Box Calculus with Coloured Buffers

The starting point of this paper is the asynchronous box calculus with multiway communication (MBC), a formalism suitable for modelling compositionally distributed systems using both synchronous and asynchronous communication and a number of control flow operators. MBC is composed of two semantically consistent models: an algebra of lowlevel Petri nets and an associate algebra of process terms whose constants and operators directly correspond to the Petri net ones. In this paper, we extend the Petri net algebra of MBC by allowing the communication buffers to carry coloured tokens which can be used for both synchronous and asynchronous communications. In asynchronous ones, coloured tokens can be used through high-level links making easy, for instance, the representation of program variables (e.g., counters), allowing a compact representation of large (possibly infinite) systems. In synchronous ones, coloured tokens may be used as parameters of synchronising actions, allowing a simple and compositional expression of interprocess communication. We also extend the MBC process terms and their associate structured operational semantics. The obtained high-level framework, called box calculus with data, BCD, is coherent with respect to MBC through the unfolding operation. Moreover, the resulting algebra of BCD terms is consistent with the net algebra in the sense that a term and the corresponding net generate isomorphic transition systems.