Toward a Modal Theory of Types for the pi-Calculus

We study the problem of specifying and verifying properties of -calculus processes while relying on a bisimulation semantics. As our property speci cation language we use a version of the modal -calculus adapted to the -calculus. We show that the logical language is su ciently expressive to characterize by means of a nite formula a process up to any approximation of the bisimulation relation. We consider the problem of checking that a process of the -calculus satis es a speci cation expressed in this modal -calculus. We develop an algorithm which is sound in general, and complete for processes having a nite reachability property. Finally, we present a proof system which can be applied to prove non-recursive properties of arbitrary processes. We show that the system is complete on the non-recursive fragment of the logical language.