Advertisement

Homeomorphic Embedding Modulo Combinations of Associativity and Commutativity Axioms

  • María Alpuente
  • Angel Cuenca-Ortega
  • Santiago EscobarEmail author
  • José Meseguer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11408)

Abstract

The Homeomorphic Embedding relation has been amply used for defining termination criteria of symbolic methods for program analysis, transformation, and verification. However, homeomorphic embedding has never been investigated in the context of order-sorted rewrite theories that support symbolic execution methods modulo equational axioms. This paper generalizes the symbolic homeomorphic embedding relation to order–sorted rewrite theories that may contain various combinations of associativity and/or commutativity axioms for different binary operators. We systematically measure the performance of increasingly efficient formulations of the homeomorphic embedding relation modulo associativity and commutativity axioms. From our experimental results, we conclude that our most efficient version indeed pays off in practice.

References

  1. 1.
    Alpuente, M., Ballis, D., Frechina, F., Sapiña, J.: Exploring conditional rewriting logic computations. J. Symbolic Comput. 69, 3–39 (2015)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Alpuente, M., Cuenca-Ortega, A., Escobar, S., Meseguer, J.: Partial evaluation of order-sorted equational programs modulo axioms. In: Hermenegildo, M.V., Lopez-Garcia, P. (eds.) LOPSTR 2016. LNCS, vol. 10184, pp. 3–20. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-63139-4_1CrossRefGoogle Scholar
  3. 3.
    Alpuente, M., Falaschi, M., Vidal, G.: Partial evaluation of functional logic programs. ACM TOPLAS 20(4), 768–844 (1998)CrossRefGoogle Scholar
  4. 4.
    Bouhoula, A., Jouannaud, J.-P., Meseguer, J.: Specification and proof in membership equational logic. Theor. Comput. Sci. 236(1–2), 35–132 (2000)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Clavel, M., et al.: All About Maude - A High-Performance Logical Framework. LNCS, vol. 4350. Springer, Heidelberg (2007).  https://doi.org/10.1007/978-3-540-71999-1CrossRefzbMATHGoogle Scholar
  6. 6.
    Dershowitz, N., Jouannaud, J.-P.: Rewrite systems. In: van Leeuwen, J. (ed.) Handbook of Theoretical Computer Science. Volume B: Formal Models and Semantics, pp. 243–320. Elsevier, Amsterdam (1990)Google Scholar
  7. 7.
    Dershowitz, N.: A note on simplification orderings. Inf. Process. Lett. 9(5), 212–215 (1979)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Eker, S.: Single elementary associative-commutative matching. J. Autom. Reasoning 28(1), 35–51 (2002)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Bürckert, H.J., Herold, A., Schmidt-Schau, M.: On equational theories, unification, and (un)decidability. J. Symbolic Comput. 8(1–2), 3–49 (1989)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Kruskal, J.B.: Well-quasi-ordering, the tree theorem, and Vazsonyi’s conjecture. Trans. Am. Math. Soc. 95, 210–225 (1960)MathSciNetzbMATHGoogle Scholar
  11. 11.
    Leuschel, M.: On the power of homeomorphic embedding for online termination. In: Levi, G. (ed.) SAS 1998. LNCS, vol. 1503, pp. 230–245. Springer, Heidelberg (1998).  https://doi.org/10.1007/3-540-49727-7_14CrossRefGoogle Scholar
  12. 12.
    Leuschel, M.: Homeomorphic embedding for online termination of symbolic methods. In: Mogensen, T.Æ., Schmidt, D.A., Sudborough, I.H. (eds.) The Essence of Computation. LNCS, vol. 2566, pp. 379–403. Springer, Heidelberg (2002).  https://doi.org/10.1007/3-540-36377-7_17CrossRefzbMATHGoogle Scholar
  13. 13.
    Leuschel, M., Martens, B., De Schreye, D.: Controlling generalization and polyvariance in partial deduction of normal logic programs. ACM TOPLAS 20(1), 208–258 (1998)CrossRefGoogle Scholar
  14. 14.
    Middeldorp, A., Gramlich, B.: Simple termination is difficult. Appl. Algebra Eng. Commun. Comput. 6(2), 115–128 (1995)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Sørensen, M.H., Glück, R.: An algorithm of generalization in positive supercompilation. In: Lloyd, J.W. (ed.) Proceedings of International Symposium on Logic Programming, ILPS 1995, pp. 465–479. MIT Press, Cambridge (1995)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • María Alpuente
    • 1
  • Angel Cuenca-Ortega
    • 1
    • 3
  • Santiago Escobar
    • 1
    Email author
  • José Meseguer
    • 2
  1. 1.DSIC-ELP, Universitat Politècnica de ValènciaValenciaSpain
  2. 2.University of Illinois at Urbana-ChampaignUrbanaUSA
  3. 3.Universidad de GuayaquilGuayaquilEcuador

Personalised recommendations