We present a rule-based Huet’s style anti-unification algorithm for simply typed lambda-terms, which computes a least general higher-order pattern generalization. For a pair of arbitrary terms of the same type, such a generalization always exists and is unique modulo $$\alpha $$α-equivalence and variable renaming. With a minor modification, the algorithm works for untyped lambda-terms as well. The time complexity of both algorithms is linear.

中文翻译：

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线性时间的高阶模式反统一

我们针对简单类型的 lambda 项提出了一种基于规则的 Huet 风格反统一算法，该算法计算最不通用的高阶模式泛化。对于一对相同类型的任意项，这样的泛化始终存在，并且是唯一的模 $$\alpha $$α 等价和变量重命名。经过较小的修改，该算法也适用于非类型化 lambda 项。两种算法的时间复杂度都是线性的。