In earlier work we explored the expressiveness and algebraic theory Psi-calculi, which form a parametric framework for extensions of the pi-calculus. In the current paper we consider higher-order psi-calculi through a technically surprisingly simple extension of the framework, and show how an arbitrary psi-calculus can be lifted to its higher-order counterpart in a canonical way. We illustrate this with examples and establish an algebraic theory of higher-order psi-calculi. The formal results are obtained by extending our proof repositories in Isabelle/Nominal.

Isabelle/HOL augments classical higher-order logic with ad-hoc overloading of constant definitions— that is, one constant may have several definitions for non-overlapping types. In this paper, we present a mechanised proof that HOL with ad-hoc overloading is consistent. All our results have been formalised in the HOL4 theorem prover.

Psi-calculi is a parametric framework for extensions of the picalculus, with arbitrary data structures and logical assertions for facts about data. In this paper we add primitives for broadcast communication in order to model wireless protocols. The additions preserve the purity of the psi-calculi semantics, and we formally prove the standard congruence and structural properties of bisimilarity. We demonstrate the expressive power of broadcast psi-calculi by modelling the wireless ad-hoc routing protocol LUNAR and verifying a basic reachability property.

Psi-calculi is a parametric framework for extensions of the picalculus, with arbitrary data structures and logical assertions for facts about data. In this paper we add primitives for broadcast communication in order to model wireless protocols. The additions preserve the purity of the psi-calculi semantics, and we formally prove the standard congruence and structural properties of bisimilarity. We demonstrate the expressive power of broadcast psi-calculi by modelling the wireless ad-hoc routing protocol LUNAR and verifying a basic reachability property.