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

Reference99 articles.

1. Martín Abadi , Anindya Banerjee , Nevin Heintze , and Jon G. Riecke . 1999. A Core Calculus of Dependency. In POPL ’99 , Proceedings of the 26th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages , San Antonio, TX, USA , January 20-22, 1999 . 147–160. Martín Abadi, Anindya Banerjee, Nevin Heintze, and Jon G. Riecke. 1999. A Core Calculus of Dependency. In POPL ’99, Proceedings of the 26th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, San Antonio, TX, USA, January 20-22, 1999. 147–160.

2. Andreas Abel and Jean-Philippe Bernardy . 2020 . A unified view of modalities in type systems . Proc. ACM Program. Lang., 4, ICFP (2020), 90:1–90:28. Andreas Abel and Jean-Philippe Bernardy. 2020. A unified view of modalities in type systems. Proc. ACM Program. Lang., 4, ICFP (2020), 90:1–90:28.

3. Samson Abramsky. 2002. Predicative Copying and Polynomial Time. Clifford Lectures Tulane. Samson Abramsky. 2002. Predicative Copying and Polynomial Time. Clifford Lectures Tulane.

4. Geometry of Interaction and linear combinatory algebras

5. Peter Aczel. 1978. A general Church-Rosser theorem. Draft Manchester. Peter Aczel. 1978. A general Church-Rosser theorem. Draft Manchester.

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