Reversibility for Concurrent Interacting Systems Ivan Lanese Focus research group Computer Science and Engineering Department University of Bologna/INRIA Bologna, Italy 1 Contributors My coauthors: Elena Giachino (Italy), Michael Lienhardt (Italy), Claudio Antares Mezzina (Italy), Jean-Bernard Stefani (France), Alan Schmitt (France), Francesco Tiezzi (Italy)
Other groups working on similar topics In France: Jean Krivine, Daniele Varacca, Ioana Cristescu, ... In UK: Irek Ulidowski, Iain Phillips, ... Part of the work has been done inside the French ANR Project REVER INRIA Grenoble, PPS, CEA, Bologna Map of the talk 1. Causal-consistent reversibility
What is reversibility for us? The possibility of executing a computation both in the standard, forward direction, and in the backward direction, going back to a past state What does it mean to go backward? If from state S1 we go forward to state S2, then from state S2 we should be able to go back to state S1 Reversibility everywhere Reversibility widespread in the world
Chemistry/biology Quantum phenomena Circuits Robots ... Why reversibility for concurrent systems? Modelling concurrent systems
Programming concurrent systems Suitable for systems which are naturally reversible Biological, chemical, ... State space exploration, such as in Prolog Define reversible functions Build reliable systems Debugging concurrent systems Avoid the Gosh, I should have put the breakpoint at an earlier command problem
Reversibility for reliability: the idea To make a system reliable we want to avoid bad states If a bad state is reached, reversibility allows one to go back to some past state Far enough, so that the decisions leading to the bad state has not been taken yet When we restart computing forward, we should try new directions Reversibility and patterns for reliability
Reversibility seems related to some patterns for programming reliable systems Checkpointing Rollback-recovery We save the state of a program to restore it in case of errors We combine checkpointing with logs to recover a program state
Transactions [see Rudis talk] Computations which are executed all or nothing In case of error their effect should be undone Both in database systems (ACID transactions) and in service oriented computing (long running transactions) Some other manifestation of reversibility? Application undo
Backup Allows one to go back to a past version of a file SVN and the like Allows you to undo a wrong command in your favorite editor More refined techniques to go back to past versions of files Understanding reversibility will shed some light on these mechanisms too?
What is the status of approaches to reliability? A lot of approaches A bag of tricks to face different problems No clue on whether and how the different tricks compose No unifying theory for them Understanding reversibility is the key to
Understand existing patterns for programming reliable systems Combine and improve them Develop new patterns Reverse execution of a sequential program Recursively undo the last step
Computations are undone in reverse order To reverse A;B reverse first B, then reverse A First we need to undo single computation steps We want the Loop Lemma to hold From state S, doing A and then undoing A should lead back to S From state S, undoing A (if A is in the past) and then redoing A should lead back to S [Danos, Krivine: Reversible Communicating Systems. CONCUR 2004] Undoing computational steps
Computation steps may cause loss of information X=5 causes the loss of the past value of X X=X+Y causes no loss of information Old value of X can be retrieved by doing X=X-Y Different approaches to reversibility Saving a past state and redoing the same computation from there Undoing steps one by one Considering languages which are reversible Featuring only actions that cause no loss of information
Taking a language which is not reversible and make it reversible One should save information on the past configurations X=5 becomes reversible by recording the old value of X Reversibility and concurrency In a sequential setting, recursively undo the last step Which is the last step in a concurrent setting? Many possibilities
For sure, if an action A caused an action B, A could not be the last one Causal-consistent reversibility: recursively undo any action whose consequences (if any) have already been undone Proposed in [Danos, Krivine: Reversible Communicating Systems. CONCUR 2004] Causal-consistent reversibility a b b a Causal-consistent reversibility: advantages
No need to understand timing of actions Difficult since a unique notion of time may not exist Only causality has to be analyzed Easier since causality has a local effect Causal history information
Remembering history information is not enough We need to remember also causality information Actions performed by the same thread are always totally ordered by causality Actions in different threads may be related if the threads interact If thread T1 sent a message to thread T2 then T2 depends on T1
T1 cannot reverse the send before T2 reverses the receive We need to remember information on communication between threads Causal equivalence According to causal-consistent reversibility Changing the order of execution of concurrent actions should not make a difference Doing an action and then undoing it (or undoing and redoing) should not make adifference (Loop Lemma)
Two computations are causal equivalent if they are equal up to the transformations above Causal consistency theorem Causal equivalent computations should Lead to the same state Produce the same history information Computations which are not causal equivalent
Should not lead to the same state Otherwise one would wrongly reverse them in the same way If in a non reversible setting they would lead to the same state, we should add history information to distinguish the states Example If x>5 then y=2 else y=7 endif;y=0 Two possible computations, leading to the same state From the causal consistency theorem we know that we need history information to distinguish them
At least we should trace the chosen branch The amount of information to be stored in the worst case is linear in the number of steps [Lienhardt, Lanese, Mezzina, Stefani: A Reversible Abstract Machine and Its Space Overhead. FMOODS/ FORTE 2012] Many reversible calculi Reversible variants of many calculi have been studied CCS: Danos & Krivine [CONCUR 2004] CCS-like calculi: Phillips & Ulidowski [FoSSaCS 2006, JLAP 2007] HO: Lanese, Mezzina & Stefani [CONCUR 2010] Oz: Lienhardt, Lanese, Mezzina & Stefani Oz: Lienhardt, Lanese, Mezzina & Stefani [FMOODS&FORTE 2012]
-calculus: Cristescu, Krivine, Varacca [LICS 2013, see Danieles talk] Klaim: Giachino, Lanese, Mezzina, Tiezzi [PDP 2015] All applying the ideas we discussed With different technical solutions This is just uncontrolled reversibility The works above describe how to go back and forward, but not when to go back and when to go forward Non-deterministic is not enough
The program may go back and forward between the same states forever If a good state is reached, the program may go back and lose the computed result We need some form of control for reversibility Different possible ways to do it Which one is better depends on the intended application Controlling reversibility
24 A taxonomy for reversibility control Categorization according to who controls the reversibility Three different possibilities Internal control: reversibility is controlled by the programmer External control: reversibility is controlled by the environment Semantic control: reversibility control is embedded in the semantics of the language l
Internal control Reversibility is controlled by the programmer Explicit operators to specify whether to go backward and whether to go forward A few possibilities have been explored Irreversible actions [Danos, Krivine: Transactions in RCCS. CONCUR 2005] Roll operator [Lanese, Mezzina, Schmitt, Stefani: Controlling Reversibility in Higher-Order Pi. CONCUR 2011] Irreversible actions
Execution is non-deterministically backward or forward Some actions, once done, cannot be undone This allows to make a computed result permanent They are a form of commit Still most programs are divergent Suitable to model biological systems
Most reactions are reversible Some are not Roll operator Normal execution is forward Backward computations are explicitly required using a dedicated command Roll , where is a reference to a past action
Undoes action pointed by , and all its consequences Go back n steps not meaningful in a concurrent setting is a form of checkpoint This allows to make a computed result permanent If there is no roll pointing back past a given action, then the action is never undone Still most programs are divergent External control Reversibility is controlled by something outside the program
Again a few possibilities have been explored Controller processes [Phillips, Ulidowski, Yuen: A Reversible Process Calculus and the Modelling of the ERK Signalling Pathway. RC 2012] Causal-consistent reversible debugger [Giachino, Lanese, Mezzina: Causal-Consistent Reversible Debugging. FASE 2014] Controller processes
Two layered system A reversible slave process and a forward master process The slave process may execute only Actions allowed by the master In the direction allowed by the master Used to model biological systems Allows for non causal-consistent reversibility Reversible debugger
The user controls the direction of execution via the debugger commands In standard debuggers: step, run, ... A reversible debugger also provides the command step back In a concurrent setting one should specify which thread should step back (or forward) Some threads may be blocked and unable to step back (or forward) Reversible debuggers exist (e.g, gdb, UndoDB[see
Gregs talk]) Causal-consistent reversible debugger We exploit the causal information to help debugging concurrent applications We provide a debugger command like the roll Undo a given past action and all its consequences Different possible interfaces for roll
The last assignment to a given variable The last send to a given channel The last read from a given channel The creation of a given thread http://www.cs.unibo.it/caredeb/index.html Semantic control l Reversibility policy embedded in the language Again a few possibilities have been explored
Prolog State-space exploration via heuristics Energy-based control [Bacci, Danos, Kammar: On the Statistical Thermodynamics of Reversible Communicating Processes. CALCO 2011] Prolog backtracking l Prolog tries to satisfy a given goal
It explores deep-first the possible solutions When it reaches a dead end, it rollbacks and tries a different path The search is normally quite efficient Relies on the programmer expertise to avoid divergence State-space exploration via heuristics l In general, there are different ways to explore a state
space looking for a solution Strategy normally composed by a standard algorithm plus some heuristics driving it As before, if the algorithm reaches a dead end, it rollbacks and tries a different path Sample algorithm Count how many times each action has been done and undone Choose paths which have been tried less times Use heuristics in case of ties Energy-based control
l Assumes a world with a given amount of energy Forward and backward steps are taken subject to some probability The rates depend on the available amount of energy Under suitable conditions on the energy a computation is guaranteed to commit in finite average time Back to our roll Our application field: programming reliable concurrent/distributed systems
Normal computation should go forward In case of error we should go back to a past state No backward computation without errors We assume to be able to detect errors We should go to a state where the decision leading to the error has not been taken yet The programmer should be able to find such a state
The kind of algorithm we want to write : take some choice .... if we reached a bad state roll else output the result The approach based on the roll operator is suitable to our aims Not necessarily the best in all the cases Roll and loop
With the roll approach We reach a bad state We go back to a past state We may choose again the same path We reach the same bad state again We go back again to the same past state We may choose again the same path Permanent and transient errors
Going back to a past state forces us to forget everything we learned in the forward computation The approach is fine for transient errors We forget that a given path was not good We may retry again and again the same path Errors that may disappear by retrying E.g., message loss on the Internet
The approach is less suited for permanent errors Errors that occur every time a state is reached E.g., division by zero, null pointer exception We can only hope to take a different branch in a choice We should break the Loop Lemma In case of error we want to change path Not possible with the roll alone
The programmer cannot avoid to take the same path again and again We need to remember something from the past try Not allowed by the Loop Lemma Specifying alternatives 42 Alternatives
[Lanese, Lienhardt, Mezzina, Schmitt, Stefani: Concurrent Flexible Reversibility. ESOP 2013] The programmer may declare different ordered alternatives to solve a problem The first time the first alternative is chosen Undoing the choice causes the selection of the next alternative Like in Prolog We rely on the programmer for a good definition and ordering of alternatives Specifying alternatives
Actions A%B Normally, A%B behaves like A If A%B is the target of a roll, it becomes B Intuitive meaning: try A, then try B B may have alternatives too Programming with alternatives We should find the actions that may lead to bad states We should replace them with actions with alternatives We need to find suitable alternatives
Retry Retry with different resources Give up and notify the user Trace the outcome to drive future choices Example Try to book a flight to Grenoble with Airfrance A Airfrance website error makes the booking fail
Retry: try again to book with Airfrance Retry with different resources: try to book with Alitalia Give up and notify the user: no possible booking, sorry Trace the outcome to drive future choices: remember that Airfrance web site is prone to failure, next time try a different company first Application: Communicating transactions [de Vries, Koutavas, Hennessy: Communicating Transactions. CONCUR 2010] Transactions that may communicate with the environment and with other transactions while computing
In case of abort one has to undo all the effects on the environment and on other transactions To ensure atomicity Communicating transactions via reversibility We can encode communicating transactions The mapping is simple, the resulting code quite complex
We label the start of the transaction with An abort is a roll The roll undoes all the effects of the transaction A commit simply disables the roll We also need all the technical machinery for reversibility The encoding is more precise than the original semantics We avoid some useless undo Since our treatment of causality is more refined
Conclusion 49 Summary Uncontrolled reversibility for concurrent systems Mechanisms for controlling reversibility How to avoid looping using alternatives Future work: language Can we make mainstram concurrent languages reversible? Concurrent ML, Erlang, Java, ...
How to deal with data structures, modularity, type systems, ... Future work: reasoning How to reason on reversible programs? Initial works based on Behavioural equivalences [Krivine: A Verification Technique for Reversible Process Algebra. RC 2012] [Aubert, Cristescu: Reversible Barbed Congruence on Configuration Structures. ICE 2015] Logic [Abadi: The Prophecy of Undo. FASE 2015] Session types [Barbanera, Dezani-Ciancaglini, de'Liguoro: Compliance for reversible client/server interactions. BEAT 2014] [Barbanera, Dezani-Ciancaglini, Lanese, DeLiguoro: Retractable contracts. PLACES 2015]
Future work: applications Can we find some killer applications? Software transactional memories Existing algorithms for distributed checkpointing Debugging Questions Do you use sequential reversibility, causal-consistent reversibility, or something different?
Do you think that causal-consistent reversibility is meaningful in your setting? Do you need techniques to control reversibility? Which ones do you use? Finally Thanks! Questions?
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