Model Checking for π-Calculus Using Proof Search

Model checking for transition systems specified in π-calculus has been a difficult problem due to the infinite-branching nature of input prefix, name-restriction and scope extrusion. We propose here an approach to model checking for π-calculus by encoding it into a logic which supports reasoning about bindings and fixed points. This logic, called FOλ∆∇, is a conservative extension of Church’s Simple Theory of Types with a “generic” quantifier. By encoding judgments about transitions in pi-calculus into this logic, various conditions on the scoping of names and restrictions on name instantiations are captured naturally by the quantification theory of the logic. Moreover, standard implementation techniques for (higher-order) logic programming are applicable for implementing proof search for this logic, as illustrated in a prototype implementation discussed in this paper. The use of logic variables and eigenvariables in the implementation allows for exploring the state space of processes in a symbolic way. Compositionality of properties of the transitions is a simple consequence of the meta theory of the logic (i.e., cut elimination). We illustrate the benefits of specifying systems in this logic by studying several specifications of modal logics for pi-calculus. These specifications are also executable directly in the prototype implementation of FOλ∆∇.