Abstract. Psi-calculi are extensions of the pi-calculus, accommodating arbitrary nominal datatypes to represent not only data but also communication channels, assertions and conditions, giving it an expressive power beyond the applied pi-calculus and the concurrent constraint picalculus. We have formalised psi-calculi in the interactive theorem prover Isabelle using its nominal datatype package. One distinctive feature is that the framework needs to treat binding sequences, as opposed to single binders, in an efficient way. While different methods for formalising single binder calculi have been proposed over the last decades, representations for such binding sequences are not very well explored. The main effort in the formalisation is to keep the machine checked proofs as close to their pen-and-paper counterparts as possible. We discuss two approaches to reasoning about binding sequences along with their strengths and weaknesses. We also cover custom induction rules to remove the bulk of manual alpha-conversions. 1

CLF (the Concurrent Logical Framework) is a language for specifying and reasoning about concurrent systems. Its most significant feature is the first-class representation of concurrent executions as monadic expressions. We illustrate the representation techniques available within CLF by applying them to an asynchronous pi-calculus with correspondence assertions, including its dynamic semantics, safety criterion, and a type system with latent effects due to Gordon and Jeffrey.

Abstract. We formalise the pi-calculus using the nominal datatype package, a package based on ideas from the nominal logic by Pitts et al., and demonstrate an implementation in Isabelle/HOL. The purpose is to derive powerful induction rules for the semantics in order to conduct machine checkable proofs, closely following the intuitive arguments found in manual proofs. In this way we have covered many of the standard theorems of bisimulation equivalence and congruence, both late and early, and both strong and weak in a unison manner. We thus provide one of the most extensive formalisations of a process calculus ever done inside a theorem prover. A significant gain in our formulation is that agents are identified up to alpha-equivalence, thereby greatly reducing the arguments about bound names. This is a normal strategy for manual proofs about the pi-calculus, but that kind of hand waving has previously been difficult to incorporate smoothly in an interactive theorem prover. We show how the nominal logic formalism and its support in Isabelle accomplishes this and thus significantly reduces the tedium of conducting completely formal proofs. This improves on previous work using weak higher order abstract syntax since we do not need extra assumptions to filter out exotic terms and can keep all arguments within a familiar first-order logic.

We use the interactive theorem prover Isabelle to prove that the algebraic axiomatization of bisimulation equivalence in the pi-calculus is sound and complete. This is the first proof of its kind to be wholly machine checked. Although the result has been known for some time the proof had parts which needed careful attention to detail to become completely formal. It is not that the result was ever in doubt; rather, our contribution lies in the methodology to prove completeness and get absolute certainty that the proof is correct, while at the same time following the intuitive lines of reasoning of the original proof. Completeness of axiomatizations is relevant for many variants of the calculus, so our method has applications beyond this single result. We build on our previous effort of implementing a framework for the pi-calculus in Isabelle using the nominal data type package, and strengthen our claim that this framework is well suited to represent the theory of the pi-calculus, especially in the smooth treatment of bound names.

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. Acknowledgements I would like to thank my advisor, Joachim Parrow, and my co-advisor, Björn Victor for all their support, help, and advice. I would like to thank all the co-authors; Johannes Borgström, Shuqin Huang,