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Please use this identifier to cite or link to this item: http://hdl.handle.net/10119/10287

Title: Natural Inductive Theorems for Higher-Order Rewriting
Authors: Aoto, Takahito
Yamada, Toshiyuki
Chiba, Yuki
Keywords: Inductive Theorems
Higher-Order Equational Logic
Simply-Typed S- Expression Rewriting Systems
Term Rewriting Systems
Issue Date: 2011-04-26
Publisher: Schloss Dagstuhl
Magazine name: Proceedings of the 22nd International Conference on Rewriting Techniques and Applications (RTA'11)
Volume: 10
Start page: 107
End page: 121
DOI: 10.4230/LIPIcs.RTA.2011.107
Abstract: The notion of inductive theorems is well-established in first-order term rewriting. In higher-order term rewriting, in contrast, it is not straightforward to extend this notion because of extensionality (Meinke, 1992). When extending the term rewriting based program transformation of Chiba et al. (2005) to higher-order term rewriting, we need extensibility, a property stating that inductive theorems are preserved by adding new functions via macros. In this paper, we propose and study a new notion of inductive theorems for higher-order rewriting, natural inductive theorems. This allows to incorporate properties such as extensionality and extensibility, based on simply typed S-expression rewriting (Yamada, 2001).
Rights: ⓒTakahito Aoto, Toshiyuki Yamada and Yuki Chiba; licensed under Creative Commons License NC-ND. 22nd International Conference on Rewriting Techniques and Applications. Editor: M. Schmidt-Schauß; pp. 107–121.
URI: http://hdl.handle.net/10119/10287
Material Type: publisher
Appears in Collections:b11-1. 会議発表論文・発表資料 (Conference Papers)

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