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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
Colin Stirling , University of Edinburgh, UK
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.

C. Stirling, "Higher-Order Matching, Games and Automata," 2007 22nd Annual IEEE Symposium on Logic in Computer Science(LICS), Wroclaw, 2007, pp. 326-335.
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