Correctness of graph programs relative to HR+ conditions

In (Pennemann 2009), the correctness of graph programs relative to nested graph conditions is considered. Since these conditions are expressively equivalent to first-order graph formulas, non-local graph properties in the sense of Gaifman are not expressible by nested graph conditions. We generalize the concept of nested graph conditions to socalled HR+ conditions and investigate the correctness for graph programs relative to these generalized conditions.