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Probabilistic Rewriting: Relations between Normalization, Termination, and Unique Normal Forms

by   Claudia Faggian, et al.

We investigate how techniques from Rewrite Theory can help us to study calculi whose evaluation is both probabilistic and non-deterministic (think untyped probabilistic lambda-calculus, in which non-determinism arises from choosing between different redexes). We are interested in relations between weak and strong normalization, and whenever the result is unique. We provide ARS-like local conditions, which also extend to a method to compare strategies. As an application, we study the untyped lambda-calculus equipped with a probabilistic choice. We show that weak call-by-value reduction has the same striking properties it has for the standard lambda-calculus: the normal forms are unique, and weak normalization implies strong normalization.


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