一句话：提出高效完全高阶合一过程，通过限制搜索空间与集成片段判定，在 Zipperposition 中实现并优于已有方法。
高阶合一在自动化定理证明中至关重要，但完全高阶合一通常会产生大量冗余合一子，搜索空间巨大。本文在 Jensen 与 Pietrzykowski 工作的基础上，设计了一种枚举完全高阶合一子集合的过程。该方法通过仔细限制搜索空间来删除冗余合一子，并紧密集成那些具有有限完全合一子集合的片段的判定过程；作者还识别出一个新的此类片段并给出计算其合一子的过程。该过程与新的高阶项索引数据结构一起实现在 Zipperposition 定理证明器中。实验评估表明，相比 Jensen 与 Pietrzykowski 的过程具有明显优势。
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}
}