Retractable and Speculative Contracts
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1 Retractable and Speculative Contracts Ivan Lanese Computer Science Department University of Bologna/INRIA Italy Joint work with Franco Barbanera and Ugo de'liguoro
2 Map of the talk What retractable/speculative contracts are? Motivating example Results Conclusion
3 Map of the talk What retractable/speculative contracts are? Motivating example Results Conclusion
4 Contracts A contract is the abstract description of the behavior of either a client or a server A client complies with a server if all her requirements are fulfilled by reaching a distinguished satisfaction state or by running an infinite interaction without ever getting stuck A client that does not comply with its server may get stuck without succeeding Compliance is statically decidable
5 Beyond classical contracts Contracts describing basic client/server interactions have been introduced in 2006 by Carpineti, Castagna, Laneve and Padovani We want to consider two features of (some) interacting systems not covered by classic contracts: rollback, enabling one to go back to past states of the interaction till a successful path is found speculation, enabling one to try different paths concurrently till a successful path is found
6 Why retractable contracts? Undo operations are useful and widespread Undo command in your favorite editor Back button in your favorite browser Restore a backup In interacting systems (unilateral) undo may lead to unpredictable or undesired results What happens if you press the back button when reserving a flight? You don t want a client to undo her payment after a purchase Undo activities must be disciplined
7 Why speculative contracts? Speculation is used for performance reasons in many contexts Simulation, thread-level optimizations, web services Do these optimizations preserve correctness? Not trivial, think to all the issues related to weak memory models Also speculation activities must be disciplined
8 Retractable/speculative contracts: syntax Retractable and speculative contracts have very different origin and aim Yet we describe both of them with the same syntax (but different semantics) σ ::= 1 success i I ai.σi internal output choice Standard Σi I ai.σi external input choice contracts X variable rec X.σ recursion i I ai.σi internal input choice Σi I ai.σi retractable/speculative output choice
9 Retractable/speculative contracts: main idea The peculiar operator is retractable/speculative output choice: Σi I ai.σi In the retractable semantics it behaves as follows: we perform an output, but other options are stored if the computation gets stuck, the choice is undone and we try another option In the speculative semantics it behaves as follows: we perform an output, but other options are not discarded and can be activated in parallel threads
10 Map of the talk What retractable/speculative contracts are? Motivating example Results Conclusion
11 Retractable contracts: history information To give semantics to retractable contracts we need history information We add (no alternatives left) to contracts σ Histories are stacks of contracts h ::= [] h:σ Contracts with history: h σ
12 Motivating problem A buyer wants to buy either a bag or a belt She will decide whether to pay by card or cash after knowing the price Buyer = bag.price.(card cash) belt.price.(card cash) The seller accepts cards only for bags, not for belts Seller = bag.price.(card + cash) + belt.price.cash Buyer and seller are not compliant
13 Reversibility to the rescue Buyer = bag.price.(card cash) belt.price.(card cash) Seller = bag.price.(card + cash) + belt.price.cash They become compliant if we make the buyer choice between bag and belt retractable Or the one between card and cash (for belt) The buyer is still able to pay a belt with card if interacting with a seller allowing this Retractable choice facilitates compliance
14 Reversibility to the rescue Buyer = bag.price.(card cash) + belt.price.(card cash) Seller = bag.price.(card + cash) + belt.price.cash They become compliant if we make the buyer choice between bag and belt retractable Or the one between card and cash (for belt) The buyer is still able to pay a belt with card if interacting with a seller allowing this Retractable choice facilitates compliance
15 Sample retractable computation Buyer = [] bag.price.(card cash) + belt.price.(card cash) Seller = [] bag.price.(card + cash) + belt.price.cash
16 Sample retractable computation Buyer = [] bag.price.(card cash) + belt.price.(card cash) bag.price.(card cash) price.(card cash) Seller = [] bag.price.(card + cash) + belt.price.cash bag.price.(card + cash) price.cash
17 Sample retractable computation Buyer = [] bag.price.(card cash) + belt.price.(card cash) bag.price.(card cash) price.(card cash) bag.price.(card cash) : card cash Seller = [] bag.price.(card + cash) + belt.price.cash bag.price.(card + cash) price.cash bag.price.(card + cash) : cash
18 Sample retractable computation Buyer = [] bag.price.(card cash) + belt.price.(card cash) bag.price.(card cash) price.(card cash) bag.price.(card cash) : card cash bag.price.(card cash) : card Seller = [] bag.price.(card + cash) + belt.price.cash bag.price.(card + cash) price.cash bag.price.(card + cash) : cash
19 Sample retractable computation Buyer = bag.price.(card cash) : card Seller = bag.price.(card + cash) : cash
20 Sample retractable computation Buyer = bag.price.(card cash) : card bag.price.(card cash) Seller = bag.price.(card + cash) : cash bag.price.(card + cash)
21 Sample retractable computation Buyer = bag.price.(card cash) : card bag.price.(card cash) [] bag.price.(card cash) Seller = bag.price.(card + cash) : cash bag.price.(card + cash) [] bag.price.(card + cash)
22 Sample retractable computation Buyer = [] bag.price.(card cash) Seller = [] bag.price.(card + cash)
23 Sample retractable computation Buyer = [] bag.price.(card cash) price.(card cash) Seller = [] bag.price.(card + cash) price.(card + cash)
24 Sample retractable computation Buyer = [] bag.price.(card cash) price.(card cash) : card cash Seller = [] bag.price.(card + cash) price.(card + cash) : card + cash
25 Sample retractable computation Buyer = : card cash Seller = : card + cash
26 Sample retractable computation Buyer = : card cash : card Seller = : card + cash
27 Sample retractable computation Buyer = : card cash : card : : 1 Seller = : card + cash : : cash 1
28 Example under the speculative semantics At runtime contracts are composed by multiple threads We use parallel composition Each thread is identified by a unique prefix obtained by composing past actions a1@...@a2@σ Only threads with dual prefix can interact
29 Sample speculative computation Buyer = bag.price.(card cash) + belt.price.(card cash) Seller = bag.price.(card + cash) + belt.price.cash
30 Sample speculative computation Buyer = bag.price.(card cash) + belt.price.(card cash) bag.price.(card cash) belt@price.(card cash) Seller = bag.price.(card + cash) + belt.price.cash bag.price.(card + cash) belt@price.cash
31 Sample speculative computation Buyer = bag.price.(card cash) + belt.price.(card cash) bag.price.(card cash) belt@price.(card cash) bag@price.(card cash) belt@price.(card cash) Seller = bag.price.(card + cash) + belt.price.cash bag.price.(card + cash) belt@price.cash bag@price.(card + cash) belt@price.cash
32 Sample speculative computation Buyer = bag@price.(card cash) belt@price.(card cash) Seller = bag@price.(card + cash) belt@price.cash
33 Sample speculative computation Buyer = bag@price.(card cash) belt@price.(card cash) bag@price@(card cash) belt@price.(card cash) Seller = bag@price.(card + cash) belt@price.cash bag@price@(card + cash) belt@price.cash
34 Sample speculative computation Buyer = bag@price.(card cash) belt@price.(card cash) bag@price@(card cash) belt@price.(card cash) bag@price@(card cash) belt@price@(card cash) Seller = bag@price.(card + cash) belt@price.cash bag@price@(card + cash) belt@price.cash bag@price@(card + cash) belt@price@cash
35 Sample speculative computation Buyer = bag@price@(card cash) belt@price@(card cash) Seller = bag@price@(card + cash) belt@price@cash
36 Sample speculative computation Buyer = bag@price@(card cash) belt@price@(card cash) bag@price@card belt@price@(card cash) Seller = bag@price@(card + cash) belt@price@cash
37 Sample speculative computation Buyer = bag@price@(card cash) belt@price@(card cash) bag@price@card belt@price@(card cash) bag@price@card belt@price@card Seller = bag@price@(card + cash) belt@price@cash
38 Sample speculative computation Buyer = bag@price@(card cash) belt@price@(card cash) bag@price@card belt@price@(card cash) bag@price@card belt@price@card bag@price@card@1 belt@price@card Seller = bag@price@(card + cash) belt@price@cash bag@price@card@1 bag@price@cash belt@price@cash
39 Map of the talk What retractable/speculative contracts are? Motivating example Results Conclusion
40 Compliance The retractable compliance relation h σ k ρ holds iff h σ k ρ * h σ k ρ implies σ = 1 If the computation stops then the client is satisfied The retractable compliance relation on contracts is obtained by executing them with an empty history The speculative compliance relation holds iff if the computation stops then at least one of the threads of the client is in the success state 1
41 Main result The retractable compliance and the speculative compliance do coincide At first sight surprising, since they have different definitions and work on different semantics Intuition: both require the existence of a successful path Two implementations of angelic nondeterminism Whether alternatives are explored sequentially or in parallel does not make a difference Consequence: all the results we derive from the compliance hold on both the settings
42 Compliance: decidability Compliance is decidable even for contracts with recursion We use judgments of the form Γ ρ ~ σ
43 Compliance: complexity One can define a recursive proof-search algorithm reading bottom-up the rules The complexity is exponential Better solution: extend the algorithm for subtyping of recursive arrow and product types from Pierce not a trivial extension keep trace not only of past successes, but also of past failures The complexity is O(n5) Pierce s algorithm has complexity O(n2)
44 Subcontract relation Subcontract relation for servers: ρ s ρ iff for each client σ. σ ρ implies σ ρ ρ has more clients than ρ Subcontract relation for clients is dual: σ c σ iff for each server ρ. σ ρ implies σ ρ The two subcontract relations are partial orders
45 Subcontract relation: example
46 Duality We define the dual σ of a client contract σ as the minimum server compliant with σ Duality enjoys the classic simple syntactic definition Swap inputs with outputs (a a) and internal choice with external choice ( Σ)
47 Subcontract relation: results Subcontract relation for servers and for clients are related: ρ s ρ iff ρ c ρ Subcontract relation and compliance are related: ρ s ρ iff ρ ρ Also the subcontract relation can be decided in O(n5)
48 Conservative extension Retractable/speculative contracts are conservative extensions of classic contracts Syntactically Semantically From the point of view of compliance, subcontract relation and duality
49 Map of the talk What retractable/speculative contracts are? Motivating example Results Conclusion
50 Summary We presented a model of contracts with retractable/speculative choice Using retractable/speculative choice instead of normal choice ensures compliance with a larger set of partners Retractable/speculative contracts are a conservative extension of classic contracts, yet they preserve most of the good properties of contracts: decidability of compliance and subcontract relation efficient decidability algorithm easy syntactic characterization of duality
51 Future work Explore the notion of retractable/speculative contracts in multiparty sessions How can we extract a contract from a reversible/speculative application? See ICE paper on retraction in session types: Session types for orchestrated interactions, by Barbanera and de Liguoro Which is the relation between retractable contracts and process calculi for reversible computation? Preliminary result: retractable contracts can be seen as a controlled form of reversibility on classic contracts
52 End of talk
53 Most related work Franco Barbanera, Mariangiola Dezani-Ciancaglini, Ugo de'liguoro: Compliance for reversible client/server interactions. BEAT 2014 also considered contracts with rollback BEAT 2014 free rollback explicit checkpoint one checkpoint compliance harder vs vs vs vs vs COORDINATION 2017 rollback only when stuck implicit checkpoint stack of checkpoints compliance easier
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