Culling Concurrency Theory : Reusable and trustworthy meta-theory, proof techniques and separation results

Abstract: As concurrent systems become ever more complex and ever more ubiquitous, the need to understand and verify them grows ever larger. For this we need formal modelling languages that are well understood, with rigorously verified foundations and proof techniques, applicable to a wide variety of concurrent systems.Defining modelling languages is easy; there is a stupefying variety of them in the literature. Verifying their foundations and proof techniques, and developing an understanding of their interrelationship with other modelling languages, is difficult, tedious and error-prone. The contributions of this thesis support these tasks in reusable and trustworthy ways, by results that apply to a wide variety of modelling languages, verified to the highest standards of mathematical rigour in an interactive theorem prover.To this end, we extend psi-calculi - a family of process calculi with reusable foundations for formal verification - with several new language features. We prove that the bisimulation meta-theory of psi-calculi carries over to these extended settings. This widens the scope of psi-calculi to important application areas, such as cryptography and wireless communication. We develop bisimulation up-to techniques - powerful proof techniques for showing that two processes exhibit the same observable behaviour - that apply to all psi-calculi. By showing how psi-calculi can encode dynamic priorities under very strong quality criteria, we demonstrate that the expressive power is greater than previously thought. Finally, we develop a simple and widely applicable technique for showing that a process calculus adds expressiveness over another, based on little more than whether parallel components may act independently or not. Many separation results, both novel ones and strengthenings of known results from the literature, emerge as special cases of this technique.