1 / 60

Reversibility and beyond

Reversibility and beyond. Ivan Lanese Computer Science Department Focus research group Univers ity of Bologna/INRIA Bologna, Italy. Summarizing work of INRIA teams Sardes and Focus. Roadmap. Directions Rhopi Roll-pi Crop What next?. Roadmap. Directions Rhopi Roll-pi Crop

tamber
Download Presentation

Reversibility and beyond

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Reversibility and beyond Ivan Lanese Computer Science Department Focus research group University of Bologna/INRIA Bologna, Italy Summarizing work of INRIA teams Sardes and Focus

  2. Roadmap • Directions • Rhopi • Roll-pi • Crop • What next?

  3. Roadmap • Directions • Rhopi • Roll-pi • Crop • What next?

  4. Reversibility and beyond • We summarize here the thread of research done on reversibility by INRIA teams Sardes and Focus • Rhopi: making HOpi reversible • Roll-pi: introducing an operator for controlling reversibility • Crop: adding compensations

  5. Reversibility and beyond • We summarize here the thread of research done on reversibility by INRIA teams Sardes and Focus • Rhopi: making HOpi reversible • Extending reversibility techniques from CCS to more expressive calculi • Preserving structural congruence • Roll-pi: introducing an operator for controlling reversibility • Crop: adding compensations

  6. Reversibility and beyond • We summarize here the thread of research done on reversibility by INRIA teams Sardes and Focus • Rhopi: making HOpi reversible • Roll-pi: introducing an operator for controlling reversibility • To model checkpointing and rollbacking techniques • Exploiting and constraining reversibility • Crop: adding compensations

  7. Reversibility and beyond • We summarize here the thread of research done on reversibility by INRIA teams Sardes and Focus • Rhopi: making HOpi reversible • Roll-pi: introducing an operator for controlling reversibility • Crop: adding compensations • Only preliminary ideas • Keeping trace of past failures • Avoiding repeating the same errors • Going towards long running transactions

  8. The small-step approach • We start from a basic calculus: Rhopi • We add to it the smallest mechanism we can think of going in the desired direction • Rollback primitive • Compensating messages • We study how far we can go with these mechanisms

  9. Roadmap • Directions • Rhopi • Roll-pi • Crop • What next?

  10. h i P Q P : : a m e s s a g e = ; j ( ) X P i t . a r g g e r j ( j ) l l l P Q i i t p a r a e c o m p o s o n j P º a n e w n a m e : j b l X i v a r a e j l l 0 n u p r o c e s s Q h i j ( ( ) ) f = g Q X P P . a a ! X HOpi fundamentals

  11. h i j ( ( ) ) j ( j ) j j j P Q P X P P Q P X 0 . : : a a º a = ; : ¯ M N i t c o n g u r a o n s : : = ; h d P t r e a · : j [ ] k m e m o r y m ; j ( j ) l l l M N p a r a e j M i i t t r e s r c o n º u : j l l ¯ i 0 t n u c o n g u r a o n ~ j h i k h h k t ¢ a g s · : : = ; ( ( h i ) j ( ( ) ) ) d P X Q i t . a c o n r e c o r m : : · : a · : a = 1 2 Rhopi syntax

  12. ( h i ) j ( ( ) ) P X Q . m · : a · : a = 1 2 F o r w a r d : P ( h i ) j ( ( ) ) ( f = g ) j [ ] k k k P X Q Q ³ . · : a · : a º : m ; X 1 2 : ( ) j [ ] k k P B a c k w a r d : m ; m : Ã Rhopi semantics • A forward rule similar to HOpi • Creating a fresh tag for the continuation • Creating a memory storing the consumed message and trigger • A backward rule undoing a step (up to garbage collection)

  13. ( h ( i ) ) h h i h j i i k k k b b d X P X X 0 0 . . : : : a a c 3 2 1 Rhopi example

  14. [ h ( ( h h j i ) ) i i h h i h j i i ] k k k k k b b d k b d k M X X P N X 0 0 0 . . : : : : : a a c : ; 2 1 3 1 2 Rhopi example

  15. [ [ ( h ( ( h h h h h j i ) i ) i j i i i h h j h i i h ) j i i ] ] k k k k k k k b b b d d k d b d k k k M X P X N X N 0 0 0 0 0 0 . . : : : : : : : a a c c : ; : ; 3 1 4 2 1 2 3 1 4 Rhopi example

  16. [ h ( ( h h j i ) ) i i h h i h j i i ] k k k k k b b d k b d k M X X P N X 0 0 0 . . : : : : : a a c : ; 2 1 3 1 2 Rhopi example

  17. ( h ( i ) ) h h i h j i i k k k b b d X P X X 0 0 . . : : : a a c 3 2 1 Rhopi example

  18. n n Y Y ~ ~ ~ ( h i ) f g k h h h k h h h ( ) E T P ´ ¢ : ¿ º : ¿ a g = i i i 1 n : ; ; : : : ; . i i 1 1 = = Rhopi structural congruence • Used for ensuring each thread has a unique tag • Needed if the continuation of a trigger is a parallel composition • Here τ is either a message or a trigger • Other structural congruence rules are standard

  19. ³ Ã Rhopi properties • Rhopi is an extension of HOpi • Rhopi satisfies the Loop lemma • If P Q then Q P and viceversa • All states reachable from P are weak barbed equivalent to P itself • Rhopi satisfies causal consistency • Essentially the same properties of RCCS

  20. Roadmap • Directions • Rhopi • Roll-pi • Crop • What next?

  21. Limits of Rhopi • In Rhopi reversibility is wild • Forward and backward actions always enabled • Each result can always be annulled • Impossible to make a result final • We want a mechanism to control reversibility

  22. Roll-pi approach • Normal computation is forward • Backward computation on demand, to backtrack in case of errors • We use an explicit roll operator to this end • Question: how far back should we go? • In a concurrent scenario the number of steps is not meaningful • Answer: we go back to undo a communication stored in a specified memory • Memory keys allows to individuate the target memory

  23. j j j ( j ) j h i j ( ) j l l P Q X P P Q P X P 0 . r o : : º a a a ° = ° ; : j j ( j ) j j [ ] k M N M M N P 0 : : º u · : ¹ ; = ; : Roll-pi syntax • Extends Rhopi syntax • Adds the primitive roll γ for triggering rollback • Adds a γ label to triggers • The idea: roll γ takes the system back to the state before the trigger labelled by γ has been consumed • More precisely: undoes all the steps caused by the interaction involving the trigger labelled by γ

  24. ( h i ) j ( ( ) ) P X Q . m · : a · : a = 1 2 ° ( ) C & N o m k P k ( h i ) j ( ( ) ) ( f = g ) j [ ] k k k P X Q Q ³ ; . · : a · : a º : m ; X 1 2 ° ° : ; ( j [ ] j ( ) ) k k l l k N N l t I r o c o m p e e m ; · : ( ) N a i v e j [ ] j ( ) j k l l k & N N r o m ; · : m à k Giving semantics: naïve try • The forward rule uses the key k to replace the placeholder γ • A rule for roll • N ►k verifies that all the elements in N are related to k • Complete checks that the term is closed under the causal relation • contains the elements in N not related to k

  25. ( h ( i ) ) h h i j i k k k b b l l X X X 0 0 . . r o : : : a a c ° 3 2 1 ° Naïve semantics example

  26. [ h ( h ( i j ) ) i h h i j ] i k k k k k b b l l k k b l k l M X X N X 0 0 . . r o r o : : : : : a a c : ; ° 1 3 2 1 2 ° Naïve semantics example

  27. ~ ~ h [ h [ h ( h ( i i i j j ) ) i h h h i i j ] i ] k k k k k k h h b b h h l k k l k k k b l l k l k l k M M X X N N X 0 0 0 . . r o ¢ ¢ r o r o : : : : : : a a : : c : : c ; ; ° 3 2 1 1 1 2 1 4 4 2 3 1 4 ° ; ; Naïve semantics example

  28. ~ ~ h [ h [ h ( h ( i i i j j ) ) i h h h i i j ] i ] k k k k k k h h b b h h l k k l k k k b l l k l k l k M M X X N N X 0 0 0 . . r o ¢ ¢ r o r o : : : : : : a a : : c : : c ; ; ° 3 2 1 1 1 2 1 4 4 2 3 1 4 ° ; ; Naïve semantics example

  29. ( h ( i ) ) h h i j i k k k b b l l X X X 0 0 . . r o : : : a a c ° 3 2 1 ° Naïve semantics example

  30. k k l l l l k k r r o o 1 1 The concurrency anomaly

  31. k k l l l l k k r r o o 1 1 The concurrency anomaly

  32. k 1 The concurrency anomaly

  33. k k l l l l k k r r o o 1 1 The concurrency anomaly

  34. k The concurrency anomaly

  35. The concurrency anomaly • Intuitively, I have rolls for undoing every action… • …but I am not able to go back to the starting state • I miss the possibility of performing rollbacks concurrently • Forcing this sequential behavior in a distributed implementation would not be easy • Can I write a semantics capturing concurrent rollbacks?

  36. ( h i ) j ( ( ) ) P X Q . m · : a · : a = 1 2 ° ( ) C o m k P ( h i ) j ( ( ) ) ( f = g ) j [ ] k k k P X Q Q ³ ; . · : a · : a º : m ; X 1 2 ° ° : ; ( ) j [ ] ( ) j [ ] ² l l k k l l k k ( ) S t a r t r o r o · : m ; · : m ; à 1 1 ( j [ ] ) k k N N l t I c o m p e e m ; ( ) R o l l j [ ] j ² k & N N m ; m à k Giving semantics: taming concurrency • The rollback has been splitted in two steps • Tagging the memory • Executing the rollback of a tagged memory

  37. k k l l l l k k r r o o 1 1 Concurrent rollback

  38. k k l l l l k k r r o o 1 1 Concurrent rollback

  39. k k l l l l k k r r o o 1 1 Concurrent rollback

  40. k 1 Concurrent rollback

  41. Concurrent rollback

  42. 0 0 0 f h h d k d ¤ ¤ M M M M M M i i t t ³ e n w a n u n m a r e à , Properties of concurrent semantics • Correct • If I go backward from M, I reach a state able to go forward to M • Complete • I can execute any number of concurrent rollbacks • Good as abstract specification

  43. Going towards an implementation • The concurrent semantics is very high-level • Includes atomic steps involving an unbounded number of participants • Concurrently executing • Possibly distributed • Can we refine the semantics to a more distributed one? • Giving the same final result • Yes! • But technicalities are quite complex…

  44. k l l k r o Low level semantics

  45. k l l k r o Low level semantics

  46. k l l k r o Low level semantics

  47. k l l k r o Low level semantics

  48. k Low level semantics

  49. Low level semantics

  50. Low level semantics • Based on local checks and asynchronous notifications • In two phases • Top-down notification of rollback request • Bottom-up rollback • Equivalent to the concurrent one • Weak barbed congruent • Fully abstract • A good starting point for a concurrent and distributed implementation • Writing a low level semantics equivalent to the naïve one would be more difficult

More Related