(Meta)model s a nd t ransformation s ! thinking aids for the engineer - a case study

1. (Meta)modelsand transformations !thinking aids for the engineer -a case study András Pataricza Budapest University of Technology and EconomicsDepartment of Measurement and Information Systems pataric@mit.bme.hu

2. Abstract State Machines

3. References

4. Methodology

5. Guideline

6. Contents

7. Formal semantics for UML diagrams UML 2.0 provides only a verbal semantics definition. How can a formal semantics derived from it ?

9. Requirements for a specification language • Scope • Preciseness • Easy to understand • Programming language-like notations, auto-documentation • No enforced details • Hierarchical modeling, refinement • Transformability • Support of verification and validation • Support of implementation • Something in between or better SIMULTANEOUSLY mathematics and programming language

10. ASM Basics • Signature (vocabulary)  • finite collection of function names. • Each function name f: • Arity, a non-negative integer. • Nullary:„constant” • Function names: • static or • dynamic. • Static constants • {undef , true, false}2every ASM signature .

11. Function scheme f(a1 ... an) f(a’1...a’n) f(a”1...a”n) undef (x1,x2...xn)

12. Constant Boolean algebra Restriction of the domains

13. Function types

14. Static function

15. Function types

16. State • A state A for a signature  • Superuniverse: a set |A|  ; • Interpretation fA of each function name f • if f is a constant fA2 |A| • if f is a n-ary function name: fA: |A|n£ |A|

17. Update • Elementary update: a pair (l,v) • l is a location • v 2 |A| is the designated new value at l • Trivial update: v=A(l) • i.e. the new vaule is the same as the old one • U update set: • set of updates • U consistent update set: • No clashing updates: • 8 l, 8 v,w: if (l,v) 2 U and (l,w) 2 U then v=w

18. Firing • Execution of upgrades • simultaneously from the (consistent) update set, • content of the locations not included: unaltered • Consistent update set U • Initial state: A • Firing: A) (A + U) • New state: (A + U) • Contents: (A + U)(l) = if (l,v) 2 U then v • elseA(l)

19. ASM • Abstract State Machine M • signature  • initial states for  • rule declarations • main rule name of the machine • arity zero

20. ASM machine

21. Basic ASM constructs

22. Formal semantics

23. Run of an ASM • A finite or infinite sequence of states such • the initial state is A0 • either for all n 2N+ a consistent update results in a An!An+1 move • or there is no more consistent update set and Anis the final state

24. Isomorphism

25. Refinement and abstraction • Equivalence of states Correctness: each refined has an abstract counterpart Completeness: each abstract has a refined counterpart

26. Example: Dataflow models A natural way for algorithm design

27. Basic structure

28. Definition of a dataflow node

29. Definition of the FIFO

30. Previous processed ASM program of the FIFO

31. ASM program of a node Compile time

32. Interpretation is defined by: number(headi) ¸ Xin,r(i) Interpreted DFN models: Coloured tokens Number of tokens – vector Comparison – by vector components Non-interpreted DFN: Simple tokens Numbers and comparison scalars ASM program of a node

33. ≥ Uninterpreted ≥ ≥ Interpreted ≥ ≥ ≥ Abstraction - refinement • In order to show correctness: • Only to show, that • Total number of tokens is a homomorphism • Comparison as a relation is a homomorphism  

34. Some conclusions on ASM programs • Non-procedural programs • Simultaneously executed blocksand not the order of instructions • Resemble to HDLs • Signals • Interaction of modules • Synchronization • Refinement/ abstraction: • correctness / completeness proven by the check of attributes of the elements

35. UML activity diagrams Case study: how effective is ASM based modeling Done for UML 1.x by Börger et al. AUTOMATED DERIVATION OF ERROR PROPAGATION MODELS FROM UML MODELS?

37. Activity diagram • Basically: a data flow network (DFN). • representation of data and control information. • directed graph • hierarchical compositionof activity nodes • activity • action • activity edges • colouredtoken flows • Partitions • Interruptible regions and exceptions

38. Activity models • Coordination between the lower-level behaviors • event oriented , • terminationof an action producing output tokens, • events from the outsideenvironment generating tokens at interface nodes, • arrival of data or controlat an action component • Option: reentrant

39. Nodes

40. Activity levels in UML 2.0 Fork, join Object nodes Control sequencing No concurrency Structured hierarchies object flows, multicast, xform of tokens, edge weights Structured programming interruptible regions, exceptions

41. Actions • Primitive functions: • user defined transformations on data • Invocations of behavior • other activities • other types of behavior • Invocation hierarchies invoking • other activities. • inter-behavior communication by signals (multicast / multireceive). • Read, write create and delete operations on • variables, • objects • links • Flow-of-control

42. Example:variable actions

43. Example: invocation actions

44. Basic action node frame • ActionNode(n) = • FSM(n; action; next(n)) where • action = ifactive(n) andguardandcorrectMultiplicity(n) then • act • forallL2dynArgs(n) withguard(L) = truedoact(L)

45. Control nodes

46. Decision node • Selection from alternatives • node ( in; (condi) i · k ; (outi) i · k ) • ASM: • DecisionNode(n) = • FSM(n; test; next(n; min{i·k| condi})) • wheretest = ifactive(n) thenskip

47. Object node • Intermediate buffer • objects and data between activityor action nodes. • Selection policies • Simplest case: multiset • CompleteActivities: • FIFO, LIFO, user defined- a behavior associatedto the object node); • Optional upper bound on the number of tokens in the node (capacity bounded Petri-nets) • Specification of the state of tokens required • A special case: DataStoreNode, • central buffernode for non-transient information.

48. Short summary • UML diagrams can be captured by ASMs • A few of frames • Mapping of non-graphical constructs to ASMs • Guards • Additional user defined behavioral specification • Elementary proofs for standards compliance • 1 phrase ) 1 simple proof (trace) • Future: • MDA • Microsoft provides technology for .net

49. Qualitative fault modeling A natural way for abstraction in diagnosis problems CAN WE DERIVE ERROR PROPAGATION MODELS IN AN AUTOMATED WAY FROM ASM MODELS?