## Abstract

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 [2]. Decidability was shown in [7] 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].

Original language | English |
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Title of host publication | Introduction to Decidability of Higher-Order Matching |

Subtitle of host publication | FOUNDATIONS OF SOFTWARE SCIENCE AND COMPUTATIONAL STRUCTURES, PROCEEDINGS |

Editors | L Ong |

Place of Publication | BERLIN |

Publisher | Springer-Verlag GmbH |

Pages | 1-1 |

Number of pages | 1 |

ISBN (Electronic) | 978-3-642-12032-9 |

ISBN (Print) | 978-3-642-12031-2 |

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

Conference | 13th International Conference on Foundations of Software Science and Computational Structures/Joint European Conferences on Theory and Practice of Software |
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City | Paphos |

Period | 20/03/10 → 28/03/10 |