Higher-Order Pattern Anti-Unification in Linear Time

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 α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}-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.