M. Lowe, M. Kor#, and A. Wagner. An algebraic framework for the transformation of attributed graphs. In Ronan Sleep, Rinus Plasmeijer, and Marko van Eekelen, editors, Term Graph Rewriting: Theory and Practice, pages 185--199. John Wiley, New York, 1993.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....v GV . Object vertices are linked to data vertices by attributes, i.e. edges a with src(a) v and tar(a) d . Edges between object vertices are called links. We have assumed that there are no edges from data vertices. Compared with other notions of attributed graphs, like [14], where special attribute carriers are used to relate graph elements and data values, our presentation is simpler because attributed graphs are regarded as a special case of ordinary graphs. However, this limits us to attributed vertices. Typed graphs. The concept of typed graphs [2] captures the ....

M. Lowe, M. Kor#, and A. Wagner. An algebraic framework for the transformation of attributed graphs. In Term Graph Rewriting: Theory and Practice, pages 185--

....place transition nets and typed graph transformation systems, it relates (high level) environment relationship nets to typed graph transformation with attributes. This relationship, which has first been observed in the case of algebraic high level nets [8] and attributed graph transformation [17] in [18] shall enable us to transfer the modelling of time in time ER nets to typed graph transformation with attributes. Next, we review time environment relationship (TER) nets [11] in order to prepare for the transfer to typed graph transformation systems in Section 4. 2 Table 1. ....

....declarations (based on ) is a graph whose set of vertices T,Up contains . Therefore, data type symbols are vertex types so that edges, representing attribute declarations, may be drawn towards them from ordinary vertices. This is compatible with notions of attributed graphs, like [17], where attribute carriers are used to relate graph elements and data values. Notice, however, that we limit ourselves to attributed vertices, and that we do not extend but refine the notion of graph. Given a data domain for every data type symbol , an instance graph with attributes over ....

M. Lowe, M. Korff, and A. Wagner. An algebraic framework for the transformation of attributed graphs. In M. R. Sleep, M. J. Plasmeijer, and M.C. van Eekelen, editors, 14 Term Graph Rewriting: Theory and Practice, chapter 14, pages 185--199. John Wiley & Sons Ltd, 1993.

....(pictorial objects) together with connection links, a set of attribute symbols (data objects) together with operations, and a family of attribution operations coupling the lexical with attribute symbols. Formally, the VL abstract syntax is given by an attributed graph structure signature Ags (see [13]) where we allow not only algebraic signatures but specifications [1] in the attribute part, ffl VL concrete syntax comprising additional lexical symbols, called attribute carriers, with connection links to the lexical symbols of the abstract syntax, a graphic specification with graphic symbols ....

.... visual language specification VL specification = VL alphabet, VL grammar) is given by all VL sentences V LS derivable from the start sentence S with the VL rules R: V L = fV LSjS = R V LSg The derivability of VL sentences is based on derivability of attributed graph structures according to [13] concerning the abstract syntax level and on solving of constraint satisfaction problems concerning the concrete syntax level (see [1] for more details) Each derivation V LS 1 = R V LS 2 of VL sentences via VL rules is called VL transformation. 4 Example 3.6 (Visual Grammar for the AHL Net ....

M. Lowe, M. Korff, and A. Wagner. An algebraic framework for the transformation of attributed graphs. In M.R. Sleep, M.J. Plasmeijer, and M.C. van Eekelen, editors, Term Graph Rewriting: Theory and Practice, chapter 14, pages 185--199. John Wiley & Sons Ltd, 1993.

....and already existing tools dealing with algebraic specifications, graph grammars and Petri nets should be integrated into the ACT [CEW93] and PROSOFT [Nun93] environments. ffl Combination of algebraic with graphical specification techniques Combining algebraic specifications with Petri nets [LKW93] and or graph transformations [LKW93] results in high level specification formalisms with graphical components for the informal and formal specification of different aspects of software like data type and process parts in an integrated framework. The graphical components should provide increased ....

....algebraic specifications, graph grammars and Petri nets should be integrated into the ACT [CEW93] and PROSOFT [Nun93] environments. ffl Combination of algebraic with graphical specification techniques Combining algebraic specifications with Petri nets [LKW93] and or graph transformations [LKW93] results in high level specification formalisms with graphical components for the informal and formal specification of different aspects of software like data type and process parts in an integrated framework. The graphical components should provide increased comprehensibility leading to more ....

M. Lowe, M. Korff, and A. Wagner. An algebraic framework for the transformation of attributed graphs. In M.R. Sleep, M.J. Plasmeijer, and M.C. van Eekelen, editors, Term Graph Rewriting: Theory and Practice, chapter 14, pages 185--199. John Wiley & Sons Ltd, 1993.

....together with connection links, a set of attribute symbols (representing data objects) together with operations, and a family of attribution operations coupling the lexical symbols with attribute symbols. Formally, the VL abstract syntax is given by an attributed graph structure signature AGS ([13]) where we allow not only algebraic signatures but specifications in the attribute part, p VL concrete syntax comprising additional symbols, called attribute carriers, with combination links to the lexical symbols of the abstract syntax, a graphic specification with graphic symbols and a ....

.... the visual language specification VL specification = VL alphabet, VL grammar) is given by all VL sentences VLS derivable from the start sentence S with the VL rules R: VL = VLS S = R VLS The derivability of VL sentences is based on derivability of attributed graph structures according to [13] concerning the abstract syntax level, and on constraint solving concerning the concrete syntax level (see [1] for more details) Each derivation VLS 1 = R VLS 2 of VL sentences via VL rules is called VL transformation. Example 3.6 (Visual Grammar for the AHL Net Language) Figure 4 illustrates ....

M. Lwe, M. Korff, and A. Wagner. An algebraic framework for the transformation of attributed graphs. In M.R. Sleep, M.J. Plasmeijer, and M.C. van Eekelen, editors, Term Graph Rewriting: Theory and Practice, chapter 14, pages 185-199. John Wiley & Sons Ltd, 1993.

....prospect of combining the intuitive expressiveness of graphs with automatic processing and support by a machine. Therefore, graph transformation appears to be quite attractive as a formal specification technique. However, for it go be of practical use, concepts of attributes were added [LKW93] HMTW95] CL95] They allow for textual and other non graphical information to be integrated into graphs. Further extensions of the formalism include rule application conditions ( Koc97] and distribution concepts ( Tae96] 8 Chapter1. Introduction 1.2 Goals Then, the interested reader ....

....approach. This means that all attributes in a graph belong to an algebra that describes some kind of data types. This algebra remains unchanged throughout the transformation process. There are approaches which use total algebras for attributes, as in [Sch92] for the Double Pushout Approach and [LKW93] for the Single Pushout Approach. Further works extend these concepts towards partial attribute algebras [CL95] and even more general, give up the strict separation of graph and data structure, in order to obtain a partial algebra transformation [Wag97] Among the existing concepts of graph ....

[Article contains additional citation context not shown here]

M. Lowe, M. Korff, and A. Wagner. An algebraic framework for the transformation of attributed graphs. In M.R. Sleep, M.J. Plasmeijer, and M.C. van Eekelen, editors, Term Graph Rewriting: Theory and Practice, chapter 14, pages 185--199. John Wiley & Sons Ltd, 1993.

....gluing condition, the single and the double pushout approaches [CMR 97] yield the same results. See also the comparison of both approaches in [EHK 97] The attribution of nodes and arcs by Java objects and expressions follows the ideas of attributed graph grammars as stated in [LKW93] and further in [TFKV99] to a large extent. The main difference is that here, Java classes and expressions are used instead of algebraic specifications and terms. The combination of attributed graph transformation with negative application conditions has been worked out comprehensibly in ....

M. Lowe, M. Korff, and A. Wagner. An Algebraic Framework for the Transformation of Attributed Graphs. In M. Sleep, M. Plasmeijer, and M. van Eekelen (eds.), Term Graph Rewriting: Theory and Practice, chapter 14, pages 185--199. John Wiley & Sons Ltd, 1993.

....condition defines preconditions for syntactic correctness of transformations. Moreover this gluing condition appears also to be useful in proofs of behaviour preserving properties [19] The semantical aspects are integrated in the above discussed model by the use of attributed multi ported graphs [20]. Attributes of a graph are used to define its semantics in a denotational way which offers the needed compositionality. The attribute functions correspond to valuation functions of a denotational semantics [21] Attributes correspond with the semantics of the nodes and or edges. Definition: An ....

M. Lwe, Martin Korff, A. Wagner, An algebraic framework for the transformation of attributed graphs, in M.R. Sleep, M.J. Plasmeijer and M.C.J.D. van Eekelen(Eds), Term Graph Rewriting, John Wiley& Sons Ltd, 1993, pp 185-199.

.... SPOapproach was started in [EL93a] and [Wag93] The Single PushOut Approach The main theory of the SPO approach was published in [Low93] and extended to distributed derivations in [EL93] and to equationally defined graph structures in [Kor92, Kor94a] Attributed graphs were considered in [LKW91, LKW93] In [CEL 94a] and [CEL 94c] it was shown how to avoid inconsistencies for abstract graph derivations using standard representations of graphs. A new categorical framework of so called generalized graph structures generalizing comma categories w.r.t. partial morphisms was elaborated in ....

....has been generalized to a more powerful graph rewriting formalism, called ESM (Extended Structure Morphism) systems, described in the next subsection. In [Kor93] actor systems were modelled by a distinguished algebraic graph grammar following the single pushout approach in the sense of [Low93, LKW93] THE idea was to reuse the available theory for graph grammars in [Low93] attributed with algebras in the sense of [LKW93] Moreover, in [Kor93] faithfullness of the model is shown w.r.t. a suitable system of axioms. A number of consistency requirements for actor systems could advantageously ....

[Article contains additional citation context not shown here]

M. Lowe, M. Korff, and A. Wagner. An algebraic framework for the transformation of attributed graphs. In M.R. Sleep, M.J. Plasmeijer, and M.C. van Eekelen, editors, Term Graph Rewriting: Theory and Practice, chapter 14, pages 185--199. John Wiley & Sons Ltd, 1993.

....in [Low93] It shows that the whole theory for double pushout transformations can be generalized in the new framework. The SPO approach was extended to distributed derivations in [EL93] and to equationally defined graph structures in [Kor92, Kor94] Attributed graphs were considered in [LKW91, LKW93] In [CEL 94a] and [CEL 94c] it was shown how to avoid inconsistencies for abstract graph derivations using standard representations of graphs. A new categorical framework of so called generalized graph structures generalizing comma categories w.r.t. partial morphisms was elaborated in ....

....has been generalized to a more powerful graph rewriting formalism, called ESM (Extended Structure Morphism) systems, described in the next subsection. In [Kor93] actor systems were modelled by a distinguished algebraic graph grammar following the single pushout approach in the sense of [Low93, LKW93] THE idea was to reuse the available theory for graph grammars in [Low93] attributed with algebras in the sense of [LKW93] Moreover, in [Kor93] faithfullness of the model is shown w.r.t. a suitable system of axioms. A number of consistency requirements for actor systems could advantageously ....

[Article contains additional citation context not shown here]

M. Lowe, M. Korff, and A. Wagner. An algebraic framework for the transformation of attributed graphs. In M.R. Sleep, M.J. Plasmeijer, and M.C. van Eekelen, editors, Term Graph Rewriting: Theory and Practice, chapter 14, pages 185--199. John Wiley & Sons Ltd, 1993.

....preserves pushouts. 2.3 Algebraic Graph Transformation Algebraic graph transformation as presented in [Ehr79, Low93] defines the rule based manipulation of graphs as algebra transformation. Algebraic graph transformation has been extended to the manipulation of attributed graphs in [Sch92, LKW93, Wag97] Within this extension the underlying graph signature contains sort symbols for node and edge types and monadic operation symbols only. The attributes may be elements of arbitrary algebras which may be changed by corresponding operations. The attributes are connected with their graph ....

M. Lowe, M. Korff, and A. Wagner. An algebraic framework for the transformation of attributed graphs. In M.R. Sleep, M.J. Plasmeijer, and M.C. van Eekelen, editors, Term Graph Rewriting: Theory and Practice, chapter 14, pages 185--199. John Wiley & Sons Ltd, 1993.

....power for some VLs. Therefore, the following subsection considers unrestricted grammars, however not for hypergraphs as in this subsection, but for graph structures. 3.3. 4 Graph Structure Representation of Visual Sentences General attributed and labeled graph structures as introduced in [65] can be used to model all graph classes, e.g, hypergraphs as presented in the previous subsection as well as attributed graphs consisting of nodes, edges and (data) attributes. They are based on algebraic concepts as presented in [35] i.e. graph structures are algebras wrt. an algebraic ....

M. Lowe, M. Korff, and A. Wagner. An algebraic framework for the transformation of attributed graphs. In R. Sleep, R. Plasmeijer, and M. van Eekelen, editors, Term Graph Rewriting: Theory and Practice, pages 185--199. John Wiley, New York, 1993.

....specification techniques, like CCS, Petri nets, graph transformation and statecharts, have been extended by data type specification techniques. In this way several integrated formalisms have been developed, like LOTOS [LOT87] algebraic high level nets [PER95] attributed graph transformation [LKW93] where algebraic specification techniques are used for the data type aspects. A different example is SZ [BDG 96] an integration of statecharts and Z, where Z is used for functional aspects. The current and future trend is the integration of different specification techniques, which are ....

M. Lowe, M. Korff, and A. Wagner. An algebraic framework for the transformation of attributed graphs. In M.R. Sleep, M.J. Plasmeijer, and M.C. van Eekelen, editors, Term Graph Rewriting: Theory and Practice, chapter 14, pages 185--199. John Wiley & Sons Ltd, 1993.

....directly attributes. To change an attribute of a graphical object requires its deletion and its recreation with the new attribute. Because of that, special graphical sorts are introduced, called attribute holder, carrying the attributes. A more detailed treatment of this problem can be found in [LKW93] Construction 1.5.5 (context graph) Given an attributed graph signature AGS, an AGS rule p = L l I r R) and a match m : L G. The attributed context graph C is constructed as follows: ffl We define C s = G s Gamma m s (L s Gamma l s (I s ) for all graphical sorts s in SGS and op ....

M. Lowe, M. Korff, and A. Wagner. An Algebraic Framework for the Transformation of Attributed Graphs. In Term Graph Rewriting - Theory and Practice, pages 185--199. Wiley, 1993.

....a system is described as a collection of states, modeled by graphs, and state transformations, specified by graph rewrite rules. This approach is particularly well suited to model the structural part of a system, and its development. In the framework of attributed graph transformation (see [622]) graphs are attributed with algebraically specified data types in order to store and manipulate data values. Applications for such a combination are specifications of concurrent and distributed systems, where data types and dynamic behavior are described within a single framework. In [922] for ....

M. Lowe, M. Korff, and A. Wagner. An Algebraic Framework for the Transformation of Attributed Graphs. In M. Sleep, M. Plasmeijer, and M. van Eekelen1, editors, Term Graph Rewriting: Theory and Practice, chapter 14, pages 185--199. John Wiley & Sons Ltd, 1993. \Phi.

....are algebra driven. This means that all the attributes in a graph belong to an algebra describing some kinds of data type. This algebra is not changed during the transformation process. There are approaches using total algebras for attribution like [Sch92] for the double pushout approach and [LKW93] for the single pushout approach. Further developments extend these concepts towards partial attribute algebras [CL95] and, even more generally, giving up the strict separation of graph and data structure yielding partial algebra transformation in [Wag97] In our approach, we like to follow the ....

....G G p;m = H G as double pushout in category Sigma G AGS, compare [EHKP91] 2. Construct data transformation G D p;m = H D as double pushout in category Sigma D AGS, compare [EHKP91] 3. Add the attribute assignments as unique extensions of the resulting diagrams, compare [LKW93]. 3 Distributing Attributed Graph Transformation In this section, we describe how attributed graph transformation can be distributed over a network. The network graph describing the topology of the system may be attributed as well as all local state graphs, too. All these graphs may be ....

M. Lowe, M. Korff, and A. Wagner. An Algebraic Framework for the Transformation of Attributed Graphs. In M. Sleep, M. Plasmeijer, and M. van Eekelen (eds.), Term Graph Rewriting: Theory and Practice, chapter 14, pages 185--199. John Wiley & Sons Ltd, 1993.

....viewpoint and Sect. 4 presents the design of the class library. In the last section of this paper we discuss limitations of the current work and future extensions. 2 Metamodel The algebraic graph theory underlying our metamodel is given in terms of attributed graph signatures in the sense of [LKW93] and corresponding algebras and homomorphisms. Transformation of graph structures follows the single pushout approach as defined in [Low93] Rather than going into the details of this theory, we try to present the metamodel on an intuitive level. Corresponding formal definitions can be found in ....

M. Lowe, M. Korff, and A. Wagner. An algebraic framework for the transformation of attributed graphs. In M. R. Sleep, M. J. Plasmeijer, and M. C. van Eekelen, editors, Term Graph Rewriting: Theory and Practice, chapter 14, pages 185--199. John Wiley & Sons Ltd, 1993.

....power for some VLs. Therefore, the following subsection considers unrestricted grammars, however not for hypergraphs as in this subsection, but for graph structures. 1.3. 4 Graph Structure Representation of Visual Sentences General attributed and labeled graph structures as introduced in [65] can be used to model all graph classes, e.g, hypergraphs as presented in the previous subsection as well as attributed graphs consisting of nodes, edges and (data) attributes. They are based on algebraic concepts as presented in [66] i.e. graph structures are algebras wrt. an algebraic ....

M. Lowe, M. Korff, and A. Wagner. An algebraic framework for the transformation of attributed graphs. In R. Sleep, R. Plasmeijer, and M. van Eekelen, editors, Term Graph Rewriting: Theory and Practice, pages 185--199. John Wiley, New York, 1993.

....the understanding of the specification much easier. But the latter methods focus just on the description of concurrency and distribution of a system. Putting things together, that is, algebraic specifications and graph transformations or Petri nets, we obtain attributed graph transformations [LKW93] and algebraic high level nets [EPR93] Then we can describe data types and data flow in the same framework. The graphical representation is a very important component of our project because we believe that this is a decisive point in the acceptance of a method within industries. A graphical ....

....graph grammars and Petri nets. Moreover, the tools should be integrated into the ACT [Cla88] and PROSOFT [Nun93] environment. ffl Combination of algebraic with graphical specification techniques Combining algebraic specifications with Petri nets [REP93, RP93] and or Graph Transformations [LKW93] results in high level specification formalisms with graphical components for the informal and formal specification of different aspects of software like data type and process parts in an integrated framework. The graphical components should provide increased comprehensibility leading to more ....

M. Lowe, M. Korff, and A. Wagner, An algebraic framework for the transformation of attributed graphs, Term Graph Rewriting: Theroy and Practice (M.R. Sleep, M.J. Plasmeijer, and M.C. van Eekelen, eds.), John Wiley & Sons Ltd, 1993, pp. 185--199.

....algebraic specifications, graph grammars and Petri Nets should be integrated into the ACT [CEW93] and PROSOFT [Nun93] environments. ffl Combination of algebraic with graphical specification techniques Combining algebraic specifications with Petri Nets [REP93] and or Graph Transformations [LKW93] results in high level specification formalisms with graphical components for the informal and formal specification of different aspects of software like data type and process parts in an integrated framework. The graphical components should provide increased comprehensibility leading to more ....

M. Lowe, M. Korff, and A. Wagner. An algebraic framework for the transformation of attributed graphs, Term Graph Rewriting: Theory and Practice (M.R. Sleep, M.J. Plasmeijer, and M.C. van Eekelen, eds.), John Wiley & Sons Ltd, 1993, pp. 185--199.

....have to make sure that it is applied before the algorithm starts,i.e. before Rules 1 and 2 are applied. This could be done by adding control structure as it was proposed in [Kreowski and Kuske, 1996, Heckel et al. 1995] ical level as it was done for high level replacement systems in [Ehrig and Lowe, 1993]. The transformation concept is based on the notion of a rule relating the state of an object before the transformation (described in the rule s lefthand side) with the state of the object after the transformation (described in the rule s right hand side) A rule can be applied if a redex is ....

....for graphs in order to integrate a data type specification with graph transformations. There are different attribution concepts in the literature. We can divide between the categorical ones of Schneider [Schneider, 1993] and Schied [Schied, 1992] and the algebra driven approaches presented in [Lowe et al. 1993, Claen and Lowe, 1995] But within all these approaches it is impossible to instantiate parametric data types with nodes or edges of the graph. The reason for this restriction is a conflict between parametric data types instantiated with graphical elements and the principle of graph ....

[Article contains additional citation context not shown here]

Lowe, M., Korff, M., and Wagner, A. (1993). An algebraic framework for the transformation of attributed graphs. In Sleep, M., Plasmeijer, M., and van Eekelen, M., editors, Term Graph Rewriting: Theory and Practice, chapter 14, pages 185--199. 8

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M. Lowe, M. Kor#, and A. Wagner. An algebraic framework for the transformation of attributed graphs. In Ronan Sleep, Rinus Plasmeijer, and Marko van Eekelen, editors, Term Graph Rewriting: Theory and Practice, pages 185--199. John Wiley, New York, 1993.

No context found.

M. Lowe, M. Kor#, and A. Wagner. An algebraic framework for the transformation of attributed graphs. In M. R. Sleep, M. J. Plasmeijer, and M. van Eekelen, editors, Term Graph Rewriting: Theory and Practice, chapter 14, pages 185--199. John Wiley & Sons Ltd, 1993.

No context found.

M. Lowe, M. Korff, and A. Wagner. An Algebraic Framework for the Transformation of Attributed Graphs. In M.R. Sleep, M.J. Plasmeijer, and M.C. van Eekelen, editors, Term Graph Rewriting: Theory and Practice, chapter 14, pages 185--199. John Wiley & Sons Ltd, 1993.

No context found.

M. Lwe, Martin Korff, A. Wagner, An algebraic framework for the transformation of attributed graphs, in M.R. Sleep, M.J. Plasmeijer and M.C.J.D. van Eekelen(Eds), Term Graph Rewriting, John Wiley& Sons Ltd, 1993, pp 185-199.

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