Toward a Modal Theory of Types for the Pi-Calculus

We study the problem of specifying and verifying properties of ß-calculus processes while relying on a bisimulation semantics. As our property specification language we use a version of the modal ¯-calculus adapted to the ß-calculus. We show that the logical language is sufficiently expressive to characterize by means of a finite formula a process up to any approximation of the bisimulation relation. We consider the problem of checking that a process of the ß-calculus satisfies a specification expressed in this modal ¯-calculus. We develop an algorithm which is sound in general, and complete for processes having a finite 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. 1 Introduction The ß-calculus was introduced by Milner, Parrow, and Walker [MPW92] as a language for describing concurrent systems with feat..