From Pattern Invocation Networks to Rule Preconditions

Incremental (graph) pattern matchers provide a suitable, high-level platform for implementing Graph Transformation (GT) engines. All incremental pattern matchers we are aware of use a similar notion of Pattern Invocation Networks (PINs) as a specification language. Leveraging an incremental pattern matcher for GT thus requires a semantics-preserving transformation from GT rules to PINs. Although graph queries have been formally related to generalised discrimination networks (a generalisation of PINs) in the literature, practical GT engines typically support only a much more restrictive form of “flat”, i.e., non-nested graph queries. We are not aware of any formalisation that relates PINs to non-nested graph queries in a way that supports verifying semantics preservation for GT-to-PIN transformations and PIN-to-PIN optimisations in a fully automated manner. In this paper, we therefore propose a formal semantics for a specific class of “flat-equivalent” PINs by providing a flattening transformation to non-nested graph queries.