2022-01-23T15:51:01Zhttps://ipsj.ixsq.nii.ac.jp/ej/?action=repository_oaipmhoai:ipsj.ixsq.nii.ac.jp:000606372020-10-27T05:02:43Z00934:00935:00936:05590
Recognizability of Redexes for Higher-Order Rewrite SystemsRecognizability of Redexes for Higher-Order Rewrite Systemseng通常論文http://id.nii.ac.jp/1001/00060637/Articlehttps://ipsj.ixsq.nii.ac.jp/ej/?action=repository_action_common_download&item_id=60637&item_no=1&attribute_id=1&file_no=1Copyright (c) 2009 by the Information Processing Society of JapanFaculty of Information Science and Technology, Aichi Prefectural UniversityGraduate School of Information Science, Nagoya UniversityGraduate School of Information Science, Nagoya UniversityHideto, KasuyaMasahiko, SakaiKiyoshi, AgusaIt 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.It 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.AA11464814情報処理学会論文誌プログラミング（PRO）221661752009-03-231882-7802 2009-08-13