Computer Software
Print ISSN : 0289-6540
Disproving Strong Head Normalization and General Productivity Automatically in Infinitary Term Rewriting Systems
Munehiro IWAMITakahito AOTO
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2012 Volume 29 Issue 1 Pages 1_211-1_239

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Abstract

Infinitary term rewriting has been proposed to model functional programs that deal with virtually infinite data structures such as streams or lazy lists. Strong head normalization is a fundamental property of infinitary term rewriting systems and methods for proving this property have been proposed by Zantema (2008) and Endrullis et al. (2009). Endrullis et al. (2010) have proposed a class of infinitary term rewriting systems—stream term rewriting systems—and they have given a decision procedure of the productivity of streams for a class of stream term rewriting systems. In this paper, we present procedures for disproving these two properties of infinitary term rewriting systems—the strong head normalization and the productivity. The basic idea of our procedure is to construct rational counterexamples which are infinitary terms but have finite representations. The correctness of our procedures is proved and an implementation is reported. Our experiments reveal that our procedures successfully disprove the strong head normalization and the productivity automatically for some examples for which no automated disproving procedure is known.

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© Japan Society for Software Science and Technology 2012
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