A note on confluence in typed probabilistic lambda calculi

@inproceedings{Romero2021ANO,
  title={A note on confluence in typed probabilistic lambda calculi},
  author={Rafael Romero and Alejandro D'iaz-Caro},
  booktitle={LSFA},
  year={2021}
}
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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SHOWING 1-10 OF 10 REFERENCES
Decomposing Probabilistic Lambda-Calculi
TLDR
The resulting calculus, the Probabilistic Event Lambda-Calculus, is confluent, and interprets the call-by-name and call- by-value strategies through different interpretations of the probabilistic operator into the authors' generator and consumer constructs.
Probabilistic Rewriting: Normalization, Termination, and Unique Normal Forms
TLDR
This work investigates how the asymptotic behavior of different rewrite sequences starting from the same term compare w.r.t. normal forms, proposes a robust analogue of the notion of "unique normal form", and develops methods to study and compare strategies.
Pattern-based calculi with finitary matching
TLDR
The framework described in this paper imposes conditions on the solving function, obtaining a generic confluence proof for a class of pattern calculi with finitary matching.
A Lambda Calculus for Density Matrices with Classical and Probabilistic Controls
TLDR
Two flavors of a quantum extension to the lambda calculus are presented, one of which follows the approach of classical control/quantum data, and the other takes advantage of the density matrices presentation in order to follow the mixed trace of programs in a kind of generalised density matrix.
Confluence in Probabilistic Rewriting
Probabilistic Rewrite Strategies. Applications to ELAN
TLDR
An extension of the ELAN strategy language to deal with randomized systems is proposed, and it is argued through several examples that a natural setting to model systems with randomized choices is proposed.
Proving Positive Almost-Sure Termination
TLDR
This work provides several results and techniques in order to prove positive almost sure termination of a given set of probabilistic rewrite rules, including classical ones for non-probabilistic systems.
Una extensión polimórfica para los λ -cálculos cuánticos λ ρ y λ • ρ . Master's thesis
  • 2020
Una extensión polimórfica para los λ -cálculos cuánticos λ ρ y λ • ρ
  • 2020
Una extensión polimórfica para los λ -cálculos cuánticos
  • λρ y λ ◦ ρ . Master’s thesis, Universidad de Buenos Aires, Argentina
  • 2020