The Semantics of Partial Model Transformations

TheSemantics ofPartial ModelTransforma-

M.Famelis,R.Salay,

M.Chechik,

Introduction

Partial Models

TransformingPartial Models

LiftedTransformSemantics

CheckingLifted Rules

Conclusion

The Semantics of Partial ModelTransformations

Michalis Famelis, Rick Salay, and Marsha Chechik

University of Toronto

June 3rd, 2012,Models in Software Engineering Workshop at ICSE

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Introduction: Uncertainty

Uncertainty: pervasive in SE

Models with uncertainty:

– Represent choice among many possibilities

– Can be refined to many different classical models

Our goal:

Handle models with uncertainty in MDE

without having to remove uncertainty.

In this talk: Transformations of models with uncertainty

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Introduction: Transformations

Existing model (graph) transformations:

– Unambiguous model is assumed as input.

– When model contains uncertainty:

• either first remove uncertainty

– Premature commitment.– Reduced quality.

• or transform all alternatives.

– Hard to maintain.

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Motivating Example

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Motivating Example

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Motivating Example

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Motivating Example

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Motivating Example

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1 Introduction

2 Partial Models

3 Transforming Partial Models

4 “Lifted” Transformation Semantics

5 Checking Lifted Rules

6 Conclusion

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Partial Models

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Partial Models

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Partial Models

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Partial Models

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Semantics of Partial Models

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Goal of This Work

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1 Introduction

2 Partial Models

6 Conclusion

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Intuition

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Intuition

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Intuition

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Intuition

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Intuition

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Our approachSummarizing the intuition:

Correctness Criterion

Applying a transformation to a partial model M

should be the same as ifwe had created all its concretizations,

applied the transformation to each separately,and encoded the result as a partial model.

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Applying a transformation to a partial model Mshould be the same as if

we had created all its concretizations,

applied the transformation to each separately,and encoded the result as a partial model.

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we had created all its concretizations,applied the transformation to each separately,

and encoded the result as a partial model.

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Lifting Transformations

Q1: How do we transform M directly to N?

Q2: Are the concretizations of N exactly the models n1 . . . nk?

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1 Introduction

2 Partial Models

6 Conclusion

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Applying Rules to Partial Models

– Lifted semantics of transformations, using logic.

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Transfer Predicates

Represent MR ∗=⇒ N as:

ΦN = R(R,M,N) ∧ ΦM

R is a conjunction φ1 ∧ φ2 ∧ ...- One subformula at each application point:

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Transfer Predicates

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Transfer Predicates

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Transfer Predicates

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Transfer Predicates

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Transfer Predicates

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Transfer Predicates

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Example 1/2

(ΦLHS → ΦRHS) ∧ (¬ΦLHS → ΦNE )

• ΦLHS = c ∧ a ∧ ¬g ∧ ¬s

• ΦRHS = (c ′ ↔ c) ∧ (a′ ↔ a) ∧ (g ′ ↔ a) ∧ (s ′ ↔ a)

• ΦNE = (x ′ ↔ x)

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Example 2/2

After matching, grounding and simplifying:

R(R,M,N) = (Product′ ↔ Product) ∧ (Milk′ ↔ Milk)∧(A′ ↔ A) ∧ (B ′ ↔ B) ∧ (C ′ ↔ C)∧(D ′ ↔ D) ∧ (E ′ ↔ A) ∧ (F ′ ↔ A)∧(G ′ ↔ B) ∧ (H ′ ↔ B) ∧ (I ′ ↔ C)∧(J ′ ↔ C) ∧ (K ′ ↔ D) ∧ (L′ ↔ D)∧(gen Milk Product′ ↔ gen Milk Product)

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Example 2/2

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Example 2/2

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Example 2/2

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Example 2/2

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Example 2/2

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Example 2/2

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1 Introduction

2 Partial Models

6 Conclusion

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Testing Rule Application

– Check equivalence of encodings using SAT.

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Checking Using a SAT Solver

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Checking Example

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Checking Example

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Checking Example

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Checking Example

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Checking Example

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1 Introduction

2 Partial Models

6 Conclusion

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Summary

– Lifted semantics of transformations, using logic.

– Check equivalence of encodings using SAT.

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Transforming models that contain uncertainty.

• Represent uncertainty using Partial Models.

• Lift transformation rules from classical to Partial Models.

• Check Correctness Criterion for the lifted transformation .

Next steps:

• Compositionally test Correctness Criterion.

• Systematically create Transfer Predicates using FOL.

• Handle expanding/contracting model vocabularies.

• Partial Models as an Adhesive HLR Category?

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Overall Picture

Overall research goal [MoDeVVa’11]:

• Handling uncertainty...• Partial models: sets of possibilities.• Syntactic “partiality” annotations.• Other kinds of partiality (“MAVO”) [FASE’12].

• ...throughout the software lifecycle.• Partial models as first-class artifacts.

(1) Reasoning [ICSE’12]

(2) Refinement [VOLT’12]

(3) Transformation

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Questions?

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Bibliography I

M. Famelis, Shoham Ben-David, Marsha Chechik, and Rick Salay.

“Partial Models: A Position Paper”.In Proceedings of MoDeVVa’11, pages 1–6, 2011.

Michalis Famelis, Marsha Chechik, and Rick Salay.

“Partial Models: Towards Modeling and Reasoning with Uncertainty”.In Proceedings of ICSE’12, 2012.

R. Salay, M. Chechik, and J. Gorzny.

“Towards a Methodology for Verifying Partial Model Refinements”.In Proceedings of VOLT’12, 2012.

R. Salay, M. Famelis, and M. Chechik.

“Language Independent Refinement using Partial Modeling”.In Proceedings of FASE’12, 2012.

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The Semantics of Partial Model Transformations

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