Recursive Checkonly QVT-R Transformations with General when and where Clauses via the Modal Mu Calculus
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.
- 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.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
- 4.Object Management Group. Object constraint language, version 2.0, formal/2006-05-01 (May 2006)Google Scholar
- 6.OMG. MOF2.0 query/view/transformation (QVT) version 1.1. OMG document formal/2009-12-05 (2009), www.omg.org
- 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