Conference article

A Compositional Semantics for Modelica-style Variable-structureModeling

P. Pepper
Institut für Softwaretechnik. TU Berlin, Germany

A. Mehlhase
Institut für Softwaretechnik. TU Berlin, Germany

Ch. Höger
Institut für Softwaretechnik. TU Berlin, Germany

L. Scholz
Institut für Mathematik. TU Berlin, Germany

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Published in: Proceedings of the 4th International Workshop on Equation-Based Object-Oriented Modeling Languages and Tools; Zurich; Switzerland; September 5; 2011

Linköping Electronic Conference Proceedings 56:6, p. 45-54

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Published: 2011-11-03

ISBN: 978-91-7519-825-5

ISSN: 1650-3686 (print), 1650-3740 (online)


Modelica traditionally has a non-compositional semantic definition; based on so-called “flattening”. But in the realm of programming languages and theoretical computer science it is by now an accepted principle that semantics should be given in a compositional way. Such a semantics is given in this paper for Modelica-style languages. Moreover; the approach is also used to consider more general modeling concepts; namely so-called variable-structure systems. As an outlook we discuss the correspondence between such an idealized mathematical semantics and a more pragmatic numeric solver-oriented semantics.


Modelica; compositional semantics; structure dynamics; uncertainty


[1] Egidio Astesiano; Michel Bidoit; Hélène Kirchner; Bernd Krieg-Brückner; Peter D.Mosses; Donald Sannella; and Andrzej Tarlecki. CASL: the common algebraic specification language. Theor. Comput. Sci.; 286(2):153–196; 2002.

[2] Kathryn E. Brenan; Stephen L. Campbell; and Linda R. Petzold. Numerical Solution of Initial-Value Problems in Differential Algebraic Equations; volume 14 of Classics in Applied Mathematics. SIAM; Philadelphia; PA; 1996.

[3] David Broman. Meta-Languages and Semantics for Equation-Based Modeling and Simulation. PhD thesisLinköping University; 2010.

[4] David Broman and Peter Fritzson. Higher-Order Acausal Models. Simulation News Europe; 19(1):5–16; 2009.

[5] Paul Caspi; Daniel Pilaud; Nicolas Halbwachs; and JohnPlaice. Lustre: A declarative language for programming synchronous systems. In POPL; pages 178–188; 1987.

[6] George Giorgidze and Henrik Nilsson. Embedding a FunctionalHybrid Modelling language in Haskell. In Revised selected papers of the 20th international symposium on Implementation and Application of Functional Languages; Hatfield; England; volume 5836 of Lecture Notes in Computer Science. Springer; 2008.

[7] George Giorgidze and Henrik Nilsson. Mixed-levelembedding and JIT compilation for an iteratively staged DSL. In Proceedings of the 19th Workshop on Functional and (Constraint) Logic Programming (WFLP’10); pages 19–34; 2010.

[8] Vineet Gupta; Thomas A. Henzinger; and Radha Jagadeesan. Robust timed automata. In Proceedings of the First InternationalWorkshop on Hybrid and Real-time Systems (HART 97); Lecture Notes in Computer Science 1201; pages 331–345; 1997.

[9] Ernst Hairer and Gerhard Wanner. Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems. Springer-Verlag; Berlin; second edition; 1996.

[10] David Harel. Statecharts: A visual formalism for complex systems. Sci. Comput. Program.; 8(3):231–274; 1987.

[11] Thomas A. Henzinger. The theory of hybrid automata. In LICS; pages 278–292; 1996.

[12] Kestrel Institute; 3260 Hillview Ave.; Palo Alto; CA 94304 USA. Specware System and documentation; 2003.

[13] Peter Kunkel and Volker Mehrmann. Differential-Algebraic Equations — Analysis and Numerical Solution. EMS Publishing House; Zürich; Switzerland; 2006.

[14] Oded Maler; Zohar Manna; and Amir Pnueli. From timed to hybrid systems. In REX Workshop; pages 447–484; 1991.

[15] Zohar Manna and Amir Pnueli. Verifying hybrid systems. In Hybrid Systems; pages 4–35; 1992.

[16] Alexandra Mehlhase. Varying the level of detail during simulation. In to appear in Proc. ASIM 2011; 2011.

[17] Volker Mehrmann and Lena Wunderlich. Hybrid systems of differential-algebraic equations – analysis and numerical solution. Journal of Process Control; 19:1218–1228; 2009.

[18] Pieter J. Mosterman. Hybrid dynamic systems: modetransition behavior in hybrid dynamic systems. In Chick S; P. J. Sanchez; D. Ferrin; and D. J. Morrice; editors; Proc. 2003 Winter Simulation Conference; pages 623–631; 2003.

[19] Henrik Nilsson and George Giorgidze. Exploiting structural dynamism in functional hybrid modelling for simulation of ideal diodes. In Proceedings of the 7th EUROSIM Congress on Modelling and Simulation; Prague; Czech Republic. Czech Technical University Publishing House; 2010.

[20] Henrik Nilsson; John Peterson; and Paul Hudak. Functional hybrid modeling. In Proceedings of 5th Int. Workshop on Practical Aspects of Declarative Languages; volume 2562 of Lecture Notes in Computer Science; pages 376–390. Springer; 2003.

[21] Christoph Nytsch-Geusen; Andre Nordwig; Thilo Ernst; Peter Schwarz; Matthias Vetter; ChristophWittwer; Andreas Holm; Jürgen Leopold; Gerhardt Schmidt; Ulrich Doll; and Alexander Mattes. MOSILAB: Development of a Modelica based generic simulation tool supporting model structural dynamics. In Proceedings of the 4th International Modelica Conference; 2005.

[22] Dusko Pavlovic; Peter Pepper; and Douglas R. Smith.Evolving specification engineering. In AMAST; pages 299– 314; 2008.

[23] Hridesh Rajan and Gary T. Leavens. Ptolemy: A language with quantified; typed events. In ECOOP; pages 155–179; 2008.

[24] Neil Sculthorpe and Henrik Nilsson. Keeping calm in the face of change: Towards optimisation of FRP by reasoning about change. Journal of Higher-Order and Symbolic Computation (HOSC); 24(1); 2011.

[25] Dirk A. van Beek; Michel A. Reniers; Jacobus E. Rooda; and Ramon R. H. Schiffelers. Foundations of an interchange format for hybrid systems. In Alberto Bemporad; Antonio Bicchi; and Giorgio Butazzo; editors; 10th International Workshop on Hybrid Systems: Computation and Control; volume 4416 of Lecture Notes in Computer Science; pages 587–600. Springer; 2007.

[26] Dirk A. van Beek; Michel A. Reniers; Jacobus E. Rooda;and Ramon R. H. Schiffelers. Revised hybrid system interchange format. Technical Report HYCON Deliverable D3.6.3; HYCON NoE; 2007.

[27] Dirk A. van Beek; Michel A. Reniers; Jacobus E. Rooda; and Ramon R. H. Schiffelers. Concrete syntax and semantics of the compositional interchange format for hybrid systems. In Proceedings of the 17th IFAC World Congress (IFAC’08) July 11-16; 2008; Seoul; Korea; 2008.

[28] Zhanyong Wan and Paul Hudak. Functional reactive programming from first principles. In PLDI 2000: Symposium on Programming Language Design and Implementation; pages 242–252; 2000.

[29] Dirk Zimmer. Equation-Based Modeling of Variable Structure Systems. PhD thesis; ETH Zürich; 2010.

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