Hypergames and full completeness for system F (rough draft)

This paper reviews the fully complete hypergames model of system $F$, presented a decade ago in the author’s thesis. Instantiating type variables is modelled by allowing games as moves''. The uniformity of a quantified type variable $\forall X$ is modelled by copycat expansion: $X$ represents an unknown game, a kind of black box, so all the player can do is copy moves between a positive occurrence and a negative occurrence of $X$. This presentation is based on slides for a talk entitled Hypergame semantics: ten years later’’ given at `Games for Logic and Programming Languages’, Seattle, August 2006.