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Software and Systems Modeling
Published in: Software and Systems Modeling 1/2024

12-07-2023 | Regular Paper

Model projection relative to submetamodeling dimensions

A form of submodel circumscribing

Authors: Bernard Carré, Gilles Vanwormhoudt, Olivier Caron

Published in: Software and Systems Modeling | Issue 1/2024

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Abstract

Model-based engineering (MBE) recognizes models as central in software construction with the possibility of their management in libraries and repositories with proper structuring of their spaces and operations. Due to this success, models (and metamodels) are becoming larger and larger and technics are needed in order to comprehend and exploit them, such as circumscribing sub(meta)models of interest, which is the subject of this paper. Following MBE, there are mainly two ways for circumscribing submodels: only at the model level (by selecting model elements of interest) or through the meta level (by selecting a submetamodeling dimension of interest). In a preceding paper, we deeply studied the first way. Here we concentrate on the second way. Model projection deeply relies on the concepts of submodels and submetamodels with their inclusion qualities for model space structuring and has to be systematically examined from this point of view. It is important to point out that model treatment has to deal with full models (as offered by “off the shelf” libraries) but also with not necessarily well-formed ones, such as unspecified model chunks, due, for example, to the storage in repositories of incomplete engineering choices or of intermediate results of operations. It is a difficulty to encompass all these forms of models, being well-formed or not, in a homogeneous manner through MBE operations. The operation for “Model projection relative to submetamodeling dimensions” presented here does take this difficulty into account.
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Footnotes
1
The restriction to impacted attributes is for simplification.
 
2
See Marvie et al. [43] and Renaux et al. [45] for examples with similar motivation when modeling distributed component-based architectures and modeling services according to several dimensions.
 
3
Such a projection could be useful to handle the mapping of the model into relational databases (ORM mapping).
 
4
For space reasons, we omit the dependency constraints between these metaclasses.
 
5
Difference and extraction operators are typical examples that may produce resulting models that are not well-formed.
 
6
Note that relationships between (meta)model elements (associations, generalization, collaboration links, etc.) are not edges (\(\sqsubseteq _{m}\)) but nodes in the formalism. In particular, in case of multiple relations between two (meta)model elements, they may be reified by specific nodes to identify and disambiguate them.
 
7
Software models being formalized here by the standard concept of “mathematical structure” (associating a set of models elements and a set of constraints), transitivity is not ensured contrary to their constitutive sets, considered separately.
 
8
where using the standard mathematical operation of closure of subsets under an ordering relation:\(closure_{\sqsubseteq _{m'}}(\widetilde{m})=\{x\in \widetilde{m'} \mid \exists y\in \widetilde{m},y\sqsubseteq _{m'}^*x\}\),that is the set of model elements of \(m'\) whose elements of \(\widetilde{m}\) transitively depend under the dependency constraints asserted by \(m'\).
 
9
In case of metamodels having a root meta element, say r, \(meta(r)=r\). Take, for example, UML, where its root metaclass Element is instance of itself.
 
10
It was shown (Property 1 of [15]) that the closure in a surrounding model m of subsets of model elements of a closed submodel of m is bound by this submodel.
 
11
Consider a model \(m=(\widetilde{m} \sqsubseteq _{m})\), for any subset s of its model elements (\(s \subseteq \widetilde{m}\)), the operator \(model_{m}(s)\) allows to extract the submodel \(m'=(s,\sqsubseteq _{m'})\) of m such as: \(\forall x,y\in s,x\sqsubseteq _{m}y\Rightarrow x\sqsubseteq _{m'}y\), that is \(Gr(model_{m}(s))=Gr(m)/s\)
 
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Metadata
Title
Model projection relative to submetamodeling dimensions
A form of submodel circumscribing
Authors
Bernard Carré
Gilles Vanwormhoudt
Olivier Caron
Publication date
12-07-2023
Publisher
Springer Berlin Heidelberg
Published in
Software and Systems Modeling / Issue 1/2024
Print ISSN: 1619-1366
Electronic ISSN: 1619-1374
DOI
https://doi.org/10.1007/s10270-023-01116-2

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