Automated Termination Proofs Using Walther Recursion

In this thesis, I present an improved method for automatic proofs of termination through a syntactic measurement of sizing that was first developed by Walther. We discuss formal requirements for proving termination using this method and how it can be generalized to other languages. We present a simple set-theoretic language as an example which can be used to write basic Lisp-like programs. Using this language, we define strict syntactic requirements on how to prove termination and then produce inference rules that indicate how these requirements can be established. Several sample algorithms whose termination proofs are sketched using the inference rules are presented in order to show the power of the approach. Last, we discuss the issue of soundness of these rules, as well as issues of the decidability and efficiency of implementing such a system. Thesis Supervisor: David A. McAllester Title: Associate Professor Acknowledgments I would especially like to thank David McAllester, my thesis advisor, for all his help and more importantly, patience and understanding. None of this work would have been possible without his guidance. Special thanks also go to Carl Witty, Robert Givan, and Luis Rodriguez, whose showed me some of the more unusual aspects of graduate life. This work is dedicated to my sister, Cynara, who is undergoing trying times right now. I hope that everything turns out for the better. I may not be the best friend that you need right now but I still love you very much. I am also forever indebted to my parents for everything they have done for me all these years. Thanks, Mom and Dad. This is for you. Finally, a thousand thanks go to all my friends here who never gave up on me despite all the time I spent doing thesis instead of with you guys. James, maybe I still have time to pick up ultimate. Henry, once this damned thing is finished, we can play tennis. Howard, thanks for trying to make me a "Superstar". It didn't quite work but you did the best with what you had. Yong, I'm sorry I didn't have quite what it takes you are the "Chosen One" in more ways than one. To everyone that can't be named, or this thesis would double in size, you all have made these five years the best of my life. I'll always remember the great times there were.