Contextual Equivalence for the Pi-Calculus that can Stop

Abstract. The pi-calculus is a well-analyzed model for mobile processes and mobile computations. While a lot of other process and lambda calculi that are core languages of higher-order concurrent and/or functional programming languages use a contextual semantics observing the termination behavior of programs in all program contexts, traditional program equivalences in the pi-calculus are bisimulations and barbed testing equivalences, which observe the communication capabilities of processes under reduction and in contexts. There is a distance between these two approaches to program equivalence which makes it hard to compare the pi-calculus with other languages. In this paper we contribute to bridging this gap by investigating a contextual semantics of the synchronous pi-calculus with replication and without sums. To transfer contextual equivalence to the pi-calculus we add a process Stop as constant which indicates success and is used as the base to define and analyze the contextual equivalence which observes may- and should-convergence of processes. We show as a main result that contextual equivalence in the pi-calculus with Stop conservatively extends barbed testing equivalence in the (Stop-free) pi-calculus. This implies that results on con-textual equivalence can be directly transferred to the (Stop-free) pi-calculus with barbed testing equivalence. We analyze the contextual ordering, prove some nontrivial process equivalences, and provide proof tools for showing contextual equivalences. Among them are a context lemma, and new notions of sound applicative similarities for may- and should-convergence