From SOS rules to proof principles: an operational metatheory for functional languages
Proceedings of the 24th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Information and Computation
Information and Computation
On generic context lemmas for higher-order calculi with sharing
Theoretical Computer Science
On the stability by union of reducibility candidates
FOSSACS'07 Proceedings of the 10th international conference on Foundations of software science and computational structures
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It is impossible to add a combinator to PCF to achieve full abstraction for models such as Berry's stable domains in a way analogous to the addition of the "parallel-or" combinator that achieves full abstraction for the familiar complete partial order (cpo) model. In particular, we define a general notion of rewriting system of the kind used for evaluating simply typed $\lambda$-terms in Scott's PCF. Any simply typed $\lambda$-calculus with such a "PCF-like" rewriting semantics is shown necessarily to satisfy Milner's Context Lemma. A simple argument demonstrates that any denotational semantics that is adequate for PCF, and in which certain simple Boolean functionals exist, cannot be fully abstract for any extension of PCF satisfying the Context Lemma. An immediate corollary is that stable domains cannot be fully abstract for any extension of PCF definable by PCF-like rules.