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Rewriting, Inference, and Proof

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Rewriting Logic and Its Applications (WRLA 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6381))

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Abstract

Rewriting is a form of inference, and one that interacts in several ways with other forms of inference such as decision procedures and proof search. We discuss a range of issues at the intersection of rewriting and inference. How can other inference procedures be combined with rewriting? Can rewriting be used to describe inference procedures? What are some of the theoretical challenges and practical applications of combining rewriting and inference? How can rewriters, decision procedures, and their combination be certified? We discuss these problems in the context of our ongoing effort to use PVS as a metatheoretic framework to construct a proof kernel for justifying the claims of theorem provers, rewriters, model checkers, and satisfiability solvers.

This research was supported NSF Grants CSR-EHCS(CPS)-0834810 and CNS-0917375. Sam Owre commented on earlier drafts of the paper, and the participants at the 2010 Workshop on Rewriting Logic and Applications, particularly José Meseguer and Peter Ölveczky, offered valuable feedback and advice.

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References

  1. Abrial, J.-R.: The B-Book: Assigning Programs to Meanings. Cambridge University Press, Cambridge (1996)

    Book  MATH  Google Scholar 

  2. Biere, A.: PicoSAT essentials. JSAT 4(2-4), 75–97 (2008)

    MATH  Google Scholar 

  3. Bledsoe, W.W.: Non-resolution theorem proving. Artificial Intelligence 9, 1–36 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  4. Bledsoe, W.W.: Non-resolution theorem proving. Artificial Intelligence 9, 1–36 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  5. Boyer, R.S., Moore, J.S.: A Computational Logic. Academic Press, New York (1979)

    MATH  Google Scholar 

  6. Boyer, R.S., Moore, J.S.: Metafunctions: Proving them correct and using them efficiently as new proof procedures. In: Boyer, R.S., Moore, J.S. (eds.) The Correctness Problem in Computer Science. Academic Press, London (1981)

    Google Scholar 

  7. Boyer, R.S., Moore, J.S.: A Computational Logic Handbook. Academic Press, New York (1988)

    MATH  Google Scholar 

  8. Harper, R.W., Howe, D.J., Knoblock, T.B., Mendler, N.P., Panangaden, P., Sasaki, J.T., Smith, S.F.: Implementing Mathematics with the Nuprl Proof Development System. Prentice Hall, Englewood Cliffs (1986), Nuprl home page, http://www.cs.cornell.edu/Info/Projects/NuPRL/

    Google Scholar 

  9. Clavel, M., Durán, F., Eker, S., Lincoln, P., Martí-Oliet, N., Meseguer, J., Quesada, J.F.: The Maude system. In: Narendran, P., Rusinowitch, M. (eds.) RTA 1999. LNCS, vol. 1631, pp. 240–243. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  10. Davis, J.C.: A Self-Verifying Theorem Prover. PhD thesis, Computer Science Department, The University of Texas at Austin (December 2009)

    Google Scholar 

  11. Dutertre, B., de Moura, L.: The Yices SMT solver (2006), http://yices.csl.sri.com/

  12. Darbari, A., Fischer, B., Marques-Silva, J.: Industrial-strength certified sat solving through verified sat proof checking. In: Int. Colloq. on Theoretical Aspects of Computing (ICTAC) (2010) (to appear)

    Google Scholar 

  13. de Moura, L., Dutertre, B., Shankar, N.: A tutorial on satisfiability modulo theories. In: Damm, W., Hermanns, H. (eds.) CAV 2007. LNCS, vol. 4590, pp. 20–36. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  14. de Moura, L., Owre, S., Rueß, H., Rushby, J., Shankar, N., Sorea, M., Tiwari, A.: SAL 2. In: Alur, R., Peled, D.A. (eds.) CAV 2004. LNCS, vol. 3114, pp. 496–500. Springer, Heidelberg (2004), SAL home page, http://sal.csl.sri.com/

    Chapter  Google Scholar 

  15. Goguen, J., Kirchner, C., Megrelis, A., Meseguer, J., Winkler, T.: An introduction to OBJ3. In: Kaplan, S., Jouannaud, J.-P. (eds.) CTRS 1987. LNCS, vol. 308, pp. 258–263. Springer, Heidelberg (1988)

    Chapter  Google Scholar 

  16. Gordon, M.J.C., Melham, T.F. (eds.): Introduction to HOL: A Theorem Proving Environment for Higher-Order Logic. Cambridge University Press, Cambridge (1993), HOL home page, http://www.cl.cam.ac.uk/Research/HVG/HOL/

    MATH  Google Scholar 

  17. Goguen, J.A., Winkler, T.: Introducing OBJ. Technical Report SRI-CSL-88-9, Computer Science Laboratory, SRI International, Menlo Park, CA (August 1988)

    Google Scholar 

  18. Huisman, M., Jacobs, B.: Java program verfication via a hoare logic with abrupt termination. In: Maibaum, T. (ed.) FASE 2000. LNCS, vol. 1783, pp. 284–303. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  19. Hoare, C.A.R.: An axiomatic basis for computer programming. ACM Comm. 12(10), 576–583 (1969)

    Article  MATH  Google Scholar 

  20. Kaufmann, M., Manolios, P., Strother Moore, J.: Computer-Aided Reasoning: An Approach. Advances in Formal Methods, vol. 3. Kluwer, Dordrecht (2000)

    Google Scholar 

  21. Kapur, D., Zhang, H.: RRL: A rewrite rule laboratory. In: Lusk, E., Overbeek, R. (eds.) CADE 1988. LNCS, vol. 310, pp. 768–769. Springer, Heidelberg (1988)

    Chapter  Google Scholar 

  22. Mehlhorn, K.: The reliable algorithmic software challenge RASC. In: Jansen, K., Margraf, M., Mastrolli, M., Rolim, J.D.P. (eds.) WEA 2003. LNCS, vol. 2647, p. 222. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  23. Miller, D.: An extension to ML to handle bound variables in data structures: Preliminary report. In: Informal Proceedings of the Logical Frameworks BRA Workshop, Nice, France, Available as UPenn CIS technical report MS-CIS-90-59 (June 1990)

    Google Scholar 

  24. Muñoz, C.: PBS: Support for the B-method in PVS. Technical Report SRI-CSL-99-1, Computer Science Laboratory, SRI International, Menlo Park, CA (February 1999)

    Google Scholar 

  25. Owre, S., Rushby, J., Shankar, N., von Henke, F.: Formal verification for fault-tolerant architectures: Prolegomena to the design of PVS. IEEE Transactions on Software Engineering 21(2), 107–125 (1995), PVS home page, http://pvs.csl.sri.com

    Article  Google Scholar 

  26. Paulson, L.C.: Verifying the unification algorithm in LCF. Technical Report 50, University of Cambridge Computer Laboratory (1984)

    Google Scholar 

  27. Paulson, L.C. (ed.): Isabelle: A Generic Theorem Prover. LNCS, vol. 828. Springer, Heidelberg (1994), Isabelle home page, http://www.cl.cam.ac.uk/research/hvg/Isabelle/

    MATH  Google Scholar 

  28. Pnueli, A., Siegel, M., Singerman, E.: Translation validation. In: Steffen, B. (ed.) TACAS 1998. LNCS, vol. 1384, pp. 151–166. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  29. Rosu, G., Eker, S., Lincoln, P., Meseguer, J.: Certifying and synthesizing membership equational proofs. In: Araki, K., Gnesi, S., Mandrioli, D. (eds.) FME 2003. LNCS, vol. 2805, pp. 359–380. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  30. Rueß, H., Shankar, N.: Deconstructing Shostak. In: 16th Annual IEEE Symposium on Logic in Computer Science, Boston, MA, pp. 19–28. IEEE Computer Society, Los Alamitos (July 2001)

    Chapter  Google Scholar 

  31. Stringer-Calvert, D.W.J.: Mechanical Verification of Compiler Correctness. PhD thesis, University of York, Department of Computer Science, York, England (March 1998), http://www.csl.sri.com/~dave_sc/papers/thesis.html

  32. Shankar, N.: Inference systems for logical algorithms. In: Ramanujam, R., Sen, S. (eds.) FSTTCS 2005. LNCS, vol. 3821, pp. 60–78. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  33. Shankar, N.: Trust and automation in verification tools. In: Cha, S.(S.), Choi, J.-Y., Kim, M., Lee, I., Viswanathan, M. (eds.) ATVA 2008. LNCS, vol. 5311, pp. 4–17. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  34. Shankar, N.: Automated deduction for verification. ACM Comput. Surv. 41(4), 20 (2009)

    Article  Google Scholar 

  35. Shankar, N.: Fixpoint and search in pvs. In: Müller, P. (ed.) LASER 2010. LNCS, vol. 6029, pp. 140–161. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  36. Shoenfield, J.R.: Mathematical Logic. Addison-Wesley, Reading (1967)

    MATH  Google Scholar 

  37. Shostak, R.E.: Deciding combinations of theories. Journal of the ACM 31(1), 1–12 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  38. Shankar, N., Owre, S., Rushby, J.M., Stringer-Calvert, D.W.J.: PVS Prover Guide. Computer Science Laboratory, SRI International, Menlo Park, CA (September 1999)

    Google Scholar 

  39. Shankar, N., Rueß, H.: Combining Shostak Theories. In: Tison, S. (ed.) RTA 2002. LNCS, vol. 2378, pp. 1–18. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  40. The Coq Development Team. The Coq proof assistant reference manual version 8.2. Technical report, INRIA (February 2009)

    Google Scholar 

  41. Zhang, L., Malik, S.: Validating SAT solvers using an independent resolution-based checker: Practical implementations and other applications. In: DATE, pp. 10880–10885. IEEE Computer Society, Los Alamitos (2003)

    Google Scholar 

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Authors and Affiliations

  1. Computer Science Laboratory, SRI International, Menlo Park, CA, 94025, USA

    Natarajan Shankar

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  1. Natarajan Shankar
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Editors and Affiliations

  1. Department of Informatics, University of Oslo, Gaustadalléen 23, 0373, Oslo, Norway

    Peter Csaba Ölveczky

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Shankar, N. (2010). Rewriting, Inference, and Proof. In: Ölveczky, P.C. (eds) Rewriting Logic and Its Applications. WRLA 2010. Lecture Notes in Computer Science, vol 6381. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16310-4_1

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  • DOI: https://doi.org/10.1007/978-3-642-16310-4_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-16309-8

  • Online ISBN: 978-3-642-16310-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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