Liveness of Communicating Transactions

Transcription

1 (joint work with Vasileios Koutavas and Matthew Hennessy) TRINITY COLLEGE DUBLIN COLÁISTE NA TRÍONÓIDE, BAILE ÁTHA CLIATH Dublin Concurrency Workshop 2011

2 Traditional Transactions Transactions provide an abstraction for error recovery in a concurrent setting.

3 Traditional Transactions Transactions provide an abstraction for error recovery in a concurrent setting. The transactional system guarantees: Atomicity: Each transaction will either run in its entirety or not at all Consistency: Faults caused by a transaction are automatically detected and rolled-back Isolation: The effects of a transaction are concealed from the rest of the system until the transaction commits Durability: After a transaction commits, its effects are permanent.

4 Traditional Transactions Transactions provide an abstraction for error recovery in a concurrent setting. The transactional system guarantees: Atomicity: Each transaction will either run in its entirety or not at all Consistency: Faults caused by a transaction are automatically detected and rolled-back Isolation: The effects of a transaction are concealed from the rest of the system until the transaction commits Durability: After a transaction commits, its effects are permanent. However, isolation limits concurrency The semantics of traditional transactions is sequential schedules Traditional transactions do not offer an abstraction for recovery from distributed errors (e.g. deadlocks)

5 Communicating Transactions We drop isolation to increase concurrency There is no limit on the communication between a transaction and its environment The transactional system guarantees: Atomicity: Each transaction will either run in its entirety or not at all Consistency: Faults caused by a transaction are automatically detected and rolled-back, together with all effects of the transaction to its environment Durability: After all transactions that have interacted commit, their effects are permanent (coordinated checkpointing) We are interested in safety and especially liveness properties First theory of liveness in the presence of transactions We have studied the transactional properties of communicating transactions in [CONCUR 2010]

6 Safety Safety: Nothing bad will happen [Lamport 77] A safety property can be formulated as a safety test T ; which signals on channel ; when it detects the bad behaviour P passes the safety test T ; when P T ; cannot output on ; This is the negation of passing a may test [DeNicola-Hennessy 84]

7 Liveness Liveness: Something good will eventually happen [Lamport 77] A liveness property can be formulated as a liveness test T ω which detects and reports good behaviour on ω. P passes the liveness test T ω when all future states of P T ω can output on ω This is a should test [Binksma-Rensink-Vogler 95, Rensink-Vogler 07] It excludes pathological traces We will later see why must testing [DeNicola-Hennessy 84] is not appropriate for transactions

8 TransCCS [CONCUR 2010] Syntax: P, Q ::= µ i.p i guarded choice P Q parallel νa.p hiding µx.p recursion P k Q transaction (k bound in P) co k commit

9 TransCCS [CONCUR 2010] Syntax: P, Q ::= µ i.p i guarded choice P Q parallel νa.p hiding µx.p recursion P k Q transaction (k bound in P) co k commit

10 TransCCS [CONCUR 2010] Syntax: P, Q ::= µ i.p i guarded choice P Q parallel νa.p hiding µx.p recursion P k Q transaction (k bound in P) Default co k commit

11 TransCCS [CONCUR 2010] Syntax: P, Q ::= µ i.p i guarded choice P Q parallel νa.p hiding µx.p recursion P k Q transaction (k bound in P) Alternative co k commit

12 TransCCS [CONCUR 2010] Syntax: P, Q ::= µ i.p i guarded choice P Q parallel νa.p hiding µx.p recursion P k Q transaction (k bound in P) Name co k commit

13 TransCCS [CONCUR 2010] Syntax: P, Q ::= µ i.p i guarded choice P Q parallel νa.p hiding µx.p recursion P k Q transaction (k bound in P) co k commit Main reductions: R-Comm a i = b j a i.p i b j.q j P i Q j i I j J R-Co P co k k Q P R-Emb k / R P k Q R P R k Q R R-Ab P k Q Q

14 TransCCS [CONCUR 2010] Syntax: P, Q ::= µ i.p i guarded choice P Q parallel νa.p hiding µx.p recursion P k Q transaction (k bound in P) co k commit Main reductions: R-Comm a i = b j a i.p i b j.q j P i Q j i I j J R-Co P co k k Q P R-Emb k / R P k Q R P R k Q R R-Ab P k Q Q

15 TransCCS [CONCUR 2010] Syntax: P, Q ::= µ i.p i guarded choice P Q parallel νa.p hiding µx.p recursion P k Q transaction (k bound in P) co k commit Main reductions: R-Comm a i = b j a i.p i b j.q j P i Q j i I j J R-Co P co k k Q P R-Emb k / R P k Q R P R k Q R R-Ab P k Q Q

16 Simple Example a.c.ω + e.; a.c.co k + e k r

17 Simple Example a.c.ω + e.; a.c.co k + e k r

18 Simple Example a.c.ω + e.; a.c.co k + e k R-Emb a.c.ω + e.; a.c.co k + e k a.c.ω + e.; r r

19 Simple Example a.c.ω + e.; a.c.co k + e k R-Emb a.c.ω + e.; a.c.co k + e k a.c.ω + e.; r R-Comm c.ω c.co k k a.c.ω + e.; r r

20 Simple Example a.c.ω + e.; a.c.co k + e k R-Emb a.c.ω + e.; a.c.co k + e k a.c.ω + e.; r R-Comm c.ω c.co k k a.c.ω + e.; r R-Comm ω co k k a.c.ω + e.; r r

21 Simple Example a.c.ω + e.; a.c.co k + e k R-Emb a.c.ω + e.; a.c.co k + e k a.c.ω + e.; r R-Comm c.ω c.co k k a.c.ω + e.; r R-Comm ω co k k a.c.ω + e.; r R-Co ω r

22 Simple Example a.c.ω + e.; a.c.co k + e k R-Emb a.c.ω + e.; a.c.co k + e k a.c.ω + e.; r R-Comm c.ω c.co k k a.c.ω + e.; r R-Comm ω co k k a.c.ω + e.; r R-Co ω r

23 Simple Example (a second trace) a.c.ω + e.; a.c.co k + e k r

24 Simple Example (a second trace) a.c.ω + e.; a.c.co k + e k R-Emb a.c.ω + e.; a.c.co k + e k a.c.ω + e.; r r

25 Simple Example (a second trace) a.c.ω + e.; a.c.co k + e k R-Emb a.c.ω + e.; a.c.co k + e k a.c.ω + e.; r R-Comm ; k a.c.ω + e.; r r

26 Simple Example (a second trace) a.c.ω + e.; a.c.co k + e k R-Emb a.c.ω + e.; a.c.co k + e k a.c.ω + e.; r R-Comm ; k a.c.ω + e.; r r

27 Simple Example (a second trace) a.c.ω + e.; a.c.co k + e k R-Emb a.c.ω + e.; a.c.co k + e k a.c.ω + e.; r R-Comm ; k a.c.ω + e.; r R-Ab a.c.ω + e.; r r

28 Simple Example (a second trace) a.c.ω + e.; a.c.co k + e k R-Emb a.c.ω + e.; a.c.co k + e k a.c.ω + e.; r R-Comm ; k a.c.ω + e.; r R-Ab a.c.ω + e.; r r (The environment is restored)

29 Simple Example (all traces) R-Ab a.c.ω + e.; a.c.co k + e k r a.c.ω + e.; r R-Emb R-Ab R-Comm P 1 R-Comm P 2 P 2 R-Comm P 3 R-Co ω

30 Restarting transactions a.c.ω + e.; µx. a.c.co k + e k X

31 Restarting transactions a.c.ω + e.; µx. a.c.co k + e k X R-Emb R-Ab R-Comm P 1 R-Comm P 2 P 2 R-Comm P 3 R-Co ω

32 Restarting transactions a.c.ω + e.; µx. a.c.co k + e k X R-Emb R-Ab R-Comm P 1 R-Comm P 2 P 2 R-Comm P 3 R-Co ω Infinitely aborting loop

33 Compositional Semantics The embedding rule is simple but entangles the processes We need to reason about the behaviour of P Q in terms of P and Q We introduce a compositional Labelled Transition System that uses secondary transactions: P k Q

34 Compositional Semantics The embedding rule is simple but entangles the processes We need to reason about the behaviour of P Q in terms of P and Q We introduce a compositional Labelled Transition System that uses secondary transactions: P k Q a.c.ω + e.; a.c.co k + e k r emb k a.c.ω + e.; k a.c.ω + e.; k(a) c.ω k a.c.ω + e.; k(c) ω k a.c.ω + e.; co k ω emb k a.c.co k + e k r k(a) c.co k k r k(c) co k k r co k 0

35 Compositional Semantics The embedding rule is simple but entangles the processes We need to reason about the behaviour of P Q in terms of P and Q We introduce a compositional Labelled Transition System that uses secondary transactions: P k Q a.c.ω + e.; a.c.co k + e k r emb k a.c.ω + e.; k a.c.ω + e.; k(e) c.ω k a.c.ω + e.; ab k a.c.ω + e.; emb k a.c.co k + e k r k(e) k r ab k r

36 Compositional Semantics (2) The behaviour of processes in TransCCS can be understood by CCS-like Clean traces derived by the LTS that: consider only traces where all actions are eventually committed ignore transactional annotations on the traces

37 Compositional Semantics (2) The behaviour of processes in TransCCS can be understood by CCS-like Clean traces derived by the LTS that: consider only traces where all actions are eventually committed ignore transactional annotations on the traces L( a.c.co k + e k r ) = {ɛ, a c, r}

38 Compositional Semantics (2) The behaviour of processes in TransCCS can be understood by CCS-like Clean traces derived by the LTS that: consider only traces where all actions are eventually committed ignore transactional annotations on the traces L( a.c.co k + e k r ) = {ɛ, a c, r} (Non-prefix-closed set)

39 Compositional Semantics (2) The behaviour of processes in TransCCS can be understood by CCS-like Clean traces derived by the LTS that: consider only traces where all actions are eventually committed ignore transactional annotations on the traces L( a.c.co k + e k r ) = {ɛ, a c, r} (Non-prefix-closed set) L(µX. a.c.co k + e k X ) = {ɛ, a c}

40 Compositional Semantics (2) The behaviour of processes in TransCCS can be understood by CCS-like Clean traces derived by the LTS that: consider only traces where all actions are eventually committed ignore transactional annotations on the traces L( a.c.co k + e k r ) = {ɛ, a c, r} (Non-prefix-closed set) L(µX. a.c.co k + e k X ) = {ɛ, a c} (Atomicity: all-or-nothing)

41 Compositional Semantics (2) The behaviour of processes in TransCCS can be understood by CCS-like Clean traces derived by the LTS that: consider only traces where all actions are eventually committed ignore transactional annotations on the traces L( a.c.co k + e k r ) = {ɛ, a c, r} (Non-prefix-closed set) L(µX. a.c.co k + e k X ) = {ɛ, a c} (Atomicity: all-or-nothing) enable compositional reasoning: L(P Q) = L(P) zip L(Q) L(P) L(Q) implies L(P R) L(Q R)

42 Safety Definition (Basic Observable) P a iff there exists P such that P P a Basic observable actions are permanent

43 Safety Definition (Basic Observable) P a iff there exists P such that P P a Basic observable actions are permanent Definition (P passes safety test T ; ) P cannot T ; when P T ; ;

44 Safety Definition (Basic Observable) P a iff there exists P such that P P a Basic observable actions are permanent Definition (P passes safety test T ; ) P cannot T ; when P T ; ; Definition (Safety preservation) S safe I when T ;. S cannot T ; implies I cannot T ;

45 Safety Definition (Basic Observable) P a iff there exists P such that P P a Basic observable actions are permanent Definition (P passes safety test T ; ) P cannot T ; when P T ; ; Definition (Safety preservation) S safe I when T ;. S cannot T ; implies I cannot T ; Theorem (Characterization of safety preservation) S safe I iff L(S) L(I )

46 Liveness Definition (P Passes liveness Test T ω [Rensink-Vogler 07]) P shd T ω when R. P T ω R implies R ω

47 Liveness Definition (P Passes liveness Test T ω [Rensink-Vogler 07]) P shd T ω when R. P T ω R implies R ω a.c.ω + e.; µx. a.c.co k + e k X R-Emb R-Ab P 1 R-Comm R-Comm P 2 P 2 R-Comm P 3 R-Co ω

48 Liveness Definition (P Passes liveness Test T ω [Rensink-Vogler 07]) P shd T ω when R. P T ω R implies R ω a.c.ω + e.; µx. a.c.co k + e k X R-Emb R-Ab P 1 R-Comm R-Comm P 2 P 2 must testing would consider the infinite loop R-Comm P 3 R-Co ω

49 Liveness Definition (P passes liveness test T ω [Rensink-Vogler 07]) P shd T ω when R. P T ω R implies R ω Definition (Tree Failures [Rensink-Vogler 07]) (t, Ref ) is a tree failure of P when P. P t = CL P and L(P ) Ref = F(P) = {(t, Ref ) tree failure of P} Ref t

50 Liveness Definition (P passes liveness test T ω [Rensink-Vogler 07]) P shd T ω when R. P T ω R implies R ω Definition (Tree Failures [Rensink-Vogler 07]) (t, Ref ) is a tree failure of P when P. P t = CL P and L(P ) Ref = F(P) = {(t, Ref ) tree failure of P} Ref t Ref is generally non-prefix-closed

51 Liveness Definition (P passes liveness test T ω [Rensink-Vogler 07]) P shd T ω when R. P T ω R implies R ω Definition (Tree Failures [Rensink-Vogler 07]) (t, Ref ) is a tree failure of P when P. P t = CL P and L(P ) Ref = F(P) = {(t, Ref ) tree failure of P} Ref t Ref is generally non-prefix-closed Theorem (Characterization of liveness preservation) S live I iff F(S) F(I )

52 Simple Examples Let S ab = µx. a.b.co k k X L(S ab ) = {ɛ, ab} F(S ab ) = {(ɛ, S\ab), (ab, S) S A }

53 Simple Examples Let S ab = µx. a.b.co k k X L(S ab ) = {ɛ, ab} F(S ab ) = {(ɛ, S\ab), (ab, S) S A } S ab safe I 1 = a.b.co k k 0 L(I 1 ) = {ɛ, ab} S ab live I 1 F(I 1 ) = {(ɛ, S), (ab, S) S A }

54 Simple Examples Let S ab = µx. a.b.co k k X L(S ab ) = {ɛ, ab} F(S ab ) = {(ɛ, S\ab), (ab, S) S A } S ab safe I 1 = a.b.co k k 0 L(I 1 ) = {ɛ, ab} S ab live I 1 F(I 1 ) = {(ɛ, S), (ab, S) S A } S ab safe I 2 = µx. a.b.co k + e k X L(I 2 ) = L(S ab ) S ab live I 2 F(I 2 ) = F(S ab )

55 Comparison with CCS (1) Safety in TransCCS is characterized by non-prefix-closed sets of traces Safety in CCS is characterized by prefix-closed sets of traces

56 Comparison with CCS (1) Safety in TransCCS is characterized by non-prefix-closed sets of traces Safety in CCS is characterized by prefix-closed sets of traces TransCCS safety tests have the same distinguishing power as CCS safety tests If in CCS P safe Q then also in TransCCS P safe Q

57 Comparison with CCS (1) Safety in TransCCS is characterized by non-prefix-closed sets of traces Safety in CCS is characterized by prefix-closed sets of traces TransCCS safety tests have the same distinguishing power as CCS safety tests If in CCS P safe Q then also in TransCCS P safe Q No way to encode non-prefix-closed traces in CCS; thus no fully-abstract translation from TransCCS to CCS

58 Comparison with CCS (2) Liveness in TransCCS is characterized by tree failures Liveness in CCS is characterized by a more complex model [Rensink-Vogler 07]

59 Comparison with CCS (2) Liveness in TransCCS is characterized by tree failures Liveness in CCS is characterized by a more complex model [Rensink-Vogler 07] TransCCS liveness tests have more distinguishing power than CCS liveness tests In CCS a.(b.c + b.d) live a.b.c + a.b.d In TransCCS a.(b.c + b.d) live a.b.c + a.b.d (a, {bd}) F(a.(b.c + b.d)) (a, {bd}) F(a.b.c + a.b.d) TransCCS distinguishing liveness test in the paper

60 Comparison with CCS (2) Liveness in TransCCS is characterized by tree failures Liveness in CCS is characterized by a more complex model [Rensink-Vogler 07] TransCCS liveness tests have more distinguishing power than CCS liveness tests In CCS a.(b.c + b.d) live a.b.c + a.b.d In TransCCS a.(b.c + b.d) live a.b.c + a.b.d (a, {bd}) F(a.(b.c + b.d)) (a, {bd}) F(a.b.c + a.b.d) TransCCS distinguishing liveness test in the paper Thus no sound translation from TransCCS to CCS that is the identity on CCS terms

61 Also in [APLAS 2010] Canonical class of tests for liveness and safety See how restarting transactions add fault tolerance to CCS (Ex. 6) A sound, but incomplete bisimulation proof method, using the clean LTS transitions Many examples

62 Conclusions Communicating transactions: Traditional transactions without the isolation requirement No limit on communication or concurrency Simple safety and liveness theory First theory of liveness in the presence of transactions Future directions: Reference implementation/evaluation of the construct in a programming language. Advertisement Joint Trinity/Microsoft Research PhD on extending Haskell with communicating transactions. We need a good student :)

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64 ACD Properties A commit step makes the effects of the transaction permanent (Durability ) a.b.ω + e.; µx. a.b.co k + e k X R-Emb P1 R-Comm P2 R-Comm P2 R-Comm P3 R-Co ω R-Ab An abort step: restarts the transaction rolls-back embedded processes to their state before embedding (Consistency ) does not roll-back actions that happened before embedding does not affect non-embedded processes The semantics of transactions transactions are non-prefix-closed traces (Atomicity ).