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.

中文翻译：

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高效的全高阶统一

我们基于 Jensen 和 Pietrzykowski 的工作开发了一个程序来枚举完整的高阶统一子集。我们的程序通过仔细限制搜索空间并紧密集成允许有限完整统一子集的片段的决策程序来删除许多冗余统一子。我们确定了一个新的这样的片段，并描述了计算其统一体的过程。我们的统一程序与新的高阶项索引数据结构一起在拉链位置定理证明器中实现。实验评估显示出优于 Jensen 和 Pietrzykowski 程序的明显优势。