Abstract
In this article we examine some consequences of computation order of two different conceptual implementations of the fold function. We explore a set of performance- and accuracy-based experiments on two implementations of this function. In particular, we contrast the traditional fold-left implementation with another approach we refer to as tree-fold. It is often implicitly supposed that the binary operation in question has constant complexity. We explore several application areas which diverge from that assumption: rational arithmetic, floating-point arithmetic, and Binary Decisions Diagram construction. These are binary operations which degrade in performance as the fold iteration progresses. We show that these types of binary operations are good candidates for tree-fold.