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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. Adoi:10.1137/s0097539791224212 fatcat:dbtdasi7wrgk5ht7lj43qwu764