Software model transformation operations are central operations in Model-Driven approaches. In order to represent software models, graphical modeling notations, for example UML, are used. Quality of software model, obtained after transformation, influences on further operations with this model. Thus, it is important to design formal approaches for model to model transformation that are grounded on analytical and mathematical tools. These approaches should provide a background for flexible adopting software model transformational techniques for peculiarities of specific software development lifecycle model. Challenges to mathematical tools and transformation rules that are involved to designing of model to model transformation approaches are formulated in this paper. The ground of mathematical tools choice that is based on these challenges is performed. An approach for performing model to model transformation, which is based on graph transformation, is presented in this paper. Transformational operations are considered on meta-level and concrete level. On meta-level choosing of mathematical tools for representing of transformation stages and transformational artifacts are grounded. Software models are represented as graphs. Initial information for transformation is represented as a set of sub-graphs. Transformation rules are composed using second and first order logics. On the level of the first-order logic all software model elements that participate in transformation are considered. In the level of second-order logic transformation rule considers types of software model element that are participate in the transformation. Proposed approach is extensible and may be used for extend functionality of model to model tools that process software models. For example in MEDINI QVT there is no direct ways to compose a model to model transformation rule that considers those software models elements that have no direct links.
the stakeholders should use information from previous software development stages;
different types of UML diagrams (UML 2.5) for successfully performing of specific tasks of some software development process.
Each type of UML diagram covers different scale of software project and expresses specific part of software project (structure or behavior). Automatizing of transformation operations lets quickly obtain software model, containing information from previously generated models. Also it can facilitate other model processing information, namely model refactoring, merging, comparing and others, i.e. transformations with the same type of software models.
In order to achieve this goal the following model transformation activities are implemented: Model to Model
(M2M), Model to Text (M2T), and Text to Model (T2M) transformations. Text in M2T and T2M transformations
means analytical representation of software model or skeleton of program. In the first case, the role of text is to be
subsidiary artefact that saves information about model. In the second case the role of text is to be target of
transformation
Other transformation’ aspects are horizontal and vertical software model transformations. A horizontal
transformation is a transformation where the source and target models reside at the same abstraction level. Typical
examples are refactoring (an endogenous transformation) and language migration (an exogenous transformation). A
vertical transformation is a transformation where the source and target models reside at different abstraction levels. A
typical example is refinement, where a specification is gradually refined into a full-fledged implementation, by means
of successive refinement steps that add more concrete information. Also code generation operations are considered as
vertical software model transformation
Many papers, proposing strong contribution in model to model transformational approach, consider transformational tasks, relating to concrete transformational languages (for example QVT, ATL or ATLAS). Also, transformational rules are implemented, by means of concrete transformational environments (for example MEDINI QVT). Respectively, transformational results are visualized in concrete modeling environments (for example eclipse or visual studio) and software models are represented in concrete formats (XML or XMI).
Such approaches depend on possibilities of concrete tools, formats or transformational languages. Variety of transformational operations is limited by supported features of chosen practical tools.
From other side, development of analytical approaches let avoiding transformation environment limitations and composing transformational rules with different levels of complexity. When operation with software models are defined, proper math apparatus for performing them is chosen. If one math approach can not satisfy all requirements, additional operations with this approach are introduced, for example, creating of new algebras of spreading existing ones. Other way is to define rules for transforming of one analytical representation to another.
Analytical transformation approaches let to provide a background for improving existing and designing new transformational languages, environments and tools. Also additional operations of software model processing such as model verification, validation may be described. These operations may be integrated into transformational approaches to estimate software model before or after transformation.
Consequence: designing foundation for software model transformation lets support flexible adoption of transformation techniques to business needs.
The paper is organized as follows: section two represents related works, section three contains task and challenges to transformational approach, section four describes proposed approach and choosing of analytical background for performing transformation operation. The last, fivth section represents conclusion and further researches.
Papers, related to software model transformation, can be divided to two classes, namely those which make strong contribution in transformation techniques and those that develop analytical tools for designing new and improving existing transformational approaches and techniques.
Detail review of papers, devoting to designing transformation methods and techniques grounded on
practical tools and environments is represented in paper
Also represent review of papers, making strong contribution in development of transformational techniques.
Paper
Described approach tries to prevent information loss during round-trip engineering by using a so called
trace model which is used to synchronize the Platform Independent and the Platform Specific Models.
Furthermore, the source code is updated using a fine grained bidirectional incremental merge. Also, information
loss is prevented by using Javadoc tags as annotations. Case model and code are changed simultaneously and the
changes are contradicting, one transformation direction has to be chosen, which causes that some changes might
get lost
The contribution of the survey
The classification is aimed to include the user’s point of view and support the notation selection in teams. In total, authors found 14 new notations compared to previous surveys: Alf, Alloy, AUML, Clafer, Dcharts, HUTN, IOM/T, Nomnoml, pgf-umlcd, pgf-umlsd, tUML, txtUML, UML/P, and uml-sequence-diagram-dsl-txl. Authors presented each of the twenty categories in detail including objectively checkable conditions that cover the level of UML support, the editing experience, and the applicability in an engineering team.
Paper
A technique that enables metamodel instances to be generated so that they satisfy partition-based coverage A technique for generating metamodel instances which satisfy graph properties.
A metamodel is a structural diagram and can be depicted using the UML class diagram notation. Thus, the
coverage criteria defined for UML class diagram can also be borrowed for metamodels. To facilitate the
transformation from class diagrams with OCL constraints to Satisfiability Modulo Theories (SMT) formulas authors
use a bounded typed graph as an intermediate representation
Paper
A review of mathematical foundations for providing realization of model transformation techniques is outlined
in
A review of metamodeling tools is represented in paper
To define steps to perform model to model transformational operation and provide the following analysis for
every step:
1. Propose analytical tools for describing operations that are performed in every step.
2. To involve formal tools for representation of transformational rules and software models used in this step.
Challenges for mathematical tools
For software model representation:
support both compact and detailed software model representation;
allow flexible choosing set of diagram notation elements that participate in transformation;
be convenient for model proceeding (analysis of structure, comparing, merging and so on);
provide easy machine processing;
be convenient for cognitive human perception
For transformational rules: support both compact and detailed transformational operations; allow matching elements of compact and detailed view; be compatible with representation of rules in natural language. Namely reflect all transformational conditions and details of transformational process.
This work continues investigations, started in papers
To perform successfully software model to model transformation operation it is proposed to use the principle of
graph transformation
To develop this approach it is necessary to propose:
Denote software model(SM) as: SM(O,L), where O – a set of software model objects. Objects are elements of software model (SM) notations that can be expressed as graph vertexes.
L – a set of links between O, that can be expressed as graph edges. Links are elements of software model notation that can be expressed as edges.
As in transformation operation there are two software models define them as initial ( SMinitial ) and resulting ( SM resulting ). SMinitial is a software model from which transformation is started. This model contains initial information for transformation. SM resulting is the model which is obtained after transformation. Thus: SM initial (O1, L1);O1 {o1,i | i 1,..., n1}; L {l1, j | j 1,..., m1}; n1 | O1 |; m1 | L1 | 1 SM resulting (O2 , L2 ) ;O1 {o2,k | k 1,..., n2} L2 {l2, p | p 1,..., m2}; n2 | O2 |; m2 | L2 | , where O1 – set of SM initial objects, O2 – set of SM resulting objects.
Initial and resulting are types of software models. For example if transformation performed from use case to collaboration diagram we write transform SM use _ case to SMcollaboration .
Graph representation of software model is not new approach. Contribution of proposed one consists in allowing forming parts of graph, namely sub-graphs that are important for particular transformation operation.
Thus, propose general representation of sub-graphs for some software model: where O1 – set of SM initial objects, O2 – set of SM resulting objects.
2
Where: Osub – a set of objects that are chosen from SM . Respectively Lsub – a set of links between elements osub Osub . Denote SMIsub -– sub-graphs of SMinitial , respectively SMRsub – sub-graphs of SM resulting . Thus:
SMI sub (OI , LI ); OI {oIi | i 1, ..., nI}; LI {lI j | j 1, ..., mI} (1) (2) (3)
The purpose for designing SMIsub is the forming sub-graphs for further transformation. They are formed by rules of choosing proper sub-graphs from SM(O,L) for concrete transformation operation. Denote these rules as initial selecting rules.
Denote transformation operation as . Thus: Representation of transformation rule in details: ( ( o I 1 , l I 1 ) , . . . , ( o I n , l I n ) ) ( ( o R 1 , l R 1 ) , . . . , ( o R m , l R m ) ) ; o I i O I , l I i L I , o R j O R , l R j L R ; i 1, . . . , n ; j 1, . . . , m ; n | O I | , m | O R |
OR {oRi | i 1,..., nR}; LR {lRj | j 1,..., mR}
(OI , LI ) (OR, LR);
OI O1, OR O2 , LI L1, LR L2
(4)
(5)
(6)
(7)
(8)
(9)
To represent transformation rules transformational grammar
Transformation rules are syntax of this grammar
Initial selecting rules define how to choose SMIsub from SMinitial for performing transformational operation. Denote initial selecting rule as R(SMinitial ) . Thus, operation of selecting SMIsub applying R on SMinitial is written
Usually initial selecting rules are composed as conditional statements, defining which parts of SMinitial form
S (OS , LS )
OS {oS i | i 1,..., ns }, ns | O | LS {lS j | j 1,..., ms}, ms | Ls | s
S – is a mask which is applied to every pair (o1, l1); o1 O1, l1 L1 . A mask may contain more than one graph pair.
Graph SMIsub is formed by the next: every pair (o1, l1); o1 O1, l1 L1 of SMinitial is compared with (oS, lS ); oS O1, lS L1 . If considered pairs are the same, then (o1, l1); o1 O1, l1 L1 is added to SMIsub .
Thus statement (5) can be written as follows:
Analogously with transformation rules also first and second logics for representation of initial selecting rules are used. rules as TRANS.
5. General description of model to model transformation according to proposed formalization Describe steps of model to model transformation approaches, that is based on formalisms, proposed above in Chapter 4. 1. Transformation rules for transforming SMinitial to SM resulting are composed. Denote a set of transformation
TRANS {i ) | i 1,..., t}; t | TRANS | .
Formal representation of transformation rules is proposed in (6) and (7). 2. A set of initial selecting rules is formed. Denote it as RULES. Thus:
RULES {Ri (SM initial ) | i 1,..., q}; q | RULES | . 3. RULES are applied to SMinitial to form set of SMIsub for further transformation.
Every Ri (SMinitial ) forms graph SMIsub,i . Denote a set of received SMIsub as SMIselected . Thus: SMI selected {SMIsub,i | i 1,..., q}; | SMI selected || RULES | SMI selected ,i {(oSMI j , lSMI j ) | j 1,..., nselectted ,i} .
(10) (11) (12) (13) (14) (15) (16) (17) where q – is the number of sub-graphs in SMIsub,i , nselected ,i – is a number of pairs of sub-graph SMIselected ,i .
4. SMIselected is verified by deleting duplicated chains of pairs, that were obtained applying different initial selecting rules. One chain can be considered as path of sub-graph.
5. SMIselected is transformed to set of sub-graphs in SM resulting notation applying TRANS. Denote all obtained sub-graphs in SM resulting notation as SMR. Thus:
i 1,..., q; , q | SMI | SMRsub,i {(oSMR j , lSMR j ) | j 1,..., nSMRi } .
6. From SMR SM resulting is composed. Analytical approach for performing this operation will be proposed in where nSMRi – is a number of pairs of sub-graph SMRsub,i . further works.
Formal foundations and corresponded approach for model to model transformation is proposed in this paper.
They are grounded on analytical representation of software models, transformation and initial selecting rules. It is
proposed to represent software models as graphs. Expressions (1) and (2) let describing software model both in general
and detailed view. In comparison with other approaches, for example
Representation of transformation rules, proposed in other papers for instance
From the other side, methods of performing transformation tasks involving concrete transformation languages (for instance ATLAS, QVT, QVT-R and others) and environments (MEDINIQVT, WEBDBF) are limited by possibilities of considered modeling language and transformation environment.
The approach, proposed in this paper, allows considering transformation process both on metalevel and model
level
Considering of sub-graphs and software models at level of elements lets analyzing transformations in details. Doing this existing rules can be refined and new transformation rules also can be designed.
Develop a full analytical approach of model to model transformation that is grounded on collaboration of mathematical tools, used for transformation operations. In order to accomplish this goal to do the following:
propose an algorithm for designing of SM resulting that is grounded on ontology analysis. This algorithm
should consider possibilities of human cognitive abilities for perception of software models
define operations that are used for analysis of software model before and after transformation, namely
software model verification and semantic checking. Propose and analytical tool for performing these operation;
verify collaboration of proposed approaches with model of problem domain “Model-Driven Architecture
formal methods and approaches” proposed in paper
Number of publications approaximatelly 65: in foreign journals – approximately 25, in Ukrainian 35. ttps://orcid.org/0000-0002-9873-6010