One of the contribution of my DPhil is a novel presentation of Game Semantics based on a generalization of the theory of traversals introduced by Ong. The unpublished technical report (pdf) contains the full technical details. The concepts are summarized in the deck (pdf) of the talk I gave at Galop 2008.
Higher-order recursion schemes
The study of the safety restriction led me to the study of higher-order recursion schemes. In an unpublished paper I showed that the type homogeneity constraint included as part of the original definition by Knapik et al. is in fact not necessary. The 12-page proof (pdf) consists in a game semantic argument based on the theory of traversals which is presented in details in my DPhil thesis.
The safe lambda calculus
My DPhil concerns the study of a syntactic constraint for higher-order computations called the safety restiction. I refer you to the thesis on the publication page for the nitty gritty details.
Termination analysis of higher-order programs
Based on the work of Jones and Bohr, I propose an extension of the size-change principle introduced by Lee, Jones and Ben-Amram to a subset of ML featuring ground type values, higher-order type values and recursively defined functions. This constitutes the first attempt to adapt the size-change principle to a higher-order functional language ala ML featuring if-then-else branching and let rec definitions. I have implemented a tool based on the this work which is able to prove termination of non-trivial higher-order programs of both ground and higher-order types. This gives a termination decision tool for some subset of recursively defined function on natural numbers.
This is research was pursued as part of my Master in Computer Science (2004).