Higher-order pattern generalization modulo equational theories

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.

One or Nothing: Anti-unification over the Simply-Typed Lambda Calculus

“…Examples: associative, commutative, and associative-commutative AU [1], AU with a single unit equation [13], unranked Term-graphs AU [8], hedges [18] • Infinitary: The mcsg R (s, t) exists for all s, t and there exists at least one pair of terms for which it is infinite.…”