The paper develops an abstract (over-approximating) semantics for double-pushout rewriting of graphs and graph-like objects. The focus is on the so-called materialization of left-hand sides from abstract graphs, a central concept in previous work. The first contribution is an accessible, general explanation of how materializations arise from universal properties and categorical constructions, in particular partial map classifiers, in a topos. Second, we introduce an extension by enriching objects with annotations and give a precise characterization of strongest post-conditions, which are effectively computable under certain assumptions.
CITATION STYLE
Corradini, A., Heindel, T., König, B., Nolte, D., & Rensink, A. (2019). Rewriting Abstract Structures: Materialization Explained Categorically. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 11425 LNCS, pp. 169–188). Springer Verlag. https://doi.org/10.1007/978-3-030-17127-8_10
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