A Sorted Semantic Framework for Applied Process Calculi

Abstract

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.

The Applied Pi Calculus

“…In psi calculi, one can avoid such counterintuitive disclosures by explicitly creating and using aliases. A recent extension of psi calculi (Borgström et al 2014(Borgström et al , 2016 addresses these difficulties with a new form of pattern matching. In contrast, the management of aliases is built into the applied pi calculus, facilitating the modeling of security protocol attackers as contexts.…”