Game Semantics and Normalization by Evaluation

Overview & Synopsis

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 low-level game-theoretic machinery. As an illustration, we give a Haskell program computing the application of innocent strategies.