Higher-order unification is the problem given an equation t = u containing free variables is there a solution substitution theta such that t theta and u theta 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 beta eta-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 . Decidability was shown in  via a game-theoretic analysis of beta-reduction when component terms are in eta-long normal form.
In the talk we outline the proof of decidability. Besides the use of games to understand beta-reduction, we also emphasize how tree automata can recognize terms of simply typed lambda calculus as developed in [1, 3-6].
|Title of host publication||Introduction to Decidability of Higher-Order Matching|
|Subtitle of host publication||FOUNDATIONS OF SOFTWARE SCIENCE AND COMPUTATIONAL STRUCTURES, PROCEEDINGS|
|Place of Publication||BERLIN|
|Number of pages||1|
|Publication status||Published - 2010|
|Event||13th International Conference on Foundations of Software Science and Computational Structures/Joint European Conferences on Theory and Practice of Software - Paphos|
Duration: 20 Mar 2010 → 28 Mar 2010
|Conference||13th International Conference on Foundations of Software Science and Computational Structures/Joint European Conferences on Theory and Practice of Software|
|Period||20/03/10 → 28/03/10|