A Per Model of Polymorphism and Recursive Types

The ideal model provides an interpretation for a rich type system, with polymorphism and recursion [12], but not a model of the typed λ-calculus. In search for a satisfactory semantics for λ-calculi with recursive and polymorphic types, it seems natural, then, to consider partial equivalence relations (pers) instead of ideals. As ideals are certain subsets of a universal domain D, we replace them with certain pers over D (rather than over ω, as in [8, 19]). For example, in order to interpret recursion, only the pers over D that satisfy a completeness axiom should be considered. This study was begun by Amadio and Cardone [1, 5]. They left open how to find complete partial orders on pers so that recursive types could be obtained by applying the usual inverselimit construction [18]. In the case of models