Preface

This volume contains the proceedings of the 9th Conference on Category Theory and Computer Science (CTCS'02), which was held at the University of Ottawa from August 15-17, 2002. The purpose of this conference series is the advancement of the foundations of computing using the tools of category theory. Indeed, category theory provides one of the key tools in the analysis of the interaction between logic and the theory of computation. The extent to which category theory has influenced these areas can be seen from the following list of topics, which are typical of the interests of this conference: • coalgebras and computing • concurrent and distributed systems • constructive mathematics • declarative programming and term rewriting • domain theory and topology • foundations of computer security • linear logic • modal and temporal logics • models of computation • program logics, data refinement, and specification • programming language semantics • type theory The list is by no means exhaustive. The vitality of the field is well displayed by the extremely high quality and the diversity of the 18 papers in this volume. For the first time in the history of CTCS, this year's conference was preceded by a “Graduate Student Preconference”, which took place from August 12-14 and which offered introductory courses in areas of importance to the conference. The response to this preconference was extraordinary, with more than 50 students and interested others taking part. This certainly suggests that the field of research of this conference will be strong and active for many years to come. The preconference offered courses in: • Introductory category theory (Susan Niefield) • Categorical logic (Philip Scott) • Concurrency theory (Peter Selinger) • Coalgebraic methods (Jiri Adamek) • Game theory (Robin Cockett) • Linear logic (Rick Blute) To hold this preconference, we received substantial funding from the Centre de Recherches Mathématiques (CRM). We thank them and Jacques Hurtubise, the Director of CRM, for their kind support. Without the help of many individuals in many different capacities, this conference would not have been possible. The editors would especially like to thank the following people: • The organizing committee: ◦ E. Moggi, Chair, (Genova) ◦ S. Abramsky (Oxford) ◦ P. Dybjer (Chalmers) ◦ B. Jay (Sydney) ◦ A. Pitts (Cambridge) • Local organizers: ◦ Rick Blute ◦ Philip Scott • The programme committee: ◦ Rick Blute, Chair (Ottawa) ◦ Robin Cockett (Calgary) ◦ Thierry Coquand (Chalmers) ◦ Andrea Corradini (Pisa) ◦ Thomas Ehrhard (Luminy) ◦ Ryu Hasegawa (Tokyo) ◦ Martin Hofmann (Munich) ◦ Bart Jacobs (Nijmegen) ◦ Michael Johnson (Macquarie) ◦ Dusko Pavlovic (Kestrel Institute) ◦ Alex Simpson (Edinburgh) • Lecturers in the student preconference: ◦ Susan Niefield (Union) ◦ Philip Scott (Ottawa) ◦ Robin Cockett (Calgary) ◦ Rick Blute (Ottawa) ◦ Jiri Adamek (Braunschweig) ◦ Peter Selinger (Ottawa) Invited speakers CTCS'02 was also lucky to have 4 distinguished invited speakers. They were Eric Goubault (CEA/Saclay), Guy McCusker (Sussex), Peter Selinger (Ottawa), and Paul Syverson (Naval Research Laboratory). Here are the titles and abstracts of their talks: • Eric Goubault - The fundamental category of concurrent processes In this talk, I will present some of the recent advances in the understanding of concurrent computations made with geometric (and of course category-theoretic) reasoning. One very important tool is the fundamental category functor which associates a category of “essential schedules” to the semantics of concurrent processes (seen as some form of partially ordered topological space for instance); hence giving a lot of information about how processes coordinate themselves. I will show how to compute inductively, in some simple cases, this fundamental category; this is part of the “compositionality” problem in concurrency theory. One of the defects is that this category is huge, so I will show how to “compress it” through several constructions of categories of fractions, which again reveal to be fundamental and natural constructions in this framework. This is joint work with Martin Raussen and Emmanuel Haucourt. • Guy McCusker - A graph model for imperative computation. Scott's P-omega graph model is a lambda-algebra based on the observation that continuous endofunctions on P-omega can be represented via their graphs . A graph consists of a set of pairs (S, n) where n is a natural and S is a finite set of naturals. We consider a similar model based on sets of pairs (s,n) , where s is a finite sequence rather than a set. Intuitively, this alteration means that we are taking into account the order in which observations are made. This new notion of graph gives rise to a model of affine lambda-calculus which admits an interpretation of imperative constructs including variable assignment, dereferencing and allocation. The category arising as the Karoubi envelope of this untyped model provides a model of typed higher-order imperative computation with an affine type system. An appropriate language of this kind is Reynolds's Syntactic Control of Interference . Our model turns out to be fully abstract for this language. At a concrete level, the model is the same as Reddy's object spaces model, which was the first “state-free” model of a higher-order imperative programming language and an important precursor of games models. Our graph model can therefore be seen as a universal domain for Reddy's model. We also give a simple construction of a category of monoids and relations in which all of this work can be seen to live. • Peter Selinger - Towards a quantum programming language The field of quantum computation suffers from a lack of syntax. In the absence of a convenient programming language, algorithms are frequently expressed in terms of circuits or Turing machines. Neither approach particularly encourages structured programming or abstractions such as data types. In this talk, I describe the syntax and semantics of a simple quantum programming language. The semantics is interesting because it combines notions from geometry of interaction, linear algebra, category theory, and complete partial orders. • Paul Syverson - The Formalization of Anonymity Anonymous communication techniques obscure who is talking to whom and are an important aspect of secure communication. This talk will be an introduction to anonymous communications theory and will be in two parts. The first part of the talk will introduce some of the basic building blocks of anonymous communications systems: proxies, Chaum mixes, DC nets, etc. These offer varying amounts of protection. Typically the stronger the protection afforded by some primitive, the less practical the system that uses it. We will also briefly describe implemented systems, such as Onion Routing and Crowds. In the second part of the talk we will look at some of the ways that have been proposed to define anonymity and related properties. As difficult as it has been to define notions such as authentication and confidentiality, anonymity is even more subtle. For example, protection generally depends on other legitimate users of the system. Otherwise the communicants are exposed. We will set out the various properties in the area, e.g., unobservability or plausible deniability, as well as the attempts to formalize them, e.g., using notions from process algebra and epistemic logic. We will also describe some of the nonformal work on probabilistic and information-theoretic characterizations of anonymity properties. List of accepted papers for CTCS'02 • S. Abramsky and B. Coecke - Physical traces: Quantum vs. classical information processing. • J. Adámek, S. Milius and J. Velebil - On rational monads and free iterative theories. • S. L. Bloom and Z. Ésik - Unique, guarded fixed points in an additive setting. • P. Boudes - Non-uniform hypercoherences. • M. Coccia, F. Gadducci and U. Montanari - GS. Lambda theories: A syntax for higher-order graphs. • R. Cockett and L. Santocanale - Induction, coinduction and adjoints. • E. Haghverdi, P. Tabuada and G. Pappas - Bisimulation relations for dynamical and control systems. • M. Hasegawa - The uniformity principle on traced monoidal categories. • J. Hughes and B. Jacobs - Factorization systems and fibrations: Toward a fibred Birkhoff variety theorem. • J. Koslowski - A monadic approach to polycategories. • J. Laird - A categorical semantics of higher order store. • F. Lamarche - Multiplicative linear logics and fibrations. • P. B. Levy - Adjunction models for call-by-push-value with stacks. • M. E. Maietti - Joyal's arithmetic universes via type theory. • S. Milius - On iteratable endofunctors. • L. Schröder - Classifying categories for partial equational logic. • P. Taylor - Local compactness and the Baire category theorem in abstract Stone duality. • K. Worytkiewicz - Paths and simulations.

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