Static Dependency Pair Method Based on Strong Computability for Higher-Order Rewrite Systems

Keiichirou KUSAKARI  Yasuo ISOGAI  Masahiko SAKAI  Frederic BLANQUI  

IEICE TRANSACTIONS on Information and Systems   Vol.E92-D   No.10   pp.2007-2015
Publication Date: 2009/10/01
Online ISSN: 1745-1361
DOI: 10.1587/transinf.E92.D.2007
Print ISSN: 0916-8532
Type of Manuscript: PAPER
Category: Computation and Computational Models
higher-order rewrite system,  termination,  static dependency pair,  plain function-passing,  strong computability,  subterm criterion,  

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Higher-order rewrite systems (HRSs) and simply-typed term rewriting systems (STRSs) are computational models of functional programs. We recently proposed an extremely powerful method, the static dependency pair method, which is based on the notion of strong computability, in order to prove termination in STRSs. In this paper, we extend the method to HRSs. Since HRSs include λ-abstraction but STRSs do not, we restructure the static dependency pair method to allow λ-abstraction, and show that the static dependency pair method also works well on HRSs without new restrictions.