Logical Full Abstraction and PCF

Kripke Logical Relations and PCF

Sieber has described a model of PCF consisting of continuous functions that are invariant under certain ((nitary) logical relations, and shown that it is fully abstract for closed terms of up to third-order types. We show that one may achieve full abstraction at all types using a form of \Kripke logical relations" introduced by Jung and Tiuryn to characterize-deenability.

Full Abstraction and the Context Lemma 1

It is impossible to add a combinator to PCF to achieve full abstraction for models such asBerry's stable domains in a way analogous to the addition of the \parallel-or" combinatorthat achieves full abstraction for the familiar cpo model. In particular, we de ne a generalnotion of rewriting system of the kind used for evaluating simply typed -terms in Scott'sPCF. Any simply t...

Inductive Definition and Domain Theoretic Properties of Fully Abstract Models for PCF and PCF+

A construction of fully abstract typed models for PCF and PCF+ (i.e., PCF + “parallel conditional function”), respectively, is presented. It is based on general notions of sequential computational strategies and wittingly consistent non-deterministic strategies introduced by the author in the seventies. Although these notions of strategies are old, the definition of the fully abstract models is...

Full abstraction, totality and PCF

Inspired by a question of Riecke, we consider the interaction of totality and full abstraction, asking whether full abstraction holds for Scott’s model of cpos and continuous functions if one restricts to total programs and total observations. The answer is negative, as there are distinct operational and denotational notions of totality. However, when two terms are each total in both senses the...

Full Abstraction for Pcf ? (extended Abstract)