Algebraic Higher-Order Nets: Graphs and Petri Nets as Tokens

Petri nets and Algebraic High-Level Nets are well-known to model parallel and concurrent systems. In this paper, we introduce the concept of Algebraic Higher-Order Nets, which allow to have dynamical tokens like graphs or (ordinary low-level) Petri nets. For this purpose, we specify graphs and Petri nets in the higher-order algebraic specification language HasCasl such that graphs and Petri nets become first-class citizens, i.e. members of algebras (rather than algebras themselves). As an example, we model hospital therapeutic processes by a single higher-order net. Individual care plans for each patient are tokens modeled by low-level nets.