http://swrc.ontoware.org/ontology#Article
Recognizability of Redexes for Higher-Order Rewrite Systems
en
通常論文
Faculty of Information Science and Technology, Aichi Prefectural University
Graduate School of Information Science, Nagoya University
Graduate School of Information Science, Nagoya University
Hideto Kasuya
Masahiko Sakai
Kiyoshi Agusa
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.
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）
2
2
166-175
2009-03-23
1882-7802