The Semantics of Nondeterminism

Paul Levy has held the position of Lecturer in the School of Computer Science, University of Birmingham, since 2002. Prior to this, he carried out research at Queen Mary, University of London (as a PhD student) and in Boston and Paris (as a postdoctoral research associate). Much of his work has used denotational semantics and category theory to find and exploit connections between disparate areas of research in theoretical computer science, including various structures for computational effects [1, 11]. His discovery of the “call-bypush-value” (CBPV) language [5, 3], underlying previous call-by-value and call-by-name languages, led to fine-grained accounts of domains, continuations, game semantics, possible worlds and nondeterminism. It has proved useful both for analyzing existing semantics and for developing new ones, such as the model for general references in [7]. These applications of call-by-push-value were described in his wide-ranging PhD thesis [6]. In particular, he described the utility of CBPV for analyzing game semantics, one of the themes of this proposal. The two CBPV operations of forcing a thunk and returning a value correspond directly to the two kinds of move in game semantics, “question” and “answer”. A radical simplification of the algebra [8, 2], using adjunction models, led to a book [9] published in “Semantic Structures in Computation” in 2004. The book describes CBPV semantics for nondeterminism using may-testing equivalence, and reveals the adjunction structure in Hyland and Ong’s well-bracketed game semantics, both relevant to this proposal. He is currently working on some of the major open problems in the semantics of nondeterminism, such as the modelling of infinite trace equivalence [10], bisimilarity and ambiguous choice. He was recently awarded a New Lecturer grant by the Nuffield Foundation for this work.