1. SEAA 2014
Automatic Production of Transformation Chains Using Structural Constraints on Output Models
Cuauhtémoc Castellanos
Etienne Borde
Thomas Vergnaud
Thomas Derive
Laurent Pautet
2014/08/27

2. Context In Model Driven Development refactoring model is common
Automated with model transformations
Model refactoring using multiple design patterns
Ex: adapter, composite patterns
Design pattern are generic solutions to specific problem
Can be applied multiple times in one model: multiple instances
Ex : adapter pattern
SEAA 2014

3. Model Transformations
Operation on model
Refinement for analysis
Code generation
Model fusion
Model modification
Advocate reusability
Model transformation is a design pattern
Can be applied multiple times
Applying multiple patterns  applying multiple transformations
Nedd to chain transformations
We have to express the transformation rule in a comsume/produce semantic
SEAA 2014

4. Chaining Model Transformations
Non-commutative composition of transformations
T1(T2(In)) ≠ T2(T1(In))
Problems to Identify chains:
Precedence: the output model of a transformation must conforms to the application conditions of another transformation
Validity: last model must verify user defined constraints
Complexity: number of possible chains grows rapidly: !n A B C B C A C B A C B C A A B
out
out
out
out
out
out
Validation
SEAA 2014

5. Chain Identification Using Constraints
Precedence
Abstract chaining process as an ordered set
Abstract transformations in constraints between elements
Validity
Post-conditions constraints on last model
Complexity:
Use of Satisfiability Solver to identify a chain
Need to abstract involved artifacts as constraints
Objective: formalize chain of transformations (models, meta-models, trasformations…) with a set of satisfiability constraints (relational algebra, binary relations, first order logic…) to identify valid chains.
SEAA 2014

6. Involved artifacts to abstraction
Input model and meta-model
Oriented object semantic
Constraints on elements to express the model architecture
Model transformations
Consumption/production semantic
Chaining process and validity post-conditions
Ordering
Constraints on models
Implementation choice: Alloy
Signature and atoms
Relational algebra
Facts and predicates
First order logic with quantifiers
Objective: formalize chain of transformations (models, meta-models, trasformations…) with a set of satisfiability constraints (relational algebra, binary relations, first order logic…) to identify valid chains.
SEAA 2014

7. Illustrative example UML subset Pattern adapter
Diagram, class, interface
Pattern adapter
Adapter transformation
Chaining process: ordered set of transformations
SEAA 2014

8. Meta-model Typed elements : Relation between elements
Type Class is a signatures
Relation between elements
Class inheritance is a relation
Architectural constraints:
Quantification is enforced with first order logic on relations
abstract sig Element {} abstract sig UMLElement extends Element { composed : set UMLElement } sig Class extends UMLElement{ inherits : lone Class, implements : set Interface}
SEAA 2014

9. Input Model Abstraction of the real model
Particular instance of signatures: atoms
Set of atoms with particular relations
Constraints on first model of the chain
Use of a predicate on first model
Constraints must be sharp: avoid multiple solutions
Each relation must be initialized
pred init (d : one Diagram){ no d.Interface some disj A, B : d.Class { A.composed = B A.interface = none A.inherits = none B.composed = none B.interface = none B.inherits = none } }
SEAA 2014

10. Adapter Pattern Transformation
Adapter and adapter applied decorator
Each decorator is a pattern instance
Target elements identification
Traceability
Signature
Adapter pre-conditions
Context: Client, Adaptee
Clients and Adaptee must be in relation
Predicate
SEAA 2014

11. Model transformation as constraints
Transformations
Implemented with matching/production rules : ATL
Rule foo from A to B
Relations between 2 oriented labeled graphs
Arcs are relations between elements within a graph
Relational algebra
Matching rules are a binary relation set: mapping
Output graph arcs are relation through mapping relation juncture and constraints
Constraints depends on the transformation
R’ = mappingt . R . mapping ╞ C
SEAA 2014

12. Model transformation as binary relations: example
The mapping relation:
Client  Client’
Adaptee  Adaptee’
Adaptee  Adapter’
Adaptee  IAdapter’
AdapterPattern  AdapterPatternApplied
Input model relations:
Client  Adaptee
Output model relations:
Client’  IAdapter’
Adapter’  IAdapter’
Adapter’  Adaptee’
We have to express the transformation rule in a comsume/produce semantic
SEAA 2014

13. Chaining Process
Precedence: Pre-conditions verify applicability of next transformations
Each transformation has pre-conditions
To apply one transformation another must be applicable next
Validity: post-conditions on last model
Complexity: The solver search a chain by ordering the list
Sizing of the solving universe for the chain: maximum atoms possible
Ex : M0 = 5 atoms, T1 : 3, T2 : 1, 3 times T1 and 2 times T2
T1  T1  T1  T2  T2 : = 69
T2  T2  T1  T1  T1 : = 57
SEAA 2014

14. Conclusion and future works
Abstract model transformations chaining using relational algebra
Identify valid transformation chain using SAT solving technique
Time consuming due to the number of manipulated element
2 design patterns modeled:
Adapter pattern
Composite pattern
Future works
Anticipate the number of elements generated
Improve performance to treat bigger chains
Automate DSL and transformation language to relational algebra transformation
SEAA 2014