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Term Rewriting with Logical Constraints

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Frontiers of Combining Systems (FroCoS 2013)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 8152))

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Abstract

In recent works on program analysis, transformations of various programming languages to term rewriting are used. In this setting, constraints appear naturally. Several definitions which combine rewriting with logical constraints, or with separate rules for integer functions, have been proposed. This paper seeks to unify and generalise these proposals.

The research in this paper is supported by the Austrian Science Fund (FWF) international project I963 and the Japan Society for the Promotion of Science.

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References

  1. Community. SMT-LIB, http://www.smtlib.org/

  2. Dershowitz, N.: Orderings for term rewriting systems. Theor. Comput. Sci. 17(3), 279–301 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  3. Falke, S., Kapur, D.: A term rewriting approach to the automated termination analysis of imperative programs. In: Schmidt, R.A. (ed.) CADE 2009. LNCS, vol. 5663, pp. 277–293. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  4. Falke, S., Kapur, D.: Rewriting induction + linear arithmetic = decision procedure. In: Gramlich, B., Miller, D., Sattler, U. (eds.) IJCAR 2012. LNCS (LNAI), vol. 7364, pp. 241–255. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  5. Falke, S., Kapur, D., Sinz, C.: Termination analysis of C programs using compiler intermediate languages. In: Schmidt-Schauß, M. (ed.) Proc. RTA 2011. LIPIcs, vol. 10, pp. 41–50. Dagstuhl (2011)

    Google Scholar 

  6. Falke, S., Kapur, D., Sinz, C.: Termination analysis of imperative programs using bitvector arithmetic. In: Joshi, R., Müller, P., Podelski, A. (eds.) VSTTE 2012. LNCS, vol. 7152, pp. 261–277. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  7. Fuhs, C., Giesl, J., Parting, M., Schneider-Kamp, P., Swiderski, S.: Proving Termination by Dependency Pairs and Inductive Theorem Proving. Journal of Automated Reasoning 47(2), 133–160 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  8. Fuhs, C., Giesl, J., Plücker, M., Schneider-Kamp, P., Falke, S.: Proving termination of integer term rewriting. In: Treinen, R. (ed.) RTA 2009. LNCS, vol. 5595, pp. 32–47. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  9. Furuichi, Y., Nishida, N., Sakai, M., Kusakari, K., Sakabe, T.: Approach to procedural-program verification based on implicit induction of constrained term rewriting systems. IPSJ Trans. Program. 1(2), 100–121 (2008)

    Google Scholar 

  10. Giesl, J., Raffelsieper, M., Schneider-Kamp, P., Swiderski, S., Thiemann, R.: Automated termination proofs for Haskell by term rewriting. ACM Transactions on Programming Languages and Systems 33(2), 7:1–7:39 (2011)

    Google Scholar 

  11. Kirchner, C., Kirchner, H., Rusinowitch, M.: Deduction with symbolic constraints. Revue Française d’Intelligence Artificielle 4(3), 9–52 (1990)

    Google Scholar 

  12. Nakabayashi, N., Nishida, N., Kusakari, K., Sakabe, T., Sakai, M.: Lemma generation method in rewriting induction for constrained term rewriting systems. Computer Software 28(1), 173–189 (2010) (in Japanese)

    Google Scholar 

  13. Otto, C., Brockschmidt, M., von Essen, C., Giesl, J.: Automated termination analysis of java bytecode by term rewriting. In: Lynch, C. (ed.) Proc. RTA 2010. LIPIcs, vol. 6, pp. 259–276. Dagstuhl (2010)

    Google Scholar 

  14. Sakata, T., Nishida, N., Sakabe, T.: On proving termination of constrained term rewrite systems by eliminating edges from dependency graphs. In: Kuchen, H. (ed.) WFLP 2011. LNCS, vol. 6816, pp. 138–155. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  15. Schneider-Kamp, P., Giesl, J., Ströder, T., Serebrenik, A., Thiemann, R.: Automated termination analysis for logic programs with cut. Theory and Practice of Logic Programming 10(4-6), 365–381 (2010)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Innsbruck, Technikerstraße 21a, 6020, Innsbruck, Austria

    Cynthia Kop

  2. Graduate School of Information Science, Nagoya University, Furo-cho, Chikusa-ku, 4648603, Japan

    Naoki Nishida

Authors
  1. Cynthia Kop
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  2. Naoki Nishida
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Editor information

Editors and Affiliations

  1. LORIA, Inria Nancy Grand Est, Université de Lorraine, 615 rue du Jardin Botanique, 54602, Villers-les-Nancy, France

    Pascal Fontaine

  2. LORIA, Inria Nancy Grand Est, 615 rue du Jardin Botanique, 54602, Villers-lès-Nancy, France

    Christophe Ringeissen

  3. School of Computer Science, The University of Manchester, Oxford Rd, Kilburn Building, M13 9PL, Manchester, UK

    Renate A. Schmidt

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Kop, C., Nishida, N. (2013). Term Rewriting with Logical Constraints. In: Fontaine, P., Ringeissen, C., Schmidt, R.A. (eds) Frontiers of Combining Systems. FroCoS 2013. Lecture Notes in Computer Science(), vol 8152. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40885-4_24

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  • DOI: https://doi.org/10.1007/978-3-642-40885-4_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-40884-7

  • Online ISBN: 978-3-642-40885-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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