Theorem Proving for Verification: The Early Days

Abstract

Summary form only given. Since Turing, computer scientists have understood that the question "does this program satisfy its specifications?" could be reduced to the question "are these formulas theorems?" But the theorem proving technology of the 50s and 60s was inadequate for the task. In 1971, here in Edinburgh, Boyer and I started building the first general-purpose theorem prover designed for a computational logic. This project continues today, with Matt Kaufmann as a partner; the current version of the theorem prover is ACL2 (A Computational Logic for Applicative Common Lisp). In this talk I'll give a highly personal view of the four decade long "Boyer-Moore Project," including our mechanization of inductive proof, support for recursive definitions, rewriting with previously proved lemmas, integration of decision procedures, efficient representation of logical constants, fast execution, and other proof techniques. Along the way we'll see several interesting side roads: the founding of the Edinburgh school of logic programming, a structureshared text editor that played a role in the creation of Word, and perhaps most surprisingly, the use of our "Lisp theorem prover" to formalize and prove theorems about commercial microprocessors and virtual machines via deep embeddings, including parts of processors by AMD, Centaur, IBM, Motorola, Rockwell-Collins, Sun, and others. The entire project helps shed light on the dichotomy between general-purpose theorem pro vers and special-purpose analysis tools.