By reading literature on (denotational) semantics of types, I see that people tried to give several models of types. Reynolds showed that types in general cannot be given a set semantics in classical set theory. However, it was shown later that constructive sets could be used. Now, I also stumbled upon papers where types are seen as complete partial orders and Scott domains. Further, Cardelli presents types as ideals, but acknowledges that retracts should be used to handle parametric types.
I understand that one can give different models depending on the type system, but is there a known model of types that handles parametric types, universal parametric polymorphism, existential polymorphism, recursive types, and subtyping? For instance, where would I start if I want to give a denotational model for OCaml types (but without the side-effect features)?
Also, how does Reynolds' relational model relate (no pun intended) to the existing models?