Corradini, A., Ehrig, H., Lowe, M., Montanari, U., Padberg, J.: The category of typed graph grammars and their adjunction with categories of derivations. In: Proceedings 5th International Workshop on Graph Grammars and their Application to Computer Science. Volume 1073 of Lecture Notes in Computer Science., Springer-Verlag (1996) 56--74  Home/Search   Document Not in Database   Summary   Related Articles   Check

....that an operation node or attribute node must always be nested in a class node or object node. Other obvious constraints are that hasa edges can only be placed between class nodes, and similarly for isa edges and uses edges. All these constraints can be expressed formally in a socalled type graph [5, 6, 9]. From an intuitive point of view, the type graph is a metagraph which puts extra restrictions on the kind of graphs that are allowed. Type graphs are very important to customise our formalism to different domains. For each specific domain, a type graph must be defined that expresses the ....

Corradini, A., Ehrig, H., Lwe, M., Montanari, U., Padberg, J.: The category of typed graph grammars and their adjunction with categories of derivations. In [11] (1996)

....model (or framework) for a certain application domain, to refine this reference model in a second step by different design views on the system to be developed, and to integrate these design views to the system model. Using concepts and results from the theory of typed graph transformation systems [5, 6, 7] we give precise definitions for views and view relations and support the integration of views by a general automatic construction. We explain this approach informally in Section 2. In Section 3, 4, and 5 we present the formal base of our approach together with illustrating examples. The basic ....

....embed embed embed rename view2 system model define views integrate views integrate views rename rename Figure 1: A view oriented approach to system modelling. graphs and modifying operations by graph transformations. In particular our approach is based on typed graph transformation systems [5, 6, 7] which allow to define a set of graphs by a type (scheme) graph together with type consistent operations on these graphs. Compared to most of the currently popular object oriented modelling techniques, typed graph transformation systems really support an integrated modelling of static and dynamic ....

A. Corradini, H. Ehrig, M. Lowe, U. Montanari, and J. Padberg. The category of typed graph grammars and their adjunction with categories of derivations. In 5th Int. Workshop on Graph Grammars and their Application to Computer Science, Williamsburg '94, LNCS 1073, pages 56--74, 1996.

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A. Corradini, H. Ehrig, M. Lowe, U. Montanari, and J. Padberg. The category of typed graph grammars and their adjunction with categories of derivations. In 5th Int. Workshop on Graph Grammars and their Application to Computer Science, Williamsburg '94, LNCS 1073, pages 56--74, 1996.

....i.e. T S(GG) provides a minimal representation of all possible behaviours of GG. It is worth summarising here some advantages of having defined the category of models GraTS(GG) via coalgebraic instead of algebraic techniques, obtaining for example an initial model by a free construction, as in [9,10]. First of all, the free construction in the mentioned papers only generates finite sequences, while the full transition system contains both finite and infinite sequences. But more importantly, in the algebraic approach all models have to include a homomorphic image of all the computations of the ....

....approach [15] It could be an interesting future topic to extend our approach of coalgebraic semantics to this language. Moreover, the coalgebraic semantics has still to be extended to graph grammar morphisms. There are various notions of such morphisms to contend with in literature ([9,16,10,6]) We only mention that in the category proposed in [6] pullbacks are used for describing a sort of parallel composition with synchronisation of systems. Since the final coalgebra semantics can be characterised via a cofree construction (that preserves pullbacks) this semantics would be ....

A. Corradini, H. Ehrig, M. Lowe, U. Montanari, and J. Padberg, "The category of typed graph grammars and their adjunction with categories of derivations," in 5th Int. Workshop on Graph Grammars and their Application to Computer Science, Williamsburg '94, LNCS 1073, 1996.

....type in TG 1 has no preimage in TG 0 and then retype the remaining elements according to r. Below, the first part of this type conversion is described by the inverse image of TG 0 TG 1 under g 1 leading to the graph g 0 : G 2 TG 0 typed over TG 0 , while the second step is realized Heckel, Corradini, Ehrig, and Lowe 10 G1 0 G2 0 G1 G2 TG1 TG0 TG2 l r l 0 g 0 2 g 0 1 g 0 0 l g2 g1 g0 k1 k2 g0 (1) 2) TG3 TG2 TG23 TG1 TG12 TG13 G1 G2 G3 g1 g 1 g 1 fR f R gR g L f L g L fL gL f g (5) 4) 3) Fig. 7. Construction of the type conversion functor hfi and functor property of h i : ....

....the productions associated with ins D i and del D i are obtained by replacing each vertex type D in D (ins D ) and D (del D ) by type D i using the type conversion functor hin i TG i. That is, hin i TG i( D (ins D ) D D (ins D i ) and hin i TG i( D (del D ) D D (del D i ) Heckel, Corradini, Ehrig, and Lowe 20 In the second step the types D 1 and D 2 of GD D are renamed according to their intended meaning to E and R, respectively. Changing the types in the productions accordingly leads to the isomorphic graph transformation system GE R . Thus the renaming of GD D into GE R is formally represented ....

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Corradini, A., Ehrig, H., Lowe, M., Montanari, U., and Padberg, J. (1996a). The category of typed graph grammars and their adjunction with categories of derivations. In 5th Int. Workshop on Graph Grammars and their Application to Computer Science, Williamsburg '94, LNCS . Accepted.

....subsystems, which are specified separately and have some meaning in their own right. Structuring mechanisms for graph transformation systems based on colimits in the category of graph grammars are investigated in [34,35] and are shown to be compatible with the functorial semantics introduced in [36]. Analysis A main advantage of formal specification methods is the possibility of formal reasoning about properties of the specified systems. ffl Consistency conditions describe properties of all derived graphs. The problem of specifying these conditions and of analyzing them w.r.t. a given ....

....composition p 1 ; p 2 as above, the following statements are equivalent: 1. There is a direct derivation G p1 ;p 2 ;m1 = H 2 . 2. There is a derivation G p1;m1 = H 1 p2 ;m 1 = H 2 such that m 1 is the co match of m 1 w.r.t. p 1 . Proof sketch. By the 3 cube pushout pullback lemma [36]. ut Combining directly derived productions by sequential composition we now define derived productions for derivations of length greater than one: The derived production haei of a derivation ae = G 0 p1;m0 = Delta Delta Delta pk ;mk Gamma1 = G k ) is defined as the sequential ....

A. Corradini, H. Ehrig, M. Lowe, U. Montanari, and J. Padberg. The Category of Typed Graph Grammars and their Adjunction with Categories of Derivations. In Proceedings of the Fifth International Workshop on Graph Grammars and their Application to Computer Science, Lecture Notes in Computer Science. Springer Verlag, 1996. To appear.

No context found.

A. Corradini, H. Ehrig, M. Lowe, U. Montanari, and J. Padberg. The category of typed graph grammars and their adjunction with categories of derivations. In LNCS, 1996. Accepted.

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Corradini, A., Ehrig, H., Lowe, M., Montanari, U., Padberg, J.: The category of typed graph grammars and their adjunction with categories of derivations. In: Proceedings 5th International Workshop on Graph Grammars and their Application to Computer Science. Volume 1073 of Lecture Notes in Computer Science., Springer-Verlag (1996) 56--74

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