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Region-Based Model AbstractionPowerPoint Presentation

Region-Based Model Abstraction

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### Region-BasedModel Abstraction

Jeremy Condit

Jim Larus

Sriram Rajamani

Jakob Rehof

OSQ Lunch

7 September 2003

Model Checking for C#

- Want to check properties of a C# program
- e.g., conformance checking for web services

- The model checking approach:
- Produce a simplified version of program with respect to the property
- Check all possible executions of this model

Our Abstraction Technique

- We abstract a program by throwing away irrelevant code
- Relevant data is identified by a third party
- Programmer annotations
- Program analysis
- Counterexample-driven refinement

- Relevant statements and expressions are those that deal with relevant data
- Easy, right?

Two Problems

- Problem 1: Aliasing
- Statements that affect aliasing can be relevant

if (…) x = y;

x.relevant_field = true;

y.relevant_field = false;

- Problem 2: Indirection
- Relevant data can be buried within other nonsense

x.y.z.relevant_field = true;

Transaction x;

Transaction y;

if (…) {

Transaction t1 = new Transaction();

t1.s = new State(); t1.s.b = true; x = t1;

} else { Transaction t2 = new Transaction();

t2.s = new State(); t2.s.b = false; x = t2;

}

if (…) {

Transaction t3 = new Transaction();

t3.s = new State(); t3.s.b = true; y = t3;

} else { Transaction t4 = new Transaction();

t4.s = new State(); t4.s.b = false; y = t4;

}

if (x.s.b) …

if (y.s.b) …

if (x.s.b) …

Program slicing

Transaction x;

Transaction y;

if (…) {

Transaction t1 = new Transaction();

t1.s = new State(); t1.s.b = true; x = t1;

} else { Transaction t2 = new Transaction();

t2.s = new State(); t2.s.b = false; x = t2;

}

if (…) {

Transaction t3 = new Transaction();

t3.s = new State(); t3.s.b = true; y = t3;

} else { Transaction t4 = new Transaction();

t4.s = new State(); t4.s.b = false; y = t4;

}

if (x.s.b) …

if (y.s.b) …

if (x.s.b) …

Include all statements!

Alias analysis

Compute alias sets for x and y:

Transaction x;

Transaction y;

if (…) {

Transaction t1 = new Transaction();

t1.s = new State(); t1.s.b = true; x = t1;

} else { Transaction t2 = new Transaction();

t2.s = new State(); t2.s.b = false; x = t2;

}

if (…) {

Transaction t3 = new Transaction();

t3.s = new State(); t3.s.b = true; y = t3;

} else { Transaction t4 = new Transaction();

t4.s = new State(); t4.s.b = false; y = t4;

}

if (x.s.b) …

if (y.s.b) …

if (x.s.b) …

x = {t1, t2}

y = {t3, t4}

if (choose({t1,t2}).s.b)

if (choose({t3,t4}).s.b)

if (choose({t1,t2}).s.b)

Example

class Transaction[] {

…

Statehi s;

…

}

class State[] at {

…

relevant bool b;

…

}

Example

Transactionhr1ix;

Transactionhr2iy;

if (…) {

Transactionhr1i t1 = new Transactionh1i();

t1.s = new Stateh1i(); t1.s.b = true; x = t1;

} else { Transactionhr1i t2 = new Transactionh1i();

t2.s = new Stateh1i(); t2.s.b = false; x = t2;

}

if (…) {

Transactionhr2i t3 = new Transactionh2i();

t3.s = new Stateh2i(); t3.s.b = true; y = t3;

} else { Transactionhr2i t4 = new Transaction();

t4.s = new Stateh2i(); t4.s.b = false; y = t4;

}

if (x.s.b) …

if (y.s.b) …

if (x.s.b) …

Regions

Transactionhr1ix;

Transactionhr2iy;

if (…) {

Transactionhr1i t1 = new Transactionh1i();

t1.s = new Stateh1i(); t1.s.b = true; x = t1;

} else { Transactionhr1i t2 = new Transactionh1i();

t2.s = new Stateh1i(); t2.s.b = false; x = t2;

}

if (…) {

Transactionhr2i t3 = new Transactionh2i();

t3.s = new Stateh2i(); t3.s.b = true; y = t3;

} else { Transactionhr2i t4 = new Transaction();

t4.s = new Stateh2i(); t4.s.b = false; y = t4;

}

if (x.s.b) …

if (y.s.b) …

if (x.s.b) …

if (…) {

s = new State();

s.b = true; r1[= s;

} else { s = new State();

s.b = false; r1[= s;

}

if (…) {

s = new State();

s.b = true; r2[= s;

} else { s = new State();

s.b = false; r2[= s;

}

if (choose(r1).b) …

if (choose(r2).b) …

if (choose(r1).b) …

Why Regions?

- Two phase alias analysis
- Static: Identify scope of alias sets
- Dynamic: Populate alias sets with objects

- Beneficial for model checker
- Avoid loss of precision when generating models
- Produce more precise alias information by exploiting the power of the model checker

- Solves aliasing and indirection problems
- Allows fine-grained tuning of trade-off between precision and performance

Our Abstraction

- Based on RegJava
- Region type system for a Java-like language
- Includes proof of soundness

- Given a statement or expression p, we define «p¬ to be its abstraction
- Distinguish three cases:
1. Relevant data

2. References to relevant data

3. All others

Example: Expressions

Example:

Example: Statements

Example:

Soundness Theorem

- Theorem: For any execution of the original RegJava program, there is a corresponding execution of the model
- Proof Sketch: Since we replace occurrences of variables and fields with a choice over the corresponding region, any possible value in the original program will be considered by the model

Context-Sensitivity

- Region type systems make our approach context-sensitive

void foo[1, 2](Stateh1i s1, Stateh2i s2) {

s1.b = true;

if (s2.b) …

}

void foo_model(Set 1, Set2) {

choose(1).b = true;

if (choose(2).b) …

}

Context-Sensitivity, Part 2

- But we still have problems now and then:

void foo[](Statehi s1, Statehi s2) {

Statehi tmp;

if (…) { tmp = s1; } else { tmp = s2; }

tmp.b = true;

}

void foo_model(Set ) {

choose().b = true;

}

Context-Sensitivity, Part 3

- We can create an even more dynamic model

void foo[1, 2](Stateh1i s1, Stateh2i s2) {

Statehi tmp;

if (…) { tmp = s1; } else { tmp = s2; }

tmp.b = true;

}

void foo_model(Set 1, Set 2) {

Set ;

if (…) { [= 1; } else { [= 2; }

choose().b = true;

}

Capturing Correlations

- Need to represent important correlations in the model
- Solution: Introduce local variables

Statehi s = …;

s.b = true;

s.f = 42;

Source:

choose().b = true;

choose().f = 42;

Statehi s = choose();

s.b = true;

s.f = 42;

Model:

Implementation

- Based on Dave Hanson and Todd Proebsting’s research C# compiler
- Five stages:
- Introduce region variables
- Gather constraints and solve
- Determine live regions at each AST node
- Insert letregion statements to limit region scope
- Translate to Zing

The Fine Print

- RegJava’s regions use a stack discipline
- Letregion statements tend to accumulate near the most general scopes in the program
- We’re looking at less restrictive region systems

- Region parameters accumulate upward in the class hierarchy
- Interfaces can’t be modeled properly
- We’re looking at alternative approaches to object-oriented region systems

Related Work

- Other model checking projects
- SLAM, BLAST, Bandera

- Regions in Cyclone
- Flow-sensitive Cqual

Conclusion

- Region type systems solves several model generation problems:
- Aliasing
- Indirection

- Efficient division of labor:
- Model generation phase (static)
- Model checking phase (dynamic)

- Other compiler analyses may benefit from this approach!

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