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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.

In this paper we propose a visual language CFSL for specifying control flow semantics of programming languages. We also present a translation from CFSL to graph production systems (GPS) for flow graph construction; that is, any CFSL specification, say for a language L, gives rise to a GPS that constructs from any L-program (represented as an abstract syntax graph) the corresponding flow graph. The specification language is rich enough to capture complex language constructs, including all of Java.

We present an algorithm for partial order reduction in the context of a countable universe of deterministic actions, of which finitely many are enabled at any given state. This means that the algorithm is suited for a setting in which resources, such as processes or objects, are dynamically created and destroyed, without an a priori bound. The algorithm relies on abstract enabling and disabling relations among actions, rather than associated sets of concurrent processes. It works by selecting so-called probe sets at every state, and backtracking in case the probe is later discovered to have missed some possible continuation.We show that this improves the potential reduction with respect to persistent sets. We then instantiate the framework by assuming that states are essentially sets of entities (out of a countable universe) and actions test, delete and create such entities. Typical examples of systems that can be captured in this way are Petri nets and (more generally) graph transformation systems. We show that all the steps of the algorithm, including the estimation of the missed actions, can be effectively implemented for this setting. This work has been carried out in the context of the GROOVE project funded by the Dutch NWO (project number 612.000.314).

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We offer an alternative to the standard way of formalising attributed graphs. We propose to represent them as graphs with a marked sub-graph that represents the data domain, rather than as tuples of graph and algebra. This is a general construction which can be shown to preserve adhesiveness of categories; it has the advantage of uniformity and gives more flexibility in defining data abstractions. We show equivalence of our formalisation with the standard one, under a suitable encoding of algebras as graphs.