Presentation slides used at SLE17: In model-driven engineering (MDE), models abstract the rel- evant features of software artefacts and model management operations, including model transformations, act on them automating large tasks of the development process. Flexible reuse of such operations is an important factor to improve productivity when developing and maintaining MDE solu- tions. In this work, we revisit the traditional notion of object subtyping based on subsumption, discarded by other ap- proaches to model subtyping. We re ne a type system for object-oriented programming, with multiple inheritance, to support model types in order to analyse its advantages and limitations with respect to reuse in MDE. Speci cally, we ex- tend type expressions with referential constraints and with OCL constraints. Our approach has been validated with a tool that extracts model types from (EMF) metamodels, paired with their OCL constraints, automatically and that exploits the extended subtyping relation to reuse model management operations. We show that structural model subtyping is ex- pressive enough to support variants of model subtyping, including multiple, partial and dynamic model subtyping. The tool has received the ACM badge "Artifacts Evaluated − Functional".

1. Structural Model Subtyping with OCL
Constraints
Artur Boronat

2. The Problem
Given two independent metamodel specifications…
are they compatible?
name : String
Node
name : String
Edgename : String
Graph
*
nodes * edgessource
target
name: String
State
name : String
isCompletion : Bool
Transition
1..*
nodes
1..* edges
source
target
name : String
StateMachine
final
initial
*
Mark
marking marks
*
Observation
marking
*
marks
0..1
0..1
context Transition inv determism:
not(Transition.allInstances()->exists(t | t.source=self.source and t.target<>self.target))
context Transition inv eventTransition:
name <> '' implies isCompletion=false
context Edge inv map:
not(Edge.allInstances()->exists(t | t.source=self.source and t.target<>self.target))

3. evolution
(backward/forward
compatibility)
translation
metamodel
Use Cases
name : String
Node
name : String
Edgename : String
Graph
*
nodes * edgessource
target
name: String
State
name : String
isCompletion : Bool
Transition
1..*
nodes
1..* edges
source
target
name : String
StateMachine
final
initial
*
Mark
marking marks
*
Observation
marking
*
marks
0..1
0..1
context Transition inv determism:
not(Transition.allInstances()->exists(t | t.source=self.source and t.target<>self.target))
context Transition inv eventTransition:
name <> '' implies isCompletion=false
context Edge inv map:
not(Edge.allInstances()->exists(t | t.source=self.source and t.target<>self.target))
with OCL
simulation
syntax
semantics
reuse
https://mde-subtyping.github.io/web/

4. M!metamodels
name: String
State
name : String
isCompletion : Bool
Transition
1..*
nodes
1..* edges
source
target
name : String
StateMachine
final
initial
*
Observation
marking
*
marks0..1
Our Solution
M<
model type expressions
linguistic typing t : ⌧
name = A
:State
name = 'a->b'
isCompletion = false
Transition
nodes edges
source
target
:StateMachine
initial
name = A
:State
nodes
ontological typing
OCL
multiple inheritance
[Cardelli’88]
Structural Model
Subtyping
Structural Subtyping with OCL
Constraints
Tool
M!
sub : M!
super (M!
sub, ⌦sub) : (M!
super , ⌦super )

5. Our Solution
Structural Model
Subtyping
M!
sub : M!
super

6. Structural Model Subtyping (I)
name: String
State
name : String
isCompletion : Bool
Transition
1..*
nodes
1..* edges
source
target
name : String
StateMachine
final
initial
*
Observation
marking
*
marks0..1
metamodel
Extension with referential constraints and generalization to model types:
M<
= (roots, type)Model Type Expression:
model type expression referential
constraints:
multiplicity,
order,
uniqueness
containment
reference
attribute:
primitive types,
enumerations
[Cardelli. A Semantics of Multiple Inheritance. 1988]

7. Structural Model Subtyping:
M<
sub : M<
super () µ(M<
sub) :; µ(M<
super )
Structural Model Subtyping (II)
Model Type JM<
K = Jµ(M<
)K = J[
[
c2roots
(c : unique c[0..⇤])]K
Adds a memory to
ensure decidability
when traversing
references
Extends subtyping
with inconsistency
checking for
referential constraints

8. Our Solution
Structural Subtyping with OCL
Constraints
(M!
sub, ⌦sub) : (M!
super , ⌦super )

9. ontological semantics
[Richters’02] name = A
:State
name = 'a->b'
isCompletion = false
Transition
nodes edges
source
target
:StateMachine
initial
name = A
:State
nodes
name: String
State
name : String
isCompletion : Bool
Transition
1..*
nodes
1..* edges
source
target
name : String
StateMachine
final
initial
*
Observation
marking
*
marks0..1
metamodel M!
Structural Subtyping with OCL Constraints (I)
JM<
K
linguistic semantics
*<
!
model type expression M<
decl
J K
Semantic Model Subtyping: M!
sub : M!
super ) JM!
subK ✓ JM!
super K
Syntactic Model Subtyping: M!
sub : M!
super ) decl(M!
sub) : decl(M!
super )
Model Type: JM!
K = *<
! ( (M!
))

10. • Satisfaction of OCL constraints
Structural Subtyping with OCL Constraints (II)
[Richters’02]

11. • Satisfaction of OCL constraints
• Extension metamodel
• reifies structural subtyping as generalization
• enables the analysis of OCL constraints from subtype
and supertype
Structural Subtyping with OCL Constraints (II)
M!
sub,super
[Richters’02]

12. • Satisfaction of OCL constraints
• Extension metamodel: synthesis procedure
Structural Subtyping with OCL Constraints (II)
name : String
Node
name : String
Edgename : String
Graph
*
nodes * edgessource
target
name: String
State
name : String
isCompletion : Bool
Transition
1..*
nodes
1..* edges
source
target
name : String
StateMachine
final
initial
*
Mark
marking marks
*
Observation
marking
*
marks
0..1
0..1
[Richters’02]

13. • Satisfaction of OCL constraints
• Extension metamodel: initialization
Structural Subtyping with OCL Constraints (II)
name : String
Node
name : String
Edgename : String
Graph
*
nodes * edgessource
target
name: String
State
name : String
isCompletion : Bool
Transition
1..*
nodes
1..* edges
source
target
name : String
StateMachine
final
initial
*
Mark
marking marks
*
Observation
marking
*
marks
0..1
0..1
multiple
typing
[Richters’02]

14. • Satisfaction of OCL constraints
• Extension metamodel: extraction of virtual classes
Structural Subtyping with OCL Constraints (II)
Node Edge
Graph
*
nodes * edgessource
target
name: String
State
name : String
isCompletion : Bool
Transition
1..*
nodes
1..* edges
source
target
name : String
StateMachine
final
initial
*
Mark
marking
marks*
Observation
marking
*
marks
0..1
0..1
«abstract»
GraphNode
name : String
«abstract»
GraphNodeEdge
[Richters’02]

15. • Satisfaction of OCL constraints
• Extension metamodel: refactoring
Structural Subtyping with OCL Constraints (II)
«abstract»
GraphNode
name: String
«abstract»
GraphNodeEdge
Node Edge
Graph
1..*
nodes 1..*edges
source
target
State TransitionStateMachine final
initial
*
Mark
marking *
Observation
marks
0..1
[Richters’02]

16. • Satisfaction of OCL constraints
• Extension metamodel
• Properties:
Structural Subtyping with OCL Constraints (II)
«abstract»
GraphNode
name: String
«abstract»
GraphNodeEdge
Node Edge
Graph
1..*
nodes 1..*edges
source
target
State TransitionStateMachine final
initial
*
Mark
marking *
Observation
marks
0..1
M!
sub,super
[Richters’02]

17. • Satisfaction of OCL constraints
• Extension metamodel
• Complements of subtype (and supertype):
Structural Subtyping with OCL Constraints (II)
«abstract»
GraphNode
name: String
«abstract»
GraphNodeEdge
Node Edge
Graph
1..*
nodes 1..*edges
source
target
State TransitionStateMachine final
initial
*
Mark
marking *
Observation
marks
0..1
M!
sub,super
StateStateMachine
final
initial
*
[Richters’02]

18. • Satisfaction of OCL constraints
• Extension metamodel
• Complements of subtype (and supertype):
• Strict subtypings, ranked
Structural Subtyping with OCL Constraints (II)
«abstract»
GraphNode
name: String
«abstract»
GraphNodeEdge
Node Edge
Graph
1..*
nodes 1..*edges
source
target
State TransitionStateMachine final
initial
*
Mark
marking *
Observation
marks
0..1
M!
sub,super
StateStateMachine
final
initial
*
[Richters’02]

19. Structural Subtyping with OCL Constraints (III)
Semantic model subtyping with OCL constraints
Semantics of metamodel specifications
Syntactic model subtyping with OCL constraints

20. Our Solution
Tool

21. Tool support
name : String
Node
name : String
Edgename : String
Graph
*
nodes * edgessource
target
name: String
State
name : String
isCompletion : Bool
Transition
1..*
nodes
1..* edges
source
target
name : String
StateMachine
final
initial
*
Mark
marking marks
*
Observation
marking
*
marks
0..1
0..1
context Transition inv determism:
not(Transition.allInstances()->exists(t | t.source=self.source and t.target<>self.target))
context Transition inv eventTransition:
name <> '' implies isCompletion=false
context Edge inv map:
not(Edge.allInstances()->exists(t | t.source=self.source and t.target<>self.target))
( ,USE OCL)
Provide metamodel specs
(M!
sm , ⌦sm )
:
(M!
g , ⌦g )?
Inspect extension metamodel,
complement supertype,
solutions for recommended
strict typings
StateStateMachine
final
initial
*
in metamodel
Where is
the problem?
«abstract»
GraphNode
name: String
«abstract»
GraphNodeEdge
Node Edge
Graph
1..*
nodes 1..*edges
source
target
State TransitionStateMachine final
initial
*
Mark
marking *
Observation
marks
0..1
M!
sub,super
Compatibility guarantee
Safe reuse
https://mde-subtyping.github.io/web/
Inspect witness
attr = "string2"
:StateMachine
attr = "string1"
:State
attr = "string5"
:State
attr = "string1"
:Transition
attr = "string2"
:Transition
source
source
target
target
nodes
nodes
edges
edges
in an OCL constraint
[TOTEM-MDE ‘17]

22. Concluding Remarks
ToolStructural Subtyping with OCL
Constraints
(M!
sub, ⌦sub) : (M!
super , ⌦super )
Structural Model
Subtyping
M!
sub : M!
super
Limitations
Number of inferred subtypings
Bounded analysis
inference: adaptations for free
Structural model subtyping with OCL constraints when metamodels are not related a priori
flexible modelling: dynamic, partial and multiple model typing
user support:
insight
prioritization and recommendation
effective metamodel, retyping

23. Structural Model Subtyping with OCL
Constraints
Artur Boronat
https://mde-subtyping.github.io/web/