# IEEE Symposium on Logic in Computer Science

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# Logic in Computer Science (LICS 2007)

## Invited Paper: Higher-Order Matching, Games and Automata (at LICS 2007)

Authors: Colin Stirling

### 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.

### BibTeX

  @InProceedings{Stirling-HigherOrderMatching,
author = 	 {Colin Stirling},
title = 	 {Higher-Order Matching, Games and Automata},
booktitle =  {Proceedings of the Twenty-Second Annual IEEE Symposium on Logic in Computer Science (LICS 2007)},
year =	 {2007},
month =	 {July},
pages =      {326--335},
location =   {Wroclaw, Poland},
note =       {Invited Talk},
publisher =	 {IEEE Computer Society Press}
}