Semantics Of Visual Languages Research Articles

Rule-based transformation of graph rewriting rules: Towards higher-order graph grammars

Higher-order functions – the ones which manipulate other functions – have a fundamental role in Computer Science, specially in areas such as functional programming and theory of computation. Graph transformation – the rule-based modification of graphs – is also an important approach used in many contexts, as for instance, the definition of syntax and semantics of visual languages and the modelling and analysis of concurrent and non-deterministic systems. Although the algebraic double-pushout (DPO) approach to graph transformation has a vast theory, it does not present a notion of higher-order transformation, i.e., transformation of graph rewriting rules themselves. Higher-order would be required, for instance, to ease the modelling of dynamic systems through graph transformation systems, and to describe model transformations that modify graph rewriting rules. The main contribution of this work is a notion of double-pushout transformation for graph rewriting rules, where the result of the rewriting is a valid graph rule. We use DPO diagrams in the category of graph spans to describe rule transformations, and negative application conditions (NACs) in the second-order rules to enforce preservation of the rule structure. We define a model named second-order graph grammars, capable of first- and second-order derivations. Finally, we discuss alternative ways of defining second-order transformations.

Enforced generative patterns for the specification of the syntax and semantics of visual languages

We present the new notion of enforced generative pattern, a structure that declares positive or negative conditions that must be satisfied by a model. Patterns are applied to transformation rules resulting in new rules that modify models according to the pattern specification. In the case of a negative pattern, an application condition is added to the rule. In the case of a positive one, the rule is modified to consider additional context in its left-hand side and to increase its effects. We have defined these patterns in an abstract setting, which enables their instantiation for different structures, like graphs, triple graphs and graph transformation rules. We apply the previous concepts to the specification of the syntax and semantics of visual languages. In particular, we show instantiations for: (i) graphs, with applications at the syntactical level; (ii) triple graphs, for the coordination of syntax and static semantics; and (iii) rules, for the incremental construction of execution rules. We present some examples that illustrate the usefulness of the combination of these three instantiations. In particular, we show the specification of environments for visual languages with token-holder semantics, discrete-event semantics and communication semantics.

Abstract Syntax and Semantics of Visual Languages

The effective use of visual languages requires a precise understanding of their meaning. Moreover, it is impossible to prove properties of visual languages like soundness of transformation rules or correctness results without having a formal language definition. Although this sounds obvious, it is surprising that only little work has been done about the semantics of visual languages, and even worse, there is no general framework available for the semantics specification of different visual languages. We present such a framework that is based on a rather general notion of abstract visual syntax. This framework allows a logical as well as a denotational approach to visual semantics, and it facilitates the formal reasoning about visual languages and their properties. We illustrate the concepts of the proposed approach by defining abstract syntax and semantics for the visual languages VEX, Show and Tell and Euler circles. We demonstrate the semantics in action by proving a rule for visual reasoning with Euler circles and by showing the correctness of a Show and Tell program.