Abstract

We show that Friedman's proof of the existence of non-trivial βη-complete models of λ→ can be extended to system F. We isolate a set of conditions which are sufficient to ensure βη-completeness for a model of F (and α-completeness at the level of types), and we discuss which class of models we get. In particular, the model introduced in [5], having as polymorphic maps exactly all possible Scott continuous maps, is βη-complete and is hence the first known complete nonsyntactic model of F. In order to have a suitable framework where to express the conditions and develop the proof, we also introduce the very natural notion of "polymax models" of System F.

Citations