A Note on Confluence in Typed Probabilistic Lambda Calculi
Rafael Romero, Alejandro D\'iaz-Caro
TL;DR
This paper investigates how small modifications in probabilistic rewriting rules, variable usage, and strategies affect confluence in a strongly normalizing lambda calculus modeling quantum computation.
Contribution
It provides an analysis of confluence properties in a probabilistic lambda calculus with quantum computation features, considering various modifications.
Findings
Probabilistic rewriting can maintain confluence under certain conditions.
Affine variables influence the confluence in probabilistic lambda calculi.
Strategies and rule modifications impact the confluence and normalization properties.
Abstract
On the topic of probabilistic rewriting, there are several works studying both termination and confluence of different systems. While working with a lambda calculus modelling quantum computation, we found a system with probabilistic rewriting rules and strongly normalizing terms. We examine the effect of small modifications in probabilistic rewriting, affine variables, and strategies on the overall confluence in this strongly normalizing probabilistic calculus.
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