# The consistent use of names and polymorphism in the definition of Object Petri Nets

## Abstract

This paper seeks to present a more elegant and general definition of Object Petri Nets than previously. It is more general since it supports transition fusion as well as place fusion. It is more elegant because it captures all the notions of place substitution, transition substitution, place fusion, and transition fusion under the single notion of binding. This is achieved by explicitly supporting names in the formalism, in line with the π-calculus which recognises that names are pervasive and should be explicitly included in a formalism in order to model object mobility. The definition in this paper is also more consistent in its use of polymorphism and embodies a more obvious duality between states and changes of state. Object Petri Nets represent a complete integration of object-oriented concepts into Petri Nets. They have a single class hierarchy which includes both token types and subnet types, and which readily supports modelling systems with multiple levels of activity. Interaction between subnets can be synchronous or asynchronous depending on whether the subnet is defined as a super place or a super transition. While not presented in this paper, Object Petri Nets can be transformed into behaviourally equivalent Coloured Petri Nets, thus providing a basis for adapting existing analysis techniques.

## Keywords

Theory of High-Level Petri Nets Object-Orientation Multiple Levels of Abstraction## Preview

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## References

- [1]G. Agha, S. Frølund, W. Y. Kim, R. Panwar, A. Patterson, and D. Sturman
*Abstraction and Modularity Mechanisms for Concurrent Computing*Research Directions in Concurrent Object-Oriented Programming, G. Agha, P, Wegner, and A. Yonezawa (eds.), pp 3–21, MIT Press (1993).Google Scholar - [2]G.A. Agha
*Actors: A Model of Concurrent Computation in Distributed Systems*The MIT Press series in artificial intelligence, MIT Press (1986).Google Scholar - [3]E. Battiston, A. Chizzoni, and F.D. Cindio
*Inheritance and Concurrency in CLOWN*Proceedings of Workshop on Object-Oriented Programming and Models of Concurrency, Torino, Italy (1995).Google Scholar - [4]E. Battiston and F. de Cindio
*Class Orientation and Inheritance in Modular Algebraic Nets*Proceedings of IEEE International Conference on Systems, Man and Cybernetics2, pp 717–723, Le Touquet, France, IEEE (1993).Google Scholar - [5]E. Battiston, F. de Cindio, and G. Mauri
*OBJSA Nets: A Class of High-level Nets having Objects as Domains*Advances in Petri Nets 1988, G. Rozenberg (ed.), Lecture Notes in Computer Science 340, pp 20–43, Springer-Verlag (1988).Google Scholar - [6]M. Bever, K. Geihs, L. Heuser, M. Mühlhäuser, and A. Schill
*Distributed Systems, OSF DCE, and Beyond*Proceedings of International DCE Workshop: DCE — the OSF distributed computing environment: Client/Server Model and Beyond, Lecture notes in computer science 731, Karlsruhe, Germany, Springer-Verlag (1993).Google Scholar - [7]O. Biberstein and D. Buchs
*Structured Algebraic Nets with Object-Orientation*Proceedings of Workshop on Object-Oriented Programming and Models of Concurrency, Torino, Italy (1995).Google Scholar - [8]D. Buchs and N. Guelfi
*CO-OPN: A Concurrent Object Oriented Petri Net Approach*Proceedings of 12th International Conference on the Application and Theory of Petri Nets, Gjern, Denmark (1991).Google Scholar - [9]D. Buchs and N, Guelfi
*Open Distributed Programming Using the Object Oriented Specification Formalism CO-OPN*Proceedings of 5th International Conference on Putting into Practice Methods and Tools for Information System Design, Nantes (1992).Google Scholar - [10]S. Christensen and N. D. Hansen
*Coloured Petri Nets Extended with Channels for Synchronous Communication*Proceedings of 15th International Conference on the Application and Theory of Petri Nets, Lecture Notes in Computer Science 815, pp 159–178, Zaragoza, Springer-Verlag (1994).Google Scholar - [11]P.A. Fishwick
*Computer Simulation: Growth Through Extension*Proceedings of Modelling and Simulation (European Simulation Multiconference), pp 3–20, Barcelona, Society for Computer Simulation (1994).Google Scholar - [12]S. Haddad
*A Reduction Theory for Coloured Nets*. Advances in Petri Nets 1989, G. Rozenberg (ed.), Lecture Notes in Computer Science 424, pp 209–235, Springer-Verlag (1990).Google Scholar - [13]K. Jensen
*Coloured Petri Nets: Basic Concepts, Analysis Methods and Practical Use — Volume 1: Basic Concepts*EATCS Monographs in Computer Science, Vol. 26, Springer-Verlag (1992).Google Scholar - [14]K. Jensen, S. Christensen, P. Huber, and M. Holla Design/CPN™:
*A Reference Manual*MetaSoftware Corporation (1992).Google Scholar - [15]C. Lakos and S. Christensen
*A General Systematic Approach to Arc Extensions for Coloured Petri Nets*Proceedings of 15th International Conference on the Application and Theory of Petri Nets, Lecture Notes in Computer Science 815, pp 338–357, Zaragoza, Springer-Verlag (1994).Google Scholar - [16]C. Lakos and C. Keen
*LOOPN*++:*A New Language for Object-Oriented Petri Nets*Proceedings of Modelling and Simulation (European Simulation Multiconference), pp 369–374, Barcelona, Society for Computer Simulation (1994).Google Scholar - [17]C.A. Lakos
*Object Petri Nets — Definition and Relationship to Coloured Nets*Technical Report TR94-3, Computer Science Department, University of Tasmania (1994).Google Scholar - [18]C.A. Lakos
*The Consistent Use of Names and Polymorphism to Achieve an Elegant Definition of Object Petri Nets*Technical Report R95-12, Computer Science Department, University of Tasmania (1995).Google Scholar - [19]C.A. Lakos
*From Coloured Petri Nets to Object Petri Nets*Proceedings of 16th International Conference on the Application and Theory of Petri Nets, Lecture Notes in Computer Science 935, pp 278–297, Torino, Italy, Springer-Verlag (1995).Google Scholar - [20]C.A. Lakos
*Pragmatic Inheritance Issues for Object Petri Nets*Proceedings of TOOLS Pacific 1995, Melbourne, Australia, Prentice-Hall (1995).Google Scholar - [21]B. Meyer
*Object-Oriented Software Construction*Prentice Hall (1988).Google Scholar - [22]B. Meyer
*Eiffel: The Language*Prentice Hall (1992).Google Scholar - [23]
- [24]R. Milner, J. Parrow, and D. Walker
*A Calculus of Mobile Processes, I*Information and Computation,**100**, 1, pp 1–40 (1992).Google Scholar - [25]C.A. Petri “Forgotten”
*Topics of Net Theory*Advances in Petri Nets 1986Lecture Notes in Computer Science, Springer-Verlag (1986).Google Scholar - [26]W. Reisig
*Petri nets: An Introduction*EATCS Monographs on Theoretical Computer Science, Vol. 4, Springer-Verlag (1985).Google Scholar - [27]C. Sibertin-Blanc
*A Client-Server Protocol for the Composition of Petri Nets*Proceedings of 14th International Conference on the Application and Theory of Petri Nets, Lecture Notes in Computer Science 691, pp 377–396, Chicago, Springer-Verlag (1993).Google Scholar - [28]C. Sibertin-Blanc
*Cooperative Nets*Proceedings of 15th International Conference on the Application and Theory of Petri Nets, Lecture Notes in Computer Science 815, pp 471–490, Zaragoza, Spain, Springer-Verlag (1994).Google Scholar - [29]C. Sibertin-Blanc, N. Hameurlain, and P. Touzeau
*SYROCO: A C++ Implementation of Cooperative Objects*Proceedings of Workshop on Object-Oriented Programming and Models of Concurrency, Torino, Italy (1995).Google Scholar - [30]P.A. Swatman, P.M.C. Swatman, and R. Duke
*Electronic Data Interchange: A High-level Formal Specification in Object-Z*Proceedings of 6th Australian Software Engineering Conference, pp 341–354, Sydney, Australia, Springer-Verlag (1991).Google Scholar - [31]R. Valk
*Modelling Concurrency by Task/Flow EN Systems*3rd Workshop on Concurrency and Compositionality, 1991, E. Best, et al. (ed.), GMD-Studien 191, pp 207–215 (1991).Google Scholar - [32]R. Valk
*Petri Nets as Dynamical Objects*Proceedings of Workshop on Object-Oriented Programming and Models of Concurrency, Torino, Italy (1995).Google Scholar - [33]P. Wegner
*Dimensions of Object-Based Language Design*Proceedings of OOPSLA 87, pp 168–182, Orlando, Florida, ACM (1987).Google Scholar - [34]P. Wegner
*Inheritance as an Incremental Modification Mechanism, or What Like Is and Isn't Like*Proceedings of ECOOP '88 — European Conference on Object Oriented Programming, Lecture Notes in Computer Science 322, pp 55–77, Oslo, Norway, Springer Verlag (1988).Google Scholar