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 metamodelling 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

An Algebra of Design Patterns

In a pattern-oriented software design process, design decisions are made by selecting and instanti- ating appropriate patterns, and composing them together. In our previous work, we enabled these decisions to be formalised by dening a set of operators on patterns with which instantiations and compositions can be represented. In this paper, we investigate the algebraic properties of these operators. We provide and prove a complete set of algebraic laws so that equivalence between pattern expressions can be proven. Furthermore, we dene an always-terminating normalisation of pattern expressions to a canonical form, which is unique modulo equivalence in rst-order logic. By a case study, the pattern-oriented design of an extensible request-handling framework, we demonstrate two practical applications of the algebraic framework. Firstly, we can prove the correctness of a nished design with respect to the design decisions made and the formal specication of the patterns. Secondly, we can even derive the design from these components