Advertisement

Recursive Checkonly QVT-R Transformations with General when and where Clauses via the Modal Mu Calculus

  • Julian Bradfield
  • Perdita Stevens
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7212)

Abstract

In earlier work we gave a game-based semantics for checkonly QVT-R transformations. We restricted when and where clauses to be conjunctions of relation invocations only, and like the OMG standard, we did not consider cases in which a relation might (directly or indirectly) invoke itself recursively. In this paper we show how to interpret checkonly QVT-R – or any future model transformation language structured similarly – in the modal mu calculus and use its well-understood model-checking game to lift these restrictions. The interpretation via fixpoints gives a principled argument for assigning semantics to recursive transformations. We demonstrate that a particular class of recursive transformations must be ruled out due to monotonicity considerations. We demonstrate and justify a corresponding extension to the rules of the QVT-R game.

References

  1. 1.
    Bradfield, J.C., Stirling, C.: Modal mu-calculi. In: Blackburn, P., van Benthem, J., Wolter, F. (eds.) Handbook of Modal Logic, vol. 3, pp. 721–756. Elsevier (2007)Google Scholar
  2. 2.
    Bradfield, J., Stevens, P.: Recursive checkonly QVT-R transformations with general when and where clauses via the modal mu calculus. Technical Report EDI–INF–RR–1410, University of Edinburgh, Includes Appendix (2012)Google Scholar
  3. 3.
    Cabot, J., Clarisó, R., Guerra, E., de Lara, J.: Verification and validation of declarative model-to-model transformations through invariants. Journal of Systems and Software 83(2), 283–302 (2010)CrossRefGoogle Scholar
  4. 4.
    Object Management Group. Object constraint language, version 2.0, formal/2006-05-01 (May 2006)Google Scholar
  5. 5.
    Kozen, D.: Results on the propositional mu-calculus. Theor. Comput. Sci. 27, 333–354 (1983)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    OMG. MOF2.0 query/view/transformation (QVT) version 1.1. OMG document formal/2009-12-05 (2009), www.omg.org
  7. 7.
    Stevens, P.: A simple game-theoretic approach to checkonly QVT Relations. Journal of Software and Systems Modeling (SoSyM) (March 16, 2011), doi: 10.1007/s10270-011-0198-8Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Julian Bradfield
    • 1
  • Perdita Stevens
    • 1
  1. 1.School of InformaticsUniversity of EdinburghUK

Personalised recommendations