Ensuring Correctness of Model Transformations While Remaining Decidable

  • Jon Haël Brenas
  • Rachid Echahed
  • Martin Strecker
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9965)

Abstract

This paper is concerned with the interplay of the expressiveness of model and graph transformation languages, of assertion formalisms making correctness statements about transformations, and the decidability of the resulting verification problems. We put a particular focus on transformations arising in graph-based knowledge bases and model-driven engineering. We then identify requirements that should be satisfied by logics dedicated to reasoning about model transformations, and investigate two promising instances which are decidable fragments of first-order logic.

Keywords

Graph transformation Model transformation Program verification Classical logic Modal logic 

References

  1. 1.
    Ahmetaj, S., Calvanese, D., Ortiz, M., Simkus, M.: Managing change in graph-structured data using description logics. In: Proceedings of the Twenty-Eighth AAAI Conference on Artificial Intelligence, Québec City, Québec, Canada, 27–31 July 2014, pp. 966–973 (2014)Google Scholar
  2. 2.
    Areces, C., Blackburn, P., Marx, M.: Hybrid logics: characterization, interpolation and complexity. J. Symb. Log. 66(3), 977–1010 (2001)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Baader, F., Calvanese, D., McGuinness, D.L., Nardi, D., Patel-Schneider, P.F. (eds.): The Description Logic Handbook: Theory, Implementation, and Applications. Cambridge University Press, Cambridge (2003)MATHGoogle Scholar
  4. 4.
    Balbiani, P., Echahed, R., Herzig, A.: A dynamic logic for termgraph rewriting. In: Ehrig, H., Rensink, A., Rozenberg, G., Schürr, A. (eds.) ICGT 2010. LNCS, vol. 6372, pp. 59–74. Springer, Heidelberg (2010). doi:10.1007/978-3-642-15928-2_5 CrossRefGoogle Scholar
  5. 5.
    Baresi, L., Spoletini, P.: On the use of alloy to analyze graph transformation systems. In: Corradini, A., Ehrig, H., Montanari, U., Ribeiro, L., Rozenberg, G. (eds.) ICGT 2006. LNCS, vol. 4178, pp. 306–320. Springer, Heidelberg (2006). doi:10.1007/11841883_22 CrossRefGoogle Scholar
  6. 6.
    Brenas, J.H., Echahed, R., Strecker, M.: On the closure of description logics under substitutions. In: Proceedings of the 29th International Workshop on Description Logics, Cape Town, South Africa, 22–25 April 2016Google Scholar
  7. 7.
    Brenas, J.H., Echahed, R., Strecker, M.: Proving correctness of logically decorated graph rewriting systems. In: 1st International Conference on Formal Structures for Computation and Deduction, FSCD 2016, Porto, Portugal, 22–26 June 2016, pp. 14:1–14:15 (2016)Google Scholar
  8. 8.
    Börger, E., Grädel, E., Gurevich, Y.: The Classical Decision Problem. Springer, New York (2000)Google Scholar
  9. 9.
    Corradini, A., Heindel, T., Hermann, F., König, B.: Sesqui-pushout rewriting. In: Corradini, A., Ehrig, H., Montanari, U., Ribeiro, L., Rozenberg, G. (eds.) ICGT 2006. LNCS, vol. 4178, pp. 30–45. Springer, Heidelberg (2006). doi:10.1007/11841883_4 CrossRefGoogle Scholar
  10. 10.
    Courcelle, B.: The monadic second-order logic of graphs. I. Recognizable sets of finite graphs. Inf. Comput. 85(1), 12–75 (1990)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    de Moura, L., Bjørner, N.: Z3: an efficient SMT solver. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 337–340. Springer, Heidelberg (2008). doi:10.1007/978-3-540-78800-3_24 CrossRefGoogle Scholar
  12. 12.
    Echahed, R.: Inductively sequential term-graph rewrite systems. In: Ehrig, H., Heckel, R., Rozenberg, G., Taentzer, G. (eds.) ICGT 2008. LNCS, vol. 5214, pp. 84–98. Springer, Heidelberg (2008). doi:10.1007/978-3-540-87405-8_7 CrossRefGoogle Scholar
  13. 13.
    Ghamarian, A.H., de Mol, M., Rensink, A., Zambon, E., Zimakova, M.: Modelling and analysis using GROOVE. STTT 14(1), 15–40 (2012)CrossRefGoogle Scholar
  14. 14.
    Grädel, E., Otto, M., Rosen, E.: Two-variable logic with counting is decidable. In: Proceedings of 12th IEEE Symposium on Logic in Computer Science, LICS 1997, Warschau (1997)Google Scholar
  15. 15.
    Habel, A., Pennemann, K.: Correctness of high-level transformation systems relative to nested conditions. Math. Struct. Comput. Sci. 19(2), 245–296 (2009)MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Itzhaky, S., Banerjee, A., Immerman, N., Nanevski, A., Sagiv, M.: Effectively-propositional reasoning about reachability in linked data structures. In: Sharygina, N., Veith, H. (eds.) CAV 2013. LNCS, vol. 8044, pp. 756–772. Springer, Heidelberg (2013). doi:10.1007/978-3-642-39799-8_53 CrossRefGoogle Scholar
  17. 17.
    Jackson, D.: Software Abstractions. MIT Press, Cambridge (2011)Google Scholar
  18. 18.
    Leino, K.R.M.: Dafny: an automatic program verifier for functional correctness. In: Clarke, E.M., Voronkov, A. (eds.) LPAR 2010. LNCS (LNAI), vol. 6355, pp. 348–370. Springer, Heidelberg (2010). doi:10.1007/978-3-642-17511-4_20 CrossRefGoogle Scholar
  19. 19.
    Piskac, R., de Moura, L.M., Bjørner, N.: Deciding effectively propositional logic using DPLL and substitution sets. J. Autom. Reason. 44(4), 401–424 (2010)MathSciNetCrossRefMATHGoogle Scholar
  20. 20.
    Poskitt, C.M., Plump, D.: A Hoare calculus for graph programs. In: Ehrig, H., Rensink, A., Rozenberg, G., Schürr, A. (eds.) ICGT 2010. LNCS, vol. 6372, pp. 139–154. Springer, Heidelberg (2010). doi:10.1007/978-3-642-15928-2_10 CrossRefGoogle Scholar
  21. 21.
    Poskitt, C.M., Plump, D.: Verifying monadic second-order properties of graph programs. In: Giese, H., König, B. (eds.) ICGT 2014. LNCS, vol. 8571, pp. 33–48. Springer, Heidelberg (2014). doi:10.1007/978-3-319-09108-2_3 Google Scholar
  22. 22.
    Reynolds, J.C.: An overview of separation logic. In: Meyer, B., Woodcock, J. (eds.) VSTTE 2005. LNCS, vol. 4171, pp. 460–469. Springer, Heidelberg (2008). doi:10.1007/978-3-540-69149-5_49 CrossRefGoogle Scholar
  23. 23.
    Semeráth, O., Barta, Á., Szatmári, Z., Horváth, Á., Varró, D.: Formal validation of domain-specific languages with derived features and well-formedness constraints. Int. J. Softw. Syst. Model., July 2015Google Scholar
  24. 24.
    Tschannen, J., Furia, C.A., Nordio, M., Polikarpova, N.: AutoProof: auto-active functional verification of object-oriented programs. In: Baier, C., Tinelli, C. (eds.) TACAS 2015. LNCS, vol. 9035, pp. 566–580. Springer, Heidelberg (2015). doi:10.1007/978-3-662-46681-0_53 Google Scholar
  25. 25.
    Varró, D.: Automated formal verification of visual modeling languages by model checking. Softw. Syst. Model. 3(2), 85–113 (2004)Google Scholar

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Jon Haël Brenas
    • 1
  • Rachid Echahed
    • 1
  • Martin Strecker
    • 2
  1. 1.CNRS and Université de Grenoble AlpesGrenobleFrance
  2. 2.Université de Toulouse / IRITToulouseFrance

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