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Psi-calculi is a parametric framework for extensions of the pi-calculus, with arbitrary data structures and logical assertions for facts about data. This thesis presents broadcast psi-calculi and higher-order psi-calculi, two extensions of the psi-calculi framework, allowing respectively one-to-many communications and the use of higher-order process descriptions through conditions in the parameterised logic. Both extensions preserve the purity of the psi-calculi semantics; the standard congruence and structural properties of bisimilarity are proved formally in Isabelle. The work going into the extensions show that depending on the specific extension, working out the formal proofs can be a work-intensive process. We find that some of this work could be automated, and implementing such automation may facilitate the development of future extensions to the psi-calculi framework.

Psi-calculi is a parametric framework for process calculi similar to popular pi-calculus extensions such as the explicit fusion calculus, the applied pi-calculus and the spi calculus. Remarkably, machine-checked proofs of standard algebraic and congruence properties of bisimilarity apply to every instance of the framework.

The contribution of this licentiate thesis is to significantly extend the applicability and expressiveness of psi-calculi by incorporating several advanced language features into the framework: broadcasts, higher-order communication, generalised pattern matching, sorts and priorities. The extensions present several interesting technical challenges, such as negative premises. The machine-checked proofs for standard results about bisimilarity are generalised to each of these new settings, and the proof scripts are freely available online.

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.