Sorted Psi-calculi with Generalised Pattern Matching with proofs

Psi-calculi is a formally verified parametric framework for extensions of the pi-calculus, with arbitrary data structures and logical assertions for facts about data. Although this framework in its original form exhibits considerable expressiveness, many applied computational models cannot be directly represented in it. In this paper we extend the applicability of psi-calculi in three ways. Firstly, we introduce patterns and pattern matching, in order to allow modelling of computations on the term language. Secondly, we add sorts to the data term language, to remove processes containing nonsensical terms from consideration. We demonstrate a sequence of examples, including fully abstract representations of extensions of the pi-calculus. Thirdly, we provide a prototype implementation of the framework, where user-defined instances are automatically provided with symbolic execution and bisimilarity checking algorithms. Substantial parts of the meta-theory of sorted psi-calculi have been machine-checked using Nominal Isabelle.