Automated Theorem Proving In Software Engineering

Growing demands for the quality, safety, and security of software can only be satisfied by the rigorous application of formal methods during software design. This book methodically investigates the potential of first-order logic automated theorem provers for applications in software engineering. Illustrated by complete case studies on protocol verification, verification of security protocols, and logic-based software reuse, this book provides techniques for assessing the prover's capabilities and for selecting and developing an appropriate interface architecture.

1. BASIC CONCEPTS OF INTERACTIVE THEOREM PROVING Interactive Theorem Proving ultimately aims at the construction of powerful reasoning tools that let us (computer scientists) prove things we cannot prove without the tools, and the tools cannot prove without us. Interaction typi cally is needed, for example, to direct and control the reasoning, to speculate or generalize strategic lemmas, and sometimes simply because the conjec ture to be proved does not hold. In software verification, for example, correct versions of specifications and programs typically are obtained only after a number of failed proof attempts and subsequent error corrections. Different interactive theorem provers may actually look quite different: They may support different logics (first-or higher-order, logics of programs, type theory etc.), may be generic or special-purpose tools, or may be tar geted to different applications. Nevertheless, they share common concepts and paradigms (e.g. architectural design, tactics, tactical reasoning etc.). The aim of this chapter is to describe the common concepts, design principles, and basic requirements of interactive theorem provers, and to explore the band width of variations. Having a 'person in the loop', strongly influences the design of the proof tool: proofs must remain comprehensible, - proof rules must be high-level and human-oriented, - persistent proof presentation and visualization becomes very important.

Abstract: "The thesis describes the production of a large prototype proof system for Z, and a tactic language in which the proof tactics used in a wide range of systems (including the system described here) can be discussed. The details of the construction of the tool -- using the W logic for Z, and implemented in 20BJ -- are presented, along with an account of some of the proof tactics which enable W to be applied to typical proofs in Z.A case study gives examples of such proofs. Special attention is paid to soundness concerns, since it is considerably easier to check that a program such as this one produces sound proofs, than to check that each of the impenetrable proofs which it creates is indeed sound. As the first such encoding of W, this helped to find bugs in the published presentations of W, and to demonstrate that W makes proof in Z tractable. The second part of the thesis presents a tactic language, with a formal semantics (independent of any particular tool) and a set of rules for reasoning about tactics written in this language. A small set of these rules is shown to be complete for the finite (non-recursive) part of the language. Some case studies are included, as are some ideas on how this tactic language can give rise to lightweight implementations of theorem proving tools. The tool described in some detail is another theorem-prover for Z, this time based on LittleZ."

There are many kinds of books on formal logic. Some have philosophers as their intended audience, some mathematicians, some computer scientists. Although there is a common core to all such books they will be very dif ferent in emphasis, methods, and even appearance. This book is intended for computer scientists. But even this is not precise. Within computer sci ence formal logic turns up in a number of areas, from program verification to logic programming to artificial intelligence. This book is intended for computer scientists interested in automated theorem proving in classical logic. To be more precise yet, it is essentially a theoretical treatment, not a how-to book, although how-to issues are not neglected. This does not mean, of course, that the book will be of no interest to philosophers or mathematicians. It does contain a thorough presentation of formal logic and many proof techniques, and as such it contains all the material one would expect to find in a course in formal logic covering completeness but not incompleteness issues. The first item to be addressed is, what are we talking about and why are we interested in it. We are primarily talking about truth as used in mathematical discourse, and our interest in it is, or should be, self-evident. Truth is a semantic concept, so we begin with models and their properties. These are used to define our subject.

An overview of ATP techniques for the non-specialist, it discusses all the main approaches to proof: resolution, natural deduction, sequentzen, and the connection calculi. Also discusses strategies for their application and three major implemented systems. Looks in detail at the new field of ``inductionless induction'' and brings out its relationship to the classical approach to proof by induction.

This text and software package introduces readers to automated theorem proving, while providing two approaches implemented as easy-to-use programs. These are semantic-tree theorem proving and resolution-refutation theorem proving. The early chapters introduce first-order predicate calculus, well-formed formulae, and their transformation to clauses. Then the author goes on to show how the two methods work and provides numerous examples for readers to try their hand at theorem-proving experiments. Each chapter comes with exercises designed to familiarise the readers with the ideas and with the software, and answers to many of the problems.

As computers increasingly control the systems and services we depend upon within our daily lives like transport, communications, and the media, ensuring these systems function correctly is of utmost importance. This book consists of twelve chapters and one historical account that were presented at a workshop in London in 2015, marking the 25th anniversary of the European ESPRIT Basic Research project ‘ProCoS’ (Provably Correct Systems). The ProCoS I and II projects pioneered and accelerated the automation of verification techniques, resulting in a wide range of applications within many trades and sectors such as aerospace, electronics, communications, and retail. The following topics are covered: An historical account of the ProCoS project Hybrid Systems Correctness of Concurrent Algorithms Interfaces and Linking Automatic Verification Run-time Assertions Checking Formal and Semi-Formal Methods Provably Correct Systems provides researchers, designers and engineers with a complete overview of the ProCoS initiative, past and present, and explores current developments and perspectives within the field.

This text and software package introduces readers to automated theorem proving, while providing two approaches implemented as easy-to-use programs. These are semantic-tree theorem proving and resolution-refutation theorem proving. The early chapters introduce first-order predicate calculus, well-formed formulae, and their transformation to clauses. Then the author goes on to show how the two methods work and provides numerous examples for readers to try their hand at theorem-proving experiments. Each chapter comes with exercises designed to familiarise the readers with the ideas and with the software, and answers to many of the problems.