1. Modular reasoning in the presence of event subtyping 14 th international conference on Modularity 1 Mehdi Bagherzadeh Robert Dyer Rex D. Fernando Jose Sanchez Hridesh Rajan

2. Event types: separation of crosscutting concerns a subject announces an event (using announce expression) observers (zero or more) register for the event observers run in a chain, when the event is announced, and can invoke each other (using invoke expressions) subject (base) observer (crosscutting) observer event type announce invoke

3. Modular reasoning about behavior Modular subject reasoning : {P} announce ev {?} using only subject implementation and event ev Modular observer reasoning : {P} invoke {?} using only observer implementation and event ev subject (announce ev) observer ev announce ev observer (invoke) observer ev ob

4. Event specification, previous work Modular subject reasoning : {P} announce ev {Q} Modular observer reasoning : {P} invoke {Q} announce ev ev specify spec (P,Q) invoke P Q Q P ob1 observer Q P ob2

5. Event subtyping For observer reuse, announcement of ev runs not only its observers but also all observers of its superevents. announce ev observer ev ev’ observer subtype

6. Subject modular reasoning & event subtping Can we still say {P} announce ev {Q} ? NO announce ev ev ev’ (P,Q) (P’,Q’)

7. Observer modular reasoning & event subtyping Can we still say {P} invoke {Q} ? NO ev ev’ invoke (P,Q) (P’,Q’) ob

8. Problems of modular reasoning in presence of event subtyping 1.Combinatorial reasoning 2.Behavioral invariance

9. Combinatorial reasoning problem {P} announce ev {?} announce ev ev ev’ (P,Q) (P’,Q’)

10. Combinatorial reasoning 1 {P} announce ev {Q} announce ev ev ev’ (P,Q) (P’,Q’) Q P ob Q’ P’ ob’

11. Combinatorial reasoning 2 {P} announce ev {Q’} if P => P’ announce ev ev ev’ (P,Q) (P’,Q’) Q P ob Q’ P’ ob’

12. Combinatorial reasoning {P} announce ev {Q or Q’ or Q ∞ Q’} – all execution orders of observers must be considered. – caused by arbitrary execution orders of observers announce ev ev ev’ (P,Q) (P’,Q’)

13. Behavioral invariance problem ob: {P} invoke {?} ob’:{P’} invoke {?} ev ev’ (P,Q) (P’,Q’) invoke ob invoke ob’

14. Behavioral invariance 1 ob: {P} invoke {Q} requires (P => P’ and Q’ => Q) ev ev’ (P,Q) (P’,Q’) invoke P Q Q P ob Q’ P’ ob’

15. Behavioral invariance 2 ob’: {P’} invoke {Q’} requires (P’ => P and Q=> Q’) ev ev’ (P,Q) (P’,Q’) invoke P’ Q’ P’ ob’ Q P ob

16. Behavioral invariance ev ev’ (P,Q) (P’,Q’) ob runs before ob’P => P’ and Q’ => Q ob’ runs before obP’ => P and Q => Q’ arbitrary execution orderP = P’ and Q = Q’ invoke P Q Q P ob Q’ P’ ob’ invoke P’ Q’ P’ ob’ Q P ob

17. Solution 1. Non-decreasing relation on execution orders of observers of an event and its superevents Problem: arbitrary execution orders of observers 2. Refining relation among event specifications of an event and its superevents. Problem: unrelated behaviors of observers

18. Non-decreasing order An observer ob of ev run before any observer ob’ of ev’. – Backward compatible: observers of ev run according to their dynamic registration order. observer ev ev’ observer non-decreasing ob ob’

19. Refining relation, behavior 1. Behavior of an event refines the behavior of its superevent. – P => P’ && Q’ => Q (P strengthens P’ and Q weakens Q’) – inverse of blackbox behavioral subtyping ev ev’ (P’,A’,Q’) (P,A,Q) refines Q’ P’ Q P strengthen weaken

20. Refining relation, control 2. Control effects of an event refines control effects of its superevents – Behavior (R,S) refines its corresponding (R’,S’) as shown previously – program expression pe textually refines corresponding pe’. – Blackbox behavioral subtyping does not control effect refinement. ev ev’ (P’,A’,Q’) (P,A,Q) refines A’ A refines (R’,S’) pe’ (R,S) pe

21. Combinatorial reasoning solved {P} announce ev {Q} Non-decreasing relation: observer ob’ cannot run before ob. announce ev ev ev’ (P,Q) (P’,Q’) Q P ob Q’ P’ ob’ Q P ob Q’ P’ ob’

22. Behavioral invariance solved {P} invoke {Q} Refining relation: P => P’ && Q => Q’ ev ev’ (P,Q) (P’,Q’) invoke P Q Q P ob Q’ P’ ob’ Q P ob Q’ P’ ob’

23. Non-decreasing alone Non-decreasing alone: does not allow ob’ to run before ob, but does not guarantee (P => P’ and Q => Q’ ). ev ev’ (P’,A’,Q’) invoke P Q Q P ob Q’ P’ ob’ invoke P’ Q’ P’ ob’ Q P ob  

24. Refining alone Refining alone: guarantees (P = >P’ and Q => Q’ ) but does not guarantee that ob’ does not run before ob. ev ev’ (P’,A’,Q’) invoke P Q Q P ob Q’ P’ ob’ invoke P’ Q’ P’ ob’ Q P ob  

25. Modular reasoning is enabled {P} announce ev {Q} ? Yes ob: {P} invoke {Q} ? Yes ob’: {P’} invoke {Q’} ? Yes announce ev invoke ev ev’ invoke (P’,A’,Q’) (P,A,Q) ob ob’ non-decreasing refining 1 2

26. Control effect reasoning Our technique enables modular reasoning about control effects in addition to reasoning about behaviors.

27. Applicability Applicable to other event-based systems including: joint point types Joint point interfaces

28. Summary Problems in modular reasoning in the presence of event subtyping: 1.Combinatorial reasoning 2.Behavioral invariance Solution: 1.Non-decreasing relation for observers’ execution order 2.Refining relation for event specifications

29. Thank you & Questions 29