An Automatic Mapping Mechanism for Formalizing Domain-Specific Metamodels
Tao Jiang Xin Wang Lidong Huang
School of Mathematics and Computer Science
Yunnan Minzu University
Kunming, P.R.China
jtzwyinternet73@163.com wxkmyn@163.com hldwinter@163.com
Abstract—Due to informal definition of Domain-Specific
Metamodeling Language (DSMML), properties of metamodels
built based on DSMML cannot be precisely and automatically
analyzed. In response, based on formalization of DSMML
named XMML, the paper proposes an automatic mapping
mechanism for formalizing metamodels to automatically
translate metamodels to the corresponding first-order logic
system. Firstly, we briefly present our approach for verifying
metamodels consistency, and then, an automatic mapping
mechanism for formalizing metamodels is established, finally,
we design and implement an automatic mapping engine for
formalizing metamodels.
Keywords- Domain-Specific Modeling Language (DSML);
metamodel; consistency; automatic mapping
I. INTRODUCTION
As a metamodeling language for DSM [1] and a
metalanguage used to build Domain-Specific Modeling
Languages (DSMLs), DSMML plays an important role in
software system modeling of specific domains.
There are several problems that have not been solved
well for DSMML, which include precise mathematical
foundation of its semantics, tool-independent formal
descriptions, and analysis techniques for metamodels syntax,
and automatic mapping mechanism and its implementation
and so on. Here are some examples that illustrate this. The
precise structural semantics of the mature
metaprogrammable Generic Modeling Environment (GME)
[2] depend on the implementation of complex tools.
Standards such as the UML superstructure [3] and Meta-
Object Facility (MOF) [4] do not provide sufficiently rigid
formal definitions of the DSML process.
One of my papers published in the Journal of Software
proposes a formal representation of the structural semantics
of DSMML named XMML based on first-order logic [5],
and another one of my papers published in Electrical Review
proposes an approach for verifying metamodels consistency
by first-order logical inference based on formalization of
XMML [6].
In this paper, based on research results of my published
papers, we propose an automatic mapping mechanism for
formalizing metamodels to automatically translate
metamodels to the corresponding first-order logic system
based on formalization of XMML, and then we illustrate it
by a case, based on this we design and implement the
corresponding formalization automatic mapping engine for
metamodels.
II. R
ELATED WORKS
In UML domain, there are much typical works on
formalization and analysis, such as L Shan’s formalization
and checking of UML metamodels and models based on
first-order logic [7] and so on.
In DSM domain, most of the DSMLs are defined and
verified by informal way, for example, GME [2] developed
by Vanderbilt university uses expanded OCL to check
model, and MetaEdit+ [8] of MetaCase company uses fixed
declarative rules to verify model properties. There is also
some typical work on formalization of DSMLs, such as
Jackson and Sztipanovits’s formalization of DSML based on
Horn logic [9]. Without considering formalization of
metamodeling language and automatic translation from
metamodels to the corresponding formal semantic domain,
these approaches have lower level of automated analysis.
III. F
ORMALIZATION OF XMML AND ITS METAMODELS
We design a DSMML named extensible markup language
based meta-modeling language (XMML) [10].
Metamodeling elements of XMML are divided into two
types: entity type and association type, the former is used to
describe modeling entities in metamodels and the latter
concerns relationships between modeling entities.
Metamodeling element of entity type consists of four types
such as model type, entity type and so on. Metamodeling
element of association type includes six types such as source
role assignment association and so on. We finish
formalization of structural semantics of XMML based on
the above ten elements. Details of definition and
formalization can be seen in [5].
Because we can prove logical consistency of XMML,
XMML must have metamodels that can be satisfied, thus it
is meaningful to discuss properties of metamodels built
based on XMML.
Based on theory and method of first-order logic [11], we
can only determine whether a metamodel is a legitimate
instance of XMML by examining relationship that the
metamodel satisfies XMML. From the perspective of
formalization, a metamodel is an interpretation of
formalized system of XMML named T
X
, and a legal
metamodel is an interpretation that satisfies all constraint
2015 International Conference on Intelligent Systems and Knowledge Engineering
978-1-4673-9323-2/15 $31.00 © 2015 IEEE
DOI 10.1109/ISKE.2015.26
274