Reasoning about higher-order processes

We address the specification and verification problem for process calculi such as Chocs, CML and Facile where processes or functions are transmissible values. Our work takes place in the context of a static treatment of restriction and of a bisimulation-based semantics. As a paradigmatic and simple case we concentrate on (Plain) Chocs. We show that Chocs bisimulation can be characterized by an extension of Hennessy-Milner logic including a constructive implication, or function space constructor. This result is a non-trivial extension of the classical characterization result for labelled transition systems. In the second part of the paper we address the problem of developing a proof system for the verification of process specifications. Building on previous work for CCS we present a sound proof system for a Chocs sub-calculus not including restriction. We present two completeness results: one for the full specification language using an infinitary system, and one for a special class of so-called well-described specifications using a finitary system.