Skip to main content
SpringerLink
Log in
Book cover

Scalable Techniques for Formal Verification pp 65–79Cite as

Operational Semantics and Assertional Reasoning

  • Chapter
  • First Online:

  • 708 Accesses

Abstract

We present a method to convert (a) an operational semantics for a given machine language, and (b) an off-the-shelf theorem prover, into a high assurance verification condition generator (VCG). Given a program annotated with assertions at cutpoints, we show how to use the theorem prover directly on the operational semantics to generate verification conditions analogous to those produced by a custom-built VCG. Thus, no separate VCG is necessary, and the theorem prover can be employed both to generate and to discharge the verification conditions. The method handles both partial and total correctness. It is also compositional in that the correctness of a subroutine needs to be proved once, rather than at each call site.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   119.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Notes

  1. 1.

    Although we describe all proofs in this book in terms of the ACL2 logic, most of our techniques are portable to other theorem provers. In particular, the derivation of assertional reasoning methods for operational semantics has been formalized by John Matthews in the Isabelle theorem prover.

  2. 2.

    Functions preand posthere take an extra argumentkwhile our generic proofs used unary functions. This is admissible since one can functionally instantiate constraints with concrete functions having extra arguments, as long as such arguments do not affect the parameters (in this cases) involved in the constraints [19].

References

  1. A. W. Appel. Foundational Proof-Carrying Code. InProceedings of the 16th IEEE International Symposium on Logic in Computer Science (LICS 2001), pages 247–258, Washington, DC, 2001. IEEE Computer Society Press.

    Google Scholar 

  2. T. Ball and S. K. Rajamani. Automatically Validating Temporal Safety Properties of Interfaces. In M. B. Dwyer, editor,Proceedings of the 8th International SPIN Workshop on Model Checking of Software, volume 2057 ofLNCS, pages 103–122, Toronta, ON, 2001. Springer-Verlag.

    Google Scholar 

  3. R. S. Boyer, D. Goldshlag, M. Kaufmann, and J. S. Moore. Functional Instantiation in First Order Logic. In V. Lifschitz, editor,Artificial Intelligence and Mathematical Theory of Computation: Papers in Honor of John McCarthy, pages 7–26. Academic Press, 1991.

    Google Scholar 

  4. C. Colby, P. Lee, G. C. Necula, F. Blau, M. Plesko, and K. Cline. A Certifying Compiler for Java. InACM SIGPLAN 2000 Conference on Programming Language Design and Implementation (PLDI 2000), pages 95–107. ACM Press, 2000.

    Google Scholar 

  5. D. L. Detlefs, K. R. M. Leino, G. Nelson, and J. B. Saxe. Extended Static Checking for Java. Technical Report 159, Compaq Systems Research Center, December 1998.

    Google Scholar 

  6. E. W. Dijkstra. Guarded Commands, Non-determinacy and a Calculus for Derivation of Programs.Language Hierarchies and Interfaces, pages 111–124, 1975.

    Google Scholar 

  7. C. Flanagan and J. B. Saxe. Avoiding Exponential Explosion: Generating Compact Verification Conditions. InProceedings of the 28th ACM SIGPLAN-SIGACT symposium on Principles of Programming Languages (POPL 2001), pages 193–205, London, UK, 2001. ACM Press.

    Google Scholar 

  8. R. Floyd. Assigning Meanings to Programs. InMathematical Aspects of Computer Science, Proceedings of Symposia in Applied Mathematcs, volume XIX, pages 19–32, Providence, Rhode Island, 1967. American Mathematical Society.

    Google Scholar 

  9. P. Y. Gloess. Imperative Program Verification in PVS. Technical Report, École Nationale Supérieure Électronique, Informatique et Radiocommunications de bordeaux, 1999. See URL http://-dept-info.labri.-u.bordeaux.fr/-imperative/-index.html.

    Google Scholar 

  10. H. H. Goldstein and J. von Neumann. Planning and Coding Problems for an Electronic Computing Instrument. InJohn von Neumann, Collected Works, Volume V. Pergamon Press, Oxford, 1961.

    Google Scholar 

  11. D. Greve, M. Wilding, and D. Hardin. High-Speed, Analyzable Simulators. In M. Kaufmann, P. Manolios, and J. S. Moore, editors,Computer-Aided Reasoning: ACL2 Case Studies, pages 89–106, Boston, MA, June 2000. Kluwer Academic Publishers.

    Google Scholar 

  12. D. Hardin, E. W. Smith, and W. D. Young. A Robust Machine Code Proof Framework for Highly Secure Applications. In P. Manolios and M. Wilding, editors,Proceedings of the 6th International Workshop on the ACL2 Theorem Prover and Its Applications (ACL2 2006), pages 11–20, Seattle, WA, July 2006. ACM.

    Google Scholar 

  13. C. A. R. Hoare. An Axiomatic Basis for Computer Programming.Communications of the ACM, 12(10):576–583, 1969.

    Article  MATH  Google Scholar 

  14. P. Homeier and D. Martin. A Mechanically Verified Verification Condition Generator.The Computer Journal, 38(2):131–141, July 1995.

    Article  Google Scholar 

  15. J. C. King.A Program Verifier. PhD thesis, Carnegie-Melon University, 1969.

    Google Scholar 

  16. P. Manolios and J. S. Moore. Partial Functions in ACL2.Journal of Automated Reasoning, 31(2):107–127, 2003.

    Article  MathSciNet  MATH  Google Scholar 

  17. J. Matthews, J. S. Moore, S. Ray, and D. Vroon. Verification Condition Generation via Theorem Proving. In M. Hermann and A. Voronkov, editors,Proceedings of the 13th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning (LPAR 2006), volume 4246 ofLNCS, pages 362–376, Phnom Penh, Cambodia, November 2006. Springer.

    Google Scholar 

  18. J. Matthews and D. Vroon. Partial Clock Functions in ACL2. In M. Kaufmann and J. S. Moore, editors,5th International Workshop on the ACL2 Theorem Prover and Its Applications (ACL2 2004), Austin, TX, November 2004.

    Google Scholar 

  19. F. Mehta and T. Nipkow. Proving Pointer Programs in Higher Order Logic. In F. Baader, editor,Proceedings of the 19th International Conference on Automated Deduction (CADE 2003), volume 2741 ofLNAI, pages 121–135, Miami, FL, 2003. Springer-Verlag.

    Google Scholar 

  20. J. S. Moore. Inductive Assertions and Operational Semantics. In D. Geist, editor,Proceedings of the 12th International Conference on Correct Hardware Design and Verification Methods, volume 2860 ofLNCS, pages 289–303, L‘Aquila, Italy, October 2003. Springer-Verlag.

    Google Scholar 

  21. J. S. Moore. Proving Theorems About Java and the JVM with ACL2. In M. Broy and M. Pizka, editors,Models, Algebras, and Logic of Engineering Software, pages 227–290. IOS Press, 2003.

    Google Scholar 

  22. G. Necula.Compiling with Proofs. PhD thesis, Carnegie-Melon University, September 1998.

    Google Scholar 

  23. G. C. Necula. Proof-Carrying Code. InProceedings of the 24th ACM SIGPLAN SIGACT Conference on Principles of Programming Languages (POPL 1997), pages 106–119, Paris, France, 1997. ACM Press.

    Google Scholar 

  24. M. Norrish.C Formalised in HOL. PhD thesis, University of Cambridge, 1998.

    Google Scholar 

  25. B. Schneier.Applied Cryptography (2nd ed.): Protocols, Algorithms, and Source Code in C. John Wiley & Sons, Inc., 1995.

    Google Scholar 

  26. K. Slind and J. Hurd. Applications of Polytypism in Theorem Proving. In D. Basin and B. Wolff, editors,Proceedings of the 16th International Conference on Theorem Proving in Higher Order Logics (TPHOLs 2003), volume 2978 ofLNCS, pages 103–119, Rom, Italy, 2003. Springer-Verlag.

    Chapter  Google Scholar 

  27. D. Toma and D. Borrione. Formal verification of a SHA-1 Circuit Core Using ACL2. In J. Hurd and T. Melham, editors,Proceedings of the 18th International Conference on Theorem Proving in Higher-Order Logics (TPHOLS 2005), volume 3603 ofLNCS, pages 326–341, Oxford, UK, 2005. Springer-Verlag.

    Chapter  Google Scholar 

  28. A. M. Turing. Checking a Large Routine. InReport of a Conference on High Speed Automatic Calculating Machine, pages 67–69, University Mathematical Laboratory, Cambridge, England, June 1949.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Sciences, University of Texas, Austin, University Station 1 MS C0500, 78712-0233, Austin, Texas, USA

    Dr. Sandip Ray

Authors
  1. Dr. Sandip Ray
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sandip Ray .

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer Science+Business Media, LLC

About this chapter

Cite this chapter

Ray, S. (2010). Operational Semantics and Assertional Reasoning. In: Scalable Techniques for Formal Verification. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-5998-0_5

Download citation

  • DOI: https://doi.org/10.1007/978-1-4419-5998-0_5

  • Published:

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4419-5997-3

  • Online ISBN: 978-1-4419-5998-0

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation