Formal Methods for Automated Program Improvement

Systems supporting the manipulation of non-trivial program code are complex and are at best semi-automatic. However, formal methods, and in partieular theorem proving, are providing a growing foundation of techniques for automatie program development (synthesis, improvement, transformation and verification). In this paper we report on novel research concerning: (1) the exploitation of synthesis proofs for the purposes of automatie program optimization by the transformation of proofs, andj (2) the automatie synthesis of efficient programs from standard equational definitions. A fundamental theme exhibited by our research is that mechanical program construction, whether by direct synthesis or transformation, is tantamount to program verification plus higher-order reasoning. The exploitation of the proofs-as-programs paradigm lends our approach numerous advantages over more traditional approaches to program improvement. For example, we are able to automate the identification of efficient recursive data-types which usua11y correspond to eureka steps in "pure" transformational techniques such as unfoldjfold. Furthermore, a11 transformed, and synthesized, programs are guaranteed correct with respect to their specifications.