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Interface Theories With Component Reuse

This paper presents a novel perspective on component-based design through the lens of interface theories. It discusses motivation, components reuse, and shared refinements for stateless and stateful interfaces. By introducing new operators and foundational concepts, the work highlights the nuances of compatible interfaces and dynamic behaviors in component design. Key points include definitions of interface automata, refinement relations, and their implications on system composition. The insights aim to advance the understanding and application of interface theories for more robust software design.

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Interface Theories With Component Reuse

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  1. Interface Theories With Component Reuse Laurent Doyen EPFL Thomas Henzinger EPFL Barbara Jobstmann EPFL Tatjana Petrov EPFL

  2. Outline • Motivation • Interface theories and component-based design • New operator: component reuse • Shared refinement: Stateless Interfaces • Shared refinement: Stateful Interfaces • Conclusions and future work 2

  3. Interfaces Odd(x)? x int y boolean  Signature Divide x int  Assertional z real y int, y!=0 • analogy with type systems • static checking at compile-time • well-formed: usable in some environment 3

  4. Interface Automaton FIFO enq deq E F Size2Buffer (enq,deq), (!enq,!deq) (enq,deq), (!enq,!deq) (enq,deq), (!enq,!deq) enq (enq,!deq) (enq,!deq) deq EF EF EF E F (enq,deq) (!enq,deq) Transition guards Assumption: !(deq,!enq) Guarantee: (E,!F) 4

  5. Component-Based Design I1 I2 I1 I12 I2 I11 I21 I22 I13 I11 I112 I111 5

  6. Interface Theories If A and B are compatible and A'  A and B'  B, then A’ and B' are compatible and A'||B'  A||B. A B A’ B’ 6

  7. Component-Based Design I1 I2 I1 I12 I2 I11 I21 I22 I13 I11 I112 I22 Π I112 I111 7

  8. Interface Theories • Parallel composition and feedback, Contravariant refinement relation => independent implementiability => stepwise refinement [de Alfaro, Henzinger, 2001] • Shared refinement => greatest lower bound in the refinement lattice => associativity => distributivity 8

  9. Stateless Interface • Predicates over input and output variables • Wellformedness • Inputs and outputs disjoint • Assumption satisfiable • Guarantee satisfiable Guarantee over outputs Assumption about inputs Divide x int z real y int, y!=0 9

  10. Parallel Composition A y mod 3 = 0 even(x) B z mod 4 = 0 x > 0 A||B A y even(x) & (x>0) y mod 3 = 0 & z mod 4 = 0 x B z 10

  11. Parallel Composition A y mod 3 = 0 even(x) B z mod 4 = 0 odd(x) INCOMPATIBLE ! A||B A y y mod 3 = 0 & z mod 4 = 0 x FALSE B z 11

  12. Connection A x z y x=0 => y=0 TRUE Ac x z y forall x,z. (TRUE & (x=z)) => (x=0 => y=0) TRUE & (x=z) y=0 12

  13. Connection Ac z y = 0 TRUE INCOMPATIBLE ! 13

  14. Refinement Relation A even(y) even(x) B y mod 4 = 0 x int B refines A 14

  15. Refinement Relation C y mod 3 = 0 even(x) B y mod 4 = 0 x int Implementation must obey output guarantee → B does not refine C 15

  16. Refinement Relation D even(y) even(x) B y mod 4 = 0 odd(x) Implementation must accept all permissible inputs → B does not refine D 16

  17. Shared Refinement A y mod 3 = 0 even(x) even(x) OR x>0 A Π B y mod 12 = 0 B y mod 4 = 0 x>0 (A Π B) can be used in any design as an implementation of A, and as an implementation of B 17

  18. Shared Refinement A odd(y) even(x) B y mod 4 = 0 x>0 18

  19. Shared Refinement A odd(y) even(x) even(x) OR x>0 A Π B FALSE B y mod 4 = 0 x>0 NOT SHARED-REFINABLE ! 19

  20. Shared Refinement: Properties Greatest lower bound in the refinement lattice Associativity: Distributivity: A1 A2 a1 g1 a2 g2 A1 Π A2 a1 OR a2 g1 & g2 A1 x A2 (A Π B) Π C = A Π (B Π C)‏ A || (B Π C) = (A || B) Π (A || C) A Π (B || C) = (A Π B) || (A Π C) 20

  21. Shared Refinement: Properties Greatest lower bound in the refinement lattice A B A Π B for all C, if C ≤ A and C ≤ B then C ≤ A Π B 21

  22. Shared Refinement: Properties Greatest lower bound in the refinement lattice A B A Π B C 22

  23. Shared Refinement: Properties Associativity A3 A1 B2 B1 A1 Π B1 Π B2 Π A3 23

  24. Stateful Interface FIFO enq deq E F Size2Buffer (enq,deq), (!enq,!deq) (enq,deq), (!enq,!deq) (enq,deq), (!enq,!deq) enq (enq,!deq) (enq,!deq) deq EF EF EF E F (enq,deq) (!enq,deq) Transition guards Assumption: !(deq,!enq) Guarantee: (E,!F) 24

  25. Interface Theories • Define • Refinement relation • Composition of interfaces so that… • Ensure If A and B is are compatible and A'  A and B'  B, then A’ and B' are compatible and A'||B'  A||B. • [de Alfaro, Henzinger, 2001] 25

  26. Stateful Interface • Wellformedness • Satisfiable assumption in each state = non-stopping • Satisfiable guarantee in each state • Deterministic Size2Buffer (enq,deq), (!enq, !deq) (enq,deq), (!enq, !deq) (enq,deq), (!enq, !deq) enq deq (enq ,!deq) (enq, !deq) E EF EF EF F (enq ,deq) (!enq, deq) 26

  27. Stateful Interfaces: Refinement • Alternating simulation relation [Alur, Henzinger, Kupferman, Vardi, 1998] • N refines M if there exists a relation R between the states such that if (p,q) is in R, then • a(p) => a(q)‏ • g(q) => g(p)‏ • a(p) & g(q) & (p → p’) & (q → q’) => (p’,q’) in R 27

  28. Stateful Interfaces: Refinement p1 x even A y int x: int y : int q1 ≤ p1 q1 x int y odd p2 p3 x int x even y int y odd q3 ≤ p3 q2 ≤ p2 q2 q3 x even x int y odd y int 28

  29. Stateful Interfaces: Refinement SlowBuffer (!enq ,!deq) enq or deq T T (!enq ,!deq) Size2Buffer (enq,deq), (!enq,!deq) (enq,deq), (!enq,!deq) (enq,deq), (!enq,!deq) enq enq deq deq (enq,!deq) (enq,!deq) E E EF EF EF F F (enq,deq) (!enq,deq) 29

  30. Shared Refinement I1 I2 I1 I12 I2 I11 I21 SlowBuffer I13 I11 Size2Buffer Size2Buffer Π SlowBuffer I111 30

  31. Stateful Interface !e!d e!d,!ed,ed T T e!d !e!d !e!d !e!d !ed !e!d !ed EF EF EF e!d !ed Size2Buffer Π SlowBuffer ed !e!d ed e!d !e!d !e!d ed EF EF EF !ed !ed ed !ed !ed ed ed e!d e!d EF EF EF !ed !ed 31

  32. Shared Refinement: Properties Greatest lower bound in the refinement lattice Associativity: Distributivity: (A Π B) Π C = A Π(B Π C)‏ A || (B Π C) ≤ (A || B) Π(A || C) (A Π B) || (A ΠC) ≤ A Π (B || C) 32

  33. Shared Refinement: Properties Distributivity A || (B Π C) ≤ (A || B) Π (A || C) A B A C (A||B) Π (A||C) 33

  34. Shared Refinement: Properties Distributivity A || (B Π C) ≤ (A || B) Π (A || C) A B A C (A||B) Π (A||C) A B Π C A || (B Π C) 34

  35. View-Points Timing T Power P Functional F F Π T Π P 35

  36. Conclusions • We extended the existing theory Possible Applications • Implementation of view-points • Refactoring of systems • Use of standard components 36

  37. Future Work • Implementation of an automatic checker for shared refinability • Asynchronous case • Relationship to modal interfaces [Benveniste et al.: Residual for Component Specifications, 2007] 37

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