A mechanized proof of loop freedom of the (untimed) AODV routing protocol

The Ad hoc On-demand Distance Vector (AODV) routing protocol allows the nodes in a Mobile Ad hoc Network (MANET) or a Wireless Mesh Network (WMN) to know where to forward data packets. Such a protocol is 'loop free' if it never leads to routing decisions that forward packets in circles. This paper describes the mechanization of an existing pen-and-paper proof of loop freedom of AODV in the interactive theorem prover Isabelle/HOL. The mechanization relies on a novel compositional approach for lifting invariants to networks of nodes. We exploit the mechanization to analyse several improvements of AODV and show that Isabelle/HOL can re-establish most proof obligations automatically and identify exactly the steps that are no longer valid.Comment: The Isabelle/HOL source files, and a full proof document, are available in the Archive of Formal Proofs, at http://afp.sourceforge.net/entries/AODV.shtm

A Framework for Verifying Data-Centric Protocols

International audienceData centric languages, such as recursive rule based languages, have been proposed to program distributed applications over networks. They simplify greatly the code, while still admitting efficient distributed execution. We show that they also provide a promising approach to the verification of distributed protocols, thanks to their data centric orientation, which allows us to explicitly handle global structures such as the topology of the network. We consider a framework using an original formalization in the Coq proof assistant of a distributed computation model based on message passing with either synchronous or asynchronous behavior. The declarative rules of the Netlog language for specifying distributed protocols and the virtual machines for evaluating these rules are encoded in Coq as well. We consider as a case study tree protocols, and show how this framework enables us to formally verify them in both the asynchronous and synchronous setting

Mechanizing a Process Algebra for Network Protocols

This paper presents the mechanization of a process algebra for Mobile Ad hoc Networks and Wireless Mesh Networks, and the development of a compositional framework for proving invariant properties. Mechanizing the core process algebra in Isabelle/HOL is relatively standard, but its layered structure necessitates special treatment. The control states of reactive processes, such as nodes in a network, are modelled by terms of the process algebra. We propose a technique based on these terms to streamline proofs of inductive invariance. This is not sufficient, however, to state and prove invariants that relate states across multiple processes (entire networks). To this end, we propose a novel compositional technique for lifting global invariants stated at the level of individual nodes to networks of nodes.Comment: This paper is an extended version of arXiv:1407.3519. The Isabelle/HOL source files, and a full proof document, are available in the Archive of Formal Proofs, at http://afp.sourceforge.net/entries/AWN.shtm

LFTOP: An LF based approach to domain specific reasoning

Specialized vocabulary, notations and inference rules tailored for the description, analysis and reasoning of a domain is very important for the domain. For domain-specific issues researchers focus mainly on the design and implementation of domain-specific languages (DSL) and pay little attention to the reasoning aspects. We believe that domain-specific reasoning is very important to help the proofs of some properties of the domains and should be more concise, more reusable and more believable. It deserves to be investigated in an engineering way. Type theory provides good support for generic reasoning and verification. Many type theorists want to extend uses of type theory to more domains, and believe that the methods, ideas, and technology of type theory can have a beneficial effect for computer assisted reasoning in many domains. Proof assistants based on type theory are well known as effective tools to support reasoning. But these proof assistants have focused primarily on generic notations for representation of problems and are oriented towards helping expert type theorists build proofs efficiently. They are successful in this goal, but they are less suitable for use by non-specialists. In other words, one of the big barriers to limit the use of type theory and proof assistant in domain-specific areas is that it requires significant expertise to use it effectively. We present LFTOP ― a new approach to domain-specific reasoning that is based on a type-theoretic logical framework (LP) but does not require the user to be an expert in type theory. In this approach, users work on a domain-specific interface that is familiar to them. The interface presents a reasoning system of the domain through a user-oriented syntax. A middle layer provides translation between the user syntax and LF， and allows additional support for reasoning (e.g. model checking). Thus, the complexity of the logical framework is hidden but we also retain the benefits of using type theory and its related tools, such as precision and machine-checkable proofs. The approach is being investigated through a number of case studies. In each case study, the relevant domain-specific specification languages and logic are formalized in Plastic. The relevant reasoning system is designed and customized for the users of the corresponding specific domain. The corresponding lemmas are proved in Plastic. We analyze the advantages and shortcomings of this approach, define some new concepts related to the approach, especially discuss issues arising from the translation between the different levels. A prototype implementation is developed. We illustrate the approach through many concrete examples in the prototype implementation. The study of this thesis shows that the approach is feasible and promising, the relevant methods and technologies are useful and effective

Proceedings of the 11th International Conference, TPHOLs’98 Canberra, Australia, September–October 1998. Supplementary Proceedings

Mechanical theorem provers for higher order logics have been successfully applied in many areas including hardware verification and synthesis; verification of security and communications protocols; software verification, transformation and refinement; compiler construction; and concurrency. The higher order logics used to reason about these problems and the underlying theorem prover technology that support them are also active areas of research. The International Conference on Theorem Proving in Higher Order Logics (TPHOLs) brings together people working in these and related areas for the discussion and dissemination of new ideas in the field. TPHOLs'98 continues the conference tradition of having both a completed work and work-in-progress stream. The Papers from the first stream were formally refereed, and published as volume 1479 of LNCS. This, supplementary, proceedings records work accepted under the work-in-progress category, and is intended to document emerging trends in higher-order logic research. Papers in the work-in-progress stream are vetted for relevance and contribution before acceptance. The work-in-progress stream is regarded as an important feature of the conference as it provides a venue for the presentation of ongoing research projects, where researchers invite discussion of preliminary results. Although the TPHOLs conferences have their genesis in meetings of the users of the HOL theorem proving system, each successive year has seen a higher rate of contribution from the other groups with similar goals, particularly the user communities of Coq, Isabelle, Lambda, Lego, NuPrl, and PVS. Since 1993 the proceedings have been published by Springer as volumes in Lecture Notes in Computer Science series. Bibliographic details of these publications can be found at the back of this book; more history of TPHOLs can be found with further information about the 1998 event at http://cs.anu.edu.au/TPHOLs98/.Conference Papers: Integrating TPS with Omega By Christoph Benzmuller and Volker Sorge Some Theorem Proving Aids By Paul E. Black and Phillip J. Windley Verification of the MDG Components Library in HOL By Paul Curzon, Sofiene Tahar, and Otmane Ait Mohamed Simulating Term-Rewriting in LPF and in Display Logic By Jeremy E. Dawson A Prototype Generic Tool Supporting the Embedding of Formal Notations By Andrew M. Gravell and Chris H. Pratten Embedding a Formal Notation: Experiences of Automating the Embedding of Z in the Higher Order Logics of PVS and HOL By Andrew M. Gravell and Chris H. Pratten Building HOL90 Everywhere Easily (Well Almost) By Elsa L. Gunter Program Composition in COQ-UNITY : By Francois Marques Formally Analysed Dynamic Synthesis of Hardware By Kong Woei Susanto and Tom Melham Requirements for a Simple Proof Checker By Geoffrey Watson Integrating HOL and RAISE: a practitioner's approach By Wai Wong and Karl R. P. H. Leung Effective Support for Mutually Recursive Types By Peter V. Homeie