The PBPO graph transformation approach

We propose a new algebraic approach to graph transformation, called the Pullback-Pushout ( pbpo ) approach, where we combine smoothly the classical modifications to a host graph specified by a first part of a rule, defined as a span of graph morphisms, with the cloning of structures specified by a second span. The motivation behind this new approach is to support cloning of structures in an elegant and efficient way. After a formal definition of the proposed approach, we demonstrate that pbpo rewriting is a conservative extension of agree and the Sesqui-Pushout approaches. Contrary to agree, we show that the proposed pbpo transformation can easily be extended to cope with attributed graphs. In general, totally attributed graphs are not closed under pbpo transformation. We propose sufficient conditions which guarantee that the attribution of transformed graphs is total. Furthermore, a pbpo transformation can affect all parts of a host graph including non local parts (i.e., parts which are outside the image of the left-hand side of a rule). We propose and discuss some conditions which ensure a form of locality of pbpo transformations.