Efficient Full Higher-Order Unification

TL;DR

This paper presents a new, efficient procedure for higher-order unification that reduces redundancy, introduces a novel unification fragment, and demonstrates improved performance in a theorem prover.

Contribution

It introduces a restricted, more efficient unification procedure with a new finite unification fragment and integrates it into the Zipperposition prover.

Findings

Experimental results show improved efficiency over previous methods.

The new fragment admits a finite complete set of unifiers.

Implementation in Zipperposition enhances theorem proving performance.

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, 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.