Folding an e-graph in pure egglog

Abstract: Folding over a recursive data structure (also known as "catamorphism") is an essential operation in functional programming. It allows one to declaratively define a recursive computation by focusing on how solutions of subproblems are combined into the solution of the parent problem. Folding in the context of e-graphs can have several benefits. Not only do we get memoization for free, but also computation is drastically reduced since the subproblems are defined over e-classes as opposed to concrete sub-terms. This short report presents our initial attempt at defining and implementing catamorphism, a general notion of a fold, in pure egglog. We discuss a reusable implementation trick to stage the inference rules so that there is no re-propagation of updated values.