# Efficient Full Higher-Order Unification

arXiv: https://arxiv.org/abs/2011.09507 · HTML: https://mlsanity.com/paper/2011.09507/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Nov 2020.

## Built on by (most cited first, 1 of 1)

- [Superposition with Lambdas](https://mlsanity.com/paper/2102.00453/) (2021)

## Abstract (arXiv)

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.