public void Run()
{
using (Context ctx = new Context()) {
ctx.UpdateParamValue("DL_ENGINE", "1");
ctx.UpdateParamValue("DL_PDR_USE_FARKAS", "true");
// ctx.UpdateParamValue("VERBOSE","2");
var s = ctx.MkFixedpoint();
BoolSort B = ctx.BoolSort;
IntSort I = ctx.IntSort;
FuncDecl mc = ctx.MkFuncDecl("mc", new Sort[] { I, I }, B);
ArithExpr x = (ArithExpr)ctx.MkBound(0, I);
ArithExpr y = (ArithExpr)ctx.MkBound(1, I);
ArithExpr z = (ArithExpr)ctx.MkBound(2, I);
s.RegisterRelation(mc);
BoolExpr gt = ctx.MkGt(x, ctx.MkInt(100));
s.AddRule(ctx.MkImplies(gt, (BoolExpr)mc[x, ctx.MkSub(x, ctx.MkInt(10))]));
s.AddRule(ctx.MkImplies(ctx.MkAnd(ctx.MkNot(gt),
(BoolExpr)mc[ctx.MkAdd(x, ctx.MkInt(11)), y],
(BoolExpr)mc[y, z]),
(BoolExpr)mc[x, z]));
Console.WriteLine(s.Query(ctx.MkAnd((BoolExpr)mc[x, y], ctx.MkGt(y, ctx.MkInt(100)))));
Console.WriteLine(s.GetAnswer());
Console.WriteLine(s.Query(ctx.MkAnd((BoolExpr)mc[x, y], ctx.MkLt(y, ctx.MkInt(91)))));
Console.WriteLine(s.GetAnswer());
}
}
public void Run()
{
Dictionary <string, string> cfg = new Dictionary <string, string>()
{
{ "AUTO_CONFIG", "true" }
};
using (Context ctx = new Context(cfg))
{
IntExpr x = ctx.MkIntConst("x");
IntExpr y = ctx.MkIntConst("y");
Console.WriteLine(ctx.MkAdd(x, y) == ctx.MkAdd(x, y));
Console.WriteLine(ctx.MkAdd(x, y) == ctx.MkAdd(y, x));
ArithExpr n = ctx.MkAdd(x, y);
Console.WriteLine(n == ctx.MkAdd(x, y));
IntExpr x2 = ctx.MkIntConst("x");
Console.WriteLine(x == x2);
Console.WriteLine(ctx.MkIntConst("x") == ctx.MkRealConst("x"));
}
}
public static BoolExpr GetSpec(ERelationalOperators opr, ArithExpr arg_1, ArithExpr arg_2, Context ctx)
{
switch (opr)
{
case (ERelationalOperators.Eq):
return(ctx.MkEq(arg_1, arg_2));
case (ERelationalOperators.Gt):
return(ctx.MkGt(arg_1, arg_2));
case (ERelationalOperators.L):
return(ctx.MkLt(arg_1, arg_2));
case (ERelationalOperators.GtEq):
var first = ctx.MkEq(arg_1, arg_2);
var second = ctx.MkGt(arg_1, arg_2);
return(ctx.MkOr(first, second));
case (ERelationalOperators.LEq):
var firsts = ctx.MkEq(arg_1, arg_2);
var seconds = ctx.MkLt(arg_1, arg_2);
return(ctx.MkOr(firsts, seconds));
}
return(null);
}
public BoolExpr IsNearerThan(Z3Point3D that, double distanceThreshold)
{
ArithExpr distance = this.CalcApproximateDistance(that);
BoolExpr result = Z3.Context.MkLt(distance, Z3Math.Real(distanceThreshold));
return(result);
}
public void Run()
{
Dictionary<string, string> cfg = new Dictionary<string, string>() {
{ "AUTO_CONFIG", "true" } };
using (Context ctx = new Context(cfg))
{
IntExpr[] X = new IntExpr[5];
for (uint i = 0; i < 5; i++)
X[i] = ctx.MkIntConst(string.Format("x_{0}", i));
RealExpr[] Y = new RealExpr[5];
for (uint i = 0; i < 5; i++)
Y[i] = ctx.MkRealConst(string.Format("y_{0}", i));
BoolExpr[] P = new BoolExpr[5];
for (uint i = 0; i < 5; i++)
P[i] = ctx.MkBoolConst(string.Format("p_{0}", i));
foreach (Expr x in X)
Console.WriteLine(x);
foreach (Expr x in Y)
Console.WriteLine(x);
foreach (Expr x in P)
Console.WriteLine(x);
foreach (ArithExpr y in Y)
Console.WriteLine(ctx.MkPower(y, ctx.MkReal(2)));
ArithExpr[] Yp = new ArithExpr[Y.Length];
for (uint i = 0; i < Y.Length; i++)
Yp[i] = ctx.MkPower(Y[i], ctx.MkReal(2));
Console.WriteLine(ctx.MkAdd(Yp));
}
}
private BoolExpr handleRealRectangularObstacle(RectangularObstacle obstacle, Context ctx, IntExpr[] sourcesX,
IntExpr[] sourcesY, IntExpr[] destinationsX, IntExpr[] destinationsY)
{
RealExpr obstacleLeftX = ctx.MkReal(obstacle.realLocation.x.ToString(new CultureInfo("en-US")));
RealExpr obstacleRightX = ctx.MkReal((obstacle.realLocation.x + obstacle.width).ToString(new CultureInfo("en-US")));
RealExpr obstacleLeftY = ctx.MkReal(obstacle.realLocation.y.ToString(new CultureInfo("en-US")));
RealExpr obstacleRightY = ctx.MkReal((obstacle.realLocation.y + obstacle.length).ToString(new CultureInfo("en-US")));
RealExpr passDistance = ctx.MkReal(obstaclePassDistance);
BoolExpr[] avoidingObstaclesX = new BoolExpr[pathSegments];
BoolExpr[] avoidingObstaclesY = new BoolExpr[pathSegments];
BoolExpr[] avoidingObstaclesCombined = new BoolExpr[pathSegments];
for (int i = 0; i < pathSegments; i++)
{
ArithExpr xl_minus_xs = ctx.MkSub(obstacleLeftX, sourcesX[i]);
ArithExpr xl_minus_xd = ctx.MkSub(obstacleLeftX, destinationsX[i]);
ArithExpr xs_minus_xh = ctx.MkSub(sourcesX[i], obstacleRightX);
ArithExpr xd_minus_xh = ctx.MkSub(destinationsX[i], obstacleRightX);
avoidingObstaclesX[i] = ctx.MkOr(ctx.MkAnd(ctx.MkGe(xl_minus_xs, passDistance), ctx.MkGe(xl_minus_xd, passDistance)),
ctx.MkAnd(ctx.MkGe(xs_minus_xh, passDistance), ctx.MkGe(xd_minus_xh, passDistance)));
ArithExpr yl_minus_ys = ctx.MkSub(obstacleLeftY, sourcesY[i]);
ArithExpr yl_minus_yd = ctx.MkSub(obstacleLeftY, destinationsY[i]);
ArithExpr ys_minus_yh = ctx.MkSub(sourcesY[i], obstacleRightY);
ArithExpr yd_minus_yh = ctx.MkSub(destinationsY[i], obstacleRightY);
avoidingObstaclesY[i] = ctx.MkOr(ctx.MkAnd(ctx.MkGe(yl_minus_ys, passDistance), ctx.MkGe(yl_minus_yd, passDistance)),
ctx.MkAnd(ctx.MkGe(ys_minus_yh, passDistance), ctx.MkGe(yd_minus_yh, passDistance)));
avoidingObstaclesCombined[i] = ctx.MkOr(avoidingObstaclesX[i], avoidingObstaclesY[i]);
}
return(ctx.MkAnd(avoidingObstaclesCombined));
}
//internal static SimpleBodyRestriction TouchRestriction(JointType jointType, JointSide handSide)
//{
// double maxY = TrigonometryHelper.GetSine(5);
// return new TouchBodyRestriction(jointType, handSide);
//}
internal static BoolExpr EvaluateNorms(Z3Body body1, Z3Body body2)
{
double normsThreshold = 0.1;
BoolExpr result = Z3Math.True;
var jointTypes = EnumUtil.GetValues <JointType>();
foreach (var jointType in jointTypes)
{
// Calc the distance between the two norms
ArithExpr distance =
Z3Math.Abs(
Z3Math.Sub(
body1.Norms[jointType],
body2.Norms[jointType]));
// Create the boolean expression to evaluate the distance
result =
Z3.Context.MkAnd(
result,
Z3.Context.MkLt(
distance,
Z3Math.Real(normsThreshold)));
}
return(result);
}
/// <summary>
/// Adds a MSF variable with the coresponding assertion to the Z3 variables.
/// </summary>
/// <param name="vid">The MSF id of the variable</param>
internal void AddVariable(int vid)
{
// Is the variable an integer
bool isInteger = _model.GetIntegrality(vid);
// Construct the sort we will be using
Sort sort = isInteger ? (Sort)_context.IntSort : (Sort)_context.RealSort;
// Get the variable key
object key = _model.GetKeyFromIndex(vid);
// Try to construct the name
string name;
if (key != null)
{
name = String.Format("x_{0}_{1}", key, vid);
}
else
{
name = String.Format("x_{0}", vid);
}
ArithExpr variable = (ArithExpr)_context.MkConst(name, sort);
// Create the variable and add it to the map
Debug.Assert(!_variables.ContainsKey(vid), "Variable names should be unique.");
_variables.Add(vid, variable);
AssertArith(vid, variable);
}
/// <summary>
/// Get corresponding Z3 formula of a MSF row.
/// </summary>
/// <param name="rid">The MSF row id</param>
private ArithExpr MkGoalRow(int rid)
{
// Start with the 0 term
List <ArithExpr> row = new List <ArithExpr>();
// Now, add all the entries of this row
foreach (LinearEntry entry in GetRowEntries(rid))
{
// Get the variable and constant in the row
ArithExpr e = _solver.GetVariable(entry.Index);
if (!entry.Value.IsOne)
{
e = _solver.Context.MkMul(_solver.GetNumeral(entry.Value, e.Sort), e);
}
row.Add(e);
}
switch (row.Count)
{
case 0: return(_solver.GetNumeral(new Rational()));
case 1: return(row[0]);
default: return(_solver.Context.MkAdd(row.ToArray()));
}
}
/// <summary>
/// Adds a MSF row to the Z3 assertions.
/// </summary>
/// <param name="rid">The MSF row id</param>
private void AddRow(int rid)
{
// Start with the 0 term
ArithExpr row = MkGoalRow(rid);
_solver.AssertArith(rid, row);
}
public Z3Point3D GetInverted()
{
ArithExpr invertedX = Z3Math.Neg(this.X);
ArithExpr invertedY = Z3Math.Neg(this.Y);
ArithExpr invertedZ = Z3Math.Neg(this.Z);
return(new Z3Point3D(invertedX, invertedY, invertedZ));
}
public override void ToSMTConstraints(Context z3Context, Solver z3Solver, int maxNumVars, VariableCache variableGenerator)
{
this.constraintVariable = variableGenerator.GetVarChoiceVariable(orgId);
ArithExpr myVariable = z3Context.MkIntConst(this.constraintVariable);
z3Solver.Assert(z3Context.MkLe(z3Context.MkInt(0), myVariable));
z3Solver.Assert(z3Context.MkLe(myVariable, z3Context.MkInt(maxNumVars - 1)));
}
private static BoolExpr CreateAssignmentFormula(Context z3Context, Model lastModel, string choiceVariable)
{
ArithExpr z3Variable = z3Context.MkIntConst(choiceVariable);
ArithExpr assignment = (ArithExpr)lastModel.ConstInterp(z3Variable);
BoolExpr currentAssignment = z3Context.MkEq(z3Variable, assignment);
return(currentAssignment);
}
private static Dictionary <JointType, ArithExpr> CreateSyntheticNorms()
{
var result = new Dictionary <JointType, ArithExpr>();
ArithExpr spineBase = Z3Math.Real(0.0);
ArithExpr spineMid = Z3Math.Real(0.3);
ArithExpr spineShoulder = Z3Math.Real(0.3);
ArithExpr neck = Z3Math.Real(0.15);
ArithExpr head = Z3Math.Real(0.15);
ArithExpr shoulderLeft = Z3Math.Real(0.25);
ArithExpr elbowLeft = Z3Math.Real(0.25);
ArithExpr wristLeft = Z3Math.Real(0.25);
ArithExpr handLeft = Z3Math.Real(0.05);
ArithExpr handTipLeft = Z3Math.Real(0.05);
ArithExpr thumbLeft = Z3Math.Real(0.05);
ArithExpr hipLeft = Z3Math.Real(0.25);
ArithExpr kneeLeft = Z3Math.Real(0.35);
ArithExpr ankleLeft = Z3Math.Real(0.35);
ArithExpr footLeft = Z3Math.Real(0.1);
ArithExpr shoulderRight = Z3Math.Real(0.25);
ArithExpr elbowRight = Z3Math.Real(0.25);
ArithExpr wristRight = Z3Math.Real(0.25);
ArithExpr handRight = Z3Math.Real(0.05);
ArithExpr handTipRight = Z3Math.Real(0.05);
ArithExpr thumbRight = Z3Math.Real(0.05);
ArithExpr hipRight = Z3Math.Real(0.25);
ArithExpr kneeRight = Z3Math.Real(0.35);
ArithExpr ankleRight = Z3Math.Real(0.35);
ArithExpr footRight = Z3Math.Real(0.1);
result.Add(JointType.SpineBase, spineBase);
result.Add(JointType.SpineMid, spineMid);
result.Add(JointType.SpineShoulder, spineShoulder);
result.Add(JointType.Neck, neck);
result.Add(JointType.Head, head);
result.Add(JointType.ShoulderLeft, shoulderLeft);
result.Add(JointType.ElbowLeft, elbowLeft);
result.Add(JointType.WristLeft, wristLeft);
result.Add(JointType.HandLeft, handLeft);
result.Add(JointType.HandTipLeft, handTipLeft);
result.Add(JointType.ThumbLeft, thumbLeft);
result.Add(JointType.HipLeft, hipLeft);
result.Add(JointType.KneeLeft, kneeLeft);
result.Add(JointType.AnkleLeft, ankleLeft);
result.Add(JointType.FootLeft, footLeft);
result.Add(JointType.ShoulderRight, shoulderRight);
result.Add(JointType.ElbowRight, elbowRight);
result.Add(JointType.WristRight, wristRight);
result.Add(JointType.HandRight, handRight);
result.Add(JointType.HandTipRight, handTipRight);
result.Add(JointType.ThumbRight, thumbRight);
result.Add(JointType.HipRight, hipRight);
result.Add(JointType.KneeRight, kneeRight);
result.Add(JointType.AnkleRight, ankleRight);
result.Add(JointType.FootRight, footRight);
return(result);
}
/// <summary>
/// The method aims at finding a configuration which is similar to the given configuration, but does not contain the optionToBeRemoved. If further options need to be removed from the given configuration, they are outputed in removedElements.
/// </summary>
/// <param name="optionToBeRemoved">The binary configuration option that must not be part of the new configuration.</param>
/// <param name="originalConfig">The configuration for which we want to find a similar one.</param>
/// <param name="removedElements">If further options need to be removed from the given configuration to build a valid configuration, they are outputed in this list.</param>
/// <param name="vm">The variability model containing all options and their constraints.</param>
/// <returns>A configuration that is valid, similar to the original configuration and does not contain the optionToBeRemoved.</returns>
public List <BinaryOption> GenerateConfigWithoutOption(BinaryOption optionToBeRemoved, List <BinaryOption> originalConfig, out List <BinaryOption> removedElements, VariabilityModel vm)
{
removedElements = new List <BinaryOption>();
var originalConfigWithoutRemoved = originalConfig.Where(x => !x.Equals(optionToBeRemoved));
List <BoolExpr> variables;
Dictionary <BoolExpr, BinaryOption> termToOption;
Dictionary <BinaryOption, BoolExpr> optionToTerm;
Tuple <Context, BoolExpr> z3Tuple = Z3Solver.GetInitializedBooleanSolverSystem(out variables, out optionToTerm, out termToOption, vm, this.henard);
Context z3Context = z3Tuple.Item1;
BoolExpr z3Constraints = z3Tuple.Item2;
List <BoolExpr> constraints = new List <BoolExpr>();
constraints.Add(z3Constraints);
constraints.Add(z3Context.MkNot(optionToTerm[optionToBeRemoved]));
ArithExpr[] minGoals = new ArithExpr[variables.Count];
for (int r = 0; r < variables.Count; r++)
{
BinaryOption currOption = termToOption[variables[r]];
ArithExpr numericVariable = z3Context.MkIntConst(currOption.Name);
int weight = -1000;
if (!originalConfigWithoutRemoved.Contains(currOption))
{
weight = 1000;
}
else if (currOption.Equals(optionToBeRemoved))
{
weight = 100000;
}
constraints.Add(z3Context.MkEq(numericVariable, z3Context.MkITE(variables[r], z3Context.MkInt(weight), z3Context.MkInt(0))));
minGoals[r] = numericVariable;
}
Optimize optimizer = z3Context.MkOptimize();
optimizer.Assert(constraints.ToArray());
optimizer.MkMinimize(z3Context.MkAdd(minGoals));
if (optimizer.Check() != Status.SATISFIABLE)
{
return(null);
}
else
{
Model model = optimizer.Model;
List <BinaryOption> similarConfig = RetrieveConfiguration(variables, model, termToOption);
removedElements = originalConfigWithoutRemoved.Except(similarConfig).ToList();
return(similarConfig);
}
}
// Arithmetic helpers
public static ArithExpr Abs(ArithExpr expr)
{
Expr result = Z3.Context.MkITE(
Z3.Context.MkGe(expr, Z3Math.Zero),
expr,
Z3Math.Neg(expr));
return(result as ArithExpr);
}
public static ArithExpr Max(ArithExpr expr1, ArithExpr expr2)
{
Expr result = Z3.Context.MkITE(
Z3.Context.MkGe(expr1, expr2),
expr1,
expr2);
return(result as ArithExpr);
}
public static double GetRealValue(ArithExpr expr, Context localContext)
{
RatNum xRatNum = expr.Simplify() as RatNum;
IntNum d = xRatNum.Denominator;
IntNum n = xRatNum.Numerator;
BigRational bigRational = new BigRational(n.BigInteger, d.BigInteger);
return((double)bigRational);
}
public override void ToSMTConstraints(Context z3Context, Solver z3Solver, int maxNumVars, VariableCache variableGenerator)
{
this.constraintVariable = variableGenerator.GetFreshVariableName();
ArithExpr myVariable = z3Context.MkIntConst(this.constraintVariable);
z3Solver.Assert(z3Context.MkLe(z3Context.MkInt(0), myVariable));
z3Solver.Assert(z3Context.MkLe(myVariable, z3Context.MkInt(1)));
this.condition.ToSMTConstraints(z3Context, z3Solver, maxNumVars, variableGenerator);
}
//public Z3Point3D GetApproximateNormalized()
//{
// Z3Point3D result = this.GetManhattanNormalized();
// result.X = CalcApproximateCoordFromManhattanToEuclidianSystem(result.X, result.Y, result.Z);
// result.Y = CalcApproximateCoordFromManhattanToEuclidianSystem(result.Y, result.X, result.Z);
// result.Z = CalcApproximateCoordFromManhattanToEuclidianSystem(result.Z, result.Y, result.X);
// return result;
//}
public ArithExpr Norm()
{
ArithExpr result =
Z3Math.Max(
Z3Math.Abs(CalcApproximateCoordFromManhattanToEuclidianSystem(this.X, this.Y, this.Z)),
Z3Math.Abs(CalcApproximateCoordFromManhattanToEuclidianSystem(this.Y, this.X, this.Z)),
Z3Math.Abs(CalcApproximateCoordFromManhattanToEuclidianSystem(this.Z, this.Y, this.X)));
return(result);
}
public void Run()
{
Dictionary<string, string> cfg = new Dictionary<string, string>() {
{ "AUTO_CONFIG", "true" } };
using (Context ctx = new Context(cfg))
{
ArithExpr[] a = new ArithExpr[5];
for (uint x = 0; x < 5; x++)
a[x] = ctx.MkInt(x+1);
foreach (Expr e in a)
Console.WriteLine(e);
ArithExpr[] X = new ArithExpr[5];
for (uint i = 0; i < 5; i++)
X[i] = ctx.MkIntConst(string.Format("x{0}", i));
ArithExpr[] Y = new ArithExpr[5];
for (uint i = 0; i < 5; i++)
Y[i] = ctx.MkIntConst(string.Format("y{0}", i));
foreach (Expr e in X)
Console.WriteLine(e);
ArithExpr[] X_plus_Y = new ArithExpr[5];
for (uint i = 0; i < 5; i++)
X_plus_Y[i] = ctx.MkAdd(X[i], Y[i]);
foreach (Expr e in X_plus_Y)
Console.WriteLine(e);
BoolExpr[] X_gt_Y = new BoolExpr[5];
for (uint i = 0; i < 5; i++)
X_gt_Y[i] = ctx.MkGt(X[i], Y[i]);
foreach (Expr e in X_gt_Y)
Console.WriteLine(e);
Console.WriteLine(ctx.MkAnd(X_gt_Y));
Expr[][] matrix = new Expr[3][];
for (uint i = 0; i < 3; i++) {
matrix[i] = new Expr[3];
for (uint j = 0; j < 3; j++)
matrix[i][j] = ctx.MkIntConst(string.Format("x_{0}_{1}", i + 1, j + 1));
}
foreach(Expr[] row in matrix) {
foreach(Expr e in row)
Console.Write(" " + e);
Console.WriteLine();
}
}
}
public static void Run()
{
Z3Point3D constPoint = Z3Point3D.MkZ3Const("const"); // ("const X", "const Y", "const Z")
Z3Point3D normalized = new Z3Point3D();
ArithExpr higherCoord =
Z3Math.Max(
Z3Math.Max(
Z3Math.Abs(constPoint.X),
Z3Math.Abs(constPoint.Y)),
Z3Math.Abs(constPoint.Z));
normalized.X = Z3.Context.MkDiv(constPoint.X, constPoint.Y);
normalized.Y = Z3Math.One;//Z3.Context.MkDiv(constPoint.Y, higherCoord);
normalized.Z = Z3.Context.MkDiv(constPoint.Z, constPoint.Y);
normalized.X = CalcApproximateCoordFromManhattanToEuclidianSystem(normalized.X, normalized.Y, normalized.Z);
normalized.Y = CalcApproximateCoordFromManhattanToEuclidianSystem(normalized.Y, normalized.X, normalized.Z);
normalized.Z = CalcApproximateCoordFromManhattanToEuclidianSystem(normalized.Z, normalized.Y, normalized.X);
Z3Point3D up = Z3Point3D.DirectionPoint(Direction.Up); // (0, 1, 0)
Z3Point3D distVec = normalized - up;
ArithExpr distance =
Max(
Abs(CalcApproximateCoordFromManhattanToEuclidianSystem(distVec.X, distVec.Y, distVec.Z)),
Abs(CalcApproximateCoordFromManhattanToEuclidianSystem(distVec.Y, distVec.X, distVec.Z)),
Abs(CalcApproximateCoordFromManhattanToEuclidianSystem(distVec.Z, distVec.Y, distVec.X)));
BoolExpr expr = Z3.Context.MkLt(distance, Z3.Context.MkReal(1, 2));
Solver solver = Z3.Context.MkSolver();
solver.Assert(expr);
Status status = solver.Check();
Statistics stats = solver.Statistics;
switch (status)
{
case Status.UNKNOWN:
Console.WriteLine("Solver check for witness returned Status.UNKNOWN because: " + solver.ReasonUnknown);
throw new ArgumentException("Test Failed Expception");
case Status.UNSATISFIABLE:
Console.WriteLine("There is no valid witness for " + expr);
throw new ArgumentException("Test Failed Expception");
case Status.SATISFIABLE:
Console.WriteLine("OK, model: " + solver.Model);
break;
}
}
public void Run()
{
Dictionary <string, string> cfg = new Dictionary <string, string>()
{
{ "AUTO_CONFIG", "true" }
};
using (Context ctx = new Context(cfg))
{
IntExpr[] X = new IntExpr[5];
for (uint i = 0; i < 5; i++)
{
X[i] = ctx.MkIntConst(string.Format("x_{0}", i));
}
RealExpr[] Y = new RealExpr[5];
for (uint i = 0; i < 5; i++)
{
Y[i] = ctx.MkRealConst(string.Format("y_{0}", i));
}
BoolExpr[] P = new BoolExpr[5];
for (uint i = 0; i < 5; i++)
{
P[i] = ctx.MkBoolConst(string.Format("p_{0}", i));
}
foreach (Expr x in X)
{
Console.WriteLine(x);
}
foreach (Expr x in Y)
{
Console.WriteLine(x);
}
foreach (Expr x in P)
{
Console.WriteLine(x);
}
foreach (ArithExpr y in Y)
{
Console.WriteLine(ctx.MkPower(y, ctx.MkReal(2)));
}
ArithExpr[] Yp = new ArithExpr[Y.Length];
for (uint i = 0; i < Y.Length; i++)
{
Yp[i] = ctx.MkPower(Y[i], ctx.MkReal(2));
}
Console.WriteLine(ctx.MkAdd(Yp));
}
}
public override void ToSMTConstraints(Context z3Context, Solver z3Solver, int maxNumVars, VariableCache variableGenerator)
{
this.constraintVariable = variableGenerator.GetConstChoiceVariable(orgValue);
ArithExpr myVariable = z3Context.MkIntConst(this.constraintVariable);
//range for variation of constants
//TODO: allow 0?
int lowerBound = Math.Max((int)(this.orgValue / 2), 0);
int upperBound = Math.Max((int)(this.orgValue * 2), 0);
z3Solver.Assert(z3Context.MkLe(z3Context.MkInt(lowerBound), myVariable));
z3Solver.Assert(z3Context.MkLe(myVariable, z3Context.MkInt(upperBound)));
}
public override void ToSMTConstraints(Context z3Context, Solver z3Solver, int maxNumVars, VariableCache variableGenerator)
{
/* constraint variable in { 0, 1 }
* 0 -> increment
* 1 -> decrement
*/
this.constraintVariable = variableGenerator.GetFreshVariableName();
ArithExpr myVariable = z3Context.MkIntConst(this.constraintVariable);
z3Solver.Assert(z3Context.MkLe(z3Context.MkInt(0), myVariable));
z3Solver.Assert(z3Context.MkLe(myVariable, z3Context.MkInt(1)));
this.arg.ToSMTConstraints(z3Context, z3Solver, maxNumVars, variableGenerator);
}
/// <summary>
/// Based on a given (partial) configuration and a variability, we aim at finding all optimally maximal or minimal (in terms of selected binary options) configurations.
/// </summary>
/// <param name="config">The (partial) configuration which needs to be expanded to be valid.</param>
/// <param name="vm">Variability model containing all options and their constraints.</param>
/// <param name="minimize">If true, we search for the smallest (in terms of selected options) valid configuration. If false, we search for the largest one.</param>
/// <param name="unwantedOptions">Binary options that we do not want to become part of the configuration. Might be part if there is no other valid configuration without them</param>
/// <returns>A list of configurations that satisfies the VM and the goal (or null if there is none).</returns>
public List <List <BinaryOption> > MaximizeConfig(List <BinaryOption> config, VariabilityModel vm, bool minimize, List <BinaryOption> unwantedOptions)
{
List <BoolExpr> variables;
Dictionary <BoolExpr, BinaryOption> termToOption;
Dictionary <BinaryOption, BoolExpr> optionToTerm;
Tuple <Context, BoolExpr> z3Tuple = Z3Solver.GetInitializedBooleanSolverSystem(out variables, out optionToTerm, out termToOption, vm, this.henard);
Context z3Context = z3Tuple.Item1;
BoolExpr z3Constraints = z3Tuple.Item2;
List <BoolExpr> constraints = new List <BoolExpr>();
constraints.Add(z3Constraints);
List <BoolExpr> requireConfigs = new List <BoolExpr>();
if (config != null)
{
foreach (BinaryOption option in config)
{
requireConfigs.Add(optionToTerm[option]);
}
constraints.Add(z3Context.MkAnd(requireConfigs.ToArray()));
}
ArithExpr[] optimizationGoals = new ArithExpr[variables.Count];
for (int r = 0; r < variables.Count; r++)
{
BinaryOption currOption = termToOption[variables[r]];
ArithExpr numericVariable = z3Context.MkIntConst(currOption.Name);
constraints.Add(z3Context.MkEq(numericVariable, z3Context.MkITE(variables[r], z3Context.MkInt(1), z3Context.MkInt(0))));
optimizationGoals[r] = numericVariable;
}
Optimize optimizer = z3Context.MkOptimize();
optimizer.Assert(constraints.ToArray());
optimizer.MkMaximize(z3Context.MkAdd(optimizationGoals));
if (optimizer.Check() != Status.SATISFIABLE)
{
return(null);
}
List <BinaryOption> solution = RetrieveConfiguration(variables, optimizer.Model, termToOption);
return(new List <List <BinaryOption> >
{
solution
});
}
public void Run()
{
Dictionary <string, string> cfg = new Dictionary <string, string>()
{
{ "AUTO_CONFIG", "true" }
};
using (Context ctx = new Context(cfg))
{
ArithExpr[] Q = new ArithExpr[8];
for (uint i = 0; i < 8; i++)
{
Q[i] = ctx.MkIntConst(string.Format("Q_{0}", i + 1));
}
BoolExpr[] val_c = new BoolExpr[8];
for (uint i = 0; i < 8; i++)
{
val_c[i] = ctx.MkAnd(ctx.MkLe(ctx.MkInt(1), Q[i]),
ctx.MkLe(Q[i], ctx.MkInt(8)));
}
BoolExpr col_c = ctx.MkDistinct(Q);
BoolExpr[][] diag_c = new BoolExpr[8][];
for (uint i = 0; i < 8; i++)
{
diag_c[i] = new BoolExpr[i];
for (uint j = 0; j < i; j++)
{
diag_c[i][j] = (BoolExpr)ctx.MkITE(ctx.MkEq(ctx.MkInt(i), ctx.MkInt(j)),
ctx.MkTrue(),
ctx.MkAnd(ctx.MkNot(ctx.MkEq(ctx.MkSub(Q[i], Q[j]),
ctx.MkSub(ctx.MkInt(i), ctx.MkInt(j)))),
ctx.MkNot(ctx.MkEq(ctx.MkSub(Q[i], Q[j]),
ctx.MkSub(ctx.MkInt(j), ctx.MkInt(i))))));
}
}
Solver s = ctx.MkSolver();
s.Assert(val_c);
s.Assert(col_c);
foreach (var c in diag_c)
{
s.Assert(c);
}
Console.WriteLine(s.Check());
Console.WriteLine(s.Model);
}
}
public override void ToSMTConstraints(Context z3Context, Solver z3Solver, int maxNumVars, VariableCache variableGenerator)
{
/* constraint variable in { 0, 1 }
* 0 -> and
* 1 -> or
*/
this.constraintVariable = variableGenerator.GetFreshVariableName();
ArithExpr myVariable = z3Context.MkIntConst(this.constraintVariable);
z3Solver.Assert(z3Context.MkLe(z3Context.MkInt(0), myVariable));
z3Solver.Assert(z3Context.MkLe(myVariable, z3Context.MkInt(Enum.GetNames(typeof(WCCompound.Logic)).Length - 1)));
this.cond1.ToSMTConstraints(z3Context, z3Solver, maxNumVars, variableGenerator);
this.cond2.ToSMTConstraints(z3Context, z3Solver, maxNumVars, variableGenerator);
}
public override void ToSMTConstraints(Context z3Context, Solver z3Solver, int maxNumVars, VariableCache variableGenerator)
{
/* constraint variable in { 0, ..., 5 }
* -> eq, l, leq, neq, g, geq
*/
this.constraintVariable = variableGenerator.GetFreshVariableName();
ArithExpr myVariable = z3Context.MkIntConst(this.constraintVariable);
z3Solver.Assert(z3Context.MkLe(z3Context.MkInt(0), myVariable));
z3Solver.Assert(z3Context.MkLe(myVariable, z3Context.MkInt(Enum.GetNames(typeof(WCComparison.CompareType)).Length - 1)));
this.arg1.ToSMTConstraints(z3Context, z3Solver, maxNumVars, variableGenerator);
//Currently, arg2 may be concretized to a 0 constant, possibly resulting in an '== 0' or '!= 0' condition, which is a simple condition.
this.arg2.ToSMTConstraints(z3Context, z3Solver, maxNumVars, variableGenerator);
}
public override void ToSMTConstraints(Context z3Context, Solver z3Solver, int maxNumVars, VariableCache variableGenerator)
{
/* constraint variable in { 0, 1 }
* 0 -> plus
* 1 -> minus
*/
this.constraintVariable = variableGenerator.GetFreshVariableName();
ArithExpr myVariable = z3Context.MkIntConst(this.constraintVariable);
z3Solver.Assert(z3Context.MkLe(z3Context.MkInt(0), myVariable));
z3Solver.Assert(z3Context.MkLe(myVariable, z3Context.MkInt(Enum.GetNames(typeof(WEArith.ArithOp)).Length - 1)));
this.lhs.ToSMTConstraints(z3Context, z3Solver, maxNumVars, variableGenerator);
this.arg1.ToSMTConstraints(z3Context, z3Solver, maxNumVars, variableGenerator);
this.arg2.ToSMTConstraints(z3Context, z3Solver, maxNumVars, variableGenerator);
}
Expr ParseMulExpr()
{
Expr left = ParsePrimExpr();
if (!Is("*") && !Is("/"))
{
return(left);
}
ArithExpr expr = new ArithExpr();
expr.Op = (string)tokens[ix++].Value;
expr.Left = left;
expr.Right = ParsePrimExpr();
return(expr);
}
public static void ProveExample2(Context ctx)
{
Console.WriteLine("ProveExample2");
/* declare function g */
Sort I = ctx.IntSort;
FuncDecl g = ctx.MkFuncDecl("g", I, I);
/* create x, y, and z */
IntExpr x = ctx.MkIntConst("x");
IntExpr y = ctx.MkIntConst("y");
IntExpr z = ctx.MkIntConst("z");
/* create gx, gy, gz */
Expr gx = ctx.MkApp(g, x);
Expr gy = ctx.MkApp(g, y);
Expr gz = ctx.MkApp(g, z);
/* create zero */
IntExpr zero = ctx.MkInt(0);
/* assert not(g(g(x) - g(y)) = g(z)) */
ArithExpr gx_gy = ctx.MkSub((IntExpr)gx, (IntExpr)gy);
Expr ggx_gy = ctx.MkApp(g, gx_gy);
BoolExpr eq = ctx.MkEq(ggx_gy, gz);
BoolExpr c1 = ctx.MkNot(eq);
/* assert x + z <= y */
ArithExpr x_plus_z = ctx.MkAdd(x, z);
BoolExpr c2 = ctx.MkLe(x_plus_z, y);
/* assert y <= x */
BoolExpr c3 = ctx.MkLe(y, x);
/* prove z < 0 */
BoolExpr f = ctx.MkLt(z, zero);
Console.WriteLine("prove: not(g(g(x) - g(y)) = g(z)), x + z <= y <= x implies z < 0");
Prove(ctx, f, c1, c2, c3);
/* disprove z < -1 */
IntExpr minus_one = ctx.MkInt(-1);
f = ctx.MkLt(z, minus_one);
Console.WriteLine("disprove: not(g(g(x) - g(y)) = g(z)), x + z <= y <= x implies z < -1");
Disprove(ctx, f, c1, c2, c3);
}
public void Run()
{
Dictionary<string, string> cfg = new Dictionary<string, string>() {
{ "AUTO_CONFIG", "true" } };
using (Context ctx = new Context(cfg))
{
ArithExpr[] Q = new ArithExpr[8];
for (uint i = 0; i < 8; i++)
Q[i] = ctx.MkIntConst(string.Format("Q_{0}", i + 1));
BoolExpr[] val_c = new BoolExpr[8];
for (uint i = 0; i < 8; i++)
val_c[i] = ctx.MkAnd(ctx.MkLe(ctx.MkInt(1), Q[i]),
ctx.MkLe(Q[i], ctx.MkInt(8)));
BoolExpr col_c = ctx.MkDistinct(Q);
BoolExpr[][] diag_c = new BoolExpr[8][];
for (uint i = 0; i < 8; i++)
{
diag_c[i] = new BoolExpr[i];
for (uint j = 0; j < i; j++)
diag_c[i][j] = (BoolExpr)ctx.MkITE(ctx.MkEq(ctx.MkInt(i), ctx.MkInt(j)),
ctx.MkTrue(),
ctx.MkAnd(ctx.MkNot(ctx.MkEq(ctx.MkSub(Q[i], Q[j]),
ctx.MkSub(ctx.MkInt(i), ctx.MkInt(j)))),
ctx.MkNot(ctx.MkEq(ctx.MkSub(Q[i], Q[j]),
ctx.MkSub(ctx.MkInt(j), ctx.MkInt(i))))));
}
Solver s = ctx.MkSolver();
s.Assert(val_c);
s.Assert(col_c);
foreach (var c in diag_c)
s.Assert(c);
Console.WriteLine(s.Check());
Console.WriteLine(s.Model);
}
}
private Expr ParseExpr()
{
if (_index == _tokens.Count) throw new Exception("expected expression, got EOF");
var nexttoken = _tokens[_index + 1];
var isLoop = nexttoken is string && (string)nexttoken == "up" ||
nexttoken is string && (string)nexttoken == "down";
//check if this is a arithmetic-expr or simple expr
if ((nexttoken is string && (string)nexttoken == "to")|| isLoop || // loop
(nexttoken is Scanner.ArithToken && (Scanner.ArithToken)nexttoken == Scanner.ArithToken.Semi))
{
if (isLoop)
SetLoopType(nexttoken);
return ParseSimpleExpr();
}
var binexpr = new ArithExpr();
binexpr.Op = GetArithOperator(nexttoken);
binexpr.Left = ParseSimpleExpr();
_index++;
binexpr.Right = ParseExpr();
return binexpr;
}
Expr ParseMulExpr()
{
Expr left = ParsePrimExpr();
if (!Is("*") && !Is("/")) return left;
ArithExpr expr = new ArithExpr();
expr.Op = (string)tokens[ix++].Value;
expr.Left = left;
expr.Right = ParsePrimExpr();
return expr;
}
