Extended pi-Calculi

We demonstrate a general framework for extending the picalculus with data terms. In this we generalise and improve on several related efforts such as the spi calculus and the applied pi-calculus, also including pattern matching and polyadic channels. Our framework uses a single untyped notion of agent, name and scope, an operational semantics without structural equivalence and a simple definition of bisimilarity. We provide general criteria on the semantic equivalence of data terms; with these we prove algebraic laws and that bisimulation is preserved by the operators in the usual way. The definitions are simple enough that an implementation in an automated proof assistant is feasible.