@**techreport**{RISC5918,author = {David M. Cerna and Temur Kutsia},

title = {{Higher-Order Pattern Generalization Modulo Equational Theories}},

language = {english},

abstract = {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.
The algorithm does not depend on the number of idempotent function symbols in the input terms. The
language generated by the grammar is the minimal complete set of generalizations of the given
anti-unification problem, which implies that idempotent anti-unification is infinitary.},

year = {2019},

keywords = {Anti-unification Lambda Calculus},

length = {40},

type = {RISC Report Series},

institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},

address = {Altenberger Straße 69, 4040 Linz, Austria},

issn = {2791-4267 (online)}

}