We consider anti-unification for simply typed lambda terms in theories defined by associativity, commutativity, identity (unit element) axioms and their combinations and develop a sound and complete algorithm which takes two lambda terms and computes their equational generalizations in the form of higher-order patterns. The problem is finitary: the minimal complete set of such generalizations contains finitely many elements. We define the notion of optimal solution and investigate special restrictions of the problem for which the optimal solution can be computed in linear or polynomial time.

中文翻译：

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高阶模式泛化模方程理论

我们在由关联性、交换性、同一性（单位元素）公理及其组合定义的理论中考虑了简单类型 lambda 项的反统一，并开发了一个健全且完整的算法，该算法采用两个 lambda 项并以更高的形式计算它们的等式推广订单模式。问题是有限的：这种概括的最小完整集包含有限多个元素。我们定义了最优解的概念，并研究了可以在线性或多项式时间内计算最优解的问题的特殊限制。