Francesco Parisi Presicce

Formal Software Specification with Refinements and Modules of Typed Graph Transformation Systems

Graph transformation systems are a formal specification technique for software systems that support the rule based specification of the dynamic behaviour of a system.Their main advantages are the intuitive visual representation of states and state transformations as graphs on the one hand, and the fully formal semantics on the other hand, that allow precise statements about the specification and tool support. In this paper we introduce refinements and modules for typed graph transformation systems to support the software specification development in both dimensions: modules for the horizontal structuring of a specification, i.e., its composition from feasible parts, and refinements for the development over time.

Refinements and modules for typed graph transformation systems

Petri Nets as a Uniform Approach to High-Level Petri Nets . . . . . 241 J. PadbergSpatial and temporal refinement relations between typed graph transformation systems have been introduced in [6,7]. In a spatial refinement a transformation rule is refined by an amalgamation of rules while in a temporal refinement it is refined by a sequence of rules: in both cases, the refinement relation supports the modeling of implementation. In the first part of this paper, we further investigate the properties of spatial and temporal refinements while, in the second part, we employ them for the development of a module concept for typed graph transformation systems. Finally, as a first step towards an algebra of modules, we introduce the operations of union and composition of modules.

High-level replacement units and their termination properties

Visual rewriting techniques, in particular graph transformations, are increasingly used to model transformations of systems specified through diagrammatic sentences. Several rewriting models have been proposed, differing in the expressivity of the types of rules and in the complexity of the rewriting mechanism; yet, for many of them, basic results concerning the formal properties of these models are still missing. In this paper, we give a contribution towards solving the termination problem for rewriting systems with external control mechanisms. In particular, we obtain results of more general validity by extending the concept of transformation unit to high-level replacement systems, a generalization of graph transformation systems. For high-level replacement units, we state and prove several abstract properties based on termination criteria. Then, we instantiate the high-level replacement systems by attributed graph transformation systems and present concrete termination criteria. We explore some types of rules and replacement units for which the criterion can be established. These are used to show the termination of some replacement units needed to express model transformations formalizing refactoring.

Annotation processes for flexible management of contextual information

We propose the use of annotations as a way to flexibly enrich a domain of interest with information concerning different contexts of use for its elements. We provide a formal model of annotation in the framework of typed graphs, in which the presence of annotations is reified through nodes and edges of specific types, relating nodes from different domains. This allows the flexible activation and de-activation of annotations, as well as the addition of several annotations from different domains on the same element. We show that annotations give rise to a category, where pushouts are the basic construct for the composition of annotation-related processes. We prove some properties of annotated graphs and discuss examples drawn from several fields.

A Termination Criterion for Graph Transformations with Negative Application Conditions

Termination of graph transformations is in general undecidable, but it is possible to prove it for specific systems by checking for sufficient conditions. In the presence of rules with negative application conditions, the difficulties increase. In this paper we propose a different approach to the identification of a (sufficient) criterion for termination, based on the construction of a labelled transition system whose states represent overlaps between the negative application condition and the right hand side that can give rise to cycles.

Spider Graphs: a graph transformation system for spider diagrams

The use of diagrammatic logic as a reasoning mechanism to produce inferences on subsets of some universe could provide a way to overcome the current limitations of visual modelling methods, which have to be integrated with textual languages to express complex constraints. On the other hand, graph transformations are becoming widespread as a way to express formal semantics for visual modelling languages, so that a mechanisation of diagrammatic logic based on graph transformation would facilitate language integration, based on a common underlying machinery. In this paper, we propose such a mechanisation for spider diagrams (SDs), an established language for reasoning with diagrams modelling relations between sets and constraints on their cardinalities. The concrete syntax of SDs extends that of Euler diagrams that use closed curves and the enclosed regions to represent sets and their intersections. The language is augmented with reasoning rules, i.e. syntactic transformation rules corresponding to logical inference rules. However, these rules are typically defined in procedural terms, so that a completely formal specification and an adequate mechanisation of them has not been achieved yet. We propose an abstract syntax for SDs in terms of typed graphs and define the corresponding language of Spider Graphs (SGs), expressing reasoning rules for SDs as graph transformation units. This enables a direct realisation of the reasoning system via graph transformation tools without resorting to ad hoc implementations, and we provide an implementation in AGG. Techniques for static analysis become available to reason on proof strategies and on possible optimisations.

Annotations on Complex Patterns

Modelers of systems often want to isolate specific parts of a model to be treated as a whole, for example to protect them from accidental changes,to constrain them to specific policies, or to identify them as instances of a general pattern. In particular, we study here the case in which these parts are annotated with information from some external model. In a previous paper, we have discussed the use of annotations on individual model elements, represented as nodes in a graph; in this paper we model annotation processes involving also annotations themselves or whole configurations. To address the latter problem, we enrich the notion of graph by introducing a third sort of elements, called boxes, encompassing subgraphs, and associate them with annotations, too. We show how annotations on boxes support the modeling of complex policies,adapting the previous constructions for notation-aware rewriting to include boxes. The paper illustrates these concepts on the concrete modeling scenario of an organisation with security and temporal annotations.

Resource-aware Policies

Abstract In previous papers, we proposed an extension of Spider Diagrams to object-oriented modelling, called Modelling Spider Diagrams (MSDs), as a visual notation for specifying admissible states of instances of types, and for verifying the conformance of configurations of instances with such specifications. Based on this formalisation, we developed a notion of transformation of MSDs, modelling admissible evolutions of configurations. In the original version of MSD, individual instances evolve independently, but in reality evolutions often occur in the context of available resources, so transformations must be extended to take this into account. In this paper we provide an abstract syntax for MSDs, in terms of typed attributed graphs, and a semantics for the specification of policies based on notions from the theory of graph transformations, and we associate with them a notion of resources. We also introduce a synchronisation mechanism, based on annotation of instances with resources, so that the transformations required by a policy occur with respect to available resources. In particular, resources can be atomically produced or consumed or can change their state consistently with the evolution of the spiders subject to the policy.