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The Semantics of Partial Model Transforma- tions M.Famelis, R.Salay, M.Chechik, The Semantics of Partial Model Introduction Transformations Partial Models Transforming Partial Models Michalis Famelis, Rick Salay, and Marsha Chechik

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The Semantics of Partial Model Transforma- tions M.Famelis, R.Salay, M.Chechik, Introduction Partial Models Transforming Partial Models Lifted Transform Semantics Checking Lifted Rules Conclusion

The Semantics of Partial Model Transformations

Michalis Famelis, Rick Salay, and Marsha Chechik

University of Toronto

June 3rd, 2012,

Models in Software Engineering Workshop at ICSE

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The Semantics of Partial Model Transforma- tions M.Famelis, R.Salay, M.Chechik, Introduction Partial Models Transforming Partial Models Lifted Transform Semantics Checking Lifted Rules Conclusion

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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The Semantics of Partial Model Transforma- tions M.Famelis, R.Salay, M.Chechik, Introduction Partial Models Transforming Partial Models Lifted Transform Semantics Checking Lifted Rules Conclusion

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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The Semantics of Partial Model Transforma- tions M.Famelis, R.Salay, M.Chechik, Introduction Partial Models Transforming Partial Models Lifted Transform Semantics Checking Lifted Rules Conclusion

Motivating Example

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The Semantics of Partial Model Transforma- tions M.Famelis, R.Salay, M.Chechik, Introduction Partial Models Transforming Partial Models Lifted Transform Semantics Checking Lifted Rules Conclusion

Motivating Example

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The Semantics of Partial Model Transforma- tions M.Famelis, R.Salay, M.Chechik, Introduction Partial Models Transforming Partial Models Lifted Transform Semantics Checking Lifted Rules Conclusion

Motivating Example

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Motivating Example

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The Semantics of Partial Model Transforma- tions M.Famelis, R.Salay, M.Chechik, Introduction Partial Models Transforming Partial Models Lifted Transform Semantics Checking Lifted Rules Conclusion

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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The Semantics of Partial Model Transforma- tions M.Famelis, R.Salay, M.Chechik, Introduction Partial Models Transforming Partial Models Lifted Transform Semantics Checking Lifted Rules Conclusion

Partial Models

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The Semantics of Partial Model Transforma- tions M.Famelis, R.Salay, M.Chechik, Introduction Partial Models Transforming Partial Models Lifted Transform Semantics Checking Lifted Rules Conclusion

Partial Models

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The Semantics of Partial Model Transforma- tions M.Famelis, R.Salay, M.Chechik, Introduction Partial Models Transforming Partial Models Lifted Transform Semantics Checking Lifted Rules Conclusion

Partial Models

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The Semantics of Partial Model Transforma- tions M.Famelis, R.Salay, M.Chechik, Introduction Partial Models Transforming Partial Models Lifted Transform Semantics Checking Lifted Rules Conclusion

Partial Models

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The Semantics of Partial Model Transforma- tions M.Famelis, R.Salay, M.Chechik, Introduction Partial Models Transforming Partial Models Lifted Transform Semantics Checking Lifted Rules Conclusion

Semantics of Partial Models

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The Semantics of Partial Model Transforma- tions M.Famelis, R.Salay, M.Chechik, Introduction Partial Models Transforming Partial Models Lifted Transform Semantics Checking Lifted Rules Conclusion

Semantics of Partial Models

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The Semantics of Partial Model Transforma- tions M.Famelis, R.Salay, M.Chechik, Introduction Partial Models Transforming Partial Models Lifted Transform Semantics Checking Lifted Rules Conclusion

Semantics of Partial Models

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The Semantics of Partial Model Transforma- tions M.Famelis, R.Salay, M.Chechik, Introduction Partial Models Transforming Partial Models Lifted Transform Semantics Checking Lifted Rules Conclusion

Semantics of Partial Models

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The Semantics of Partial Model Transforma- tions M.Famelis, R.Salay, M.Chechik, Introduction Partial Models Transforming Partial Models Lifted Transform Semantics Checking Lifted Rules Conclusion

Goal of This Work

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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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The Semantics of Partial Model Transforma- tions M.Famelis, R.Salay, M.Chechik, Introduction Partial Models Transforming Partial Models Lifted Transform Semantics Checking Lifted Rules Conclusion

Intuition

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The Semantics of Partial Model Transforma- tions M.Famelis, R.Salay, M.Chechik, Introduction Partial Models Transforming Partial Models Lifted Transform Semantics Checking Lifted Rules Conclusion

Intuition

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The Semantics of Partial Model Transforma- tions M.Famelis, R.Salay, M.Chechik, Introduction Partial Models Transforming Partial Models Lifted Transform Semantics Checking Lifted Rules Conclusion

Intuition

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The Semantics of Partial Model Transforma- tions M.Famelis, R.Salay, M.Chechik, Introduction Partial Models Transforming Partial Models Lifted Transform Semantics Checking Lifted Rules Conclusion

Intuition

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The Semantics of Partial Model Transforma- tions M.Famelis, R.Salay, M.Chechik, Introduction Partial Models Transforming Partial Models Lifted Transform Semantics Checking Lifted Rules Conclusion

Intuition

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The Semantics of Partial Model Transforma- tions M.Famelis, R.Salay, M.Chechik, Introduction Partial Models Transforming Partial Models Lifted Transform Semantics Checking Lifted Rules Conclusion

Our approach

Summarizing the intuition: Applying a transformation to a partial model M

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The Semantics of Partial Model Transforma- tions M.Famelis, R.Salay, M.Chechik, Introduction Partial Models Transforming Partial Models Lifted Transform Semantics Checking Lifted Rules Conclusion

Our approach

Summarizing the intuition: Applying a transformation to a partial model M should be the same as if we had created all its concretizations,

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The Semantics of Partial Model Transforma- tions M.Famelis, R.Salay, M.Chechik, Introduction Partial Models Transforming Partial Models Lifted Transform Semantics Checking Lifted Rules Conclusion

Our approach

Summarizing the intuition: Applying a transformation to a partial model M should be the same as if we had created all its concretizations, applied the transformation to each separately,

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The Semantics of Partial Model Transforma- tions M.Famelis, R.Salay, M.Chechik, Introduction Partial Models Transforming Partial Models Lifted Transform Semantics Checking Lifted Rules Conclusion

Our approach

Summarizing the intuition: Applying a transformation to a partial model M should 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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The Semantics of Partial Model Transforma- tions M.Famelis, R.Salay, M.Chechik, Introduction Partial Models Transforming Partial Models Lifted Transform Semantics Checking Lifted Rules Conclusion

Our approach

Summarizing the intuition:

Correctness Criterion

Applying a transformation to a partial model M should 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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The Semantics of Partial Model Transforma- tions M.Famelis, R.Salay, M.Chechik, Introduction Partial Models Transforming Partial Models Lifted Transform Semantics Checking Lifted Rules Conclusion

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 3 Transforming Partial Models 4 “Lifted” Transformation Semantics 5 Checking Lifted Rules 6 Conclusion

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The Semantics of Partial Model Transforma- tions M.Famelis, R.Salay, M.Chechik, Introduction Partial Models Transforming Partial Models Lifted Transform Semantics Checking Lifted Rules Conclusion

Applying Rules to Partial Models

Q1: How do we transform M directly to N? – Lifted semantics of transformations, using logic. Q2: Are the concretizations of N exactly the models n1 . . . nk?

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The Semantics of Partial Model Transforma- tions M.Famelis, R.Salay, M.Chechik, Introduction Partial Models Transforming Partial Models Lifted Transform Semantics Checking Lifted Rules Conclusion

Transfer Predicates

Represent M R ∗ = ⇒ N as: ΦN = R(R, M, N) ∧ ΦM R is a conjunction φ1 ∧ φ2 ∧ ...

  • One subformula at each application point:

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The Semantics of Partial Model Transforma- tions M.Famelis, R.Salay, M.Chechik, Introduction Partial Models Transforming Partial Models Lifted Transform Semantics Checking Lifted Rules Conclusion

Transfer Predicates

Represent M R ∗ = ⇒ N as: ΦN = R(R, M, N) ∧ ΦM R is a conjunction φ1 ∧ φ2 ∧ ...

  • One subformula at each application point:

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The Semantics of Partial Model Transforma- tions M.Famelis, R.Salay, M.Chechik, Introduction Partial Models Transforming Partial Models Lifted Transform Semantics Checking Lifted Rules Conclusion

Transfer Predicates

Represent M R ∗ = ⇒ N as: ΦN = R(R, M, N) ∧ ΦM R is a conjunction φ1 ∧ φ2 ∧ ...

  • One subformula at each application point:

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The Semantics of Partial Model Transforma- tions M.Famelis, R.Salay, M.Chechik, Introduction Partial Models Transforming Partial Models Lifted Transform Semantics Checking Lifted Rules Conclusion

Transfer Predicates

Represent M R ∗ = ⇒ N as: ΦN = R(R, M, N) ∧ ΦM R is a conjunction φ1 ∧ φ2 ∧ ...

  • One subformula at each application point:

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The Semantics of Partial Model Transforma- tions M.Famelis, R.Salay, M.Chechik, Introduction Partial Models Transforming Partial Models Lifted Transform Semantics Checking Lifted Rules Conclusion

Transfer Predicates

Represent M R ∗ = ⇒ N as: ΦN = R(R, M, N) ∧ ΦM R is a conjunction φ1 ∧ φ2 ∧ ...

  • One subformula at each application point:

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The Semantics of Partial Model Transforma- tions M.Famelis, R.Salay, M.Chechik, Introduction Partial Models Transforming Partial Models Lifted Transform Semantics Checking Lifted Rules Conclusion

Transfer Predicates

Represent M R ∗ = ⇒ N as: ΦN = R(R, M, N) ∧ ΦM R is a conjunction φ1 ∧ φ2 ∧ ...

  • One subformula at each application point:

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The Semantics of Partial Model Transforma- tions M.Famelis, R.Salay, M.Chechik, Introduction Partial Models Transforming Partial Models Lifted Transform Semantics Checking Lifted Rules Conclusion

Transfer Predicates

Represent M R ∗ = ⇒ N as: ΦN = R(R, M, N) ∧ ΦM R is a conjunction φ1 ∧ φ2 ∧ ...

  • One subformula at each application point:

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The Semantics of Partial Model Transforma- tions M.Famelis, R.Salay, M.Chechik, Introduction Partial Models Transforming Partial Models Lifted Transform Semantics Checking Lifted Rules Conclusion

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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The Semantics of Partial Model Transforma- tions M.Famelis, R.Salay, M.Chechik, Introduction Partial Models Transforming Partial Models Lifted Transform Semantics Checking Lifted Rules Conclusion

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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The Semantics of Partial Model Transforma- tions M.Famelis, R.Salay, M.Chechik, Introduction Partial Models Transforming Partial Models Lifted Transform Semantics Checking Lifted Rules Conclusion

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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The Semantics of Partial Model Transforma- tions M.Famelis, R.Salay, M.Chechik, Introduction Partial Models Transforming Partial Models Lifted Transform Semantics Checking Lifted Rules Conclusion

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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The Semantics of Partial Model Transforma- tions M.Famelis, R.Salay, M.Chechik, Introduction Partial Models Transforming Partial Models Lifted Transform Semantics Checking Lifted Rules Conclusion

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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The Semantics of Partial Model Transforma- tions M.Famelis, R.Salay, M.Chechik, Introduction Partial Models Transforming Partial Models Lifted Transform Semantics Checking Lifted Rules Conclusion

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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The Semantics of Partial Model Transforma- tions M.Famelis, R.Salay, M.Chechik, Introduction Partial Models Transforming Partial Models Lifted Transform Semantics Checking Lifted Rules Conclusion

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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The Semantics of Partial Model Transforma- tions M.Famelis, R.Salay, M.Chechik, Introduction Partial Models Transforming Partial Models Lifted Transform Semantics Checking Lifted Rules Conclusion

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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1 Introduction 2 Partial Models 3 Transforming Partial Models 4 “Lifted” Transformation Semantics 5 Checking Lifted Rules 6 Conclusion

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The Semantics of Partial Model Transforma- tions M.Famelis, R.Salay, M.Chechik, Introduction Partial Models Transforming Partial Models Lifted Transform Semantics Checking Lifted Rules Conclusion

Testing Rule Application

Q1: How do we transform M directly to N? Q2: Are the concretizations of N exactly the models n1 . . . nk? – Check equivalence of encodings using SAT.

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Checking Using a SAT Solver

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Checking Using a SAT Solver

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The Semantics of Partial Model Transforma- tions M.Famelis, R.Salay, M.Chechik, Introduction Partial Models Transforming Partial Models Lifted Transform Semantics Checking Lifted Rules Conclusion

Checking Using a SAT Solver

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Checking Using a SAT Solver

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The Semantics of Partial Model Transforma- tions M.Famelis, R.Salay, M.Chechik, Introduction Partial Models Transforming Partial Models Lifted Transform Semantics Checking Lifted Rules Conclusion

Checking Using a SAT Solver

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Checking Using a SAT Solver

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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 3 Transforming Partial Models 4 “Lifted” Transformation Semantics 5 Checking Lifted Rules 6 Conclusion

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The Semantics of Partial Model Transforma- tions M.Famelis, R.Salay, M.Chechik, Introduction Partial Models Transforming Partial Models Lifted Transform Semantics Checking Lifted Rules Conclusion

Summary

Q1: How do we transform M directly to N? – Lifted semantics of transformations, using logic. Q2: Are the concretizations of N exactly the models n1 . . . nk? – Check equivalence of encodings using SAT.

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Conclusion

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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The Semantics of Partial Model Transforma- tions M.Famelis, R.Salay, M.Chechik, Introduction Partial Models Transforming Partial Models Lifted Transform Semantics Checking Lifted Rules Conclusion

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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The Semantics of Partial Model Transforma- tions M.Famelis, R.Salay, M.Chechik, Introduction Partial Models Transforming Partial Models Lifted Transform Semantics Checking Lifted Rules Conclusion

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. 27 / 27