Building continuous webbed models for system F

AbstractWe present here a large family of concrete models for Girard and Reynolds polymorphism (system F), in a noncategorical setting. The family generalizes the construction of the model of Barbanera and Berardi (Tech. Report, University of Turin, 1997), hence it contains complete models for Fη (A βη-complete model for system F, preprint, June, 1998) and we conjecture that it contains models which are complete for F. It also contains simpler models, the simplest of them, E2, being a second-order variant of the Engeler–Plotkin model E. All the models here belong to the continuous semantics and have underlying prime algebraic domains, all have the maximum number of polymorphic maps. The class contains models which can be viewed as two intertwined compatible webbed models of untyped λ-calculus (in the sense of Berline (From computations to foundations: the λ-calculus and its webbed models, revised version, Theoret. Comput. Sci. 86 pp., to appear)), but it is much larger than this. Finally, many of its models might be read as two intertwined strict intersection type systems