A. Corradini and R. Heckel. A compositional approach to structuring and refinement of typed graph grammars. Proc. of SEGRAGRA'95 "Graph Rewriting and Computation", Electronic Notes of TCS, 2, 1995. http://www.elsevier.nl/locate/entcs/volume2.html .  Home/Search   Document Not in Database   Summary   Related Articles   Check

....e.g. allowing analysis of the specified languages is as important as tool support. This theory is based on well developed concepts and tools for algebraic graph transformations ( 8, 5, 11] and can be used for further analysis of the language like consistency checks, layout constraints, etc. [10, 27]) A more comprehensive discussion on the definition of VLs by algebraic specification techniques and graph grammars in combination with GENGED, e.g. Petri nets, Statecharts, Sequence Diagrams, etc. is presented in ( 2] To our point of view a visual specification is a sentence of the GENGED ....

....solver PARCON ( 9] Moreover, the theory of algebraic graph transformation offers analysis techniques, for example for consistency checks. Consistency conditions concerning the existence and non existence of graph parts can be proven for all graphs within a graph grammar produced language ([10, 27]) The idea is to transform a condition into equivalent application conditions for rules in the sense that given a consistent graph a condition satisfying graph transformation with these rules yields a consistent graph again. GENGED can be used to define several kinds of VLs because it allows any ....

R. Heckel and A. Wagner. Ensuring Consistency of Conditional Graph Grammars -- A Constructive Approach. Proc. of SEGRAGRA'95 "Graph Rewriting and Computation", Electronic Notes of TCS, 2, 1995. http://www.elsevier.nl/locate/entcs/volume2.html.

....of nodes or edges. Moreover, the theory of algebraic graph transformation offers analysis techniques, for example for consistency checks. Consistency conditions concerning the existence and non existence of graph parts can be proven for all graphs within a graph grammar produced language ( HW95,Wag97] Using consistency conditions it is possible to ensure, e.g. that two classes do not have the same name. A first prototype of GENGED is realized within a student s project which is the basis for the current (re)implemention of GENGED. The following extensions of the GENGED environment ....

R. Heckel and A. Wagner. Ensuring Consistency of Conditional Graph Grammars -- A constructive Approach. Proc. of SEGRAGRA'95 "Graph Rewriting and Computation", Electronic Notes of TCS, 2, 1995. http://www.elsevier.nl/locate/entcs/volume2.html.

....of nodes or edges. Moreover, the theory of algebraic graph transformation offers analysis techniques, for example for consistency checks. Consistency conditions concerning the existence and non existence of graph parts can be proven for all graphs within a graph grammar produced language ( HW95, Wag97] Using consistency conditions it is possible to ensure, e.g. that two classes do not have the same name. A first prototype of GENGED is realized within a student s project which is the basis for the current (re)implemention of GENGED, partially founded by a DFG grant. The following ....

R. Heckel and A. Wagner. Ensuring Consistency of Conditional Graph Grammars -- A Constructive Approach. Proc. of SEGRAGRA'95 "Graph Rewriting and Computation", Electronic Notes of TCS, 2, 1995. http://www.elsevier.nl/locate/entcs/volume2.html.

....application conditions are investigated with respect to their generative power. The embedding properties of graph grammars with application conditions have been studied in [Hec95b] In [Wag95] the expressive power of graph grammars with different kinds of application conditions are compared. In [HW95] a construction is presented how consistency conditions can be transfered into application conditions, i.e. a given conditional graph grammar is transfered into a conditional graph grammar that satisfies the given consistency conditions. In [HMTW95] a combination of attributed graph ....

R. Heckel and A. Wagner. Ensuring consistency of conditional graph grammars -- a constructive approach. Proc. of SEGRAGRA'95 "Graph Rewriting and Computation", Electronic Notes of TCS, 2, 1995. http://www.elsevier.nl/locate/entcs .

....can be proven for all graphs within a graph grammar produced language. The idea is to transform a condition into equivalent application conditions for rules in the sense that given a consistent graph a condition satisfying graph transformation with these rules yields a consistent graph again ( HW95, Wag97] Using consistency conditions it is possible to ensure for example that two classes do not have the same name. By means of consistency conditions it is possible to support more convenient editing by allowing incorrect graphics during editing. The tool environment we sketched in our work ....

R. Heckel and A. Wagner. Ensuring consistency of conditional graph grammars -- a constructive approach. Proc. of SEGRAGRA'95 "Graph Rewriting and Computation", Electronic Notes of TCS, 2, 1995. http://www.elsevier.nl/locate/entcs/volume2.html.

....to be considered. Especially for the development of distributed systems, consistency is a very important aspect. A notion of consistency conditions, logical formulas on the existence and non existence of graph structures, and a constructive approach to ensure these conditions are presented in [HW95] It is due to future work to extend this work to distributed graph transformation. Currently, we are working on an implementation of our ideas which will be based on the AGG language and environment [TER98] Of course, this implementation is designed such that it can run in a really distributed ....

R. Heckel and A. Wagner. Ensuring consistency of conditional graph grammars -- a constructive approach. Proc. of SEGRAGRA'95 "Graph Rewriting and Computation", Electronic Notes of TCS, 2, 1995. http://www.elsevier.nl/locate/entcs/volume2.html.

....is possible to force that two objects in a rule should not be mapped to one and the same. Consider e.g. the third diagram in Figure 3 which is a test on different persons with the same names. More advanced application conditions allowing also predicate logic formulae on diagrams can be found in [HW95] Attribute conditions Often it is not enough to restrict the matching structures for a rule, but also the matching attribute values may be restricted by additional conditions. An attribute condition may be any boolean expression which may contain rule variables.Moreover, object roles defined ....

....rule applications. Logical formulas may be used to ensure additional properties of the rule set, e.g. to ensure that a certain object is created only if another is existing. If a rule set does not ensure the validity of a certain set of formulas, the rule set is automatically corrected ( HW95] Visual editing of graph rules and their application are supported by the graph transformation machine AGG [TER99] which is implemented in Java. The visual layout of the rules is very similar to that one used in this contribution and thus, to UML. As a next step we intend to extend AGG by ....

R. Heckel and A. Wagner. Ensuring Consistency of Conditional Graph Grammars -- A constructive Approach. Proc. of SEGRAGRA'95 "Graph Rewriting and Computation", Electronic Notes of TCS, 2, 1995. http://www.elsevier.nl/locate/entcs/volume2.html.

....are only a subset of the constraints we want to be able to define in PROGRES. Another serious disadvantage of G Log is that there is no implementation yet. Another inspiring approach for this work was the integration of graphical constraints to graph grammars based on the category theory [4]. Although some ideas could be taken over this approach aims for different goals such as verification of graph grammars. Furthermore there is no implementation currently available. We will discuss the visual representation of constraints w.r.t. visual programming with the graph rewriting system ....

....all parts of a specification are well typed . Integrity constraints as well as pre and postconditions of rules allow a run time checking of the specification . An automatic verification of a subset of PROGRES specifications is feasible but its description is out of the scope of this paper (cf. [4]) Constraints are also interesting for generating a prototype from a specification. With the help of these constraints the user can make sure that the prototype will not produce an erroneous hostgraph. This leads to much safer generated visual programming environments. Currently we are ....

R. Heckel, A. Wagner: Ensuring consistency of conditional graph grammars - a constructive approach, Proc. of SEGRAGRA '95 "Graph Rewriting and Computation", Electronic Notes of TCS, 2, 1995, http://www.elsevier.nl/locate/ entcs/volume2.html

....are based on the use of appropriate morphisms, colimits, and their compatibilities. For formal specifications in the spirit of algebraic specification for instance this is shown in [Ehr89, EG94] and state based specification approaches like graph grammars use the same categorical techniques (see [CH95, HCEL96]) The framework of algebra transformation systems is developed in an institutional style ( GB84, GB92] That means, signatures and model categories are introduced first, then signatures are organized into categories, i.e. they are supplied with morphisms, and their model categories are related ....

.... Figure 2: Parallel composition of transitions Note that in this case also the set of states is enlarged, and the functionality of the transition label function becomes lab T : T (ME T Sigma ) Phi . For the definition of refinement relations of graph transformation systems (see [CH95, Par96]) further operations on transformations have been investigated, like taking instances or subproductions, which could be defined in the same way for algebra transformations. Each of these closure operations, or combinations thereof, yields an extended notion of transformation system morphism as ....

A. Corradini and R. Heckel. A compositional approach to structuring and refinement of typed graph grammars. Proc. of SEGRAGRA'95 "Graph Rewriting and Computation", Electronic Notes of TCS, 2, 1995. http://www.elsevier.nl/locate/entcs/volume2.html .

....that the number of steps of a refinement does not depend on the rule but its application in different contexts. Then the automatic construction of rules that preserve data constraints from a given rewrite specification with active data constraints as discussed above should be investigated. cf. HW95] for the construction of graph rewrite rules that preserve consistency conditions. A fundamental feature of formal specification techniques are composition operations. In [Gro98] these have been introduced on the semantical level for algebra transformation systems. Sequential composition and ....

R. Heckel and A. Wagner. Ensuring consistency of conditional graph grammars -- a constructive approach. Proc. of SEGRAGRA'95 "Graph Rewriting and Computation", Electronic Notes of TCS, 2, 1995. http://www.elsevier.nl/locate/entcs/volume2.html.

....means for the construction of graph processes. This typing, however, may also be considered as a structuring means for graph transformation systems in the usual sense of typing. Morphisms and refinements of graph transformation systems with type graphs as structuring means have been introduced in [CH95, HCEL96, Rib96] A type system for graphs, rules, and graph transformation systems is itself given by a graph TG whose nodes and edges are considered as node and edge types respectively. A TG typed graph is then a graph homomorphism g : G TG, i.e. the typing of a graph G is an assignment of ....

A. Corradini and R. Heckel. A compositional approach to structuring and refinement of typed graph grammars. Proc. of SEGRAGRA'95 "Graph Rewriting and Computation", Electronic Notes of TCS, 2, 1995. http://www.elsevier.nl/locate/entcs/volume2.html .

....in their different variations, have become a well accepted approach to the formal modeling of systems. For a survey see [Roz97] In this paper we investigate refinement relations between graph transformation systems, a question that has been addressed only few in the literature up to now (see [CH95,HCEL96,Par96,Rib96] Our main concern are refinement relations that preserve the full behaviour of graph transformation systems, as opposed to [CH95,HCEL96] for instance, whose refinement relation guarantees only the existence of specialised transformations in the refining system, not the whole ....

.... investigate refinement relations between graph transformation systems, a question that has been addressed only few in the literature up to now (see [CH95,HCEL96,Par96,Rib96] Our main concern are refinement relations that preserve the full behaviour of graph transformation systems, as opposed to [CH95,HCEL96] for instance, whose refinement relation guarantees only the existence of specialised transformations in the refining system, not the whole behaviour. Using typed graph transformation systems ( CEL 96] refinement also supports the implementation of a more abstract system by another ....

[Article contains additional citation context not shown here]

A. Corradini and R. Heckel. A compositional approach to structuring and refinement of typed graph grammars. Proc. of SEGRAGRA'95 "Graph Rewriting and Computation", Electronic Notes of TCS, 2, 1995. http://www.elsevier.nl/locate/entcs/volume2.html .

....structuring is shown. Then, Section 6 investigates the compatibility of horizontal and vertical structuring and the properties of vertical refinements, i.e. preservation of consistency and completeness. Finally let us note that a short version of this paper has appeared as (Corradini and Heckel, 1995) already. 2. Typed Graph Transformation Systems This section reviews basic notions and definitions of the algebraic approaches to graph transformation (Ehrig, 1979; Lowe, 1993) It introduces the concept of typed graph transformation (Corradini et al. 1996b; Lowe, 1994; Corradini et al. 1996a) ....

....is defined w.r.t. a certain consistency condition for the more concrete graph transformation system. Since consistency conditions are treated in pure semantical terms (as classes of consistent graphs) in this paper, a suitable specification technique for consistency conditions is needed, see (Heckel and Wagner, 1995) for example. The construction proposed in (Heckel and Wagner, 1995) translating global consistency conditions into preconditions for individual productions, can be considered as a refinement step as well since it preserves the consistency of the original graph transformation system. The ....

[Article contains additional citation context not shown here]

Heckel, R. and Wagner, A. (1995). Ensuring consistency of conditional graph grammars -- a constructive approach. Proc. of SEGRAGRA'95 "Graph Rewriting and Computation", Electronic Notes of TCS, 2. http://www.elsevier.nl/locate/entcs/volume2.html.

....w.r.t. the horizontal structuring is shown. Then, Section 6 investigates the compatibility of horizontal and vertical structuring and the properties of vertical refinements, i.e. preservation of consistency and completeness. Finally let us note that a short version of this paper has appeared as (Corradini and Heckel, 1995) already. 2. Typed Graph Transformation Systems This section reviews basic notions and definitions of the algebraic approaches to graph transformation (Ehrig, 1979; Lowe, 1993) It introduces the concept of typed graph transformation (Corradini et al. 1996b; Lowe, 1994; Corradini et al. 1996a) ....

Corradini, A. and Heckel, R. (1995). A compositional approach to structuring and refinement of typed graph grammars. Proc. of SEGRAGRA'95 "Graph Rewriting and Computation", Electronic Notes of TCS, 2. http://www.elsevier.nl/locate/entcs/volume2.html .

....be syntactically simple, i.e. there should be as few redundancies as possible. Traceability: It should be possible to distinguish in OP INV between those parts originating from OP and those constructed from the invariant INV. The solution we propose is motivated by a verification technique [6] for algebraic graph rewriting systems which provide a semantical basis for the specification and analysis of state oriented systems, including concurrent and distributed ones. In the following section we explain the integration of safety invariants into Z specifications in some more detail and ....

R. Heckel, A. Wagner: Ensuring Consistency of Conditional Graph Grammars -- A Constructive Approach. To appear in: Electronic Notes in Theoretical Computer Science 1 1995. Proc. of SEGRAGRA'95 "Graph Rewriting and Computation", Electronic Notes of TCS Vol.2 1995, http://www.elsevier.nl/locate/entcs/volume2.html

....reason we study behavioural constraints for graph transformation systems. We introduce logics of behavioural constraints as a general framework including, for example, start graphs, explicit frame conditions (as introduced in Section 3) application and consistency conditions (as studied in [HHT96,HW95] and temporal logic constraints. These constraints are defined explicitly at the end of this section. The main result of this section (see Theorem 16) shows that the full transition system can be restricted to those transition sequences satisfying the behavioural constraints such that we obtain ....

....A(p)i iff first(s) G p=d ; H implies that the match dL : L G for p satisfies A(p) Then, AC = hConstr; j= I i defined according to Proposition 23 forms a logic of behavioural constraints of type I. Proof. Directly from Proposition 23. 2 Proposition 27 (graphical consistency conditions [HW95] Let Constr(G) be the set of all injective morphisms c : X Y 2 Graph TG . An 21 assignment for X in a graph G is an injective morphism a : X G. It is a solution for c if there is an injective b : Y G such that b ffi c = a. Now, define j= seq G S Theta Constr(G) by s j= seq G c ....

R. Heckel and A. Wagner. Ensuring consistency of conditional graph grammars -- a constructive approach. Proc. of SEGRAGRA'95 26 "Graph Rewriting and Computation", Electronic Notes of TCS, 2, 1995. http://www.elsevier.nl/locate/entcs/volume2.html.

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