Asynchronous Timed Session Types & Processes Laura Bocchi - PowerPoint PPT Presentation


 ABCD Meeting, London, 17/12/2018 Asynchronous Timed Session Types & Processes Laura Bocchi University of Kent 
 Maurizio Murgia University of Kent Vasco Thudichum Vasconcelos University of Lisbon Nobuko Yoshida Imperial College London 1

Agenda • Session types ♥ Time • Synchronous [Bartoletti,Cimoli&Murgia@FORTE’13] • Multiparty asynchronous [Bocchi,Yang,Yoshida@CONCUR’14] • restriction to types/protocols that could be used for type-checking • limitations to the expressiveness of the calculus • Today • Designing timed protocols : asynchronous timed duality • Checking timed programs : a time-sensitive calculus & typing system 2

Time & trouble • A timed protocol is not correct by definition S = ! 홸횗횝 .? 횂횝횛횒횗횐 S = ! 홸횗횝 ( x ≤ 3) . ? 횂횝횛횒횗횐 ( x ≤ 2) Usually this is handled by adding some conditions • feasibility [Bocchi, Yang, Yoshida@CONCUR’14], 
 interaction-enabledness (CTA) [Bocchi, Lange, Yoshida@CONCUR’15], 
 compliance [Bartoletti, Cimoli, Murgia@FORTE’16] 
 formation + duality [Bocchi, Murgia, Yoshida, Vasconcelos’18] S = ! 홸횗횝 ( x ≤ 3) . ? 횂횝횛횒횗횐 ( x ≤ 3) 3

Duality & progress • Duality characterises well-behaved systems S = ! 홸횗횝 .? 횂횝횛횒횗횐 S = ? 홸횗횝 .! 횂횝횛횒횗횐 S = ! 홸횗횝 ( x ≤ 1, x ) . ? 횂횝횛횒횗횐 ( x ≤ 2) S = ? 홸횗횝 ( y ≤ 1, y ) . ! 횂횝횛횒횗횐 ( y ≤ 2) Synchronous Int String 0.4 S ∣ S ⟶ S ∣ S 2 ⟶ ? 횂횝횛횒횗횐 ( x ≤ 2) ∣ ! 횂횝횛횒횗횐 ( y ≤ 2) ⟶ ⟶ 4

Duality & progress • Duality characterises well-behaved systems S = ! 홸횗횝 .? 횂횝횛횒횗횐 S = ? 홸횗횝 .! 횂횝횛횒횗횐 S = ! 홸횗횝 ( x ≤ 1, x ) . ? 횂횝횛횒횗횐 ( x ≤ 2) S = ? 홸횗횝 ( y ≤ 1, y ) . ! 횂횝횛횒횗횐 ( y ≤ 2) Synchronous Int String 0.4 S ∣ S ⟶ S ∣ S 2 ⟶ ? 횂횝횛횒횗횐 ( x ≤ 2) ∣ ! 횂횝횛횒횗횐 ( y ≤ 2) ⟶ ⟶ Asynchronous 0.4 !Int S ∣ S ⟶ S ∣ S ⟶ ? 횂횝횛횒횗횐 ( x ≤ 2) ∣ ? 홸횗횝 ( y ≤ 1, y ) . ! 횂횝횛횒횗횐 ( y ≤ 2) !String ? 횂횝횛횒횗횐 ( x ≤ 2) ?Int 0.6 2 ⟶ ⟶ ? 횂횝횛횒횗횐 ( x ≤ 2) ∣ ! 횂횝횛횒횗횐 ( y ≤ 2) ⟶ ⟶ 0.4 0 0 2 1 2.6 0.6 0.4 0 0 x y

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 a<-10 fmt.Printf("sent int 10 at time %s\n", t.Sub(start)) select{ case c:=<-b : t := time.Now() fmt.Printf("received string %s at time %s\n", c, t.Sub(start)) case <-time.After(2 * time.Second) : 
 fmt.Println("S Failed! String not received within deadline") } } } 6

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Urgent receive semantics • Urgent receive semantics: messages are received as soon as • they are in a channel, and • the time constraint of the receiver is satisfied Urgent receive semantics yields executions that are • are a bit more synchronous … • … but as asynchronous as when using (common) receive primitives • !Int 0.4 S ∣ S ⟶ S ∣ S ⟶ ? 횂횝횛횒횗횐 ( x ≤ 2) ∣ ? 홸횗횝 ( y ≤ 1, y ) . ! 횂횝횛횒횗횐 ( y ≤ 2) ?Int !String 0.6 2 ? 횂횝횛횒횗횐 ( x ≤ 2) ⟶ ⟶ ? 횂횝횛횒횗횐 ( x ≤ 2) ∣ ! 횂횝횛횒횗횐 ( y ≤ 2) ⟶ ⟶ 0 0.4 0 y x 8