In Model-Driven Engineering (MDE), metamodels de ne the structure of software models such as Petri Nets. This paper proposes a new approach to extract correspondences from metamodels, in order to automatically derive transformations on models. We present the approach on an example of two versions of metamodels for Petri Nets, and evaluate it on benchmark examples of metamodel matching.
A few tools have been created for the synthesis of model transformations from
metamodels. AML [
For similarity measures we considered several di erent alternatives: Graph
structural similarity (GSS) tests if two classes have similar graph structure
metrics [
Graph similarity measures treat a metamodel as a graph of nodes (classes) and edges (associations, aggregations and inheritances).
We evaluated the di erent measures on a large collection of di erent
metamodel pairs. We found that data-structure similarity (DSS) was the consistently
best approach. GSS overall has a poor average. GES is quite accurate, however it
has exponential time complexity [
The state of the art in metamodel matching is represented by [
Flattening a class is the process of representing the class in a form which
represents all of its recursively inherited and composed features [
(a) source metamodel
(b) target metamodel In assessing similarity, it is only necessary to look at the types of the properties, not at their names. This kind of similarity is called data structure similarity (DSS). Although sometimes property names are very similar, names may be too much in uenced by human factors. For example, two completely di erent properties in di erent metamodels can have the same name if the developer chooses. In contrast, the types of properties are much more objective.
To make the similarity result more accurate, we need to consider all possible
matches of classes. Eg., if we assume that class E1 matches class E2, then type
E1 is considered fully similar (value 1 equivalent) to type E2. However, equality
of types can be fuzzy, for example, a type E property with 0..1 multiplicity could
be considered 0.75 similar to a type E property with 1 multiplicity. This allows
more exible matches than strict equality of the types. In this paper we use xed
similarity values for types (see Table 2).
We sum the individual class DSS similarities to obtain a mapping score.
However, sometimes there are multiple mappings with the same highest map score.
In this case, calculating name similarity is used to choose one map. To calculate
the name similarity, we use string edit distance [
N SS =
A:size + B:size ed(A; B)
A:size + B:size
The correspondences are expressed as mappings of classes and their features. Eg.: T ransition$ 7 ! T ransition1$ with
name 7 ! name src 7 ! in:src dst 7 ! out:dst where P lace$ 7 ! P lace1$. From these mappings, transformations in di erent MT languages can be synthesised. So far, we generate QVT-R, QVT-O and UML-RSDS. Eg., in QVT-R the T ransition mapping is: top relation MapTransition2Transition1 { enforce domain sourc t : Transition { name = n, src = t_src : Place {}, dst = t_dst : Place {} }; enforce domain targ t1 : Transition1 { name = n, in = t1_in : PTArc { src = t1_in_src : Place1 {} }, out = t1_out : TPArc { dst = t1_out_dst : Place1 {} } }; when { Transition2Transition1(t,t1) and
Place2Place1(t_src,t1_in_src) and
Place2Place1(t_dst,t1_out_dst) } } 6
In the Petri Net example, the source metamodel contains 3 classes, and the target metamodel contains 5 classes, meaning there are 60 potential class mappings. After calculating these 60 mappings, we found 2 mappings with the highest map score, 1.6825396825396826. The rst mapping is: Transition$ 7! Transition1$, Net$ 7! Net1$, Place$ 7! Place1$. The second mapping is: Transition$ 7! Place1$, Net$ 7! Net1$, Place$ 7! Transition1$. This arises because of the structural symmetry of the P lace and T ransition classes { they can be validly interchanged according to DSS.
By calculating name similarity, the rst result is selected as the best mapping, and its detailed correspondences are as follows: { Matching for Transition$ and Transition1$: [name, src, dst, src.name, dst.name] 7 ! [name, in.src, out.dst, in.src.name, out.dst.name]. Similarity of Transition$ and Transition1$ is: 0.5555555555555556. { Matching for Net$ and Net1$: [places, transitions, places.name, places.dst, places.src, places.dst.name, places.src.name, transitions.name, transitions.src, transitions.dst, transitions.src.name, transitions.dst.name] 7 ! [places, transitions, places.name, places.out.dst, places.in.src, places.out.dst.name, places.in.src.name, transitions.name, transitions.in.src, transitions.out.dst, transitions.in.src.name, transitions.out.dst.name]. Similarity of Net$ and Net1$ is: 0.5714285714285714. { Matching for Place$ and Place1$: [name, dst, src, dst.name, src.name] 7 ! [name, out.dst, in.src, out.dst.name, in.src.name]. Similarity of Place$ and Place1$ is: 0.5555555555555556.
Data of these and other cases may be found at nms.kcl.ac.uk/kevin.lano/mtsy nthesis. The prototype tools used are at: nms.kcl.ac.uk/kevin.lano/uml2web.
In this paper, we have presented an approach for extracting correspondences by using metamodel matching. The core step has been calculating the similarities of all possible class matches, and using name similarity or human choice to select the best matching. Evaluation has shown the feasibility and relevance of the approach.
Our future research plan involves (i) compare di erent similarity measures for metamodel matching based on graph or data structures, naming, or semantics using several cases; (ii) compare di erent evolutionary approaches and other techniques for handling larger metamodels; (iii) develop a general approach for automatically transforming correspondences to transformations in QVT-R and other MT languages, and evaluate it with several examples to verify e ciency and quality. (iv) Finally, a tool will be developed based on our approach for automated model transformation.