public void Run()
{
Dictionary<string, string> cfg = new Dictionary<string, string>() {
{ "AUTO_CONFIG", "true" } };
using (Context ctx = new Context(cfg))
{
IntExpr[] x = new IntExpr[20];
IntExpr[] y = new IntExpr[20];
for (uint i = 0; i < 20; i++)
{
x[i] = ctx.MkIntConst(string.Format("x_{0}", i));
y[i] = ctx.MkIntConst(string.Format("y_{0}", i));
}
BoolExpr f = ctx.MkAnd(ctx.MkGe(ctx.MkAdd(x), ctx.MkInt(0)),
ctx.MkGe(ctx.MkAdd(y), ctx.MkInt(0)));
Console.WriteLine("now: " + ctx.GetParamValue("PP_MAX_DEPTH"));
ctx.UpdateParamValue("PP_MAX_DEPTH", "1");
Console.WriteLine(f);
ctx.UpdateParamValue("PP_MAX_DEPTH", "100");
ctx.UpdateParamValue("PP_MAX_NUM_LINES", "10");
Console.WriteLine(f);
ctx.UpdateParamValue("PP_MAX_NUM_LINES", "20");
ctx.UpdateParamValue("PP_MAX_WIDTH", "300");
Console.WriteLine(f);
Console.WriteLine("now: " + ctx.GetParamValue("PP_MAX_WIDTH"));
}
}
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));
}
}
/// <summary>
/// Translates an ASTVector into a IntExpr[]
/// </summary>
public IntExpr[] ToIntExprArray()
{
uint n = Size;
IntExpr[] res = new IntExpr[n];
for (uint i = 0; i < n; i++)
{
res[i] = (IntExpr)Expr.Create(this.Context, this[i].NativeObject);
}
return(res);
}
/// <summary>
/// Create an expression representing <c>t1 rem t2</c>.
/// </summary>
/// <remarks>The arguments must have int type.</remarks>
public IntExpr MkRem(IntExpr t1, IntExpr t2)
{
Contract.Requires(t1 != null);
Contract.Requires(t2 != null);
Contract.Ensures(Contract.Result<IntExpr>() != null);
CheckContextMatch(t1);
CheckContextMatch(t2);
return new IntExpr(this, Native.Z3_mk_rem(nCtx, t1.NativeObject, t2.NativeObject));
}
/// <summary>
/// Coerce an integer to a real.
/// </summary>
/// <remarks>
/// There is also a converse operation exposed. It follows the semantics prescribed by the SMT-LIB standard.
///
/// You can take the floor of a real by creating an auxiliary integer Term <c>k</c> and
/// and asserting <c>MakeInt2Real(k) <= t1 < MkInt2Real(k)+1</c>.
/// The argument must be of integer sort.
/// </remarks>
public RealExpr MkInt2Real(IntExpr t)
{
Contract.Requires(t != null);
Contract.Ensures(Contract.Result<RealExpr>() != null);
CheckContextMatch(t);
return new RealExpr(this, Native.Z3_mk_int2real(nCtx, t.NativeObject));
}
/// <summary>
/// Create an <paramref name="n"/> bit bit-vector from the integer argument <paramref name="t"/>.
/// </summary>
/// <remarks>
/// NB. This function is essentially treated as uninterpreted.
/// So you cannot expect Z3 to precisely reflect the semantics of this function
/// when solving constraints with this function.
///
/// The argument must be of integer sort.
/// </remarks>
public BitVecExpr MkInt2BV(uint n, IntExpr t)
{
Contract.Requires(t != null);
Contract.Ensures(Contract.Result<BitVecExpr>() != null);
CheckContextMatch(t);
return new BitVecExpr(this, Native.Z3_mk_int2bv(nCtx, n, t.NativeObject));
}
/// <summary>
/// Conversion of a real-sorted significand and an integer-sorted exponent into a term of FloatingPoint sort.
/// </summary>
/// <remarks>
/// Produces a term that represents the conversion of sig * 2^exp into a
/// floating-point term of sort s. If necessary, the result will be rounded
/// according to rounding mode rm.
/// </remarks>
/// <param name="rm">RoundingMode term.</param>
/// <param name="exp">Exponent term of Int sort.</param>
/// <param name="sig">Significand term of Real sort.</param>
/// <param name="s">FloatingPoint sort.</param>
public BitVecExpr MkFPToFP(FPRMExpr rm, IntExpr exp, RealExpr sig, FPSort s)
{
Contract.Ensures(Contract.Result<BitVecExpr>() != null);
return new BitVecExpr(this, Native.Z3_mk_fpa_to_fp_int_real(this.nCtx, rm.NativeObject, exp.NativeObject, sig.NativeObject, s.NativeObject));
}
/// <summary>
/// Extract subsequence.
/// </summary>
public SeqExpr MkExtract(SeqExpr s, IntExpr offset, IntExpr length)
{
Contract.Requires(s != null);
Contract.Requires(offset != null);
Contract.Requires(length != null);
Contract.Ensures(Contract.Result<SeqExpr>() != null);
CheckContextMatch(s, offset, length);
return new SeqExpr(this, Native.Z3_mk_seq_extract(nCtx, s.NativeObject, offset.NativeObject, length.NativeObject));
}
/// <summary>
/// Retrieve sequence of length one at index.
/// </summary>
public SeqExpr MkAt(SeqExpr s, IntExpr index)
{
Contract.Requires(s != null);
Contract.Requires(index != null);
Contract.Ensures(Contract.Result<SeqExpr>() != null);
CheckContextMatch(s, index);
return new SeqExpr(this, Native.Z3_mk_seq_at(nCtx, s.NativeObject, index.NativeObject));
}
/// <summary>
/// A basic example of how to use quantifiers.
/// </summary>
static void QuantifierExample1(Context ctx)
{
Console.WriteLine("QuantifierExample");
Sort[] types = new Sort[3];
IntExpr[] xs = new IntExpr[3];
Symbol[] names = new Symbol[3];
IntExpr[] vars = new IntExpr[3];
for (uint j = 0; j < 3; j++)
{
types[j] = ctx.IntSort;
names[j] = ctx.MkSymbol(String.Format("x_{0}", j));
xs[j] = (IntExpr)ctx.MkConst(names[j], types[j]);
vars[j] = (IntExpr)ctx.MkBound(2 - j, types[j]); // <-- vars reversed!
}
Expr body_vars = ctx.MkAnd(ctx.MkEq(ctx.MkAdd(vars[0], ctx.MkInt(1)), ctx.MkInt(2)),
ctx.MkEq(ctx.MkAdd(vars[1], ctx.MkInt(2)),
ctx.MkAdd(vars[2], ctx.MkInt(3))));
Expr body_const = ctx.MkAnd(ctx.MkEq(ctx.MkAdd(xs[0], ctx.MkInt(1)), ctx.MkInt(2)),
ctx.MkEq(ctx.MkAdd(xs[1], ctx.MkInt(2)),
ctx.MkAdd(xs[2], ctx.MkInt(3))));
Expr x = ctx.MkForall(types, names, body_vars, 1, null, null, ctx.MkSymbol("Q1"), ctx.MkSymbol("skid1"));
Console.WriteLine("Quantifier X: " + x.ToString());
Expr y = ctx.MkForall(xs, body_const, 1, null, null, ctx.MkSymbol("Q2"), ctx.MkSymbol("skid2"));
Console.WriteLine("Quantifier Y: " + y.ToString());
}
/// <summary>
/// Sudoku solving example.
/// </summary>
static void SudokuExample(Context ctx)
{
Console.WriteLine("SudokuExample");
// 9x9 matrix of integer variables
IntExpr[][] X = new IntExpr[9][];
for (uint i = 0; i < 9; i++)
{
X[i] = new IntExpr[9];
for (uint j = 0; j < 9; j++)
X[i][j] = (IntExpr)ctx.MkConst(ctx.MkSymbol("x_" + (i + 1) + "_" + (j + 1)), ctx.IntSort);
}
// each cell contains a value in {1, ..., 9}
Expr[][] cells_c = new Expr[9][];
for (uint i = 0; i < 9; i++)
{
cells_c[i] = new BoolExpr[9];
for (uint j = 0; j < 9; j++)
cells_c[i][j] = ctx.MkAnd(ctx.MkLe(ctx.MkInt(1), X[i][j]),
ctx.MkLe(X[i][j], ctx.MkInt(9)));
}
// each row contains a digit at most once
BoolExpr[] rows_c = new BoolExpr[9];
for (uint i = 0; i < 9; i++)
rows_c[i] = ctx.MkDistinct(X[i]);
// each column contains a digit at most once
BoolExpr[] cols_c = new BoolExpr[9];
for (uint j = 0; j < 9; j++)
{
IntExpr[] column = new IntExpr[9];
for (uint i = 0; i < 9; i++)
column[i] = X[i][j];
cols_c[j] = ctx.MkDistinct(column);
}
// each 3x3 square contains a digit at most once
BoolExpr[][] sq_c = new BoolExpr[3][];
for (uint i0 = 0; i0 < 3; i0++)
{
sq_c[i0] = new BoolExpr[3];
for (uint j0 = 0; j0 < 3; j0++)
{
IntExpr[] square = new IntExpr[9];
for (uint i = 0; i < 3; i++)
for (uint j = 0; j < 3; j++)
square[3 * i + j] = X[3 * i0 + i][3 * j0 + j];
sq_c[i0][j0] = ctx.MkDistinct(square);
}
}
BoolExpr sudoku_c = ctx.MkTrue();
foreach (BoolExpr[] t in cells_c)
sudoku_c = ctx.MkAnd(ctx.MkAnd(t), sudoku_c);
sudoku_c = ctx.MkAnd(ctx.MkAnd(rows_c), sudoku_c);
sudoku_c = ctx.MkAnd(ctx.MkAnd(cols_c), sudoku_c);
foreach (BoolExpr[] t in sq_c)
sudoku_c = ctx.MkAnd(ctx.MkAnd(t), sudoku_c);
// sudoku instance, we use '0' for empty cells
int[,] instance = {{0,0,0,0,9,4,0,3,0},
{0,0,0,5,1,0,0,0,7},
{0,8,9,0,0,0,0,4,0},
{0,0,0,0,0,0,2,0,8},
{0,6,0,2,0,1,0,5,0},
{1,0,2,0,0,0,0,0,0},
{0,7,0,0,0,0,5,2,0},
{9,0,0,0,6,5,0,0,0},
{0,4,0,9,7,0,0,0,0}};
BoolExpr instance_c = ctx.MkTrue();
for (uint i = 0; i < 9; i++)
for (uint j = 0; j < 9; j++)
instance_c = ctx.MkAnd(instance_c,
(BoolExpr)
ctx.MkITE(ctx.MkEq(ctx.MkInt(instance[i, j]), ctx.MkInt(0)),
ctx.MkTrue(),
ctx.MkEq(X[i][j], ctx.MkInt(instance[i, j]))));
Solver s = ctx.MkSolver();
s.Assert(sudoku_c);
s.Assert(instance_c);
if (s.Check() == Status.SATISFIABLE)
{
Model m = s.Model;
Expr[,] R = new Expr[9, 9];
for (uint i = 0; i < 9; i++)
for (uint j = 0; j < 9; j++)
R[i, j] = m.Evaluate(X[i][j]);
Console.WriteLine("Sudoku solution:");
for (uint i = 0; i < 9; i++)
{
for (uint j = 0; j < 9; j++)
Console.Write(" " + R[i, j]);
Console.WriteLine();
}
}
else
{
Console.WriteLine("Failed to solve sudoku");
throw new TestFailedException();
}
}
protected void Clique(Context ctx, Edge[] edges, uint n)
{
uint num = 0;
foreach (Edge e in edges)
{
if (e.v0 >= num)
num = e.v0 + 1;
if (e.v1 >= num)
num = e.v1 + 1;
}
Solver S = ctx.MkSolver();
IntExpr [] In = new IntExpr[num];
for (uint i = 0; i < num; i++)
{
In[i] = ctx.MkIntConst(String.Format("in_{0}", i));
S.Assert(ctx.MkLe(ctx.MkInt(0), In[i]));
S.Assert(ctx.MkLe(In[i], ctx.MkInt(1)));
}
ArithExpr sum = ctx.MkInt(0);
foreach (IntExpr e in In)
sum = ctx.MkAdd(sum, e);
S.Assert(ctx.MkGe(sum, ctx.MkInt(n)));
IntNum[][] matrix = new IntNum[num][];
for (uint i = 0; i < num; i++)
{
matrix[i] = new IntNum[i];
for (uint j = 0; j < i; j++)
matrix[i][j] = ctx.MkInt(0);
}
foreach (Edge e in edges)
{
uint s = e.v0;
uint t = e.v1;
if (s < t) {
s = e.v1;
t = e.v0;
}
matrix[s][t] = ctx.MkInt(1);
}
for (uint i = 0; i < num; i++)
for (uint j = 0; j < i; j++)
if (i != j)
if (matrix[i][j].Int == 0)
S.Assert(ctx.MkOr(ctx.MkEq(In[i], ctx.MkInt(0)),
ctx.MkEq(In[j], ctx.MkInt(0))));
Status r = S.Check();
if (r == Status.UNSATISFIABLE)
Console.WriteLine("no solution");
else if (r == Status.UNKNOWN)
{
Console.Write("failed");
Console.WriteLine(S.ReasonUnknown);
}
else
{
Console.WriteLine("solution found");
Model m = S.Model;
Console.Write("{ ");
foreach (FuncDecl cfd in m.ConstDecls)
{
IntNum q = (IntNum)m.ConstInterp(cfd);
if (q.Int == 1)
Console.Write(" " + cfd.Name);
}
Console.WriteLine(" }");
Console.Write("{ ");
for (uint i = 0; i < num; i++)
{
IntNum q = (IntNum)m.Evaluate(In[i]);
if (q.Int == 1)
Console.Write(" " + In[i]);
}
Console.WriteLine(" }");
}
}
/// <summary>
/// Translates an ASTVector into a IntExpr[]
/// </summary>
public IntExpr[] ToIntExprArray()
{
uint n = Size;
IntExpr[] res = new IntExpr[n];
for (uint i = 0; i < n; i++)
res[i] = (IntExpr)Expr.Create(this.Context, this[i].NativeObject);
return res;
}
