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.

@article{paperbot1257,
  title = {Efficient Full Higher-Order Unification},
  author = {Petar Vukmirović and Alexander Bentkamp and Visa Nummelin},
  journal = {Logical Methods in Computer Science},
  volume = {Volume 17, Issue 4},
  year = {2021},
  doi = {10.46298/lmcs-17(4:18)2021}
}