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.