Abstract
We introduce a component model for graph rewriting that allows to model a system as a network of components with interfaces representing shared views of internal states and transformations. Their composition assembles a global view whose behaviour is equivalent to the synchronised distributed execution of local components in the network. Formally, components are arrows in a category with interfaces as objects that, with suitable component connectors, forms a Frobenius algebra. This allows the use of string diagrams to model the architecture of basic components and connectors, such that their assembly is freely generated by the algebraic structure. The compositionality of the proposed model is reflected by Structural Operational Semantic rules.
Research partly supported by MIUR PRIN project 2017FTXR7S “IT-MaTTerS”.
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Notes
- 1.
\({\mathbf {TC}}\) is obtained by applying the Grothendieck construction to the indexed category \({\mathbf {C}}^{op} \rightarrow {\mathbf {Cat}}\), mapping each object T to category \({\mathbf {C}}_T\) and each arrow to the corresponding retyping functor.
- 2.
We may drop the reference to the system if this is clear from context.
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Heckel, R., Corradini, A., Gadducci, F. (2022). Graph Rewriting Components. In: Behr, N., Strüber, D. (eds) Graph Transformation. ICGT 2022. Lecture Notes in Computer Science, vol 13349. Springer, Cham. https://doi.org/10.1007/978-3-031-09843-7_2
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