Reversible event structures, and Controlled and Uncontrolled - - PowerPoint PPT Presentation

Reversible event structures, and Controlled and Uncontrolled Reversibility in CCSK

Eva Graversen & Nobuko Yoshida April 29

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http://mrg.doc.ic.ac.uk

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Post-docs: Simon CASTELLAN David CASTRO Francisco FERREIR Raymond HU Rumyana NEYK Nicholas NG Alceste SCALA PhD Students: Assel ALTAYEV Juliana FRANCO Eva GRAVERSEN

ECOOP’16 E C O O P ’ 1 7 CC’18

POPL’17

ICSE’18

[CC’18] Rumyana Neykova , Raymond Hu, NY, Fahd Abdeljallal: Session Type Providers: Compile-time API Generation for Distributed Protocols with Interaction Refinements in F#. [FoSSaCS’18] Bernardo Toninho, NY: Depending On Session Typed Process. [ESOP’18] Bernardo Toninho, NY: On Polymorphic Sessions And Functions: A Talk of Two (Fully Abstract) Encodings. [ESOP’18] Malte Viering, Tzu-Chun Chen, Patrick Eugster, Raymond Hu , Lukasz Ziarek: A Typing Discipline for Statically Verified Crash Failure Handling in Distributed Systems. [ICSE’18] Julien Lange, Nicholas Ng, Bernardo Toninho, NY : A Static Verification Framework for Message Passing in Go using Behavioural Types [ECOOP’17] Alceste Scala, Raymond Hu, Ornela Darda, NY: A Linear Decomposition

• f Multiparty Sessions for Safe Distributed Programming..

[COORDINATION’17] Keigo Imai, NY, Shoji Yuen: Session-ocaml: a session-based library with polarities and lenses. [FoSSaCS’17] Julien Lange, NY: On the Undecidability of Asynchronous Session Subtyping. [FASE’17] Raymond Hu, NY: Explicit Connection Actions in Multiparty Session Types. [CC’17] Rumyana Neykova, NY: Let It Recover: Multiparty Protocol-Induced Recovery. [POPL’17] Julien Lange, Nicholas Ng, Bernardo Toninho, NY: Fencing off Go: Liveness and Safety for Channel-based Programming.

Selected Publications 2017/2018

[CC’18] Rumyana Neykova , Raymond Hu, NY, Fahd Abdeljallal: Session Type Providers: Compile-time API Generation for Distributed Protocols with Interaction Refinements in F#. [FoSSaCS’18] Bernardo Toninho, NY: Depending On Session Typed Process. [ESOP’18] Bernardo Toninho, NY: On Polymorphic Sessions And Functions: A Talk of Two (Fully Abstract) Encodings. [ESOP’18] Malte Viering, Tzu-Chun Chen, Patrick Eugster, Raymond Hu , Lukasz Ziarek: A Typing Discipline for Statically Verified Crash Failure Handling in Distributed Systems. [ICSE’18] Julien Lange, Nicholas Ng, Bernardo Toninho, NY : A Static Verification Framework for Message Passing in Go using Behavioural Types. [ECOOP’17] Alceste Scala, Raymond Hu, Ornela Darda, NY: A Linear Decomposition

• f Multiparty Sessions for Safe Distributed Programming.

[COORDINATION’17] Keigo Imai, NY, Shoji Yuen: Session-ocaml: a session-based library with polarities and lenses. [FoSSaCS’17] Julien Lange, NY: On the Undecidability of Asynchronous Session Subtyping. [FASE’17] Raymond Hu, NY: Explicit Connection Actions in Multiparty Session Types. [CC’17] Rumyana Neykova, NY: Let It Recover: Multiparty Protocol-Induced Recovery. [POPL’17] Julien Lange, Nicholas Ng, Bernardo Toninho, NY: Fencing off Go: Liveness and Safety for Channel-based Programming.

Selected Publications 2017/2018

Motivation

• Reversibility can be used for:
• Modelling naturally reversible systems
• Debugging
• State-space exploration
• Event structures have been used to define semantics for CCS,

π-calculus, LOTOS, etc. in forwards-only setting.

• Categorical definitions can help define choice and parallel

composition.

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CCSK

CCSK (Phillips et al. 06) uses keys to denote past actions and which actions they have synchronised with: a.b ⑤ a

τrms

Ý Ý Ý Ñ arms.b ⑤ arms

brns

Ý Ý Ñ arms.brns ⑤ arms

brns

arms.b ⑤ arms

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Forwards CCS Process as Prime Event Structure (Winskel 1982)

a.b ⑤ b Ñ E ✏ ta, b, b, τ✉ a ➔ b a ➔ τ b ✼ τ τ ✼ b Ñ ❍ ta✉ ta, b✉ tb✉ ta, b✉ ta, τ✉ ta, b, b✉

Process Event Structure Configurations

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Forwards-only Category Overview

PrimeES BundleES StableES generalES AsymmetricES ExtendedBundleES B I A Ba Be Eb 5

Category Overview

PES BES SES ES ReversiblePES RBES SRES RES AES RAES EBES REBES SConfigurationSystems FinitelyEnabledCS Pp ✪ Pb ✪ Pe ✪ B Br I I Pr Pr Ar Bar Ber A Ba Be Pa ✪ I Cr ✪ ✪ Cr Cer Φp Φb Φe Φa ✪ R✶ R✶ R Eb Eer

Previously defined Morphisms defined by us Entirely defined by us

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Outline

Configuration Systems Reversible Bundle Event Structures Event structure semantics of CCSK Roll-CCSK

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Configuration Systems

Configuration System

A configuration system has a set of events E ✏ ta, b✉, a set of reversible events F ✏ ta, b✉, which can be undone a, b, a set C ❸ 2E configurations of events, and a set Ñ❸ C ✂ ♣E ❨ Fq ✂ C transitions between them: ❍ ta✉ tb✉ ta, b✉ a b a b b a a b, a

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Morphism

Definition (Configuration system-morphism) Let ♣E0, F0, C0, Ñ0q and ♣E1, F1, C1, Ñ1q be configuration systems. A configuration system morphism is a partial function f : E0 Ñ E1 such that

• 1. for any X, Y P C0, A ❸ E0, and B ❸ F0, if X

A❨B

Ý Ý Ý Ñ0 Y then f ♣Xq

f ♣Aq❨f ♣Bq

Ý Ý Ý Ý Ý Ý Ñ1 f ♣Y q

• 2. for any X P C0, f ♣Xq P C1
• 3. for all e0, e✶

0 P E0, if f ♣e0q ✏ f ♣e✶ 0q ✘ ❑ and e0 ✘ e✶ 0 then there

exists no X P C0 such that e0, e✶

0 P X 9

Coproduct (Choice)

❍ ta✉ tb✉ ta, b✉

• ❍

tc✉ td✉ tc, d✉

✏

❍ ta✉ tb✉ ta, b✉ tc✉ td✉ tc, d✉

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Partially Synchronous Product (Parallel Composition)

❍ ta✉ tb✉ ta, b✉

✂

❍ tc✉ ✏ ❍ t♣a, ✝q✉ t♣b, ✝q✉ t♣a, cq✉ t♣b, cq✉ t♣✝, cq✉ t♣a, ✝q, ♣b, ✝q✉ t♣a, ✝q, ♣b, cq✉ t♣a, ✝q, ♣✝, cq✉ t♣a, cq, ♣b, ✝q✉ t♣b, ✝q, ♣✝, cq✉ t♣a, ✝q, ♣b, ✝q, ♣✝, cq✉

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Reversible Bundle Event Structures

Reversible Bundle Event Structure

E ✏ ♣E, F, Ðß , #, ⊲q where E ✏ ta, b, c✉, F ✏ ta, b✉, tc, b✉ Ðß a, ta✉ Ðß c, b#c, ta✉ Ðß b, c ⊲ a ❍ ta✉ tb✉ tc✉ ta, b✉ ta, c✉ b b c a a a b a

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Causal

If a CS or RBES is causal, an event can be reversed if and only if every event caused by it has been reversed. In a causal CS any reachable configuration is forwards-reachable. Most reversible process calculi are causal. The previous RBES and CS were not causal.

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Causal CS and RBES

E ✏ ♣E, F, ÞÑ, ✼, ⊲q where E ✏ ta, b✉ F ✏ ta, b✉ ta✉ Ðß b, b ⊲ a ❍ ta✉ tb✉ ta, b✉ a b a b a, b b a

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Event structure semantics of CCSK

CCSK

CCSK uses keys to denote past actions and which actions they have synchronised with: a.b ⑤ a

τrms

Ý Ý Ý Ñ arms.b ⑤ arms

brns

Ý Ý Ñ arms.brns ⑤ arms

brns

arms.b ⑤ arms

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CCSK Process as Reversible Bundle Event Structure

arms.b ⑤ arms Ñ E ✏ ta, a, τ, b✉ ta, τ✉ Ðß b a ✼ τ ✼ a b ⊲ a b ⊲ τ

Ñ

❍ ta✉ ta✉ tτ✉ ta, b✉ tτ, b✉ ta, a✉ ta, a, b✉

Process Event Structure Configurations

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Roll-CCSK

Rollback

Rollback (Lanese et al., 11) is a way to control when the process reverses, only letting tagged actions and actions caused by them reverse when the roll is reached: arms.brns ⑤ aγrms.crosroll γ

roll γ

a.b ⑤ aγ.c.roll γ ♣ ♣ ⑤ q ⑤

✶ ♣

⑤

✶q ⑤

⑤ q③t ✉

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Rollback

Rollback (Lanese et al., 11) is a way to control when the process reverses, only letting tagged actions and actions caused by them reverse when the roll is reached: arms.brns ⑤ aγrms.crosroll γ

roll γ

a.b ⑤ aγ.c.roll γ Using this method, ♣aγ.♣d.0 ⑤ c.roll γq ⑤ bγ✶.♣c ⑤ d.roll γ✶q ⑤ a ⑤ bq③ta, b, c, d✉ is not able to roll all the way back to the beginning, as executing

• ne roll undoes an action preceding the other.

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We split the roll into two actions, one triggering the roll, which is reversed when a previous action is rolled back, and one executing the roll:

♣aγrms.♣drns.0 ⑤ cros.roll γq ⑤ bγ✶rps.♣cros ⑤ drns.roll γ✶q ⑤ arms ⑤ brpsq③ta, b, c, d✉

start roll γ

♣aγrms.♣drns.0 ⑤ cros.rolling γq ⑤ bγ✶rps.♣cros ⑤ drns.roll γ✶q ⑤ arms ⑤ brpsq③ta, b, c, d✉

start roll γ✶

♣aγrms.♣drns.0 ⑤ cros.rolling γq ⑤ bγ✶rps.♣cros ⑤ drns.rolling γ✶q ⑤ arms ⑤ brpsq③ta, b, c, d✉

roll γ✶

♣aγrms.♣d.0 ⑤ c.rolling γq ⑤ bγ✶.♣c ⑤ d.roll γ✶q ⑤ arms ⑤ bq③ta, b, c, d✉

roll γ

♣aγ.♣d.0 ⑤ c.roll γq ⑤ bγ✶.♣c ⑤ d.roll γ✶q ⑤ a ⑤ bq③ta, b, c, d✉ 18

Roll-CCSK Process as Event Structure

aγ.roll γ Ñ E ✏ ta, start roll γ, roll γ✉ ta✉ Ðß start roll γ tstart roll γ✉ Ðß roll γ troll γ✉ Ðß start roll γ troll γ✉ Ðß a a ⊲ roll γ start roll γ ⊲ a roll γ ⊲ a roll γ ⊲ start roll γ

Ñ

❍ ta✉ ta, start roll γ✉ ta, start roll γ, roll γ✉ troll γ✉ ta, roll γ✉

Process Event Structure Configurations

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Splitting events in Roll-CCSK

Sometimes reversal of events is caused by multiple events

• combining. To model this, events must be spilt.

arms.brns ⑤ aγrms.rolling γ

roll γ

Ý Ý Ý Ñ a.b ⑤ aγ.roll γ arm✶s.brns ⑤ aγrms.rolling γ

roll γ

Ý Ý Ý Ñ arm✶s.brns ⑤ aγ.roll γ t ✉ Ðß t ✉ Ðß t ✉ Ðß

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Splitting events in Roll-CCSK

Sometimes reversal of events is caused by multiple events

• combining. To model this, events must be spilt.

arms.brns ⑤ aγrms.rolling γ

roll γ

Ý Ý Ý Ñ a.b ⑤ aγ.roll γ arm✶s.brns ⑤ aγrms.rolling γ

roll γ

Ý Ý Ý Ñ arm✶s.brns ⑤ aγ.roll γ This requires splitting b as it is only rolled back by roll γ if the as synchronised, meaning ta✉ Ðß ba tτ✉ Ðß bτ troll γ✉ Ðß bτ

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Result

Given a process P, which generates an event structure E and an initial state Init,

• 1. P

µ

Ý Ñ P✶ for a P✶ which generates an event structure E✶ and initial state Init✶, if and only if there exists an isomorphism f : E Ñ E✶ and an event e in E that is enabled in Init and labelled µ, such that f ♣Init ❨ te✉q ✏ Init✶

• 2. P

roll γ

Ý Ý Ý Ñ P✶ for a P✶ which generates an event structure E✶ and initial state Init✶, if and only if there exists an isomorphism f : E Ñ E✶ and a sequence of transitions in the configuration system of E, Init e0 Ý Ñ X0

e1 . . . Xn✁1 en Xn e0 X such that e0

is labelled roll γ and f ♣Xq ✏ Init✶

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Conclusion

• Causal reversible bundle event structures can describe the

semantics of CCSK

• Roll-CCSK extends CCSK to control reversibility by using

rollback

• Non-causal reversible extended bundle event structures can

model Roll-CCSK.

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Future Work

π-calculus: ♣νnq♣a①n② ⑤ b①n② ⑤ n♣yqq

• Non-structural causation
• Traditionally non-stable
• Past actions must be stored in separate memories

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