Dynamic Recursion Pattern

Everybody knows what recursion is and how it should be implemented in a procedural language. The first analysis of recursion implementations is due Kent Beck [Beck92], but no formalization was given. The other work on an OOP implementation of the subject is due to Boby Wolf [Wolf97], but his work only deals with one aspect of the problem: Structural Recursion. Structural Recursion is a particular aspect of general recursion where the recursion is performed by a set of objects (a list or a tree, for example) that is already present in the computer memory. All the participating objects must exist previously the recursion starts. As opposite to Structural Recursion, Dynamic Recursion does not put such a strong requirement on the way the recursion is performed. This is done simply by delaying the creation of the recursive elements until they are actually needed, and thus, delaying the decision of finishing the recursion until its very end. Examples of recursion that can only be handled with this pattern are the famous eight-rook problem [HVC91] or even a simple airplane-routing problem. Another important point to be taken into account is that implementing recursive behavior into an object is more or less the same as forcing it to use a certain built-in iterator instead of using the iterator pattern [GoF]. Let's start by a simple, widely known example: sorting an array by the well known MergeSort Strategy (the analysis would be identical for the QuickSort strategy)[Baa91]. The traditional way to do so in procedural programming can be translated as is to OOP by creating a new message sort: in a MergeSort class: