{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/e-unification-for-second-order-abstract","title":"E-unification for Second-Order Abstract Syntax","arxiv_id":"2302.05815","date":"2023-02-11","proceeding":null,"authors":["Nikolai Kudasov"],"abstract":"Higher-order unification (HOU) concerns unification of (extensions of) $\\lambda$-calculus and can be seen as an instance of equational unification ($E$-unification) modulo $\\beta\\eta$-equivalence of $\\lambda$-terms. We study equational unification of terms in languages with arbitrary variable binding constructions modulo arbitrary second-order equational theories. Abstract syntax with general variable binding and parametrised metavariables allows us to work with arbitrary binders without committing to $\\lambda$-calculus or use inconvenient and error-prone term encodings, leading to a more flexible framework. In this paper, we introduce $E$-unification for second-order abstract syntax and describe a unification procedure for such problems, merging ideas from both full HOU and general $E$-unification. We prove that the procedure is sound and complete.","url_abs":"https://arxiv.org/abs/2302.05815v2","url_pdf":"https://arxiv.org/pdf/2302.05815v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"e-unification-for-second-order-abstract","repo_url":"https://github.com/fizruk/rzk","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"e-unification-for-second-order-abstract","repo_url":"https://github.com/rzk-lang/rzk","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}