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Software and Systems Modeling

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01.05.2014 | Theme Section Paper

Merging of EMF models

Formal foundations

verfasst von: Bernhard Westfechtel

Erschienen in: Software and Systems Modeling | Ausgabe 2/2014

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Abstract

Inadequate version control for models significantly impedes the application of model-driven software development. In particular, sophisticated support for merging model versions is urgently needed. In this paper, we present a formal approach to both two- and three-way merging of models in the EMF framework. The approach may be applied to instances of arbitrary Ecore models. We specify context-free as well as context-sensitive rules for model merging which both detect and resolve merge conflicts. Based on these rules, a merge algorithm is developed which produces a consistent model from consistent input models. The merge algorithm does neither assume unique object identifiers, nor does it require change logs. In contrast, it relies on matchings among the input models which identify common elements (state-based approach). The requirements imposed on these matchings are reduced to a minimum, e.g., there are no restrictions on the relative positions of matched elements. Altogether, the merge algorithm is widely applicable, preserves consistency, and offers advanced features, such as merging of ordered collections in the presence of arbitrary moves and handling of context-sensitive conflicts which are hard to detect and to resolve.

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\(\bot \) denotes an undefined result.

http://download.eclipse.org/modeling/emf/emf/javadoc/2.5.0/org/eclipse/emf/ecore/package-summary.html#details.

For some set \(S\), \(SET(S)\) denotes the set of sets over \(S\).

We use the notation \(o_2 \in fv(o_1)\) also for single-valued features.

An undirected edge is a set \(\{e_1, e_2\}\). In the conditions below, we will write \(e_1 \leftrightarrow e_2\) as a shorthand for \(\{e_1, e_2\} \in M\).

\(O_b\), \(O_1\), and \(O_2\) denote the object sets of the input versions \(b\), \(a_1\), and \(a_2\), respectively.

We reuse the predicates \(n-way(o, cf)\) introduced for the merging of single-valued features. Furthermore, \(b \in \mathbb B \).

A directed graph is a pair \(g = (V, E)\), where \(V\) is a finite set of nodes and \(E \subseteq V \times V\) is a set of directed edges.

In the conditions below, \(v \rightarrow v^{\prime }\) and \(v \xrightarrow {+} v^{\prime }\) stand for \((v, v^{\prime }) \in E\) and \((v, v^{\prime }) \in E^+\), respectively; \(^+\) denotes transitive closure.

This predicate may be defined on the merged model graph by checking the visibilities of elements reachable from the root of the superimposed trees.

\(\xrightarrow {c^*}\) denotes the reflective and transitive closure over containment links.

We assume that the target type of the reference \(xr_1\) is \(C_4\) and \(C_4\) does not conform to \(C_5\).

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Titel: Merging of EMF models
Formal foundations
verfasst von: Bernhard Westfechtel
Publikationsdatum: 01.05.2014
Verlag: Springer Berlin Heidelberg
Erschienen in: Software and Systems Modeling / Ausgabe 2/2014
Print ISSN: 1619-1366
Elektronische ISSN: 1619-1374
DOI: https://doi.org/10.1007/s10270-012-0279-3

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