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Metamodeling Mathematics: A Precise and Visual Framework for Describing Semantics Domains of UML Models

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≪UML≫ 2002 — The Unified Modeling Language (UML 2002)

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Abstract

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 UML-based 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.

This work was partially carried out during the visit of the first author to Computer Science Laboratory at SRI International (333 Ravenswood Ave., Menlo Park, CA, U.S.A.) and supported by the National Science Foundation Grant (CCR-00-86096), the Hungarian Information and Communication Technologies and Applications Grant (IKTA 00065/2000) and the Hungarian National Scientific Foundation Grant (OTKA 038027).

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Author information

Authors and Affiliations

  1. Department of Measurement and Information Systems, Budapest University of Technology and Economics, H-1521, Budapest Magyar tudósok körútja 2

    Dániel Varró & András Pataricza

Authors
  1. Dániel Varró
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  2. András Pataricza
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Editor information

Editors and Affiliations

  1. Irisa - Univesité de Rennes 1, Campus de Beaulieu, 35042, Rennes cedex, France

    Jean-Marc Jézéquel

  2. Fakultät Informatik, Technische Universität Dresden, Mommsenstr. 13, 01062, Dresden, Germany

    Heinrich Hussmann

  3. IBM United Kingdom Ltd, Sunbury House, 79 Staines Road West Sunbury-on-Thames, TW16 7AN, Middlesex, UK

    Stephen Cook

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© 2002 Springer-Verlag Berlin Heidelberg

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Varró, D., Pataricza, A. (2002). Metamodeling Mathematics: A Precise and Visual Framework for Describing Semantics Domains of UML Models. In: Jézéquel, JM., Hussmann, H., Cook, S. (eds) ≪UML≫ 2002 — The Unified Modeling Language. UML 2002. Lecture Notes in Computer Science, vol 2460. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45800-X_3

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  • DOI: https://doi.org/10.1007/3-540-45800-X_3

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44254-7

  • Online ISBN: 978-3-540-45800-5

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