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Efficient Full Higher-Order Unification

Authors: Petar Vukmirović, Alexander Bentkamp, and Visa Nummelin

Published in: LIPIcs, Volume 167, 5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020)


Abstract
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 is implemented in the Zipperposition theorem prover. Experimental evaluation shows a clear advantage over Jensen and Pietrzykowski’s procedure.

Cite as

Petar Vukmirović, Alexander Bentkamp, and Visa Nummelin. Efficient Full Higher-Order Unification. In 5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 167, pp. 5:1-5:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{vukmirovic_et_al:LIPIcs.FSCD.2020.5,
  author =	{Vukmirovi\'{c}, Petar and Bentkamp, Alexander and Nummelin, Visa},
  title =	{{Efficient Full Higher-Order Unification}},
  booktitle =	{5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020)},
  pages =	{5:1--5:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-155-9},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{167},
  editor =	{Ariola, Zena M.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2020.5},
  URN =		{urn:nbn:de:0030-drops-123271},
  doi =		{10.4230/LIPIcs.FSCD.2020.5},
  annote =	{Keywords: unification, higher-order logic, theorem proving, term rewriting, indexing data structures}
}
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