AGREE – algebraic graph rewriting with controlled embedding

The several algebraic approaches to graph transformation proposed in the literature all ensure that if an item is preserved by a rule, so are its connections with the context graph where it is embedded. But there are applications in which it is desirable to specify different embeddings. For example when cloning an item, there may be a need to handle the original and the copy in different ways. We propose a conservative extension of classical algebraic approaches to graph transformation, for the case of monic matches, where rules allow one to specify how the embedding of preserved items should be carried out.