Double-pushout-rewriting in S-Cartesian functor categories: Rewriting theory and application to partial triple graphs

Abstract

A variety of restricted functor categories has been investigated independently and for different purposes to provide double-pushout-rewriting in the areas of model-driven development and graph transformation. We introduce S-cartesian functor categories as a unifying formal framework for these different examples. S-cartesian functor categories are certain subcategories of functor categories that preserve the adhesiveness of their base categories. We show the comprehensive theory of double-pushout-rewriting for S-cartesian functor categories which fulfill additional sufficient conditions. As a new application, we introduce the categories PTrG and APTrG of partial triple graphs and attributed partial triple graphs as S-cartesian functor categories and obtain all the classical results for double-pushout-rewriting in these categories by construction. Partial triple graphs have recently been used to improve model synchronization processes.