VPM: A visual, precise and multilevel metamodeling framework for describing mathematical domains and UML As UML 2.0 is evolving into a family of languages with individually specified semantics, there is an increasing need for automated and provenly correct model transformations that (i) assure the integration of local views (different diagrams) of the system into a consistent global view, and, (ii) provide a well-founded mapping from UML models to different semantic domains (Petri nets, Kripke automaton, process algebras, etc.) for formal analysis purposes as foreseen, for instance, in submissions for the OMG RFP for Schedulability, Performance and Time. However, such transformations into different semantic domains typically require the deep understanding of the underlying mathematics, which hinders the use of formal specification techniques in industrial applications. In the paper, we propose a multilevel metamodeling technique with precise static and dynamic semantics (based on a refinement calculus and graph transformation) where the structure and operational semantics of mathematical models can be defined in a UML notation without cumbersome mathematical formulae.

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  1. Horváth, Ákos; Bergmann, Gábor; Ráth, István; Varró, Dániel: Experimental assessment of combining pattern matching strategies with VIATRA2 (2010) ioport
  2. Jackson, Ethan; Sztipanovits, Janos: Formalizing the structural semantics of domain-specific modeling languages (2009) ioport
  3. Levendovszky, Tihamér; Lengyel, László; Mészáros, Tamás: Supporting domain-specific model patterns with metamodeling (2009) ioport
  4. Alanen, Marcus; Porres, Ivan: A metamodeling language supporting subset and union properties (2008) ioport
  5. Dingel, J.; Diskin, Z.; Zito, A.: Understanding and improving UML package merge (2008) ioport
  6. Montangero, Carlo; Semini, Laura: Barbed model-driven software development: a case study (2008) ioport
  7. de Lara, Juan; Bardohl, Roswitha; Ehrig, Hartmut; Ehrig, Karsten; Prange, Ulrike; Taentzer, Gabriele: Attributed graph transformation with node type inheritance (2007)
  8. Jouault, Frédéric; Kurtev, Ivan: On the interoperability of model-to-model transformation languages (2007)
  9. Varró, Dániel; Balogh, András: The model transformation language of the VIATRA2 framework (2007)
  10. Taentzer, Gabriele; Rensink, Arend: Ensuring structural constraints in graph-based models with type inheritance (2005)
  11. Varró, Dániel; Pataricza, András: VPM: a visual, precise and multilevel metamodeling framework for describing mathematical domains and UML (2003) ioport