2021-11-28T11:30:09Zhttps://nagoya.repo.nii.ac.jp/oaioai:nagoya.repo.nii.ac.jp:000190562021-03-01T16:23:58ZRecognizability of Redexes for Higher-Order Rewrite SystemsKasuya, Hideto55658Sakai, Masahiko55659Agusa, Kiyoshi55660It is known that the set of all redexes for a left-linear term rewriting system is recognizable by a tree automaton, which means that we can construct a tree automaton that accepts redexes. The present paper extends this result to Nipkow's higher-order rewrite systems, in which every left-hand side is a linear fully-extended pattern. A naive extension of the first-order method causes the automata to have infinitely many states in order to distinguish bound variables in λ-terms, even if they are closed. To avoid this problem, it is natural to adopt de Bruijn notation, in which bound variables are represented as natural numbers (possibly finite symbols, such as 0, s(0), and s(s(0))). We propose a variant of de Bruijn notation in which only bound variables are represented as natural numbers because it is not necessary to represent free variables as natural numbers.journal article一般社団法人情報処理学会2009-03application/pdf情報処理学会論文誌, プログラミング22166175http://id.nii.ac.jp/1001/00060637/http://hdl.handle.net/2237/211620387-5806https://nagoya.repo.nii.ac.jp/record/19056/files/IPSJ-TPRO0202013.pdfengここに掲載した著作物の利用に関する注意 本著作物の著作権は情報処理学会に帰属します。本著作物は著作権者である情報処理学会の許可のもとに掲載するものです。ご利用に当たっては「著作権法」ならびに「情報処理学会倫理綱領」に従うことをお願いいたします。Notice for the use of this material The copyright of this material is retained by the Information Processing Society of Japan (IPSJ). This material is published on this web site with the agreement of the author (s) and the IPSJ. Please be complied with Copyright Law of Japan and the Code of Ethics of the IPSJ if any users wish to reproduce, make derivative work, distribute or make available to the public any part or whole thereof. All Rights Reserved, Copyright (C) Information Processing Society of Japan. Comments are welcome. Mail to address editj＠ipsj.or.jp, please.