Associative unification in Maude - Eker, Steven (Journal of logical and algebraic methods in programming, 2022)
Semantic unification has been much studied since the early days of automated reasoning, and theories such as commutativity and associativity-commutativity (AC) have been built into a number of theorem provers and term rewriting engines. Associativity, which captures the notion of lists, might be considered even more basic than AC, which captures the notion of multisets. However despite being decidable, associative unification has not been widely implemented in general purpose systems, due to its infinitary nature and the high complexity of available algorithms. In this paper we describe the support for associative unification implemented in the Maude system, which is incomplete, but handles many useful cases and smoothly combines with other supported theories.