you dont have to "get around Godel's Incompleteness Theorem". (from wikipedia:): "Any effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and complete. In particular, for any consistent, effectively generated formal theory that proves certain basic arithmetic truths, there is an arithmetical statement that is true, but not provable in the theory". it says "a statement" not "every statement". So, you can make formal theories where a lot of statements are provable, including a large class of computer programs.