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Higher-order pattern generalization modulo equational theories

Published online by Cambridge University Press:  20 May 2020

David M. Cerna Open the ORCID record for David M. Cerna [Opens in a new window]  and
Temur Kutsia
David M. Cerna*
Affiliation:
RISC, Johannes Kepler University, Linz, Austria FMV, Johannes Kepler University, Linz, Austria
Temur Kutsia
Affiliation:
RISC, Johannes Kepler University, Linz, Austria
*
*Corresponding author. Email: david.cerna@risc.jku.at
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Abstract

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We consider anti-unification for simply typed lambda terms in theories defined by associativity, commutativity, identity (unit element) axioms and their combinations and develop a sound and complete algorithm which takes two lambda terms and computes their equational generalizations in the form of higher-order patterns. The problem is finitary: the minimal complete set of such generalizations contains finitely many elements. We define the notion of optimal solution and investigate special restrictions of the problem for which the optimal solution can be computed in linear or polynomial time.

Keywords

Simply typed lambda calculusanti-unificationequational theorieshigher-order patterns
Type
Paper
Information
Mathematical Structures in Computer Science , Volume 30 , Special Issue 6: Special Issue: Unification , June 2020 , pp. 627 - 663
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s) 2020. Published by Cambridge University Press

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