Abstract. This paper proposes two typing systems for session interactions in higherorder mobile processes. Session types for the HOπ-calculus capture high-level structures of communication protocols and code mobility as type abstraction, and can be used to statically check the safe and consistent process composition in communication-centric distributed software. Integration of arbitrary higher-order code mobility and sessions leads to technical difficulties in type soundness, because linear usage of session channels and completion of sessions are required in executed code. By using techniques from the linear λ-calculus, we develop a coherent and tractable session typing system for the HOπ-calculus. We also present an alternative system based on fine-grained process types. The formal comparison between the two systems offers insight on the interplay between higher-order code mobility and session types. 1

This dissertation investigates different formalisms, in the form of programming language calculi, that are aimed at providing a theoretical foundation for structured concurrent programming based on session types. The structure of a session type is essentially a process-algebraic style description of the behaviour of a single program identifier serving as a communication medium (and usually referred to as a channel): the types incorporate typed inputs, outputs, and choices which can be composed to form larger protocol descriptions. The effectiveness of session typing can be attributed to the linear treatment of channels and session types, and to the use of tractable methods such as syntactic duality to decide if the types of two connected channels are compatible. Linearity is ensured when accumulating the uses of a channel into a composite type that describes also the order of those actions. Duality provides a tractable and intuitive method for deciding when two connected channels can interact and exchange values in a statically determined type-safe way. We present our contributions to the theory of sessions, distilled into two families of programming calculi, the first based on higher-order processes and the second based on objects. Our work unifies, improves and extends, in manifold ways, the session primitives and typing systems for the Lambda-calculus, the Pi-calculus, the Object-calculus, and their combinations in multi-paradigm