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

**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} }