In Model-Driven Engineering, the potential advantages of using bidirectional transformations are largely recognized. Despite its crucial function, in certain cases bidirectionality has somewhat limited success because of the ambivalence concerning non-bijectivity. In fact, consistently propagating changes from one side to the other is typically non univocal as more than one correct solution is admitted. This gives place to a form of uncertainty which means that, rather than having a single model, we actually have a set of possible models but we do not know what is the right one. In this paper, we discuss how dealing with multiple solutions is important and requires specialized tools and support. In particular, handling a set of models explicitly is generally non-viable. Thus, we extended the JTL semantics to generate a model with uncertainty which is semantically equivalent to the set of models it represents. The approach is implemented and a metamodel-independent technique is proposed.

1. Dipartimento di Ingegneria e Scienze
Università degli Studi dell’Aquila
dell’Informazione e Matematica
Generating model with
uncertainty by means of JTL
Gianni Rosa

2. In Model-Driven Engineering (MDE)
bidirectionality in transformations
has been always regarded as a key
mechanism, but has rarely produced
anticipated benefits.
Why?

3. …probably the main reason is the
ambivalence concerning non-bijectivity.
Propagating changes from one side to the other is
typically non univocal as more than one correct
solution is admitted.

4. We discuss how dealing with multiple
solutions is important and requires
specialized tools and support

5. Gianni Rosa – University of L’Aquila - ITALY
5
Non-bijectivity
Most examples of bidirectional transformations are
non-bijective, therefore there may be multiple ways to
transform two models into a consistent state,
introducing uncertainty and non-determinism.
T-1
Δ Manual Changes
TMs Mt
Mt’
Ms1’
?Msn’
Ms1’

6. Source model Target model
Hierarchical State Machine Non-hierarchical state
machine obtained by
flattening the source model
T

7. Source model Target model
Δ Manual ChangesThe designer performs
some manual changes on
the generated model
T

8. Source model Target model
Δ Manual ChangesThe designer performs
some manual changes on
the generated model
T
Problem
How to back propagate the manual changes on
the target model towards the source models
according to the knowledge encoded in T?
What about non-bijectivity?

9. Gianni Rosa – University of L’Aquila - ITALY
9
Specifying transformation with JTL
Fragment of the HSM2NHSM transformation
specified in JTL
9
transformation hsm2nhsm(source : HSM, target : NHSM) {
top relation StateMachine2StateMachine {
enforce domain source sSM : HSM::StateMachine;
enforce domain target tSM : NHSM::StateMachine;
}
top relation State2State {
enforce domain source sourceState : HSM::State;
enforce domain target targetState : NHSM::State;
when {
sourceState.owningCompositeState.oclIsUndefined();
}
}
top relation CompositeState2State {
enforce domain source sourceState : HSM::CompositeState;
enforce domain target targetState : NHSM::State;
}
}

10. Gianni Rosa – University of L’Aquila - ITALY
10
transformation hsm2nhsm(source : HSM, target : NHSM) {
top relation StateMachine2StateMachine {
enforce domain source sSM : HSM::StateMachine;
enforce domain target tSM : NHSM::StateMachine;
}
top relation State2State {
enforce domain source sourceState : HSM::State;
enforce domain target targetState : NHSM::State;
when {
sourceState.owningCompositeState.oclIsUndefined();
}
}
top relation CompositeState2State {
enforce domain source sourceState : HSM::CompositeState;
enforce domain target targetState : NHSM::State;
}
}
Specifying transformation with JTL
Fragment of the HSM2NHSM transformation
specified in JTL
10
c
It transforms hierarchical state
machines into flat state machines and
the other way round.

11. Gianni Rosa – University of L’Aquila - ITALY
11
transformation hsm2nhsm(source : HSM, target : NHSM) {
top relation StateMachine2StateMachine {
enforce domain source sSM : HSM::StateMachine;
enforce domain target tSM : NHSM::StateMachine;
}
top relation State2State {
enforce domain source sourceState : HSM::State;
enforce domain target targetState : NHSM::State;
when {
sourceState.owningCompositeState.oclIsUndefined();
}
}
top relation CompositeState2State {
enforce domain source sourceState : HSM::CompositeState;
enforce domain target targetState : NHSM::State;
}
}
Specifying transformation with JTL
Fragment of the HSM2NHSM transformation
specified in JTL
11
c
The forward transformation is clearly non-injective:
both «State» and «CompositeState» are mapped
to the same target «State»

12. Gianni Rosa – University of L’Aquila - ITALY
12
transformation hsm2nhsm(source : HSM, target : NHSM) {
top relation StateMachine2StateMachine {
enforce domain source sSM : HSM::StateMachine;
enforce domain target tSM : NHSM::StateMachine;
}
top relation State2State {
enforce domain source sourceState : HSM::State;
enforce domain target targetState : NHSM::State;
when {
sourceState.owningCompositeState.oclIsUndefined();
}
}
top relation CompositeState2State {
enforce domain source sourceState : HSM::CompositeState;
enforce domain target targetState : NHSM::State;
}
}
Specifying transformation with JTL
Fragment of the HSM2NHSM transformation
specified in JTL
12
c
The forward transformation is clearly non-injective:
both «State» and «CompositeState» are mapped
to the same target «State»

13. Source model Target model
Δ Manual Changes
T
T
Modifications on the target are
back propagated to the source
which is consistently updated
making use of tracing
information

14. Gianni Rosa – University of L’Aquila - ITALY
14
Combinatorial explosion
Not surprisingly, there is not a unique way of updating
the source model.
Despite the changes on the target model are
relatively simple, their impact on the source model is
typically exponential.

15. Gianni Rosa – University of L’Aquila - ITALY
15
Combinatorial explosion
|print| × |completed| × |critical error| = 4 * 4 * 3 = 48
where |name| is the number of alternative model
elements called name.

16. Gianni Rosa – University of L’Aquila - ITALY
16
Combinatorial explosion
|print| × |completed| × |critical error| = 4 * 4 * 3 = 48
where |name| is the number of alternative model
elements called name.
Solution? Representing multiple solutions with
Model Uncertainty

17. Gianni Rosa – University of L’Aquila - ITALY
17
Uncertainty
Uncertainty is a consequence of non-determinism.
Dealing with a multitude of models obtained by a
non-deterministic transformation requires us to
consider uncertainty as a first-class concern.
For any metamodel M an uncertainty metamodel
U(M) can obtained by means of an automated
transformation:
U: Ecore  Ecore

18. Gianni Rosa – University of L’Aquila - ITALY
18
Uncertainty metamodel
.
HSM
Metamodel
U(HSM)
Metamodel

19. Gianni Rosa – University of L’Aquila - ITALY
19
Uncertainty metamodel
.
HSM
Metamodel
U(HSM)
Metamodel
the abstract metaclass
TracedClass with
attributes trace and ref is
added

20. Gianni Rosa – University of L’Aquila - ITALY
20
Uncertainty metamodel
.
HSM
Metamodel
U(HSM)
Metamodel
the abstract metaclass
TracedClass with
attributes trace and ref is
added
StateMachine is generalized by
TracedClass

21. Gianni Rosa – University of L’Aquila - ITALY
21
Uncertainty metamodel
.
HSM
Metamodel
U(HSM)
Metamodel
the abstract metaclass
TracedClass with
attributes trace and ref is
added
a direct sub-metaclass of
StateMachine is added
StateMachine is generalized by
TracedClass

22. Gianni Rosa – University of L’Aquila - ITALY
22
Uncertainty metamodel
.
HSM
Metamodel
U(HSM)
Metamodel
the abstract metaclass
TracedClass with
attributes trace and ref is
added
a direct sub-metaclass of
StateMachine is added
StateMachine is generalized by
TracedClass
The composition enable
the representation of a
point of uncertainty and its
alternatives
the cardinality of attributes and references are relaxed

23. Gianni Rosa – University of L’Aquila - ITALY
23
Extension of JTL Semantic
The JTL semantics has been extended in order to
factorize the solution space and generate a model
with uncertainty instead of a set of models.

24. Gianni Rosa – University of L’Aquila - ITALY
24
Extension of JTL Semantic
The JTL semantics has been extended in order to
factorize the solution space and generate a model
with uncertainty instead of a set of models.

25. Gianni Rosa – University of L’Aquila - ITALY
25
Extension of JTL Semantic
The JTL semantics has been extended in order to
factorize the solution space and generate a model
with uncertainty instead of a set of models.

26. Example

27. Gianni Rosa – University of L’Aquila - ITALY
27
Conclusion
The JTL semantics has been refined in order to be able
to generate directly the model with uncertainty
semantically corresponding to the complete solution
space.
We distinguish among two different behaviors:
- extensional, generate all the models satisfying the
relation defined in the bidirectional transformation;
- intensional (or with uncertainty), generate a model
with uncertainty wich is semantically equivalent to
the models of the extensive case
The approach is implemented on Eclipse/EMF.

28. Thank you!