Games and Full Abstraction for a Functional Metalanguage with Recursive Types

This book is a minor revision of the thesis submitted in August 1996; no major changes have been made. However, I would like to take this opportunity to mention that since the thesis was written, discoveries have been made which would allow a substantial simplification and strengthening of the results in Chapters 3 and 6. In particular, it is now possible to model sums correctly in the category I as well as in £, which means that the definability results of Chapter 6 can be stated and proved at the intensional level, making them simpler and much closer in spirit to the original proofs of Abramsky, Jagadeesan, Malacaria, Hyland, Ong and Nickau [10,61,79]. This also leads quite straightforwardly to an understanding of call-by-value languages. Details of these improvements can be found in [14,73]. It is also worth mentioning that progress has been made on some of the topics suggested for future research in Chapter 7. In particular, fully abstract models have been found for various kinds of languages with local variables [8,13-16], and a fully complete games model of the polymorphic language System F has been constructed by Hughes [59]. Guy McCusker February 1998 Acknowledgements First of all, I must thank my supervisor, Samson Abramsky. It was he who first introduced me to game semantics and suggested avenues of research in the area; this book would certainly not exist were it not for him.

Contains the first treatment of recursive types using game semantics, and the first fully abstract model of a recursively typed language The first exposition of game semantics for programming languages at such a high level of detail The mathematics required for denotational semantics of recursive types is studied at a general, categorical level * A computational adequacy result is proved at this level

Klappentext

The Distinguished Dissertation series is published on behalf of the Conference of Professors and Heads of Computing and The British Computer Society, who annually select the best British PhD dissertations in computer science for publication. The dissertations are selected on behalf of the CPHC by a panel of eight academics. Each dissertation chosen makes a noteworthy contribution to the subject and reaches a high standard of exposition, placing all results clearly in the context of computer science as a whole. In this way computer scientists with significantly different interests are able to grasp the essentials - or even find a means of entry - to an unfamiliar research topic. This book develops a theory of game semantics, a recently discovered setting for modelling and reasoning about sequential programming languages, suitable for interpreting higher-order functional languages with rich type structure, and applies it to constr uct a fully abstract model of the metalanguage FPC.

Inhalt
Introduction.- Full Abstraction.- Game Semantics.- Historical Perspective.- Contribution of This Book.- Prerequisites.- Preliminaries.- Enriched Category Theory.- Intrinsic Preorder.- Games.- Arenas, Views and Legal Positions.- Games and Strategies.- The Category.- Exponential.- A Cartesian Closed Category.- An Alternative Category.- The Extensional Category.- Sums.- Lifting.- Rational Categories and Recursive Types.- Rational Categories.- Recursive Types.- Invariant Relations.- Parameterized Invariant Relations.- IP-Categories.- Axioms for Rationality.- FPC and its Models.- The Language FPC.- Models of FPC.- Semantics of the Recursion Combinator.- Formal Approximation Relations.- Computational Adequacy.- Full Abstraction.- Conclusions.