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