Pcf Deenability via Kripke Logical Relations (after O'hearn and Riecke)

The material presented here is an exposition of an application of logical relations to the problem of full abstraction for PCF. The point is to see Kripke logical relations as introduced by Jung and Tiuryn in [5] and used by O'Hearn and Riecke in [6] to give a logical characterization of sequentiality, within the mainstream of the classical notion of logical relations. The main di erence with respect to [6] is that we give a de nition which is just a specialization of that of [5], and then we need the extensional collapse of \sequential" objects to get the fully abstract model. It is questionable whether the extensional collapse is a higher price to pay in comparison with the complex construction in [6]. As observed in [6], Jung and Tiuryn's Kripke logical relations are a special case of unary logical relations in a functor category. Since our exposition is very concrete, we avoid a strong commitment with categorical concepts, and use instead the de nition of Kripke model and of Kripke logical relation given in [4] as our starting point. The exposition is kept at an elementary level, even if familiarity with lambda-calculus and domain theory is assumed. As said before, we do not make any substantial use of category theory, but for some notation and for the use of diagrams that are of help to visualize some otherwise complex