Abstract. In this paper we describe an application of the theory of graph transformations to the practise of language design. In particular, we have defined the static and dynamic semantics of a small but realistic object-oriented language (called TAAL) by mapping the language constructs to graphs (the static semantics) and modelling their effect by graph transformation rules (the dynamic semantics). This gives rise to execution models for all TAAL-programs, which can be used as the basis for formal verification.This work constitutes a first step towards a method for defining all aspects of software languages, besides their concrete syntax, in a consistent and rigorous manner. Such a method facilitates the integration of formal correctness in the software development trajectory.
Model transformations support a model-driven design by providing an automatic translation of abstract models into more concrete ones, and eventually program code. Crucial to a successful application of model transformations is their correctness, in the sense that the meaning (semantics) of the models is preserved. This is especially important if the models not only describe the structure but also the intended behaviour of the systems. Reasoning about and showing correctness is, however, often impossible as the source and target models typically lack a precise definition of their semantics.In this paper, we take a first step towards provably correct behavioural model transformations. In particular, we develop transformations from UML Activities (which are visual models) to programs in TAAL, which is a textual Java-like programming language. Both languages come equipped with formal behavioural semantics, which, moreover, have the same semantic domain. This sets the stage for showing correctness, which in this case comes down to showing that the behaviour of every (well-formed) UML Activity coincides with that of the corresponding TAAL program, in a well-defined sense.
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