Logic in Computer Science, Symposium on (2007)

Wroclaw, Poland

July 10, 2007 to July 14, 2007

ISSN: 1043-6871

ISBN: 0-7695-2908-9

pp: 326-335

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/LICS.2007.23

Colin Stirling , University of Edinburgh, UK

ABSTRACT

Higher-order matching is the problem given t = u where t, u are terms of simply typed \lambda-calculus and u is closed, is there a substitution \theta such that t\theta and u have the same normal form with respect to \beta \eta-equality: can t be pattern matched to u? This paper considers the question: can we characterize the set of all solution terms to a matching problem? We provide an automata-theoretic account that is relative to resource: given a matching problem and a finite set of variables and constants, the (possibly infinite) set of terms that are built from those components and that solve the problem is regular. The characterization uses standard bottom-up tree automata.

INDEX TERMS

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CITATION

Colin Stirling,
"Higher-Order Matching, Games and Automata",

*Logic in Computer Science, Symposium on*, vol. 00, no. , pp. 326-335, 2007, doi:10.1109/LICS.2007.23