Recognizability of Redexes for Higher-Order Rewrite Systems
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概要
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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.
- 2009-03-23
著者
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Hideto Kasuya
Faculty of Information Science and Technology, Aichi Prefectural University
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Masahiko Sakai
Graduate School of Information Science, Nagoya University
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Kiyoshi Agusa
Graduate School of Information Science, Nagoya University
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Kiyoshi Agusa
Graduate School Of Information Science Nagoya University
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Hideto Kasuya
Faculty Of Information Science And Technology Aichi Prefectural University
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Masahiko Sakai
Graduate School Of Information Science Nagoya University
関連論文
- Recognizability of Redexes for Higher-Order Rewrite Systems
- Head-Needed Strategy of Higher-Order Rewrite Systems and Its Decidable Classes
- Context-sensitive Innermost Reachability is Decidable for Linear Right-shallow Term Rewriting Systems
- Decidability of Reachability for Right-shallow Context-sensitive Term Rewriting Systems
- Determinization of Conditional Term Rewriting Systems for Program Generation