Algebraic Proof Assistants in HOL

We explore several ways to formalize the algebraic laws of CSP-like languages in HOL. The intent of the paper is to show how HOL can be tailored to acting as a proof assistant. The emphasis is therefore on the consequences of various choices to be made during the formalization for writing tactics. We end up with a proof assistant that allows a user to make steps of the granularity of an algebraic law. It is not the purpose of this paper to show in HOL that the algebraic laws of some CSP-like language are sound; the purpose is to show how HOL can be used to apply the algebraic laws and act as a rewrite system. 0 Introduction We report on our attempts to tailor the automated proof checker HOL GM93] to the veriication of proofs in CSP-like process algebras. Although it is technically feasible to prove the correctness of processes operating in parallel, this is often a long and tedious, and therefore extremely error-prone task. Reliable tools that can assist in proving concurrent programs correct are indispensable, if we ever want the programming practitioners to prove their programs correct. The goal of making program correctness proofs common practice in industry will fail miserably, if we cannot supply adequate tool support. Toy problems and their solutions simply do not scale to problems of industrial size. For these reasons, we aim at the mechanization of reasoning about concurrent programs, CSP-like programs in particular. One can think of two approaches to achieve this goal: build something from scratch, or tailor some existing proof checker/formula manipulator to one's needs. Since the feasibility of the latter 1