Adjunction for Garbage Collection with Application to Graph Rewriting

We investigate garbage collection of unreachable parts of rooted graphs from a categorical point of view. First, we define this task as the right adjoint of an inclusion functor. We also show that garbage collection may be stated via a left adjoint, hence preserving colimits, followed by two right adjoints. These three adjoints cope well with the different phases of a traditional garbage collector. Consequently, our results should naturally help to better formulate graph transformation steps in order to get rid of garbage (unwanted nodes). We illustrate this point on a particular class of graph rewriting systems based on a double pushout approach and featuring edge redirection. Our approach gives a neat rewriting step akin to the one on terms, where garbage never appears in the reduced term.

• Type: Conference
• Year: 2007
• Where: RTA
• Authors: Dominique Duval, Rachid Echahed, Frédéric Prost
• Keywords: Garbage Collection, Right Adjoints, RTA 2007, Theoretical Computer Science, Traditional Garbage Collector