Game Semantics and Subtyping

Game Semantics is a relatively new framework for the description of the semantics of programming languages. By combining the mathematical elegance of Denotational Semantics with explicitly operational concepts, Game Semantics has made possible the direct and intuitive modelling of a large range of programming constructs. In this thesis, we show how Game Semantics is able to model subtyping. We start by designing an untyped λ-calculus with ground values that explicitly internalises the notion of typing error. We then equip this calculus with a rich typing system that includes quantification (both universal and existential) as well as recursive types. In a second part, we show how to interpret the untyped calculus; after equipping the domain of the interpretation with an ordering --- the liveness ordering --- loosely inspired from implication on process specifications, we show how our interpretation is both sound and computationally adequate. In a third part, we introduce a notion of game which we use for interpreting types, and show how the liveness ordering on games is suitable for interpreting subtyping. Finally, we prove that under the (unproved) assumption that recursive types are compatible with quantification, our interpretation is sound with respect to both subtyping and typing

Timed Session Types

Timed session types formalise timed communication protocols between two participants at the endpoints of a session. They feature a decidable compliance relation, which generalises to the timed setting the progress-based compliance between untimed session types. We show a sound and complete technique to decide when a timed session type admits a compliant one. Then, we show how to construct the most precise session type compliant with a given one, according to the subtyping preorder induced by compliance. Decidability of subtyping follows from these results

A Typed Language for Truthful One-Dimensional Mechanism Design

We first introduce a very simple typed language for expressing allocation algorithms that allows automatic verification that an algorithm is monotonic and therefore truthful. The analysis of truthfulness is accomplished using a syntax-directed transformation which constructs a proof of monotonicity based on an exhaustive critical-value analysis of the algorithm. We then define a more high-level, general-purpose programming language with typical constructs, such as those for defining recursive functions, along with primitives that match allocation algorithm combinators found in the work of Mu'alem and Nisan [10]. We demonstrate how this language can be used to combine both primitive and user-defined combinators, allowing it to capture a collection of basic truthful allocation algorithms. In addition to demonstrating the value of programming language design techniques in application to a specific domain, this work suggests a blueprint for interactive tools that can be used to teach the simple principles of truthful mechanism desig