2020/05/12 by Cyrille Chenavier, Chenavier, Cyrille, Maxime Lucas +1
Chemistry · Computer Science · Medicine · #Cancer Treatment and Pharmacology #FOS: Computer and information sciences #Logic in Computer Science (cs.LO) #Logic, programming, and type systems #Synthetic Organic Chemistry Methods
paper · pdf · doi:10.48550/arxiv.2005.05764
openalex publication_date 2020/05/12 · openalex created_date 2020/05/21 · openalex updated_date 2026/07/28
We study rewriting systems whose underlying set of terms is equipped with a vector space structure over a given field. We introduce parallel rewriting relations, which are rewriting relations compatible with the vector space structure, as well as rewriting strategies, which consist in choosing one rewriting step for each reducible basis element of the vector space. Using these notions, we introduce the S-confluence property and show that it implies confluence. We deduce a proof of the diamond's lemma, based on strategies. We illustrate our general framework with rewriting systems over rational Weyl algebras, that are vector spaces over a field of rational functions. In particular, we show that involutive divisions induce rewriting strategies over rational Weyl algebras, and using the S-confluence property, we show that involutive sets induce confluent rewriting systems over rational Weyl algebras.