Verification of behavioural elements of UML models using B

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Verification of behavioural elements of UML
models using B

• Truong, Ninh-Thuan and Souquieres, Jeanine. 2005.
• In Proceedings of the 2005 ACM Symposium on
  Applied ComputingSanta Fe, New Mexico, March 13
  - 17, 2005
• Presented by James T. OHara
• SE 510, Fall 2005

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A Tale of Two Tools

• The application of formal methods allows the
  rigorous definition and analysis of the
  functionality and the behavior of a system.
• It is capable of showing that the system is
  correct.
• B is a method for specifying, designing and
  coding software systems.
• UML is a widely accepted modeling language that
  can be used to visualize, specify, construct and
  document the artifacts of a software system.

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Combining UML with B

• The derivation from UML specification into the B
  formal method is considered as an appropriate way
  to jointly use UML and B in practical, unified
  and rigorous software development.
• The aim of the study was to use B support tools
  to analyze UML model properties.

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THE B METHOD

• B is a formal software development method,
  originally developed by J.R. Abrial.
• The B notation is based on set theory, the
  language of generalized substitutions and first
  order logic.
• Specifications are composed of abstract machines
  that are similar to modules or classes.

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The UML Metamodel

• The UML metamodel defines the complete semantics
  for representing object models using UML.
• Abstract Syntax
• Well-Formedness Rules
• Semantics

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TRANSFORMATION OF UML TO B

• The transformation of an attribute of a UML class
  to a variable of a B abstract machine can be
  performed as follows

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What is a UML Collaboration Diagram

• A collaboration diagram describes interactions
  among objects in terms of sequenced messages.
  Collaboration diagrams represent a combination of
  information taken from class, sequence, and use
  case diagrams describing both the static
  structure and dynamic behavior of a system.

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UML Collaboration Diagram

• UML collaboration diagrams, are used to explore
  the dynamic nature of your software.

Source http//www.agilemodeling.com/style/collab
orationDiagram.htm
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TRANSFORMATION OF THE COLLABORATION PACKAGE TO B

• The Collaboration package is a sub-package of the
  Behavioral Elements package

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What is a UML State Diagram
Figure 1. A seminar during registration.

• UML state machine diagrams depict the various
  states that an object may be in and the
  transitions between those states.

Source http//www.agilemodeling.com/artifacts/st
ateMachineDiagram.htm
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TRANSFORMATION OF THE STATE MACHINE PACKAGE TO B

• The State Machine package is a sub-package of the
  Behavioral Elements package.

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A CASE STUDY

• Modeling of a printing system.
• This system can be described as followsthe
  printing system is a system to print a file from
  a computer.
• The use gives a command to print a file, and the
  system will respond according to its messages.

Figure 3. Collaboration diagram of the printing
system.
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Interaction B Abstract Machine
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Verification of UML Model Properties

• The well-formedness rules of the Messages class
  applied on the Collaboration package and their B
  machines counterparts can be evaluated for
  completeness and consistency.
• UML well-formedness rules can be represented by
  system invariants.

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CONCLUSION

• In this paper, the authors have presented a
  technique to transform the UML behavioral
  diagrams to a B specification.
• With the contribution of the transformation of
  UML metamodel and their well-formedness rules
  into B, the semantics of the UML models can be
  translated into B properties.
• Formal methods can then be used to specify and
  verify object-oriented systems.

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Additional References

• The B-Book Assigning Programs to Meanings,
  Cambridge University Press 1996. ISBN
  0-521-49619-5
• The Object Primer Agile Model-Driven Development
  with UML 2.0Scott Ambler, Cambridge University
  Press, Paperback, 3rd edition, 2004