A Formal representation of the Structural Semantics of
Domain-Specific Modeling
Language*
Tao Jiang LiangLin Xiong WenYun Zheng
School of Mathematics and Computer Science School of Mathematics and Computer Science Infrared Company
Yunnan University of Nationalities Yunnan University of Nationalities Kunming Institute of Physics
Kunming, P.R.China Kunming, P.R.China Kunming, P.R.China
jtzwy123@gmail.com lianglin_5318@126.com zhengwy@sina.com
Abstract—Domain-Specific Modeling has been widely and
successfully used in system design and modeling of specific
areas. Due to informal definition of Domain-Specific Modeling
Language (DSML) and Meta-Modeling Language (DSMML),
the structural semantics of DSMLs and DSMMLs cannot be
strictly described and the properties based on it also cannot be
systematically analyzed and validated. In response, the paper
proposes a formal description method of the structural
semantics of DSML and DSMML. Firstly, a formal definition
of domain and meta-domain based on algebra is presented,
secondly, a mapping mechanism from domain and meta-
domain to the corresponding first-order logic system is
established, based on this, the method of formalization of
structural semantics of DSML based on first-order logic is
presented, finally, the formalization automatic mapping engine
is designed and relevant test is performed to show the
feasibility of our formal method.
Keywords- Domain-Specific Modeling Language (DSML);
structural semantics; domain; meta-domain
I. INTRODUCTION
As a Model-Driven Development methodology for the
specific domain, compared with the uniformity and
standardization of MDA [1], DSM [2] focuses on simplicity,
practicability and flexibility. As a modeling language for
DSM, DSMLs play an important role in system design and
modeling of specific areas.
Semantics of DSMLs can be grouped into structural
semantics [3] and behavioral semantics. The former concerns
static semantic constraints of relationship between modeling
elements based on abstract syntax, focusing on the static
structural properties; the latter concerns domain-specific
execution semantics, focusing on the dynamic behavior of
the model. Although structural semantics is very important,
research in structural semantics is not as extensive and deep
as behavioral semantics’.
There are several problems that have not been solved
well for DSMLs, which include precise mathematical
description, independence of formal specification and
validation method of properties based on formalization.
__________________
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Research supported by Yunnan Provincial Department of Education
Research Fund Key Project (2011z025) and General Project (2011y214)
The paper proposes a formal description method of the
structural semantics of DSMLs and DSMMLs, based on this,
method of formalization of structural semantics of DSML
based on first-order logic is presented, and then the
corresponding formalization automatic mapping engine and
its test are introduced to show the application of
formalization.
II. RELATED WORKS
Our view of modeling differs from existing approaches
based on instance semantics [4]. While this top-down
approach is certainly reasonable, it makes it difficult to
disassociate models from the tools used to construct them.
In the paper, we explore a bottom-up approach to
formalizing the structural semantics of DSML and DSMML.
By bottom-up, we mean that our approach does not begin
with the concepts of metamodeling, but ends with these, so
it is meta-metamodel agnostic.
Within the domain-specific language community, graph-
theoretic formalisms have received the most research
attention [5]. The majority of work focuses on model
transformations based on graph, but analysis and validation
of properties of models has not received the same attention.
There are much typical work on formalization of
modeling language and validation, such as Andre’s
formalization and validation of UML class diagram based on
ADT [6] and Paige’s formalization of BON based on PVS [7]
and Jackson.E.K’s formalization of DSML based on Horn
logic [8] and so on. Without considering automatic
translation from modeling language to the corresponding
formal semantic domain, these approaches have lower level
of automated analysis and validation.
III.
DOMAIN
A. Domain Definition
Intuitively, the domain of a DSML classifies all the
structurally legal (well-formed) models of that language. As
an example, consider the simplified metamodel describing
software system domain [10] in Figure 1. The metamodel
consists of modeling concepts such as component, interface
and interface association, and it also builds constraints over