Download presentation

Presentation is loading. Please wait.

Published byEmilia Kittleson Modified over 3 years ago

1
Structuring for Reuse: from B to Event-B Mike Poppleton, DSSE

2
Outline 1.Classical B – recap 2.Structuring in classical B 3.Event-B – recap 4.Towards structuring in Event-B 5.Fusion of events and models 6.Conclusion 2

3
Classical B: quick recap Model-based formal method, obvious LTS semantics: Unit of modularity = MACHINE Static information = SETS, CONSTANTS, PROPERTIES Dynamic state = VARIABLES, INVARIANT Behaviour = INITIALIZATION, OPERATIONS A partial Module Interconnection Language (MIL): o INCLUDES, EXTENDS, PROMOTES o IMPORTS, SEES … 3

4
Classical B: quick recap II The atom of behaviour: the substitution: x := Exp(x,s,c) x :| Pred(x 0,x,s,c) x : ∈ SetExp(…) is elaborated in the GSL (generalised substitution language): PRE Pred THEN Sub END CHOICE Sub1 OR Sub2 … END SELECT Pred1 THEN Sub1 WHEN Pred2 THEN Sub2 … ELSE... END ANY z WHERE Pred(z,x) THEN Sub(z,x) END typically x := Exp(z,x) IF Pred THEN Sub1 ELSE Sub2 END etc … 4

5
Structuring in Classical B: Operation-level Remember : B acts via call-/invocation-based preconditioned operations Event-B acts via occurrence of enabled guarded events Conditional substitutions: o IF-THEN(-ELSE), SELECT(-ELSE), CASE(-ELSE) … o Nesting of substitutions within such … o (shades of von Neumann SSIR …) Operation call (of included by including machine operation) 5

6
Structuring in B: Machine-level M INCLUDES N: internal reuse M, N variables, operations distinct: Concatenate defns, conjoin predicates operation call: o op M (i) = SubsExp (ao op N (ai)) is realised by a “substituted substitution”: [fo, fi := ao, ai] 6

7
Structuring in B: Machine-level II M INCLUDES N … But: Included N ops not externally visible from M In including op, “at most one op of a given including machine can be called” Encapsulation: included vars writable only by included ops ? Machine inclusion restriction on op call is presumably to guarantee variable distinctness ? 7

8
Structuring in B: Machine-level II M PROMOTES N.op1, N.op2 … (M INCLUDES N) M EXTENDS N : externally visible reuse named/ all included ops become full ops of including machine (ie externally visible) ? but these ops are NOT internally callable ? 8

9
Structuring in B: Machine-level III M USES N: elaborated inclusion: 2-step multiple reuse: M1, M2, M3 variables distinct M1 -USES M2 USES- M3 INCLUDES M M1, M3 reuse static part of M2 without re-copying M2’s text M1, M3 can read M2 vars, cannot use M2 ops M INCLUDES M1,M2,M3 9

10
Structuring in B: Implementation-level M SEES N: implementation-level, for flexible visibility across the development tree M, N variables distinct Seen machine independence Seeing INVARIANT cannot see seen VARIABLES Contrast with INCLUDES/USES: specification-level including/using INVARIANT can see included/used VARIABLES 10

11
Questions Why were these structuring mechanisms removed in the evolution to Event-B ? o Elaborate and awkward visibility rulesets and POs o Elaborate and awkward stucturing mechanism (haven’t discussed REFINEMENTs, IMPLEMENTATIONs, IMPORT, SEES) o And said structuring can be inconsistent ( Rouzaud, Potet, 1999 ) o ?? Should/can any of these mechanisms be introduced into Event-B (and if so, how) ? 11

12
Answers ? 1.Atomic conditional transition: o No: use separate event for each conditional branch o Rely on event scheduling o ! But lose control over invocation … 2.INCLUDES for internal operation call: o No, as for (1.) 3.PROMOTES/EXTENDS: o Yes, would like the reuse … 4.USES o Would like the reuse without awkward MIL mechanisms to avoid multiple machine text copies (ie need more sophisticated textual composition) 12

13
Event-B What’s the evolution from Classical B ? Abrial doc 13

14
Event-B events & consistency MACHINE M, axioms P, invariant I, event e, variable v: e = ANY t WHERE Q(t,v) THEN v := F(t,v) END guard G = ∃ t.Q(t,v) before-after predicate E = ∃ t.(Q(t,v) ⋀ v’ = F(t,v)) consistency: P ⋀ I(v) ⋀ G(v) ⋀ E(v,v’) ⇒ I(v’) 14

15
Event-B events & consistency MACHINE M, axioms P, invariant I, event e, variable v: e = ANY t WHERE Q(t,v) THEN v := F(t,v) END guard G = ∃ t.Q(t,v) before-after predicate E = ∃ t.(Q(t,v) ⋀ v’ = F(t,v)) consistency: P ⋀ I(v) ⋀ G(v) ⋀ E(v,v’) ⇒ I(v’) 15

16
Simple composition in Event-B (1) Variables, events disjoint: ie “PROMOTES/EXTENDS/USES” M(v, {e i }) + N(w, {f j }) = concatenate definitions, conjoin predicates No conflict: independent product of two models Enabledness “increases” Consistency is preserved trivially: I M+N (v,w) = I M (v) ⋀ I N (w) e M+N = e M || skip N 16

17
Simple composition in Event-B (2) (2) variables disjoint, events intersect ie new (to Event-B) e M = ANY t WHERE Q M (t,v) THEN v := F M (t,v) END guard: ∃ t. Q M (t,v) b-a pred: ∃ t.(Q M (t,v) ⋀ v’ = F M (t,v)) e N = ANY u WHERE Q N (u,w) THEN w := F N (u,w) END guard: ∃ u. Q N (u,w) b-a pred: ∃ u.(Q N (u,w) ⋀ w’ = F N (u,w)) e M+N =ANY t,u WHERE Q M (t,v) ⋀ Q N (u,w) THEN v := F M (t,v) || w := F N (u,w) END guard: ∃ t,u. (Q M (t,v) ⋀ Q N (u,w)) b-a pred: ∃ t,u.(Q M (t,v) ⋀ Q N (u,w) ⋀ v’ = F M (t,v) ⋀ w’ = F N (u,w)) 17

18
Consistency for composition (2) ? Enabledness OK: ∃ t. Q M (t,v), ∃ u. Q N (u,w) ⊢ ∃ t,u. (Q M (t,v) ⋀ Q N (u,w)) …(but we lose independent enabledness …) Consistency OK: distribution of ⋀ through ∃ in combined guard, b-a predicate NB: No communication between events 18

19
Fusion composition in Event-B (3) Variables intersect, events intersect ie new NB (1, 2) are special cases of (3) … 19

20
Fusion: “compositional composition” 20

21
21

Similar presentations

OK

Chapter 11 Separate Compilation and Namespaces. Copyright © 2006 Pearson Addison-Wesley. All rights reserved. 11-2 Learning Objectives Separate Compilation.

Chapter 11 Separate Compilation and Namespaces. Copyright © 2006 Pearson Addison-Wesley. All rights reserved. 11-2 Learning Objectives Separate Compilation.

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Design for ppt on deforestation Ppt on limits and derivatives for dummies Ppt on seven segment display tutorials Pps to ppt online converter Ppt on interest rate risk Ppt on power grid control through pc Waters view ppt online Ppt on word association test words Ppt on zener diode characteristics Ppt on 2nd world war video