Abstract
We consider a de’Liguoro-Piperno-style extension of the pure lambda calculus with a non-deterministic choice operator as well as a non-deterministic iterator construct, with the aim of studying its normalization properties. We provide a simple characterization of non-strongly normalizable terms by means of the so called “zoom-in” perpetual reduction strategy. We then show that this characterization implies the strong normalization of the simply typed version of the calculus. As straightforward corollary of these results we obtain a new proof of strong normalization of Gödel’s System T by a simple translation of this latter system into the former.
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Aschieri, F., Zorzi, M. (2013). Non-determinism, Non-termination and the Strong Normalization of System T. In: Hasegawa, M. (eds) Typed Lambda Calculi and Applications. TLCA 2013. Lecture Notes in Computer Science, vol 7941. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38946-7_5
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DOI: https://doi.org/10.1007/978-3-642-38946-7_5
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