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Semantics of Interaction

This is an introduction to Game Semantics based on some lecture notes given at the CLiCS II summer school in Cambridge in 1995. We will focus on the recent (1994) work on Game semantics, which has led to some striking advances in the Full Abstraction problem for PCF and other programming languages. Our aim is to give a genuinely elementary first introduction; we therefore present a simplified version of game semantics, which nonetheless contains most of the essential concepts. The more complex game semantics used by Abramsky, Jagadeesan and Malacaria and by Hyland and Ong to construct fully abstract models for PCF can be seen as refinements of what we present. Some background in category theory, type theory and linear logic would be helpful in reading these notes.