Proof-Checking, Theorem-Proving, and Program Verification

This article consists of three parts: a tutorial introduction to a computer program that proves theorems by induction; a brief description of recent applications of that theorem-prover; and a discussion of several nontechnical aspects of the problem of building automatic theorem-provers. The theorem-prover described has proved theorems such as the uniqueness of prime factorizations, Fermat’s theorem, and the recursive unsolvability of the halting problem. The article is addressed to those who know nothing about automatic theorem-proving but would like a glimpse of one such system. This article definitely does not provide a balanced view of all automatic theorem1 proving, the literature of which is already rather large and technical. Good places to start on the technical literature are [Loveland 78] and [Bledsoe 77]. Nor do we describe the details of our theorem-proving system, but they can be found in the books, articles, and technical reports that we reference. In our opinion, progress in automatic theorem-proving is largely a function of the mathematical ability of those attempting to build such systems. We encourage good mathematicians to work in the field. The work reported here was supported in part by NSF Grant MCS-8202943 and ONR Contract N00014-81K-0634.