A Sorted Semantic Framework for Applied Process Calculi

TL;DR

This paper introduces a unified, sorted semantic framework for various applied process calculi, extending psi-calculi with novel patterns, sorts, and computational features, ensuring accurate representation and analysis of complex concurrent systems.

Contribution

It extends psi-calculi with new abstract patterns, sorts, and computational primitives, enabling a unified and accurate representation of diverse process calculi.

Findings

Framework can represent several existing calculi with isomorphic transition systems.

Supports various notions of computation, including cryptography and lambda calculus.

Proves key properties like bisimulation congruence, machine-checked in Isabelle.

Abstract

Applied process calculi include advanced programming constructs such as type systems, communication with pattern matching, encryption primitives, concurrent constraints, nondeterminism, process creation, and dynamic connection topologies. Several such formalisms, e.g. the applied pi calculus, are extensions of the the pi-calculus; a growing number is geared towards particular applications or computational paradigms. Our goal is a unified framework to represent different process calculi and notions of computation. To this end, we extend our previous work on psi-calculi with novel abstract patterns and pattern matching, and add sorts to the data term language, giving sufficient criteria for subject reduction to hold. Our framework can directly represent several existing process calculi; the resulting transition systems are isomorphic to the originals up to strong bisimulation. We also demonstrate different notions of computation on data terms, including cryptographic primitives and a lambda-calculus with erratic choice. Finally, we prove standard congruence and structural properties of bisimulation; the proof has been machine-checked using Nominal Isabelle in the case of a single name sort.