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A Systematic Approach to Atomicity Decomposition in Event-B

A Systematic Approach to Atomicity Decomposition in Event-B. Asieh Salehi Fathabadi , Michael Butler and Abdolbaghi Rezazadeh (asf08r, mjb , ra3@ecs.soton.ac.uk) School of Electronics and Computer Science University of Southampton, UK SEFM 2012, Thessaloniki, Greece

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A Systematic Approach to Atomicity Decomposition in Event-B

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  1. A Systematic Approach to AtomicityDecomposition in Event-B AsiehSalehiFathabadi, Michael Butler and AbdolbaghiRezazadeh (asf08r, mjb, ra3@ecs.soton.ac.uk) School of Electronics and Computer Science University of Southampton, UK SEFM 2012, Thessaloniki, Greece Wednesday 3rd October www.event-b.org www.deploy-project.eu

  2. Overview & Road Map • Event-B Formal Method • Motivation (AtomcityDecomposition Overview) • Case Studies Overview • AD Language (ADL) • Translation Rules (TRs) • Tool Support • Evaluation • Conclusion Initial Atomicity Decomposition iFM 2009 Butler ManualDevelopments of Case Studies FMCO 2010 NFM 2011 ADLand Translation Rules SEFM 2012 AD ToolSupport Automatic Developments of Case Studies

  3. Event-B (Abrial) • A model based formal method • models the state and events of a system (state-transition model) • Simple modelling notation • Set theory and predicate logic • Mathematical proofs • Verifying correctness and consistency of models • Supported by an open tool platform (Rodin) • Extension of Eclipse IDE • Extensible • Integrated environment for modelling and proving • Proof obligation generator, automatic and interactive provers

  4. Refinement-based Development • Starts with an abstract representation of the system. • A simple view of the system • Focus on main purpose of the system • Adding details during a sequence of steps, instead of building a single large model. • During refinement steps: • Add details to current functionality • Introduce new functionality • Use proofs to verify the consistency of refinement steps

  5. Motivation Atomicity Decompositionuses a graphical notation to enhance Event-B development approach by • Introducing explicit control flows • Event-B is a state-based formal method; control flow between events is typically modelled implicitly via variables and event guards. • Introducing explicit refinement relationships • New events may be introduced in Event-B refinement; there is no explicit link between such new events and the abstract event. * Initially introduced by Butler: Butler, M. J. Decomposition Structures for Event-B. In Integrated Formal Methods iFM2009 (2009).

  6. Atomicity Decomposition Diagram* Root, abstract event, is decomposed into sub events AbstractEvent (par) refines skip refines AbstractEvent Event2 (par) Event1 (par) The sub events are read from left to right and indicate sequential control * Based on Jackson Structure Diagram (JSD): M.A Jackson: System Development. Prentice-Hall, Englewood Cliffs (1983)

  7. Case Studies Overview • The initial AD approach is evaluated and extended in development of two case studies: • Multimedia Protocol* • A media channel is established for transferring multi-media data. There are three phases in the protocol: establish, modifyand close. • BepiColombo Spacecraft** • A TeleCommand(TC) is received by the core from Earth. • The Software Core (CSW) checks the syntax of the received TC. • Further semantic checking has to be carried out on the syntactically validated TC. • For each valid TC a control TeleMessage(TM) is generated and sent to Earth. * Zave, P. & Cheung, E. Compositional Control of IP Media. IEEE Trans. Software Eng. (2009). ** ESA Media Center, Space Science. Factsheet: Bepicolombo. http://www.esa.int/esaSC/SEMNEM3MDAF_0_spk.html.

  8. Atomicity Decomposition Language (ADL) flow (p1, pn) one(p) * xor leaf leaf leaf leaf (p) leaf …

  9. Translation Rules (sequencing) BepiColombo (tc) Translation Rule1 Translation Rule1 TC_Validation_Ok (tc) ReceiveTC (tc) TR1 TR1 TR2 TR3 TR4 TR4 TR5 TR5 TR6 TR7 TR7

  10. Translation Rules (loop-constructor) Media Channel (ch) * TR8 establishMediaChannel (ch) modify (ch) close (ch)

  11. Translation Rules (solid line) TC_Validation_Ok (tc) TCCheck_Ok (tc) TCExecute_Ok (tc) TCExecOk_ReplyCtrlTM (tc) TR9 TR10

  12. Translation Rules (xor-constructor) TCExecute_Ok (tc) xor TCCore_Execute_Ok (tc) TCDevice_Execute_Ok (tc) TR11 TR12 TR12

  13. Translation Rules (one-constructor) TCExecOk_ReplyCtrlTM (tc) one(tm) TCExecOk_ProcessCtrlTM(tc, tm) TCExecOk_CompleteCtrlTM (tc) TR13 TR14

  14. Translation Rules (Overview and a closer view) TR1

  15. Tool Support • The Rodin platform is an Eclipse-based IDE for Event-B and is extendablewith plug-ins. • The AD tool support is developed as a plug-in for Rodin provides: • an environment for graphical modelling in Event-B. • automatic translation of the AD diagrams into Event-B models in terms of control flows and refinement relationships. Uses: • Eclipse Modelling Framework (EMF) • Epsilon Transformation Language (ETL) Event-B EMF Meta-model AD EMF Meta-model ETL Rules rule Leaf2Varibale transform l : Source!Leaf to v : Target!Variable{ v.name := l.name; }

  16. Evaluation • The AD plug-in provides a consistent encoding of the AD diagrams in a systematicway. The manually generated Event-B models are less systematic and less consistent. • Systematic naming protocol:each control variable has the same name as the corresponding event name. • Alternative approaches of control flow modelling in Event-B: subsets, disjoint sets, … • A merged guard versus separate guards: complicated proof obligations.

  17. The ADL (other constructors)* one(p) all(p) some(p) and or xor leaf (p) leaf (p) leaf leaf leaf … leaf … leaf … leaf leaf (p) * Available at http://eprints.soton.ac.uk/340357/

  18. Combined AD Diagram: An Overall Overview of the Refinement Process BepiColombo (tc) ReceiveTC(tc) TC_Validation_Ok(tc) TCValid_GenerateData(tc) TCValid_ReplyDataTM(tc) TCCheck_Ok(tc) TCExecute_Ok(tc) TCExecOk_ReplyCtrlTM(tc) xor TCCore_Execute_Ok (tc) TCDevice_Execute_Ok (tc) SendTC_Core_to_Device (tc) CheckTC_in_Device_Ok (tc) SendOkTC_Device_to_Core (tc)

  19. Conclusion • FM 2009: The initial AD approach is introduced by Butler. • FMCO 2010, NFM 2011: • How the AD approach provides a means of introducing explicit flow controlinto Event-B development process (in development of two complex case studies). • SEFM 2012: • The formal description of the ADL. • Translation rules from the ADL to the Event-B language. • A tool supporting the AD methodology. • Re-developthe models of the previous case studies in an automatic way (more consistent and systematic). • Future work: • Combining the AD approach and other approaches like state machine. • Applying to furtherreal world case studies. • Publishing the complete version of ADL and translation rules (as an extension of SEFM2012).

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