Full Abstraction and the Context Lemma

Trevor Jim, Albert R. Meyer
1996 SIAM journal on computing (Print)  
It is impossible to add a combinator to PCF to achieve full abstraction for models such a s Berry's stable domains in a way analogous to the addition of the parallel-or" combinator that achieves full abstraction for the familiar cpo model. In particular, we de ne a general notion of rewriting system of the kind used for evaluating simply typed -terms in Scott's PCF. Any simply typed -calculus with such a PCF-like" rewriting semantics is shown necessarily to satisfy Milner's Context Lemma. A
more » ... ontext 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 de nable by PCF-like rules.
doi:10.1137/s0097539791224212 fatcat:dbtdasi7wrgk5ht7lj43qwu764