Natural Inductive Theorems for Higher-Order Rewriting

Authors Takahito Aoto, Toshiyuki Yamada, Yuki Chiba

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Takahito Aoto
Toshiyuki Yamada
Yuki Chiba

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Takahito Aoto, Toshiyuki Yamada, and Yuki Chiba. Natural Inductive Theorems for Higher-Order Rewriting. In 22nd International Conference on Rewriting Techniques and Applications (RTA'11). Leibniz International Proceedings in Informatics (LIPIcs), Volume 10, pp. 107-121, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)


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).
  • Inductive Theorems
  • Higher-Order Equational Logic
  • Simply-Typed S-Expression Rewriting Systems
  • Term Rewriting Systems


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