University of Birmingham > Talks@bham > Theoretical computer science seminar > The recursion hierarchy for PCF is strict

The recursion hierarchy for PCF is strict

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If you have a question about this talk, please contact Neel Krishnaswami.

Let $\PCF_k$ denote the sublanguage of Plotkin’s $\PCF$ in which fixed point operators $Y_\sigma$ are admitted only for types $\sigma$ of level $\leq k$. We show that the languages $\PCF_k$ form a strict hierarchy, in the sense that for each $k$, there are closed programs of $\PCF_{k+1}$ that are not observationally equivalent to any programs of $\PCF_k$. This answers a question posed by Berger in 1999. Our proof makes substantial use of the theory of \emph{nested sequential procedures} (also called \emph{$\PCF$ B\”ohm trees}).

I plan to give the talk in two parts: first, a discussion of the result with a general overview of the method of proof, and then (for any who are interested) a closer look at some of the technical details of the proof.

This talk is part of the Theoretical computer science seminar series.

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