More on Graph Rewriting With Contextual Refinement

In GRGEN , a graph rewrite generator tool, rules have the outstandingfeature that variables in their pattern and replacement graphs may be refined withmeta-rules based on contextual hyperedge replacement grammars. A refined rule maydelete, copy, and transform subgraphs of unbounded size and of variable shape. Inthis paper, we show that rules with contextual refinement can be transformed to stan-dard graph rewrite rules that perform the refinement incrementally, and are appliedaccording to a strategy called residual rewriting. With this transformation, it is possi-ble to state precisely whether refinements can be determined in finitely many steps ornot, and whether refinements are unique for every form of refined pattern or not

Graph Rewriting with Contextual Refinement

In the standard theory of graph transformation, a rule modifies only subgraphs of constant size and fixed shape.  The rules supported by the graph-rewriting tool GrGen are far more expressive: they may modify subgraphs of unbounded size and variable shape. Therefore properties like termination and confluence cannot be analyzed as for the standard case. In order to lift such results, we formalize the outstanding feature of GrGen rules by using plain rules on two levels: schemata} are rules with variables; they are refined with meta-rules, which are based on contextual hyperedge replacement, before they are used for rewriting.We show that every rule based on single pushouts, on neighborhood-controlled embedding, or on variable substitution can be modeled by a schema with appropriate meta-rules. It turns out that the question whether schemata may have overlapping refinements is not decidable

Pattern-based Rewriting through Abstraction

Fundamenta Informaticae, vol. 144, no. 2, pp. 109-160, 2016, Copyright 2016, with permission from IOS PressModel-based development relies on models in different phases for different purposes, with modelling patterns being used to document and gather knowledge about good practices in specific domains, to analyse the quality of existing designs, and to guide the construction and refactoring of models. Providing a formal basis for the use of patterns would also support their integration with existing approaches to model transformation. To this end, we turn to the commonly used, in this context, machinery of graph transformations and provide an algebraic-categorical formalization of modelling patterns, which can express variability and required/forbidden application contexts. This allows the definition of transformation rules having patterns in left and right-hand sides, which can be used to express refactorings towards patterns, change the use of one pattern by a different one, or switch between pattern variants. A key element in our proposal is the use of operations to abstract models into patterns, so that they can be manipulated by pattern rules, thus leading to a rewriting mechanism for classes of graphs described by patterns and not just individual graphs. The proposal is illustrated with examples in object-oriented software design patterns and enterprise architecture patterns, but can be applied to any other domain where patterns are used for modelling.This work has been partially supported by the Spanish Ministry of Economy and Competitivity with projects Go-Lite (TIN2011-24139) and Flexor (TIN2014-52129-R), the Madrid Region with project SICOMORO (S2013/ICE-3006), and the EU commission with project MONDO (FP7-ICT-2013-10, #611125)

Shapely Hierarchical Graph Transformation

Diagrams can be represented by graphs, and the animation and transformation of diagrams can be modeled by graph transformation. This paper studies extensions of graphs and graph transformation that are important for programming with graphs: ¯ We extend graphs by a notion of hierarchy that supports value composition, and define hierarchical graph transformation in an intuitive way that resembles term rewriting. ¯ We require that admissable shapes for hierarchical graphs are specified by context-free graph grammars, in order to set up a type discipline for shapely hierarchical graph transformation. The resulting computational model shall be the basis of the visual language DIAPLAN for programming with graphs that represent diagrams