2026-07-19T20:30:36Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:17469 2024-03-06T11:00:03Z ddc:004 open_access

Reductions in Higher-Order Rewriting and Their Equivalence Barenbaum, Pablo Bonelli, Eduardo Term Rewriting Higher-Order Rewriting Proof terms Equivalence of Computations Proof terms are syntactic expressions that represent computations in term rewriting. They were introduced by Meseguer and exploited by van Oostrom and de Vrijer to study equivalence of reductions in (left-linear) first-order term rewriting systems. We study the problem of extending the notion of proof term to higher-order rewriting, which generalizes the first-order setting by allowing terms with binders and higher-order substitution. In previous works that devise proof terms for higher-order rewriting, such as Bruggink’s, it has been noted that the challenge lies in reconciling composition of proof terms and higher-order substitution (β-equivalence). This led Bruggink to reject "nested" composition, other than at the outermost level. In this paper, we propose a notion of higher-order proof term we dub rewrites that supports nested composition. We then define two notions of equivalence on rewrites, namely permutation equivalence and projection equivalence, and show that they coincide. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Pablo Barenbaum and Eduardo Bonelli 2023 Is Part Of LIPIcs, Volume 252, 31st EACSL Annual Conference on Computer Science Logic (CSL 2023) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CSL.2023.8 urn:nbn:de:0030-drops-174694 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2023.8 eng https://creativecommons.org/licenses/by/4.0/legalcode