The Y - hierarchy for PCF is strict ( Draft version )
نویسنده
چکیده
Let PCFk denote the sublanguage of Plotkin’s PCF in which fixed point operators Yσ are admitted only for types σ of level at most k. We show that the languages PCFk form a strict hierarchy as regards expressivity, in the sense that for each k, there are closed programs of PCFk+1 that are not observationally equivalent to any programs of PCFk. This answers positively a question posed by Berger in 1999. Our proof makes serious use of the theory of nested sequential procedures (also called PCF Böhm trees) as expounded in the forthcoming book of Longley and Normann.
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