public void Run()
{
Dictionary<string, string> cfg = new Dictionary<string, string>() {
{ "AUTO_CONFIG", "true" } };
using (Context ctx = new Context(cfg))
{
RealExpr x = ctx.MkRealConst("x");
RealExpr y = ctx.MkRealConst("y");
RealExpr z = ctx.MkRealConst("z");
RatNum zero = ctx.MkReal(0);
RatNum two = ctx.MkReal(2);
Goal g = ctx.MkGoal();
g.Assert(ctx.MkGe(ctx.MkSub(ctx.MkPower(x, two), ctx.MkPower(y, two)), zero));
Probe p = ctx.MkProbe("num-consts");
Probe p2 = ctx.Gt(p, ctx.Const(2));
Tactic t = ctx.Cond(p2, ctx.MkTactic("simplify"), ctx.MkTactic("factor"));
Console.WriteLine(t[g]);
g = ctx.MkGoal();
g.Assert(ctx.MkGe(ctx.MkAdd(x, x, y, z), zero));
g.Assert(ctx.MkGe(ctx.MkSub(ctx.MkPower(x, two), ctx.MkPower(y, two)), zero));
Console.WriteLine(t[g]);
}
}
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))
{
RealExpr x = ctx.MkRealConst("x");
RealExpr y = ctx.MkRealConst("y");
Solver s = ctx.MkSolver();
s.Assert(ctx.MkGt(x, ctx.MkReal(1)),
ctx.MkGt(y, ctx.MkReal(1)),
ctx.MkOr(ctx.MkGt(ctx.MkAdd(x, y), ctx.MkReal(1)),
ctx.MkLt(ctx.MkSub(x, y), ctx.MkReal(2))));
Console.WriteLine("asserted constraints: ");
foreach (var c in s.Assertions)
Console.WriteLine(c);
Console.WriteLine(s.Check());
Console.WriteLine(s.Statistics);
Console.WriteLine("stats for last check: ");
foreach (Statistics.Entry e in s.Statistics.Entries)
Console.WriteLine(e);
}
}
public void Run()
{
Dictionary<string, string> cfg = new Dictionary<string, string>() {
{ "AUTO_CONFIG", "true" } };
Context ctx = new Context(cfg);
RealExpr x = ctx.MkRealConst("x");
RealExpr y = ctx.MkRealConst("y");
RealExpr z = ctx.MkRealConst("z");
RatNum two = ctx.MkReal(2);
Console.WriteLine(ctx.MkAdd(ctx.MkSub(ctx.MkMul(x, y), ctx.MkPower(y, two)), ctx.MkPower(z, two)));
Console.WriteLine(ctx.MkSub(ctx.MkAdd(ctx.MkMul(x, y), ctx.MkPower(y, two)), ctx.MkPower(z, two)));
Console.WriteLine(ctx.MkMul(ctx.MkAdd(x, y), z));
}
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 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);
}
/// <summary>
/// Simplifier example.
/// </summary>
public static void SimplifierExample(Context ctx)
{
Console.WriteLine("SimplifierExample");
IntExpr x = ctx.MkIntConst("x");
IntExpr y = ctx.MkIntConst("y");
IntExpr z = ctx.MkIntConst("z");
IntExpr u = ctx.MkIntConst("u");
Expr t1 = ctx.MkAdd(x, ctx.MkSub(y, ctx.MkAdd(x, z)));
Expr t2 = t1.Simplify();
Console.WriteLine("{0} -> {1}", (t1), (t2));
}
public void Run()
{
using (Context ctx = new Context())
{
RealExpr x = ctx.MkRealConst("x");
RealExpr y = ctx.MkRealConst("y");
RealExpr z = ctx.MkRealConst("z");
IntExpr a = ctx.MkIntConst("a");
IntExpr b = ctx.MkIntConst("b");
IntExpr c = ctx.MkIntConst("c");
ctx.UpdateParamValue(":pp-flat-assoc", "false");
Console.WriteLine(ctx.MkAdd(x, y, ctx.MkInt2Real(a)));
Console.WriteLine(ctx.MkAdd(x, ctx.MkReal(1)));
Console.WriteLine(ctx.MkAdd(ctx.MkReal(2), y));
Console.WriteLine(ctx.MkMul(x, y));
Console.WriteLine(ctx.MkAdd(ctx.MkInt(2), ctx.MkInt(3)));
Console.WriteLine(ctx.MkMul(ctx.MkReal(2), x));
Console.WriteLine(ctx.MkAdd(ctx.MkInt2Real((IntExpr)ctx.MkAdd(ctx.MkInt(2), ctx.MkInt(3))), x));
Console.WriteLine(ctx.MkAdd((RealExpr)ctx.MkInt2Real((IntExpr)ctx.MkAdd(ctx.MkInt(2), ctx.MkInt(3))).Simplify(), x));
Console.WriteLine(ctx.MkAdd(a, b, ctx.MkInt(1)));
Console.WriteLine(ctx.MkDiv(x, y));
Console.WriteLine(ctx.MkDiv(x, ctx.MkReal(2)));
Console.WriteLine(ctx.MkDiv(ctx.MkReal(2), y));
Console.WriteLine(ctx.MkDiv(a, ctx.MkInt(2)));
Console.WriteLine(ctx.MkDiv(ctx.MkAdd(a, b), ctx.MkInt(2)));
Console.WriteLine(ctx.MkDiv(ctx.MkInt(3), a));
Console.WriteLine(ctx.MkMod(a, b));
Console.WriteLine(ctx.MkMod(a, ctx.MkInt(2)));
Console.WriteLine(ctx.MkMod(ctx.MkInt(3), a));
Console.WriteLine(ctx.MkSub(a, ctx.MkInt(2)));
Console.WriteLine(ctx.MkUnaryMinus(a));
Console.WriteLine(ctx.MkUnaryMinus(x));
Console.WriteLine(ctx.MkSub(a, b));
Console.WriteLine(a.IsAdd);
Console.WriteLine(ctx.MkAdd(a, b).IsAdd);
Console.WriteLine(ctx.MkSub(a, b).IsAdd);
Console.WriteLine(ctx.MkInt(10).IsAdd);
Console.WriteLine(ctx.MkMul(a, b).IsMul);
Console.WriteLine(ctx.MkMul(x, ctx.MkInt2Real(b)).IsMul);
Console.WriteLine(ctx.MkAdd(a, b).IsMul);
Console.WriteLine(ctx.MkDiv(a, ctx.MkInt(2)).IsDiv);
Console.WriteLine(ctx.MkDiv(ctx.MkReal(3), x).IsDiv);
Console.WriteLine(ctx.MkDiv(x,y).IsDiv);
Console.WriteLine(ctx.MkDiv(a, ctx.MkInt(2)).IsIDiv);
Console.WriteLine(ctx.MkAdd(ctx.MkInt(2), ctx.MkInt(3)).Simplify().IsAdd);
Console.WriteLine();
Console.WriteLine(a is ArithExpr);
Console.WriteLine(ctx.MkInt(2) is ArithExpr);
Console.WriteLine(ctx.MkAdd(a, b) is ArithExpr);
Console.WriteLine(ctx.MkBoolConst("p") is ArithExpr);
Console.WriteLine(ctx.MkInt(2) is IntNum);
Console.WriteLine(ctx.MkInt(2) is RatNum);
Console.WriteLine(ctx.MkReal(2, 3));
Console.WriteLine(ctx.MkReal(2, 3).IsReal);
Console.WriteLine(ctx.MkReal(2, 3) is ArithExpr);
Console.WriteLine(ctx.MkReal(2, 3).IsConst);
Console.WriteLine(ctx.MkReal(2, 3).Simplify() is RatNum);
Console.WriteLine(ctx.MkReal(2, 3).Simplify().IsRatNum);
Console.WriteLine(ctx.MkPower(ctx.MkReal(2), ctx.MkReal(1, 2)).Simplify().IsAlgebraicNumber);
Console.WriteLine(ctx.MkPower(ctx.MkReal(2), ctx.MkReal(1, 2)).Simplify() is AlgebraicNum);
Console.WriteLine(ctx.MkPower(ctx.MkReal(2), ctx.MkReal(1, 2)).IsAlgebraicNumber);
Console.WriteLine(ctx.MkPower(ctx.MkReal(2), ctx.MkReal(1, 2)) is AlgebraicNum);
Console.WriteLine(ctx.MkPower(ctx.MkReal(2), ctx.MkReal(1, 2)));
Console.WriteLine(ctx.MkPower(ctx.MkReal(2), ctx.MkReal(1, 3)));
}
}
/// <summary>
/// A basic example of how to use quantifiers.
/// </summary>
static void MyQuantifierExample(Context ctx)
{
Console.WriteLine("MyQuantifierExample");
RealExpr x1 = ctx.MkRealConst("x1");
RealExpr x2 = ctx.MkRealConst("x2");
BoolExpr body_vars = ctx.MkEq(ctx.MkAdd(x1, x2), ctx.MkReal(15));
BoolExpr body_const = ctx.MkEq(ctx.MkSub(x1, x2), ctx.MkReal(4));
Solver s = ctx.MkSolver();
s.Assert(body_vars);
s.Assert(body_const);
Status q = s.Check();
Model m = s.Model;
Console.WriteLine(m.ToString());
Console.WriteLine("Quantifier x1: " + m.Evaluate(x1, true));
Console.WriteLine("Quantifier x2: " + m.Evaluate(x2, true));
}
