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Chapter and Conference Paper
Proving Confluence of Term Rewriting Systems Automatically
We have developed an automated confluence prover for term rewriting systems (TRSs). This paper presents theoretical and technical ingredients that have been used in our prover. A distinctive feature of our pro...
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Chapter and Conference Paper
RAPT: A Program Transformation System Based on Term Rewriting
Chiba et al. (2005) proposed a framework of program transformation by template based on term rewriting in which correctness of the transformation is verified automatically. This paper describes RAPT (Rewriting-ba...
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Chapter and Conference Paper
Dealing with Non-orientable Equations in Rewriting Induction
Rewriting induction (Reddy, 1990) is an automated proof method for inductive theorems of term rewriting systems. Reasoning by the rewriting induction is based on the noetherian induction on some reduction orde...
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Chapter and Conference Paper
Dependency Pairs for Simply Typed Term Rewriting
Simply typed term rewriting proposed by Yamada (RTA, 2001) is a framework of higher-order term rewriting without bound variables. In this paper, the dependency pair method of first-order term rewriting introdu...
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Chapter and Conference Paper
Inductive Theorems for Higher-Order Rewriting
Based on the simply typed term rewriting framework, inductive reasoning in higher-order rewriting is studied. The notion of higher-order inductive theorems is introduced to reflect higher-order feature of simp...