Efficient Full Higher-Order Unification

We developed a procedure to enumerate complete sets of higher-order unifiers based on work by Jensen and Pietrzykowski. Our procedure removes many redundant unifiers by carefully restricting the search space and tightly integrating decision procedures for fragments that admit a finite complete set o...

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Bibliographic Details
Main Authors: Petar Vukmirović, Alexander Bentkamp, Visa Nummelin
Format: Article
Language:English
Published: Logical Methods in Computer Science e.V. 2021-12-01
Series:Logical Methods in Computer Science
Subjects:
Online Access:https://lmcs.episciences.org/6919/pdf
Description
Summary:We developed a procedure to enumerate complete sets of higher-order unifiers based on work by Jensen and Pietrzykowski. Our procedure removes many redundant unifiers by carefully restricting the search space and tightly integrating decision procedures for fragments that admit a finite complete set of unifiers. We identify a new such fragment and describe a procedure for computing its unifiers. Our unification procedure, together with new higher-order term indexing data structures, is implemented in the Zipperposition theorem prover. Experimental evaluation shows a clear advantage over Jensen and Pietrzykowski's procedure.
ISSN:1860-5974