Multi-amalgamated triple graph grammars: Formal foundation and application to visual language translation

Visual languages (VLs) facilitate software development by not only supporting communication and abstraction, but also by generating various artifacts such as code and reports from the same high-level specification. VLs are thus often translated to other formalisms, in most cases with bidirectionality as a crucial requirement to, e.g., support re-engineering of software systems. Triple Graph Grammars (TGGs) are a rule-based language to specify consistency relations between two (visual) languages from which bidirectional translators are automatically derived. TGGs are formally founded but are also limited in expressiveness, i.e., not all types of consistency can be specified with TGGs. In particular, 1-to-n correspondence between elements depending on concrete input models cannot be described. In other words, a universal quantifier over certain parts of a TGG rule is missing to generalize consistency to arbitrary size. To overcome this, we transfer the well-known multi-amalgamation concept from algebraic graph transformation to TGGs, allowing us to mark certain parts of rules as repeated depending on the translation context. Our main contribution is to derive TGG-based translators that comply with this extension. Furthermore, we identify bad smells on the usage of multi-amalgamation in TGGs, prove that multi-amalgamation increases the expressiveness of TGGs, and evaluate our tool support.