Constraint-awareSchema Transformation

Constraint-awareSchema Transformation

Tiago Alves (UMinho & SIG)Joint work with:

Paulo F. Silva & Joost Visser

Tiago Alves (UMinho & SIG)Joint work with:

Paulo F. Silva & Joost Visser

RULE 2008

About meAbout me

PhD Student Software Improvement Group, Amsterdam University of Minho, Braga

Supervisors José Nuno Oliveira Joost Visser

PhD Student Software Improvement Group, Amsterdam University of Minho, Braga

Supervisors José Nuno Oliveira Joost Visser

Software Improvement GroupSoftware Improvement Group

Company Spin-off from CWI in 2000, self-owned, independent Management consultancy grounded in source code analysis

Services Software Risk Assessments (snapshot) and Software Monitoring

(continuous) Toolset enables to analyze source code in an automated manner Experienced staff transforms analysis data into recommendations Focus on technical quality, primarily maintainability / evolvability

Company Spin-off from CWI in 2000, self-owned, independent Management consultancy grounded in source code analysis

Services Software Risk Assessments (snapshot) and Software Monitoring

(continuous) Toolset enables to analyze source code in an automated manner Experienced staff transforms analysis data into recommendations Focus on technical quality, primarily maintainability / evolvability

Observation...Observation...

A large proportion of the costs and failures in software engineering derive from the profoundly ad-hoc approach to the preservation of consistency between software artifacts as they undergo change.

This talk: Important instance of general problem Constraint-aware schema transformations

A large proportion of the costs and failures in software engineering derive from the profoundly ad-hoc approach to the preservation of consistency between software artifacts as they undergo change.

This talk: Important instance of general problem Constraint-aware schema transformations

2LT: Two Level Transformation2LT: Two Level Transformation

2LT: Coupled transformations2LT: Coupled transformations

A BT

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if A ≤ B and B ≈ C then A ≤ Cto

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from . to = id

Example ProblemExample Problem

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A → B → C( ) ≤ A → ()( ) × A × B → C( )

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Java →McCabe → 3,

LOC → 20

⎧ ⎨ ⎩

⎫ ⎬ ⎭

,

C#→FanIn → 3,

FanOut → 0

⎧ ⎨ ⎩

⎫ ⎬ ⎭

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⎨

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⎩

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Java → (),

C# → ()

⎧ ⎨ ⎪

⎩ ⎪

⎫ ⎬ ⎪

⎭ ⎪×

Java × McCabe → 3,

Java × LOC → 20,

C#×FanIn → 3,

C#×FanOut → 0

⎧

⎨ ⎪ ⎪

⎩ ⎪ ⎪

⎫

⎬ ⎪ ⎪

⎭ ⎪ ⎪

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Java → (),

C# → ()

⎧ ⎨ ⎪

⎩ ⎪

⎫ ⎬ ⎪

⎭ ⎪×

Java × McCabe → 3,

Java × LOC → 20,

C#×FanIn → 3,

C#×FanOut → 0,

C × NPath → 4

⎧

⎨

⎪ ⎪ ⎪

⎩

⎪ ⎪ ⎪

⎫

⎬

⎪ ⎪ ⎪

⎭

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Example SolutionExample Solution

€

A → B → C( ) ≤ A → ()( ) × A × B → C( )

€

A → B → C( ) ≈ A → ()( ) × A × B → C( )ϕ

ϕ = set π1 oδ oπ 2 ⊆δ oπ1

Rules catalogue (augmented)Rules catalogue (augmented)

€

A + B ≈ A? × B?ϕ 1

ϕ1 = ∈ oπ1( )⊕ ∈ oπ 2( )

€

A → B + C( ) ≈ A →1( ) × A → B( ) × A → C( )ϕ 2

ϕ 2 = δ oπ 2 ⊆δ oπ1( )∧ δ oπ 3 ⊆δ oπ1( )

€

A → B → C( ) ≈ A →1( ) × A × B → C( )ϕ 3

A → B × C → D( )( ) ≈ A → B( ) × A × C → D( )ϕ 3

ϕ 3 = δ oπ 2 ⊆δ oπ1( )∧ δ oπ 3 ⊆δ oπ1( )

ChallengesChallenges

Constraints Representation Constraint Transformation

Constraint Composition

Constraints Representation Constraint Transformation

Constraint Composition

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Aψ ≤ Bφ

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Aψ ≈ Bφ∧θ

The SolutionThe Solution

A BT

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to

2

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′ ϕ =ϕ • from

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ϕ

€

′ ϕ

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ψ

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ψ =simplify ′ ϕ

IngredientsIngredients

Data refinement

Point-free programtransformation

Generalized algebraic datatypes

Strategic termrewriting

Type representation (augmented)Type representation (augmented)

data Type t where One :: Type () List :: Type a -> Type [a] Set :: Type a -> Type (Set a) Map :: Type a -> Type b -> Type (Map a b) Either :: Type a -> Type b -> Type (Either a b) Prod :: Type a -> Type b -> Type (a,b) String :: Type String ... Tinv :: Type a -> PF (Pred a) -> Type a ...

type Pred a = a -> Bool

PF representation (augmented)PF representation (augmented)

data R f where ID :: PF (a -> a) COMP :: Type b -> PF (b -> c) -> PF (a -> b) -> PF (a -> c) FST :: PF ((a,b) -> a) AND :: PF (Pred a) -> PF (Pred a) -> PF (Pred a) InSet :: PF (a -> Set b) -> PF (a -> Set b) -> PF (Pred a) ...

Constraint-aware rewritingConstraint-aware rewriting

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′ ϕ =ϕ • from

A BT

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to

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ϕ

€

′ ϕ

€

ψ

PF simplification (augmented)PF simplification (augmented)

ContributionsContributions

Type theory enhanced with constraints Enhanced refinement rules Extended 2LT rewrite system

Constraints introduction Constraints propagation Constraints simplification

Type theory enhanced with constraints Enhanced refinement rules Extended 2LT rewrite system

Constraints introduction Constraints propagation Constraints simplification

What needs to be done...What needs to be done...

Consolidate work Proper evaluation of PF representations

Eq, Ord instances problems Revisit rules & constraints “Backwards transformation”

Constraints pattern-matching Constraints proof

Develop further front-ends Put on practice Extend application fields (MDE)

Consolidate work Proper evaluation of PF representations

Eq, Ord instances problems Revisit rules & constraints “Backwards transformation”

Constraints pattern-matching Constraints proof

Develop further front-ends Put on practice Extend application fields (MDE)

Thank youThank you

questions?questions?