Formalization of Variables in Algebraic High-Level Nets: Comparison of Di erent Approaches

The paper discusses diierent approaches to formalize the representation of variables in Algebraic High-Level nets (AHL nets). We compare the approaches formally with regard to certain quality conditions a good AHL net formalization should satisfy. These quality conditions are (1) the cocompleteness of the underlying category of AHL nets and AHL net morphisms as this is the technical basis for the formaliza-tion of structuring techniques for AHL nets; (2) the preservation of the net's ring behaviour by AHL net morphisms; (3) the possibility to rename variables via AHL net morphisms. An example shows that the usual treatment of variables as part of the algebraic speciication leads to a violation of these quality conditions. Then, diierent formal approaches are introduced to solve the problems. The approach we regard as the best solution of our problems, is based on local transition variables deening local name scopes for the variables of each transition. We present a concrete and an abstract, categorical formalization of this approach.