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International Conference on Automated Deduction

CADE 1994: Automated Deduction — CADE-12 pp 635–649Cite as

Decidable higher-order unification problems

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 814))

Abstract

Second-order unification is undecidable in general. Miller showed that unification of so-called higher-order patterns is decidable and unitary. We show that the unification of a linear higher-order pattern s with an arbitrary second-order term that shares no variables with s is decidable and finitary. A few extensions of this unification problem are still decidable: unifying two second-order terms, where one term is linear, is undecidable if the terms contain bound variables but decidable if they don't.

Research supported by the DFG under grant Br 887/4-2, Deduktive Programmentwicklung and by ESPRIT WG 6028, CCL.

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Authors and Affiliations

  1. Fakultät für Informatik, Technische Universität München, 80290, München, Germany

    Christian Prehofer

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  1. Christian Prehofer
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Alan Bundy

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© 1994 Springer-Verlag Berlin Heidelberg

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Prehofer, C. (1994). Decidable higher-order unification problems. In: Bundy, A. (eds) Automated Deduction — CADE-12. CADE 1994. Lecture Notes in Computer Science, vol 814. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58156-1_46

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  • DOI: https://doi.org/10.1007/3-540-58156-1_46

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58156-7

  • Online ISBN: 978-3-540-48467-7

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