1 Ivan Lanese Computer Science Department University of Bologna Roberto Bruni Computer Science Department University of Pisa A mobile calculus with parametric synchronization

2 Roadmap Why PRISMA calculus? Synchronization Algebras with Mobility Syntax and semantics Properties and applications Conclusions and future work

3 Roadmap Why PRISMA calculus? Synchronization Algebras with Mobility Syntax and semantics Properties and applications Conclusions and future work

4 Process calculi and synchronization Process calculi are used to model a wide range of systems –Computer networks, biological systems, service oriented architectures, workflow patterns Different systems communicate according to different synchronization policies Each calculus has its own primitive(s) –Binary synchronization, broadcast, service invocation

5 Modelling troubles Sometimes the desired primitives are not (all) available in the used calculus Either they should be implemented… –Difficult task, produces unclear models …or a new ad hoc model is proposed –Theory and tools have to be redeveloped from scratch

6 Our idea Define a (mobile) calculus where the synchronization primitives can be freely chosen, combined and compared We build on –Winskel’s work on synchronization algebras »Do not consider mobility –Our previous work on synchronization algebras with mobility in the Synchronized Hyperedge Replacement framework »Belongs to the graph transformation approach We apply the idea in the field of calculi for mobility

7 What we are claiming and NOT claiming Our calculus is NOT able to easily and faithfully simulate each possible calculus –Synchronization is not the only feature that characterize a calculus But l Real systems can be more easily modelled since the desired primitives can be defined and exploited l Shows how to use the parametric approach for mobile calculi l Is a first step towards the understanding of the commonalities / differences between different calculi

8 A sample scenario A news server takes news from providers and broadcasts them to clients Two kinds of primitives –Binary communication between providers and the server –Broadcast between server and clients l Challenging scenario for previous calculi (e.g., π calculus)

9 Roadmap Why PRISMA calculus? Synchronization Algebras with Mobility Syntax and semantics Properties and applications Conclusions and future work

10 Synchronization Algebras with Mobility Abstract formalization of a synchronization policy A SAM contains –A set of ranked actions Act –An element ε standing for “not taking part to the synchronization” –A set of action synchronizations of the form (a, b, (c, Mob,  )) »Actions a and b can interact, producing action c »The parameters of a and b are merged according to  »The parameters of c are computed as described by Mob –A subset Fin of Act containing the complete actions »Allowed on restricted channels SAMs must satisfy some coherence conditions

11 Mob and  abc  Mob

12 Milner synchronization as a SAM Actions: inputs (e.g., in), outputs (e.g., out), τ, ε No other synchronization is allowed Only τ and ε are in Fin inoutτaεa

13 Broadcast synchronization as a SAM Actions: inputs, outputs, ε ε can synchronize only with itself Only out and ε are in Fin As a result a complete synchronization involves one out and one in from each other partner inout in

14 Roadmap Why PRISMA calculus? Synchronization Algebras with Mobility Syntax and semantics Properties and applications Conclusions and future work

15 PRISMA Calculus syntax Standard process calculi operators –Parallel composition, restriction, choice, … –Prefixes x a y allowing to perform action a on channel x with parameters in y

16 PRISMA Calculus syntax Standard process calculi operators –Parallel composition, restriction, choice, … –Prefixes x a y allowing to perform action a on channel x with parameters in y Example: P = ( i n f o ) pu bl i s h ou t h i n f o i

17 PRISMA semantics Given by an LTS –Reduction semantics not suitable for multi-party synchronization The behavior of a PRISMA process depends on the chosen SAM S Inference rules parametric on S to derive labelled transitions –label (Y) x a y, π executes x a y extruding names in Y and applying fusion π – label √, π executes an action on a restricted channel applying fusion π

18 Implementing the news scenario News server: Provider: Clients: P = ( i n f o ) pu bl i s h ou t h i n f o i S = ! ( x ) pu bl i s h i n h x i : ( newsou t b h x ij S 0 [ x ]) C i = ( y ) news i n b h y i : U se i [ y ]

19 Abstract semantics Bisimilarity can be defined in a standard way Basic axioms (e.g., commutativity and associativity of parallel composition) bisimulate for any SAM Theorem Hyperbisimilarity (substitution closed bisimilarity) is a congruence for any SAM

20 Roadmap Why PRISMA calculus? Synchronization Algebras with Mobility Syntax and semantics Properties and applications Conclusions and future work

21 PRISMA vs Fusion Fusion calculus can be easily translated into Milner PRISMA –Homomorphic extension of the translation of Fusion inputs and outputs into PRISMA ones The obtained semantics is more detailed than standard Fusion one –Shows on which (free) channel a fusion is generated The induced bisimilarity is more detailed too

22 Composing SAMs SAMs can be given a categorical structure Categorical constructions allow to combine SAMs –Coproduct makes the union of the primitives –Product creates compound primitives l The SAM used in the sample application is a coproduct of a Milner SAM and a broadcast SAM

23 Translating processes A process on S 1 can be translated along a morphism H:S 1 →S 2 to a process on S 2 Allows to execute a process in a different framework Properties of the morphism ensure preservation of part of the behaviour –Translations along isomorphisms preserve bisimilarity

24 A sample application Priority SAM: many outputs synchronize with one input, the one with the highest priority is received Suppose we want to execute a Fusion process P F in this framework We can translate it into a Milner PRISMA process P M There is a morphism H n from Milner to Priority assigning priority n to each output H n (P M ) is a priority process

25 Roadmap Why PRISMA calculus? Synchronization Algebras with Mobility Syntax and semantics Properties and applications Conclusions and future work

26 Conclusions PRISMA is a mobile calculus suitable to model different kinds of systems –Heterogeneous systems Suitable for interoperability analysis Allows to reuse theory and tools for different applications

27 Future work Put PRISMA at work on more challenging case studies Exploit PRISMA to compare different synchronization models Analyze the relationships with existing calculi

28 End of talk