat the PDF as a tree structure. I've used that feature for writing some recursive functions.