An institution theory of formal meta-modelling in graphically extended BNF

Meta-modelling plays an important role in model driven software development. In this paper, a graphic extension of BNF (GEBNF) is proposed to define the abstract syntax of graphic modelling languages. From a GEBNF syntax definition, a formal predicate logic language can be induced so that meta-modelling can be performed formally by specifying a predicate on the domain of syntactically valid models. In this paper, we investigate the theoretical foundation of this meta-modelling approach. We formally define the semantics of GEBNF and its induced predicate logic languages, then apply Goguen and Burstall’s institution theory to prove that they form a sound and valid formal specification language for meta-modelling.