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On the Expressiveness of Polyadicity in Higher-Order Process Calculi Ivan Lanese, Jorge A. P erez, Davide Sangiorgi (Univ. di Bologna) Alan Schmitt (INRIA Grenoble - Rh one Alpes) ICTCS09 Cremona, September 2009 Jorge A. P erez

  1. On the Expressiveness of Polyadicity in Higher-Order Process Calculi Ivan Lanese, Jorge A. P´ erez, Davide Sangiorgi (Univ. di Bologna) Alan Schmitt (INRIA Grenoble - Rhˆ one Alpes) ICTCS’09 Cremona, September 2009 Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 1 / 30

  2. This Talk: Context Theoretical Computer Science − → Concurrency Theory − → Process Calculi − → Calculi for Mobile Processes Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 2 / 30

  3. Agenda Motivation: Two Approaches for Mobility 1 Polyadic Communication 2 A Core Calculus for Higher-Order Concurrency 3 Polyadicity in Higher-Order Communication 4 Expressiveness Results 5 Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 3 / 30

  4. Roadmap Motivation: Two Approaches for Mobility 1 Polyadic Communication 2 A Core Calculus for Higher-Order Concurrency 3 Polyadicity in Higher-Order Communication 4 Expressiveness Results 5 Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 4 / 30

  5. Motivation: Two Approaches for Mobility Two agents, A and B , and a resource that A wants to share with B. They share a communication channel c : p PDF e c c d A B Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 5 / 30

  6. Motivation: Two Approaches for Mobility Two agents, A and B , and a resource that A wants to share with B. They share a communication channel c : p PDF e c c d A B Two approaches for mobility: First-order (or name-passing) concurrency Higher-order (or process-passing) concurrency Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 5 / 30

  7. Motivation: Two Approaches for Mobility The first-order concurrency approach: send a link to the resource. p PDF e c c d A B (a) Before the interaction(s) Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 6 / 30

  8. Motivation: Two Approaches for Mobility The first-order concurrency approach: send a link to the resource. p p PDF PDF e e c c d c c d A B A B (c) Before the interaction(s) (d) After the interaction(s) Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 6 / 30

  9. Motivation: Two Approaches for Mobility The higher-order concurrency approach: send the resource. p PDF e c c d A B (e) Before the interaction(s) Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 7 / 30

  10. Motivation: Two Approaches for Mobility The higher-order concurrency approach: send the resource. p p PDF PDF PDF e e c c c d c d A B A B (g) Before the interaction(s) (h) After the interaction(s) Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 7 / 30

  11. Motivation: Two Approaches for Mobility The higher-order concurrency approach: send the resource. p p PDF PDF PDF e e c c c d c d A B A B (i) Before the interaction(s) (j) After the interaction(s) Upon reception, B can do only two things with the resource: Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 7 / 30

  12. Motivation: Two Approaches for Mobility The higher-order concurrency approach: send the resource. p p PDF PDF PDF e e c c c d c d A B A B (k) Before the interaction(s) (l) After the interaction(s) Upon reception, B can do only two things with the resource: Execute it 1 Forward it 2 Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 7 / 30

  13. Higher-Order Process Calculi Calculi in which processes can be communicated. Usual operators: parallel composition, input and output prefixes, restriction. Infinite behavior can be encoded. As in the λ -calculus, computation involves term instantiation. Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 8 / 30

  14. Roadmap Motivation: Two Approaches for Mobility 1 Polyadic Communication 2 A Core Calculus for Higher-Order Concurrency 3 Polyadicity in Higher-Order Communication 4 Expressiveness Results 5 Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 9 / 30

  15. Polyadic Communication Communicating tuples of values in a single, atomic interaction Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 10 / 30

  16. Polyadic Communication Communicating tuples of values in a single, atomic interaction In the (first-order) π -calculus, monadic communication is expressive enough to encode polyadic communication. Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 10 / 30

  17. Polyadic Communication Communicating tuples of values in a single, atomic interaction In the (first-order) π -calculus, monadic communication is expressive enough to encode polyadic communication. ◮ Let x ( z 1 , . . . , z n ). P and x � a 1 , . . . , a n � . P represent input and output prefixes in the π -calculus with n -adic communication. Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 10 / 30

  18. Polyadic Communication Communicating tuples of values in a single, atomic interaction In the (first-order) π -calculus, monadic communication is expressive enough to encode polyadic communication. ◮ Let x ( z 1 , . . . , z n ). P and x � a 1 , . . . , a n � . P represent input and output prefixes in the π -calculus with n -adic communication. ◮ The translation [ [ · ] ] from polyadic to monadic processes: [ [ x � a 1 , . . . , a n � . P ] ] = ν w xw . wa 1 . · · · . wa n . [ [ P ] ] x ( w ). w ( z 1 ). · · · . w ( z n ). [ [ [ x ( z 1 , . . . , z n ). P ] ] = [ P ] ] where [ [ · ] ] is an homomorphism for the other operators. Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 10 / 30

  19. Polyadic Communication [ · ] Features of [ ]: Robustness with respect to interferences: The encoding relies on a private name that is known by sender and receiver Operational correspondence: One n -adic synchronization is represented as n + 1 monadic synchronizations: Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 11 / 30

  20. Polyadic Communication [ · ] Features of [ ]: Robustness with respect to interferences: The encoding relies on a private name that is known by sender and receiver Operational correspondence: One n -adic synchronization is represented as n + 1 monadic synchronizations: ◮ A visible synchronization that mimics the polyadic action ◮ n internal synchronizations on the private name w Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 11 / 30

  21. This Talk A study of the expressive power of higher-order process calculi with respect to their ability to represent polyadic communication. Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 12 / 30

  22. This Talk A study of the expressive power of higher-order process calculi with respect to their ability to represent polyadic communication. Context: A core calculus for higher-order concurrency. ◮ Only processes can be communicated. ◮ No links can be passed around. Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 12 / 30

  23. This Talk A study of the expressive power of higher-order process calculi with respect to their ability to represent polyadic communication. Context: A core calculus for higher-order concurrency. ◮ Only processes can be communicated. ◮ No links can be passed around. Main Result: encodings as in the first-order case do not exist Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 12 / 30

  24. This Talk A study of the expressive power of higher-order process calculi with respect to their ability to represent polyadic communication. Context: A core calculus for higher-order concurrency. ◮ Only processes can be communicated. ◮ No links can be passed around. Main Result: encodings as in the first-order case do not exist A hierarchy of strictly increasingly expressiveness n -adic communication is strictly less expressive than n + 1-adic communication Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 12 / 30

  25. Roadmap Motivation: Two Approaches for Mobility 1 Polyadic Communication 2 A Core Calculus for Higher-Order Concurrency 3 Polyadicity in Higher-Order Communication 4 Expressiveness Results 5 Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 13 / 30

  26. Hocore : a calculus for higher-order concurrency P , Q ::= a � P � output | a ( x ). P input prefix | x process variable | P � Q parallel composition | nil 0 Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 14 / 30

  27. Hocore : a calculus for higher-order concurrency P , Q ::= a � P � output | a ( x ). P input prefix | x process variable | P � Q parallel composition | nil 0 No name passing is allowed. No output prefix: asynchronous calculus. No restriction operator Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 14 / 30

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