AToM3: A Tool for Multi-Formalism and Meta-Modelling

1
AToM3 A Tool for Multi-Formalism and
Meta-Modelling

• Juan de Lara(1,2)
• Hans Vangheluwe(2)

(2) School of Computer Science McGill
University Montreal, Canada
(1) ETS Informática Universidad Autónoma de
Madrid Madrid, Spain
2
Problems

• To model and simulate complex systems
• Many components
• Each one is better described in a particular
  formalism.
• To transform models between formalisms
  preserving behaviour.

3
Goals

• We propose Meta-Modelling Graph-Rewriting to
  solve these problems.
• To be able to automatically generate tools for
  the processing of models.
• Common framework for all these tools.

4
Index

• Problems
• Goals
• Background.
• Multi-Formalism Modelling
• Meta-Modelling.
• Graph Grammars.
• AToM3.
• Transforming NFA into DFA.
• Conclusions and Future work.

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Multi-Formalism Modelling
Formalism Transformation Graph
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Meta-Modelling (i)

• Need of multiple, heterogeneous tools for
  multi-formalism modelling?
• We solve it with Meta-Modelling
• Modelling the formalism...
• And generating automatically a tool for
  processing models in the described formalism.

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Meta-Modelling (ii)

• Introduce higher modelling layers to model the
  formalisms themselves.

Order
Description
Example
Meta-Meta Model
Models of (meta-) formalisms, which can be used
to describe other formalisms

• Models of
• Entity-Relationship Diagrams
• UML class Diagrams
• ...

• Models of
• Deterministic Finite Automata
• DFD, Structure Charts
• Ordinary Differential Equations
• ...

Models of formalisms.
Meta- Model

• f(x) -sin(x), f(0) 0 (in the
• ODEs formalism).
• ...

The description of an object in a
certain formalism.
Model
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Meta-Modelling (iii)

• Example

0..N
1..1
1
State Name String Type (I, R,
F) StateTransition.forAll(t1, t2t1.Conditionltgtt
2.Condition)
1
S0
S1
Transition Condition String
0..N
1
1..1
0
0
S2
S3
Constraints distinctStateNames State.forAll(p,
qp.Nameltgtq.Name) uniqueInitial
State.exists(nn.TypeI and State.forAll(mnltgtm
and m.TypeltgtI) existsFinal State.exists(nn.Type
F)
0

• Model Even binary numbers (DFA)

• Meta-Model DFA formalism (UML class diagram
  OCL)

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Meta-Modelling (iv)
E-R
E-R
(meta-meta-model)
E-R
DFA
(meta-model)
Meta-Modelling Tool (AToM3 Kernel)

• User Input
• Create entities
• Delete entities
• Verify conditions
• (local, global)

DFA
Even Binary Numbers
Meta-Modelling Tool (AToM3 Kernel)

• User Input
• Create entities
• Delete entities
• Verify conditions
• (local, global)

(model)
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Graph Grammars (i)

• A (meta-) model is a graph.
• Just like string grammars, but rules have graphs
  in LHSs and RHSs.
• If a matching is found between a LHS and a zone
  in the graph, this subgraph is substituted by the
  RHS.
• A Graph Rewriting System tries each rule in
  sequence until none of them is applicable.

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Graph Grammars (ii)

• We use graph grammars to
• Express operational semantics (simulator
  specification)
• Transform models into behaviourally equivalent
  models expressed in another formalism.
• Optimize models.
• Generate code for a particular tool ( ?
  denotational semantics).

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Index

• Problems
• Goals
• Background.
• AToM3.
• Meta-Modelling the DFA Formalism.
• Transforming NFAs into DFAs.
• Conclusions and Future work.

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AToM3(i)
Graphical Icons
User Interface Model
ASG Nodes Structure
ASG Structure
(meta-meta-model)
E-R
E-R
Graph Rewriting Processor
Graphical Model
Abstract Syntax Graph
(meta-model)
Meta-Modelling Tool (AToM3 Kernel)
User Interface
E-R
DFA
Constraint Manager
Code Generator

• User Input
• Create entities
• Delete entities
• Verify conditions
• (local, global)

DFA
Even Binary Numbers
Meta-Modelling Tool (AToM3 Kernel)
(model)

• User Input
• Create entities
• Delete entities
• Verify conditions
• (local, global)

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AToM3(ii)

• Types is another formalism.
• Atomic (integer, boolean, ...) or composite.
• A composite type is a model in the types
  formalism.
• Regular or Generative
• ATOM3Attribute
• ATOM3Constraint
• ATOM3Link
• ATOM3Appearance

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AToM3(iii)

• DFA Meta-Model
• Semantic information

Edit Cardinalities
Edit Properties
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AToM3(iii)

• DFA Meta-Model
• Semantic information

Constraints
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AToM3(iv)

• DFA Meta-Model
• Graphical information

Edit Appearance
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AToM3(v)

• DFA Meta-Model
• Global Semantic Information and Constraints.

Edit Model Attributes
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AToM3(vi)

• Configuring the DFA User Interface (In the
  Buttons formalism).
• Automatically generated by a Graph-Grammar
• Transforms a Model in the Eentity Relationship
  formalism into a Model in the Buttons Formalism.

Edit Entity
Config. Action
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AToM3(vii)

• The Tool to Process DFA Models.
• Create, Edit, Verify...
• Other manipulations can be defined by means of
  graph grammars
• Simulate.
• Optimize.
• Transform.
• Generate Code.
• ...

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Index

• Problems
• Goals
• Background.
• AToM3.
• Transforming NFAs into DFAs.
• Example
• Conclusions and Future work.

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Transforming NFAs into DFAs (i)
Eliminates unreachable states Joins equivalent
states Eliminates non determinism between two
different states Eliminates non determinism with
self-loops.
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Transforming NFAs into DFAs (ii)
Rule 3 Eliminates non determinism between two
different states
RHS
LHS
Condition node(2).condition
node(3).condition Action Copy inputs and outpus
from node(4) and node(5) into node(7)
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Transforming NFAs into DFAs (ii)
Example (i)
Rule 1
Rule 3
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Transforming NFAs into DFAs (ii)
Example (ii)
Rule 1
Rule 3
Rule 1
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Transforming NFAs into DFAs (ii)
Example (iii)
Rule 1
Rule 1
Rule 3
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Transforming NFAs into DFAs (ii)
Example (iv)
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Index

• Problems
• Goals
• Background.
• AToM3.
• Transforming NFAs into DFAs.
• Conclusions and Future work.

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Conclusions

• Meta-Modelling Graph Transformation is a
  powerful combination for Multi-Paradigm
  Modelling.
• AToM3 implements such a combination
• Meta-Modelling facilitates the generation of
  modelling tools.
• Graph Transformation facilitates the processing
  of models (transformation, simulation,
  optimization, code generation).

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Future Work

• Extend AToM3
• Hierarchy. Hierarchical Graph Grammars.
• Meta-Model Inheritance. Formalism inheritance.
• Collaborative Modelling. XML representation.
• Meta-Model UML Class Diagrams.
• Implement all the Formalisms and Transformations
  in the Formalism Transformation Graph.
• AToM3 is available at
• http//moncs.cs.mcgill.ca/MSDL/research/projects/A
  ToM3/