Elements of Quantitative Rewriting-Reference-Cited by-同舟云学术

Elements of Quantitative Rewriting

Published:2023-01-09 Issue:POPL Volume:7 Page:1832-1863
ISSN:2475-1421
Container-title:Proceedings of the ACM on Programming Languages
language:en
Short-container-title:Proc. ACM Program. Lang.

Author:

Gavazzo Francesco¹^ORCID,Di Florio Cecilia²^ORCID

Affiliation:

1. University of Pisa, Italy

2. University of Bologna, Italy

Abstract

We introduce a general theory of quantitative and metric rewriting systems, namely systems with a rewriting relation enriched over quantales modelling abstract quantities. We develop theories of abstract and term-based systems, refining cornerstone results of rewriting theory (such as Newman’s Lemma, Church-Rosser Theorem, and critical pair-like lemmas) to a metric and quantitative setting. To avoid distance trivialisation and lack of confluence issues, we introduce non-expansive, linear term rewriting systems, and then generalise the latter to the novel class of graded term rewriting systems. These systems make quantitative rewriting modal and context-sensitive, this way endowing rewriting with coeffectful behaviours.

Funder

European Research Council

Publisher

Association for Computing Machinery (ACM)

Subject

Safety, Risk, Reliability and Quality,Software

Link

https://dl.acm.org/doi/pdf/10.1145/3571256

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