Peter Dybjer: Game Semantics and Normalization by Evaluation

We show that Hyland and Ong's game semantics for PCF can be presented using normalization by evaluation (nbe). We use the bijective correspondence between innocent well-bracketed strategies and PCF Böhm trees, and show how operations on PCF Böhm trees, such as composition, can be computed lazily and simply by nbe. The usual equations characteristic of games follow from the nbe construction without reference to the game-theoretic machinery. As an illustration, we give a Haskell program computing the application of innocent strategies. This is joint work with Pierre Clairambault, CNRS and ENS Lyon.