{"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/quantitative-aspects-of-linear-and-affine","title":"Quantitative aspects of linear and affine closed lambda terms","arxiv_id":"1702.03085","date":"2017-02-10","proceeding":null,"authors":["Pierre Lescanne"],"abstract":"Affine $\\lambda$-terms are $\\lambda$-terms in which each bound variable occurs at most once and linear $\\lambda$-terms are $\\lambda$-terms in which each bound variables occurs once. and only once. In this paper we count the number of closed affine $\\lambda$-terms of size $n$, closed linear $\\lambda$-terms of size $n$, affine $\\beta$-normal forms of size $n$ and linear $\\beta$-normal forms of ise $n$, for different ways of measuring the size of $\\lambda$-terms. From these formulas, we show how we can derive programs for generating all the terms of size $n$ for each class. For this we use a specific data structure, which are contexts taking into account all the holes at levels of abstractions.","url_abs":"http://arxiv.org/abs/1702.03085v5","url_pdf":"http://arxiv.org/pdf/1702.03085v5.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":"quantitative-aspects-of-linear-and-affine","repo_url":"https://github.com/PierreLescanne/CountingGeneratingAfffineLinearClosedLambdaterms","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}