Abstract
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.
This work has been partly funded by the projet ARROWS of the French Agence Nationale de la Recherche.
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Duval, D., Echahed, R., Prost, F. (2007). Adjunction for Garbage Collection with Application to Graph Rewriting. In: Baader, F. (eds) Term Rewriting and Applications. RTA 2007. Lecture Notes in Computer Science, vol 4533. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73449-9_11
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DOI: https://doi.org/10.1007/978-3-540-73449-9_11
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