Introduction to Decidability of Higher-Order Matching

Colin Stirling

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 languageEnglish
Title of host publicationIntroduction to Decidability of Higher-Order Matching
Subtitle of host publicationFOUNDATIONS OF SOFTWARE SCIENCE AND COMPUTATIONAL STRUCTURES, PROCEEDINGS
EditorsL Ong
Place of PublicationBERLIN
PublisherSpringer-Verlag GmbH
Pages1-1
Number of pages1
ISBN (Electronic)978-3-642-12032-9
ISBN (Print)978-3-642-12031-2
Publication statusPublished - 2010
Event13th International Conference on Foundations of Software Science and Computational Structures/Joint European Conferences on Theory and Practice of Software - Paphos
Duration: 20 Mar 201028 Mar 2010

Conference

Conference13th International Conference on Foundations of Software Science and Computational Structures/Joint European Conferences on Theory and Practice of Software
CityPaphos
Period20/03/1028/03/10

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