The Pullback-Pushout approach to algebraic graph transformation

Some recent algebraic approaches to graph transformation include a pullback construction involving the match, that allows one to specify the cloning of items of the host graph. We pursue further this trend by proposing the Pullback-Pushout (pb-po) Approach, where we combine smoothly the classical modifications to a host graph specified by a rule (a span of graph morphisms) with the cloning of structures specified by another rule. The approach is shown to be a conservative extension of agree (and thus of the sqpo approach), and we show that it can be extended with standard techniques to attributed graphs. We discuss conditions to ensure a form of locality of transformations, and conditions to ensure that the attribution of transformed graphs is total