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-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

This research has been partially supported by the Austrian Science Fund (FWF) project SToUT (P 24087-N18), the Upper Austrian Government strategic program “Innovatives OÖ 2010plus”, the MINECO projects RASO (TIN2015-71799-C2-1-P) and HeLo (TIN2012-33042), the MINECO/FEDER UE project LoCoS (TIN2015-66293-R) and the UdG project MPCUdG2016/055