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Functional Equations in Shostak Theories

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Computer Science – Theory and Applications (CSR 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3967))

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Abstract

We consider Shostak theories introduced in [1]. The class of Shostak theories consists of decidable first order equality theories, specified by two algorithms: a canoniser and a solver. A canoniser calculates the normal form of a term. A solver tests whether an equality can be reduced to an equivalent substitution and constructs this substitution when it exists. The examples of Shostak theories are linear arithmetics of integers and rational numbers, theories of lists, arrays, ets.[2].

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References

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

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  2. Manna, Z., Zarba, C.G.: Combining decision procedures. In: Aichernig, B.K., Maibaum, T. (eds.) Formal Methods at the Crossroads. From Panacea to Foundational Support. LNCS, vol. 2757, pp. 381–422. Springer, Heidelberg (2003)

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  3. Krstić, S., Conchon, S.: Canonization for disjoint unions of theories. In: Baader, F. (ed.) CADE 2003. LNCS, vol. 2741, pp. 197–211. Springer, Heidelberg (2003)

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  4. Ganzinger, H.: Shostak light. In: Voronkov, A. (ed.) CADE 2002. LNCS, vol. 2392, pp. 332–346. Springer, Heidelberg (2002)

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  5. Rueß, H., Shankar, N.: Deconstructing Shostak. In: Proceedings of the 16th Annual IEEE Symposium on Logic in Computer Science. Boston, Massachusetts, USA, pp. 19–28. IEEE Computer Society, Los Alamitos (2001)

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Author information

Authors and Affiliations

  1. Moscow State University, Russia

    Sergey P. Shlepakov

Authors
  1. Sergey P. Shlepakov
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Editors and Affiliations

  1. IRMAR, Université de Rennes, Campus de Beaulieu, 35042, Rennes Cedex, France

    Dima Grigoriev

  2. Intel Corporation, JF1-13, 2111 NE 25th Avenue, 97124, Hillsboro, OR, USA

    John Harrison

  3. Steklov Institute of Mathematics at St. Petersburg, 27 Fontanka, St., 191023, Petersburg, Russia

    Edward A. Hirsch

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© 2006 Springer-Verlag Berlin Heidelberg

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Shlepakov, S.P. (2006). Functional Equations in Shostak Theories. In: Grigoriev, D., Harrison, J., Hirsch, E.A. (eds) Computer Science – Theory and Applications. CSR 2006. Lecture Notes in Computer Science, vol 3967. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11753728_35

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  • DOI: https://doi.org/10.1007/11753728_35

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-34166-6

  • Online ISBN: 978-3-540-34168-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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