A Higher-Order Knuth-Bendix Procedure and Its Applications

Keiichirou KUSAKARI
Yuki CHIBA

Publication
IEICE TRANSACTIONS on Information and Systems   Vol.E90-D    No.4    pp.707-715
Publication Date: 2007/04/01
Online ISSN: 1745-1361
DOI: 10.1093/ietisy/e90-d.4.707
Print ISSN: 0916-8532
Type of Manuscript: PAPER
Category: Computation and Computational Models
Keyword: 
simply-typed term rewriting system,  higher-order KB procedure,  inductive theorem,  inductionless induction,  fusion transformation,  

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Summary: 
The completeness (i.e. confluent and terminating) property is an important concept when using a term rewriting system (TRS) as a computational model of functional programming languages. Knuth and Bendix have proposed a procedure known as the KB procedure for generating a complete TRS. A TRS cannot, however, directly handle higher-order functions that are widely used in functional programming languages. In this paper, we propose a higher-order KB procedure that extends the KB procedure to the framework of a simply-typed term rewriting system (STRS) as an extended TRS that can handle higher-order functions. We discuss the application of this higher-order KB procedure to a certification technique called inductionless induction used in program verification, and its application to fusion transformation, a typical kind of program transformation.

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