1. © 2012 Metamaxim Ltd Modelling Choreography Ashley McNeile 1 st February 2012

2. © 2012 Metamaxim Ltd Background

3. © 2012 Metamaxim Ltd Agenda A little background Introduction to Protocol Modelling – A way of modelling rich interaction between state, data, and behaviour – Concerned with behaviour description using composition (composition of partial descriptions) Application to Choreography – Multiparty asynchronous collaborations – Reasoning a realizability

4. © 2012 Metamaxim Ltd “Pure” Process Algebra Closed Open B0 B1 B2 B-1 B-2 D2 D1 W2 W1 Close Ability to ExpressAbility to Reason Bank Account Balance values in range -2 to +2 Deposit events D1 and D2 Withdraw events W1 and W2 Close only possible when “in credit” ACCOUNT = Open  B0 B0 = D1  B1 | D2  B2 | W1  B-1 | W2  B-2 | Close  Closed B1 = D1  B2 | W1  B0 | W2  B-1 | Close  Closed B2 = W1  B1 | W2  B0 | Close  Closed B-1 = D1  B0 | D2  B1 | W1  B-2 B-2 = D1  B-1 | D2  B0

5. © 2012 Metamaxim Ltd Composition Tony Hoare Deterministic Choice P  Q Choice determined by the environment on the basis of the first action. Nondeterministic Choice P ∏ Q The environment has no control over the choice. Interleaving P ||| Q Completely independent concurrent activity. Interface Parallel P || Q Concurrent activity that requires synchronization between the component processes.

6. © 2012 Metamaxim Ltd Eclipsed by “OOP mania” in 1980s and 1990s. Early ideas in OO (1980s) Domain Object Behaviour JSD (Jackson System Development) Shlaer/Mellor (Recursive Design) M.A. Jackson Bank Account Transaction In UseOpenClose DepositWithdraw * oo Diagrams used to describe and formalise “object life-cycles.” Objects own data (like OO) balance := balance + Deposit.amount; balance := balance - Withdraw.amount; balance := 0; Composition not emphasized

7. © 2012 Metamaxim Ltd Protocol Modelling

8. © 2012 Metamaxim Ltd Protocol Modelling Open Active Closed Close Deposit Withdraw balance := balance + Deposit.amount; balance := balance - Withdraw.amount; balance := 0; Account Machine 1 Open Un- frozen Withdraw Account Machine 2 Frozen Release Freeze Release Close In Credit State Function: if (balance < 0) return “Overdrawn”; else return “In Credit”; Account Machine 3 Over- drawn

9. © 2012 Metamaxim Ltd Protocol Modelling Open Active Closed Close Deposit Withdraw balance := balance + Deposit.amount; balance := balance - Withdraw.amount; balance := 0; Account Machine 1 Open Un- frozen Withdraw Account Machine 2 Frozen Release Freeze Release Close In Credit State Function: if (balance < 0) return “Overdrawn”; else return “In Credit”; Account Machine 3 Over- drawn Open Active Closed Close Deposit Withdraw balance := balance + Deposit.amount; balance := balance - Withdraw.amount; balance := 0; Account Machine 1 Open Un- frozen Withdraw Account Machine 2 Frozen Release Freeze Release Close In Credit State Function: if (balance < 0) return “Overdrawn”; else return “In Credit”; Account Machine 3 Over- drawn Account = Account Machine 1 || Account Machine 2 ||Account Machine 3

10. © 2012 Metamaxim Ltd Protocol Modelling Active Closed Account Machine 1 Un- frozen Account Machine 2 Frozen In Credit State Function: if (balance < 0) return “Overdrawn”; else return “In Credit”; Account Machine 3 Over- drawn Open Release Close balance = ?? Close Deposit Withdraw Open Withdraw Release Freeze balance := balance + Deposit.amount; balance := balance - Withdraw.amount; balance := 0; Release Close balance = 0 Close Deposit Withdraw Open Withdraw Release Freeze

11. © 2012 Metamaxim Ltd Protocol Modelling Withdraw 20 Active Closed Account Machine 1 Un- frozen Account Machine 2 Frozen In Credit State Function: if (balance < 0) return “Overdrawn”; else return “In Credit”; Account Machine 3 Over- drawn balance := balance + Deposit.amount; balance := balance - Withdraw.amount; balance := 0; Release Close balance = 0 Close Deposit Withdraw Open Withdraw Release Freeze Release Close balance = -20 Close Deposit Withdraw Open Withdraw Release Freeze

12. © 2012 Metamaxim Ltd Protocol Modelling Close Active Closed Account Machine 1 Un- frozen Account Machine 2 Frozen In Credit State Function: if (balance < 0) return “Overdrawn”; else return “In Credit”; Account Machine 3 Over- drawn balance := balance + Deposit.amount; balance := balance - Withdraw.amount; balance := 0; Release Close balance = -20 Close Deposit Withdraw Open Withdraw Release Freeze X

13. © 2012 Metamaxim Ltd Protocol Modelling Freeze Active Closed Account Machine 1 Un- frozen Account Machine 2 Frozen In Credit State Function: if (balance < 0) return “Overdrawn”; else return “In Credit”; Account Machine 3 Over- drawn balance := balance + Deposit.amount; balance := balance - Withdraw.amount; balance := 0; Release Close balance = -20 Close Deposit Withdraw Open Withdraw Release Freeze Release Close balance = -20 Close Deposit Withdraw Open Withdraw Release Freeze

14. © 2012 Metamaxim Ltd Protocol Modelling What Now? Active Closed Account Machine 1 Un- frozen Account Machine 2 Frozen In Credit State Function: if (balance < 0) return “Overdrawn”; else return “In Credit”; Account Machine 3 Over- drawn balance := balance + Deposit.amount; balance := balance - Withdraw.amount; balance := 0; Release Close balance = -20 Close Deposit Withdraw Open Withdraw Release Freeze

15. © 2012 Metamaxim Ltd Protocol Modelling Open Active Closed Close Deposit Withdraw balance := balance + Deposit.amount; balance := balance - Withdraw.amount; balance := 0; Account Machine 1 Open Un- frozen Withdraw Account Machine 2 Frozen Release Freeze Release Close In Credit State Function: if (balance < 0) return “Overdrawn”; else return “In Credit”; Account Machine 3 Over- drawn Topological (State is driven by transitions) Non- Topological (State is calculated) Open Active Closed Close Deposit Withdraw balance := balance + Deposit.amount; balance := balance - Withdraw.amount; balance := 0; Account Machine 1 Open Un- frozen Withdraw Account Machine 2 Frozen Release Freeze Release Close In Credit State Function: if (balance < 0) return “Overdrawn”; else return “In Credit”; Account Machine 3 Over- drawn

16. © 2012 Metamaxim Ltd Construction of AM1||AM2 d1 Open Active Closed Close Deposit Withdraw Open Un- frozen Withdraw Frozen Release Freeze d2 Deposit Release Freeze Close Deposit Close Deposit Withdraw Open Release Freeze Release Freeze Closed, Frozen Closed, Un-frozen Active, Un-frozen Active, Frozen d1, d2 AM2 AM1||AM2 Closed, d2 Active, d2 d1, Frozen d1, Un-frozen AM1

17. © 2012 Metamaxim Ltd Choreography

18. © 2012 Metamaxim Ltd Dancer 4 Dance Choreography Dancer 1 Dancer 3 Dancer 2

19. © 2012 Metamaxim Ltd Scenario Messages are FIFO between each pair The network does not block How do we ensure that the collaboration “works”?

20. © 2012 Metamaxim Ltd Step 1: Design the Choreography PQ R m1, m6 m2 m3, m7, m8 m5 m4 P>Q:m1 Q>P:m2 Q>R:m3 P>R:m5 R>P:m4 P>Q:m6 Q>R:m7 Q>R:m8 The labels on transitions show message exchanges. P>Q:m1 denotes P sending a message of type m1 to Q.

21. © 2012 Metamaxim Ltd Q>R:m3 Q>R:m7 Q>R:m8 P>Q:m1 Q>P:m2 Step 2: Project to Participants P P>Q:m1 Q>P:m2 P>R:m5 R>P:m4 P>Q:m6 !>Q:m1 ?<R:m4 !>Q:m6 !>R:m5 ?<Q:m2

22. © 2012 Metamaxim Ltd P Step 2: Project to Participants !>Q:m1 ?<R:m4 !>Q:m6 !>R:m5 ?<Q:m2 !>Q:m1 ?<R:m4 !>Q:m6 !>R:m5 ?<Q:m2 R ?<Q:m3 !>P:m4 ?<P:m5 ?<Q:m7 ?<Q:m8 Q ?<P:m1 !>P:m2 !>R:m3 ?<P:m6 !>R:m7 !>R:m8

23. © 2012 Metamaxim Ltd P Step 3: “Enact” !>Q:m1 ?<R:m4 !>Q:m6 !>R:m5 ?<Q:m2 R ?<Q:m3 !>P:m4 ?<P:m5 ?<Q:m7 ?<Q:m8 Q ?<P:m1 !>P:m2 !>R:m3 ?<P:m6 !>R:m6 !>R:m7 Will the emergent behaviour of the collaboration follow the original choreography? Imagine a “global clock” On each tick, one thing happens: one send or one receive Does the ordering of sends match a trace of the choreography?

24. © 2012 Metamaxim Ltd Some Examples P Q P>Q:m1 Q>P:m2 m1 m2 P Q m1 m2 P>Q:m1 Q>P:m2 No! Yes! P Q m1 m2 P>Q:m1Q>P:m2 Yes!

25. © 2012 Metamaxim Ltd Some Examples P>Q:m1Q>R:m2 P>R:m3 P Q m1 m2 R m3 No! P>Q:m1Q>P:m3 R>Q:m2Q>P:m3 P Q m1 m2 R m3 Yes!

26. © 2012 Metamaxim Ltd The Rules (Simplified!) Within a single choreography machine: 1.Only one sender from given state of the choreography 2.No Send must take place from an ambiguous state - Q - Q P R P>Q:m1 Q>P:m2 Q>R:m3 P>R:m5 R>P:m4 P>Q:m6Q>R:m7 Q>R:m8 P !>Q:m1 ? <R:m4 !>Q:m6 !>R:m5 ? <Q:m2 ?<P:m1 !>P:m2 !>R:m3 ? <P:m6 !>R:m6 !>R:m7 ? <Q:m3 !>P:m4 ?<P:m5 ? <Q:m7 ? <Q:m8

27. © 2012 Metamaxim Ltd Scenario Place Order Request Cancel Request Amend Accept Order Accept Amend Accept Cancel Invoice Request Credit Check Request Deposit Payment Receipt Pay Deposit Pay Order Credit OK Deposit Paid Request Delivery Request Delivery Date Confirm Delivery Date SUPPLIERCUSTOMER DELIVERY CO BANK 9 7 2 9 8 4 5 1 3 6 1 2 3 4 5 6 7 8 9 C S B DC S B D

28. © 2012 Metamaxim Ltd C S B D Choreography 1 D] Cust > Supp: Request Cancel Supp > Cust: Accept Cancel Supp > Cust: Reject Cancel Cust > Supp: Place Order Supp > Cust: Accept Order Cust > Supp: Request Amend Supp > Cust: Accept Amend Supp > Cust: Reject Amend Supp > Cust: Reject Order

29. © 2012 Metamaxim Ltd C S B D Choreography 2 D] Supp > Cust: Accept Order Supp > Cust: Invoice Cust > Bank: Pay Order Bank > Cust: Payment Receipt Supp > Cust: Accept Cancel Supp > Cust: Accept Amend Cust > Supp: Place Order Cust > Bank: Pay Deposit Supp > Bank: Request Credit Check Bank > Supp: Credit OK Bank > Cust: Request Deposit Bank > Supp: Deposit Paid

30. © 2012 Metamaxim Ltd C S B D Choreography 3 D] Supp > Cust: Accept Order Supp > Del: Request Delivery Del > Cust: Request Delivery Date Cust > Del: Confirm Delivery Date Del > Supp: Confirm Delivery Date Supp > Cust: Invoice Supp > Cust: Accept Cancel Supp > Cust: Accept Amend

31. © 2012 Metamaxim Ltd Composition D] Supp > Cust: Accept Order Supp > Del: Request Delivery Del > Cust: Request Delivery Date Cust > Del: Confirm Delivery Date Del > Supp: Confirm Delivery Date Supp > Cust: Invoice Supp > Cust: Accept Cancel Supp > Cust: Accept Amend D] Cust > Supp: Request Cancel Supp > Cust: Accept Cancel Supp > Cust: Reject Cancel Cust > Supp: Place Order Supp > Cust: Accept Order Cust > Supp: Request Amend Supp > Cust: Accept Amend Supp > Cust: Reject Amend Supp > Cust: Reject Order D] Supp > Cust: Accept Order Supp > Cust: Invoice Cust > Bank: Pay Order Bank > Cust: Payment Receipt Supp > Cust: Accept Cancel Supp > Cust: Accept Amend Cust > Supp: Place Order Cust > Bank: Pay Deposit Supp > Bank: Request Credit Check Bank > Supp: Credit OK Bank > Cust: Request Deposit Bank > Supp: Deposit Paid C S B D S S S C B S S C B D C S S - - - - - -

32. © 2012 Metamaxim Ltd Reasoning with Data Money Transfer by Instalment 1 Request QP 2 Instalment 3 “Thanks” P sends a Request for money to Q Q starts sends instalments to P. Once the cumulative instalments sent reaches the requested amount, Q stops sending and P says “Thanks”. Process: 123123 State Function: if (toPay ≤ 0) return “done”; else return “not done”; done P>Q:“Thanks” not done Q>P:Instalment C2 P>Q:Request toPay := Request.amount; Q>P:Instalment P>Q:“Thanks” toPay := toPay - Instalment.amount; C1 CHOREOGRAPHY = C1 || C2

33. © 2012 Metamaxim Ltd C2 * (Connected Form of C2) Reasoning with Data State Function: if (toPay ≤ 0) return “done”; else return “not done”; done P>Q:“Thanks” not done Q>P:Instalment C2 P>Q:“Thanks” Q>P:Instalment P>Q:Request Q>P:Instalment not done done P>Q:Request toPay := Request.amount; Q>P:Instalment P>Q:“Thanks” toPay := toPay - Instalment.amount; C1 P>Q:“Thanks” Q>P:Instalment C1 || C2 * Q>P:Instalment QP- P>Q:Request P