1. FMCO 2005 / UpSTAIRS with Sequence Diagrams Ragnhild Kobro Runde UpSTAIRS with Sequence Diagrams Øystein Haugen, Ragnhild Kobro Runde, Ketil Stølen University of Oslo and SINTEF ICT, Norway

2. FMCO 2005 / UpSTAIRS with Sequence Diagrams / Slide 2 Ragnhild Kobro Runde Overview Interactions and trace semantics Interactions as example runs Underspecification and nondeterminism Refinement Data and guards

3. FMCO 2005 / UpSTAIRS with Sequence Diagrams / Slide 3 Ragnhild Kobro Runde Background: UML interactions Partial ordering of events: -The send event is ordered before the corresponding receive event. -Events on the same lifeline are ordered from the top and downwards. S specifies the two traces: - Lifeline (instance) Send-event (!x) Receive- event (?x) Message

4. FMCO 2005 / UpSTAIRS with Sequence Diagrams / Slide 4 Ragnhild Kobro Runde Alternatives S specifies the four traces: - First alternative Second alternative

5. FMCO 2005 / UpSTAIRS with Sequence Diagrams / Slide 5 Ragnhild Kobro Runde Example: Network communication Interactions = example runs! -Specifies a set of positive and/or negative behaviours. Positive Negative Inconclusive

6. FMCO 2005 / UpSTAIRS with Sequence Diagrams / Slide 6 Ragnhild Kobro Runde Negative behaviour Formally: (p1,n1) (p2,n2) = (p1 p2, (p1 n2)U(n1 p2)U(n1 n2) ) Note: -Inconclusive + positive/negative = inconclusive -Positive + negative = negative Positive: Negative:

7. FMCO 2005 / UpSTAIRS with Sequence Diagrams / Slide 7 Ragnhild Kobro Runde Overview Interactions and trace semantics Interactions as example runs Underspecification and nondeterminism Refinement Data and guards

8. FMCO 2005 / UpSTAIRS with Sequence Diagrams / Slide 8 Ragnhild Kobro Runde Underspecification and non-determinism Underspecification: Several alternative behaviours are considered equivalent (serve the same purpose). Inherent non-determinism: Alternative behaviours that must all be possible for the implementation. These two should be described differently!

9. FMCO 2005 / UpSTAIRS with Sequence Diagrams / Slide 9 Ragnhild Kobro Runde STAIRS Positive Negative Inconclusive Positive Negative Inconclusive Positive Negative Inconclusive Positive Negative Inconclusive Positive Negative Inconclusive Positive Negative Inconclusive xalt

10. FMCO 2005 / UpSTAIRS with Sequence Diagrams / Slide 10 Ragnhild Kobro Runde alt vs xalt Assume [[ d1 ]] = (p1,n1) [[ d2 ]] = (p2,n2) alt specifies potential behaviour: [[ d1 alt d2 ]] = [[ d1 ]] + [[ d2 ]] = (p1 U p2, n1 U n2) xalt specifies mandatory behaviour: [[ d1 xalt d2 ]] = [[ d1 ]] U [[ d2 ]] = (p1,n1) U (p2,n2) P1 N1 I1I1 P2 N2 I2I2 P1 U P2 N1 U N2 I

11. FMCO 2005 / UpSTAIRS with Sequence Diagrams / Slide 11 Ragnhild Kobro Runde Example: Network communication

12. FMCO 2005 / UpSTAIRS with Sequence Diagrams / Slide 12 Ragnhild Kobro Runde alt vs xalt A->G->N1->B Everything else A->G->N2->N3->B A->G->N2->N4->B Everything else S:network

13. FMCO 2005 / UpSTAIRS with Sequence Diagrams / Slide 13 Ragnhild Kobro Runde Overview Interactions and trace semantics Interactions as example runs Underspecification and nondeterminism Refinement Data and guards

14. FMCO 2005 / UpSTAIRS with Sequence Diagrams / Slide 14 Ragnhild Kobro Runde Refinement in STAIRS An interaction obligation o'=(p',n') is a refinement of an interaction obligation o=(p,n) iff -n n' -p p'Un' Positive Negative Inconclusive Supplementing Narrowing

15. FMCO 2005 / UpSTAIRS with Sequence Diagrams / Slide 15 Ragnhild Kobro Runde Refinement contd. An interaction d' is a refinement of an interaction d iff o [[ d ]]: o' [[ d' ]]: o o' P1 N1 I1I1 d: P2 N2 I2I2 d': P'1 N'1 I' 1 P'2 N'2 I' 2 P'3 N'3 I' 3 NOT VALID!

16. FMCO 2005 / UpSTAIRS with Sequence Diagrams / Slide 16 Ragnhild Kobro Runde Adding new obligations NEW

17. FMCO 2005 / UpSTAIRS with Sequence Diagrams / Slide 17 Ragnhild Kobro Runde Supplementing A->G->N1->B Everything else A->G->N2->N3->B A->G->N2->N4->B Everything else

18. FMCO 2005 / UpSTAIRS with Sequence Diagrams / Slide 18 Ragnhild Kobro Runde Overview Interactions and trace semantics Interactions as example runs Underspecification and nondeterminism Refinement Data and guards

19. FMCO 2005 / UpSTAIRS with Sequence Diagrams / Slide 19 Ragnhild Kobro Runde Including data Two special events: -write (for assignments) -check (for constraints) A state is a total function σ Var → Val For an expression expr, expr(σ) denotes its value in σ. Assignment: [[assign(var,expr)]] = ( { | σ'(var) = expr(σ)}, Ø}

20. FMCO 2005 / UpSTAIRS with Sequence Diagrams / Slide 20 Ragnhild Kobro Runde Constraints [[constr(c)]] = ( { |c(σ)}, { |¬c(σ)} )

21. FMCO 2005 / UpSTAIRS with Sequence Diagrams / Slide 21 Ragnhild Kobro Runde Guards A special kind of constraint May be overlapping Need not be exhaustive

22. FMCO 2005 / UpSTAIRS with Sequence Diagrams / Slide 22 Ragnhild Kobro Runde Definition of guarded xalt Assume: [[ d1 ]] = (p1,n1) [[ d2 ]] = (p2,n2) Guarded xalt: [[ g1->d1 xalt g2->d2]] = [[ constr(g1) seq d1 ]] U [[ constr(g2) seq d2 ]]

23. FMCO 2005 / UpSTAIRS with Sequence Diagrams / Slide 23 Ragnhild Kobro Runde Definition of guarded xalt Assume: [[ d1 ]] = (p1,n1) [[ d2 ]] = (p2,n2) Guarded xalt: [[ g1->d1 xalt g2->d2]] = ( { p1 | g1(σ)}, { p1 | ¬g1(σ)} U { n1 | g1(σ) v ¬g1(σ)} ) U ( { p2 | g2(σ)}, { p2 | ¬g2(σ)} U { n2 | g2(σ) v ¬g2(σ)} )

24. FMCO 2005 / UpSTAIRS with Sequence Diagrams / Slide 24 Ragnhild Kobro Runde

25. FMCO 2005 / UpSTAIRS with Sequence Diagrams / Slide 25 Ragnhild Kobro Runde Narrowing by using guards A->G->[N1 ok]->N1->B Everything else A->G->[N1 not ok]->N1->B A->G->[N2 ok]->N2->... Everything else A->G->[N2 not ok]->N2->...

26. FMCO 2005 / UpSTAIRS with Sequence Diagrams / Slide 26 Ragnhild Kobro Runde A->G->[N2 not ok]->N2->[N3 ok/not ok]->N3->B A->G->[N2 not ok]->N2->[N4 ok/not ok]->N4->B Narrowing by using guards A->G->[N2 ok]->N2->[N3 not ok]->N3->B A->G->[N2 ok]->N2->[N4 not ok]->N4->B A->G->[N2 ok]->N2->[N3 not ok and N4 not ok] A->G->[N2 ok]->N2->[N3 ok]->N3->B A->G->[N2 ok]->N2->[N4 ok]->N4->B Everything else A->G->[N2 ok]->N2->[N3 not ok]->N3->B A->G->[N2 ok]->N2->[N4 not ok]->N4->B

27. FMCO 2005 / UpSTAIRS with Sequence Diagrams / Slide 27 Ragnhild Kobro Runde xalt to ensure security

28. FMCO 2005 / UpSTAIRS with Sequence Diagrams / Slide 28 Ragnhild Kobro Runde A possible refinement

29. FMCO 2005 / UpSTAIRS with Sequence Diagrams / Slide 29 Ragnhild Kobro Runde Summary Interactions are partial specifications: -Distinguish between positive and inconclusive traces. Distinguish between underspecification (alt) and inherent non-determinism (xalt). Refinement also of partial interactions. -Supplementing -Narrowing Introducing guards should be a valid refinement step. -Traces with a false guards should be negative.

30. FMCO 2005 / UpSTAIRS with Sequence Diagrams / Slide 30 Ragnhild Kobro Runde Literature on STAIRS Øystein Haugen, Ketil Stølen: STAIRS – Steps to analyze interactions with refinement semantics (UML'2003, LNCS 2863). -Distinguishes between mandatory and potential behaviour Øystein Haugen, Knut Eilif Husa, Ragnhild Kobro Runde, Ketil Stølen: STAIRS towards formal design with sequence diagrams (SOSYM, Online First, 2005). -Denotational trace semantics for interactions -Formalizes the refinement relations in STAIRS Øystein Haugen, Knut Eilif Husa, Ragnhild Kobro Runde, Ketil Stølen: Why timed sequence diagrams require three- event semantics (Dagstuhl post-proc., LNCS 3466). Extended version as research report 309. -Extends STAIRS with time and three-event semantics

31. FMCO 2005 / UpSTAIRS with Sequence Diagrams / Slide 31 Ragnhild Kobro Runde Literature on STAIRS Ragnhild Kobro Runde, Øystein Haugen, Ketil Stølen: Refining UML interactions with explicit and implicit nondeterminism (Nordic Journal of Computing, to appear). -Extends STAIRS with data and guards -More on mandatory vs potential behaviour Ragnhild Kobro Runde, Øystein Haugen, Ketil Stølen: How to transform UML neg into a useful construct (NIK'2005, to appear). -Investigates various formal definitions for negation Atle Refsdal, Knut Eilif Husa, Ketil Stølen: Specification and refinement of soft real-time requirements using sequence diagrams (FORMATS'05). -Extends STAIRS with probabilistic alternatives

32. FMCO 2005 / UpSTAIRS with Sequence Diagrams Ragnhild Kobro Runde http://heim.ifi.uio.no/~ragnhilk/stairs/ Thank you!