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Chapter and Conference Paper
Nominal Confluence Tool
Nominal rewriting is a framework of higher-order rewriting introduced in (Fernández, Gabbay & Mackie, 2004; Fernández & Gabbay, 2007). Recently, (Suzuki et al., 2015) revisited confluence of nominal rewriting ...
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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...
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Chapter and Conference Paper
Termination of Simply Typed Term Rewriting by Translation and Labelling
Simply typed term rewriting proposed by Yamada (RTA 2001) is a framework of term rewriting allowing higher-order functions. In contrast to the usual higher-order term rewriting frameworks, simply typed term re...
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Chapter and Conference Paper
Termination transformation by tree lifting ordering
An extension of a modular termination result for term rewriting systems (TRSs, for short) by A. Middeldorp (1989) is presented. We intended to obtain this by adapting the dummy elimination transformation by M....
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Chapter and Conference Paper
Solution to the problem of Zantema on a persistent property of term rewriting systems
A property P of term rewriting systems is persistent if for any many-sorted term rewriting system R, R has the property P iff its underlying term rewriting system θ(R), which results from R by omitting its sort i...
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Chapter and Conference Paper
On composable properties of term rewriting systems
A property of term rewriting system (TRS, for short) is said to be composable if it is preserved under unions. We present composable properties of TRSs on the base of modularity results for direct sums of TRSs...