In-place Graph Rewriting with Interaction Nets

Abstract: An algorithm is in-place, or runs in-situ, when it does not need any additional memory to execute beyond a small constant amount. There are many algorithms that are efficient because of this feature, therefore it is an important aspect of an algorithm. In most programming languages, it is not obvious when an algorithm can run in-place, and moreover it is often not clear that the implementation respects that idea. In this paper we study interaction nets as a formalism where we can see directly, visually, that an algorithm is in-place, and moreover the implementation will respect that it is in-place. Not all algorithms can run in-place however. We can nevertheless still use the same language, but now we can annotate parts of the algorithm that can run in-place. We suggest an annotation for rules, and give an algorithm to find this automatically through analysis of the interaction rules.