/// <summary>
/// Tests the example in section 3.4.3 of Cousot and Halbwachs.
/// </summary>
public static void RunValidationB() {
IVariable/*!*/ X = new TestVariable("X");
IVariable/*!*/ Y = new TestVariable("Y");
IVariable/*!*/ Z = new TestVariable("Z");
Contract.Assert(X != null);
Contract.Assert(Y != null);
Contract.Assert(Z != null);
ArrayList /*LinearConstraint*/ cs = new ArrayList /*LinearConstraint*/ ();
LinearConstraint c = new LinearConstraint(LinearConstraint.ConstraintRelation.LE);
c.SetCoefficient(X, Rational.MINUS_ONE);
c.SetCoefficient(Y, Rational.ONE);
c.SetCoefficient(Z, Rational.MINUS_ONE);
c.rhs = Rational.ZERO;
cs.Add(c);
c = new LinearConstraint(LinearConstraint.ConstraintRelation.LE);
c.SetCoefficient(X, Rational.MINUS_ONE);
c.rhs = Rational.MINUS_ONE;
cs.Add(c);
c = new LinearConstraint(LinearConstraint.ConstraintRelation.LE);
c.SetCoefficient(X, Rational.MINUS_ONE);
c.SetCoefficient(Y, Rational.MINUS_ONE);
c.SetCoefficient(Z, Rational.ONE);
c.rhs = Rational.ZERO;
cs.Add(c);
c = new LinearConstraint(LinearConstraint.ConstraintRelation.LE);
c.SetCoefficient(Y, Rational.MINUS_ONE);
c.SetCoefficient(Z, Rational.ONE);
c.rhs = Rational.FromInt(3);
cs.Add(c);
LinearConstraintSystem lcs = new LinearConstraintSystem(cs);
Console.WriteLine("==================== The final linear constraint system ====================");
lcs.Dump();
}
public LinearConstraintSystem/*!*/ Widen(LinearConstraintSystem/*!*/ lcs) {
Contract.Requires(lcs != null);
Contract.Ensures(Contract.Result<LinearConstraintSystem>() != null);
#endif
if (this.IsBottom()) {
return cce.NonNull(lcs.Clone());
} else if (lcs.IsBottom()) {
return cce.NonNull(this.Clone());
} else if (this.IsTop() || lcs.IsTop()) {
return new LinearConstraintSystem(new ArrayList /*LinearConstraint*/ ());
}
// create new LCS, we will add only verified constraints to this...
ArrayList /*LinearConstraint*/ newConstraints = new ArrayList /*LinearConstraint*/ ();
Contract.Assume(this.Constraints != null);
foreach (LinearConstraint/*!*/ ccX in this.Constraints) {
Contract.Assert(ccX != null);
LinearConstraint cc = ccX;
#if DEBUG_PRINT
Console.WriteLine("Widen checking: Starting to check constraint: {0}", cc);
#endif
if (cc.IsConstant()) {
// (Can this ever occur in the stable state of a LinearConstraintSystem? --KRML)
// constraint is unaffected by the frame components
#if DEBUG_PRINT
Console.WriteLine("Widen checking: --Adding it!");
#endif
newConstraints.Add(cc);
continue;
}
// PHASE I: verify constraints against all frame vertices...
foreach (FrameElement/*!*/ vertex in cce.NonNull(lcs.FrameVertices)) {
Contract.Assert(vertex != null);
Rational lhs = cc.EvaluateLhs(vertex);
if (lhs > cc.rhs) {
// the vertex does not satisfy the inequality <=
if (cc.Relation == LinearConstraint.ConstraintRelation.LE) {
#if DEBUG_PRINT
Console.WriteLine("Widen checking: throwing out because of vertex: {0}", vertex);
#endif
goto CHECK_NEXT_CONSTRAINT;
} else {
// ... but it does satisfy the inequality >=
#if DEBUG_PRINT
Console.WriteLine("Widen checking: throwing out <= because of vertex: {0}", vertex);
#endif
cc = cc.ChangeRelationToAtLeast();
#if DEBUG_PRINT
Console.WriteLine("Widen checking: left with constraint: {0}", cc);
#endif
}
} else if (cc.Relation == LinearConstraint.ConstraintRelation.EQ && lhs < cc.rhs) {
// the vertex does not satisfy the inequality >=, and the constraint is an equality constraint
#if DEBUG_PRINT
Console.WriteLine("Widen checking: throwing out >= because of vertex: {0}", vertex);
#endif
cc = cc.ChangeRelation(LinearConstraint.ConstraintRelation.LE);
#if DEBUG_PRINT
Console.WriteLine("Widen checking: left with contraint: {0}", cc);
#endif
}
}
// PHASE II: verify constraints against all frame rays...
foreach (FrameElement/*!*/ ray in cce.NonNull(lcs.FrameRays)) {
Contract.Assert(ray != null);
// The following assumes the constraint to have some dimension with a non-zero coefficient
Rational lhs = cc.EvaluateLhs(ray);
if (lhs.IsPositive) {
// the ray does not satisfy the inequality <=
if (cc.Relation == LinearConstraint.ConstraintRelation.LE) {
#if DEBUG_PRINT
Console.WriteLine("Widen checking: throwing out because of ray: {0}", ray);
#endif
goto CHECK_NEXT_CONSTRAINT;
} else {
// ... but it does satisfy the inequality >=
#if DEBUG_PRINT
Console.WriteLine("Widen checking: throwing out <= because of ray: {0}", ray);
#endif
cc = cc.ChangeRelationToAtLeast();
#if DEBUG_PRINT
Console.WriteLine("Widen checking: left with contraint: {0}", cc);
#endif
}
} else if (cc.Relation == LinearConstraint.ConstraintRelation.EQ && lhs.IsNegative) {
// the ray does not satisfy the inequality >=, and the constraint is an equality constraint
#if DEBUG_PRINT
Console.WriteLine("Widen checking: throwing out >= because of ray: {0}", ray);
#endif
cc = cc.ChangeRelation(LinearConstraint.ConstraintRelation.LE);
#if DEBUG_PRINT
Console.WriteLine("Widen checking: left with constraint: {0}", cc);
#endif
}
}
// PHASE III: verify constraints against all frame lines...
foreach (FrameElement/*!*/ line in cce.NonNull(lcs.FrameLines)) {
Contract.Assert(line != null);
// The following assumes the constraint to have some dimension with a non-zero coefficient
Rational lhs = cc.EvaluateLhs(line);
if (!lhs.IsZero) {
// The line satisfies neither the inequality <= nor the equality ==
#if DEBUG_PRINT
Console.WriteLine("Widen checking: throwing out because of line: {0}", line);
#endif
goto CHECK_NEXT_CONSTRAINT;
}
}
// constraint has been verified, so add to new constraint system
#if DEBUG_PRINT
Console.WriteLine("Widen checking: --Adding it!");
#endif
newConstraints.Add(cc);
CHECK_NEXT_CONSTRAINT: {
}
#if DEBUG_PRINT
Console.WriteLine("Widen checking: done with that constraint");
#endif
}
return new LinearConstraintSystem(newConstraints);
}
/// <summary>
/// Clones "list" and the elements of "list".
/// </summary>
/// <param name="list"></param>
/// <returns></returns>
ArrayList /*LinearConstraint*/ DeeperListCopy_LC(ArrayList/*!*/ /*LinearConstraint*/ list) {
Contract.Requires(list != null);
ArrayList /*LinearConstraint*/ z = new ArrayList /*LinearConstraint*/ (list.Count);
foreach (LinearConstraint/*!*/ lc in list) {
Contract.Assert(lc != null);
z.Add(lc.Clone());
}
System.Diagnostics.Debug.Assert(z.Count == list.Count);
return z;
}