Higher-Order Matching and Tree Automata
CSL '97 Selected Papers from the11th International Workshop on Computer Science Logic
On Model-Checking Trees Generated by Higher-Order Recursion Schemes
LICS '06 Proceedings of the 21st Annual IEEE Symposium on Logic in Computer Science
Higher-Order Matching, Games and Automata
LICS '07 Proceedings of the 22nd Annual IEEE Symposium on Logic in Computer Science
FOSSACS '09 Proceedings of the 12th International Conference on Foundations of Software Science and Computational Structures: Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2009
LICS '09 Proceedings of the 2009 24th Annual IEEE Symposium on Logic In Computer Science
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Higher-order unification is the problem given an equation t=u containing free variables is there a solution substitution θ such that tθ and uθ have the same normal form? The terms t and u are from the simply typed lambda calculus and the same normal form is with respect to βη-equivalence. Higher-order matching is the particular instance when the term u is closed; can t be pattern matched to u? Although higher-order unification is undecidable, higher-order matching was conjectured to be decidable by Huet [2]. Decidability was shown in [7] via a game-theoretic analysis of β-reduction when component terms are in η-long normal form. In the talk we outline the proof of decidability. Besides the use of games to understand β-reduction, we also emphasize how tree automata can recognize terms of simply typed lambda calculus as developed in [1, 3-6].