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public MkGoal ( bool models = true, bool unsatCores = false, bool proofs = false ) : |
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| models | bool | Indicates whether model generation should be enabled. |
| unsatCores | bool | Indicates whether unsat core generation should be enabled. |
| proofs | bool | Indicates whether proof generation should be enabled. |
| Résultat | ||
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()
{
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");
RatNum zero = ctx.MkReal(0);
RatNum two = ctx.MkReal(2);
Goal g = ctx.MkGoal();
g.Assert(ctx.MkGt(x, zero));
g.Assert(ctx.MkGt(y, zero));
g.Assert(ctx.MkEq(x, ctx.MkAdd(y, two)));
Console.WriteLine(g);
Tactic t1 = ctx.MkTactic("simplify");
Tactic t2 = ctx.MkTactic("solve-eqs");
Tactic t = ctx.AndThen(t1, t2);
Console.WriteLine(t[g]);
}
}
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");
RealExpr zero = ctx.MkReal(0);
RealExpr one = ctx.MkReal(1);
Goal g = ctx.MkGoal();
g.Assert(ctx.MkOr(ctx.MkEq(x, zero), ctx.MkEq(x, one)));
g.Assert(ctx.MkOr(ctx.MkEq(y, zero), ctx.MkEq(y, one)));
g.Assert(ctx.MkOr(ctx.MkEq(z, zero), ctx.MkEq(z, one)));
g.Assert(ctx.MkGt(ctx.MkAdd(x, y, z), ctx.MkReal(2)));
Tactic t = ctx.Repeat(ctx.OrElse(ctx.MkTactic("split-clause"), ctx.MkTactic("skip")));
Console.WriteLine(t[g]);
t = ctx.Repeat(ctx.OrElse(ctx.MkTactic("split-clause"), ctx.MkTactic("skip")), 1);
Console.WriteLine(t[g]);
t = ctx.Then(ctx.Repeat(ctx.OrElse(ctx.MkTactic("split-clause"), ctx.MkTactic("skip"))), ctx.MkTactic("solve-eqs"));
Console.WriteLine(t[g]);
}
}
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");
RealExpr zero = ctx.MkReal(0);
RealExpr one = ctx.MkReal(1);
Goal g = ctx.MkGoal();
g.Assert(ctx.MkOr(ctx.MkEq(x, zero), ctx.MkEq(x, one)));
g.Assert(ctx.MkOr(ctx.MkEq(y, zero), ctx.MkEq(y, one)));
g.Assert(ctx.MkOr(ctx.MkEq(z, zero), ctx.MkEq(z, one)));
g.Assert(ctx.MkGt(ctx.MkAdd(x, y, z), ctx.MkReal(2)));
Tactic t = ctx.Repeat(ctx.OrElse(ctx.MkTactic("split-clause"), ctx.MkTactic("skip")));
ApplyResult ar = t[g];
foreach (var sg in ar.Subgoals)
Console.WriteLine(sg);
}
}
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");
Goal g = ctx.MkGoal();
g.Assert(ctx.MkGt(ctx.MkAdd(x, y, z), ctx.MkReal(0)));
Probe p = ctx.MkProbe("num-consts");
Console.WriteLine("num-consts: " + p.Apply(g));
Tactic t = ctx.FailIf(ctx.Gt(p, ctx.Const(2)));
try
{
t.Apply(g);
}
catch (Z3Exception ex)
{
Console.WriteLine("Tactic failed: " + ex.Message);
}
Console.WriteLine("trying again...");
g = ctx.MkGoal();
g.Assert(ctx.MkGt(ctx.MkAdd(x, y), ctx.MkReal(0)));
Console.WriteLine(t[g]);
}
}
public void Run()
{
using (Context ctx = new Context())
{
RealExpr x = ctx.MkRealConst("x");
RealExpr y = ctx.MkRealConst("y");
Goal g = ctx.MkGoal();
g.Assert(ctx.MkGt(x, ctx.MkReal(10)), ctx.MkEq(y, ctx.MkAdd(x, ctx.MkReal(1))));
g.Assert(ctx.MkGt(y, ctx.MkReal(1)));
Console.WriteLine(ctx.MkProbe("num-consts").Apply(g));
Console.WriteLine(ctx.MkProbe("size").Apply(g));
Console.WriteLine(ctx.MkProbe("num-exprs").Apply(g));
}
}
public void Run()
{
using (Context ctx = new Context())
{
RealExpr x = ctx.MkRealConst("x");
RealExpr y = ctx.MkRealConst("y");
Goal g = ctx.MkGoal();
g.Assert(ctx.MkGt(x, ctx.MkReal(10)), ctx.MkEq(y, ctx.MkAdd(x, ctx.MkReal(1))));
g.Assert(ctx.MkGt(y, ctx.MkReal(1)));
Tactic t = ctx.MkTactic("simplify");
ApplyResult r = t.Apply(g);
Console.WriteLine(r);
Console.WriteLine(g.Size);
foreach (Goal s in r.Subgoals)
Console.WriteLine(s);
Console.WriteLine("Old goal: ");
Console.WriteLine(g);
t = ctx.Then(ctx.MkTactic("simplify"), ctx.MkTactic("solve-eqs"));
r = t.Apply(g);
Console.WriteLine(r);
Solver solver = ctx.MkSolver();
foreach (BoolExpr f in r.Subgoals[0].Formulas)
solver.Assert(f);
Console.WriteLine(solver);
Console.WriteLine(solver.Check());
Console.WriteLine(solver.Model);
Console.WriteLine("applying model convert");
Console.WriteLine(r.ConvertModel(0, solver.Model));
Console.WriteLine("done");
}
}
public void Run()
{
Dictionary<string, string> cfg = new Dictionary<string, string>() {
{ "AUTO_CONFIG", "true" } };
using (Context ctx = new Context(cfg))
{
Tactic t = ctx.Then(ctx.MkTactic("simplify"),
ctx.MkTactic("normalize-bounds"),
ctx.MkTactic("solve-eqs"));
IntExpr x = ctx.MkIntConst("x");
IntExpr y = ctx.MkIntConst("y");
IntExpr z = ctx.MkIntConst("z");
Goal g = ctx.MkGoal();
g.Assert(ctx.MkGt(x, ctx.MkInt(10)));
g.Assert(ctx.MkEq(y, ctx.MkAdd(x, ctx.MkInt(3))));
g.Assert(ctx.MkGt(z, y));
ApplyResult r = t[g];
Console.WriteLine(r);
Solver s = ctx.MkSolver();
s.Assert(r.Subgoals[0].Formulas);
Console.WriteLine(s.Check());
Console.WriteLine("subgoal model");
Model sgm = s.Model;
Console.WriteLine(sgm);
Console.WriteLine("converted model");
Model m = r.ConvertModel(0, sgm);
Console.WriteLine(m);
Console.WriteLine(m.Evaluate(x));
}
}
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");
Goal g = ctx.MkGoal();
g.Assert(ctx.MkOr(ctx.MkLt(x, ctx.MkReal(0)),
ctx.MkGt(x, ctx.MkReal(0))));
g.Assert(ctx.MkEq(x, ctx.MkAdd(y, ctx.MkReal(1))));
g.Assert(ctx.MkLt(y, ctx.MkReal(0)));
Tactic t = ctx.MkTactic("split-clause");
ApplyResult ar = t[g];
foreach (var sg in ar.Subgoals)
Console.WriteLine(sg);
}
}
/// <summary>
/// Some basic tests.
/// </summary>
static void BasicTests(Context ctx)
{
Console.WriteLine("BasicTests");
Symbol qi = ctx.MkSymbol(1);
Symbol fname = ctx.MkSymbol("f");
Symbol x = ctx.MkSymbol("x");
Symbol y = ctx.MkSymbol("y");
Sort bs = ctx.MkBoolSort();
Sort[] domain = { bs, bs };
FuncDecl f = ctx.MkFuncDecl(fname, domain, bs);
Expr fapp = ctx.MkApp(f, ctx.MkConst(x, bs), ctx.MkConst(y, bs));
Expr[] fargs2 = { ctx.MkFreshConst("cp", bs) };
Sort[] domain2 = { bs };
Expr fapp2 = ctx.MkApp(ctx.MkFreshFuncDecl("fp", domain2, bs), fargs2);
BoolExpr trivial_eq = ctx.MkEq(fapp, fapp);
BoolExpr nontrivial_eq = ctx.MkEq(fapp, fapp2);
Goal g = ctx.MkGoal(true);
g.Assert(trivial_eq);
g.Assert(nontrivial_eq);
Console.WriteLine("Goal: " + g);
Solver solver = ctx.MkSolver();
foreach (BoolExpr a in g.Formulas)
solver.Assert(a);
if (solver.Check() != Status.SATISFIABLE)
throw new TestFailedException();
ApplyResult ar = ApplyTactic(ctx, ctx.MkTactic("simplify"), g);
if (ar.NumSubgoals == 1 && (ar.Subgoals[0].IsDecidedSat || ar.Subgoals[0].IsDecidedUnsat))
throw new TestFailedException();
ar = ApplyTactic(ctx, ctx.MkTactic("smt"), g);
if (ar.NumSubgoals != 1 || !ar.Subgoals[0].IsDecidedSat)
throw new TestFailedException();
g.Assert(ctx.MkEq(ctx.MkNumeral(1, ctx.MkBitVecSort(32)),
ctx.MkNumeral(2, ctx.MkBitVecSort(32))));
ar = ApplyTactic(ctx, ctx.MkTactic("smt"), g);
if (ar.NumSubgoals != 1 || !ar.Subgoals[0].IsDecidedUnsat)
throw new TestFailedException();
Goal g2 = ctx.MkGoal(true, true);
ar = ApplyTactic(ctx, ctx.MkTactic("smt"), g2);
if (ar.NumSubgoals != 1 || !ar.Subgoals[0].IsDecidedSat)
throw new TestFailedException();
g2 = ctx.MkGoal(true, true);
g2.Assert(ctx.MkFalse());
ar = ApplyTactic(ctx, ctx.MkTactic("smt"), g2);
if (ar.NumSubgoals != 1 || !ar.Subgoals[0].IsDecidedUnsat)
throw new TestFailedException();
Goal g3 = ctx.MkGoal(true, true);
Expr xc = ctx.MkConst(ctx.MkSymbol("x"), ctx.IntSort);
Expr yc = ctx.MkConst(ctx.MkSymbol("y"), ctx.IntSort);
g3.Assert(ctx.MkEq(xc, ctx.MkNumeral(1, ctx.IntSort)));
g3.Assert(ctx.MkEq(yc, ctx.MkNumeral(2, ctx.IntSort)));
BoolExpr constr = ctx.MkEq(xc, yc);
g3.Assert(constr);
ar = ApplyTactic(ctx, ctx.MkTactic("smt"), g3);
if (ar.NumSubgoals != 1 || !ar.Subgoals[0].IsDecidedUnsat)
throw new TestFailedException();
ModelConverterTest(ctx);
// Real num/den test.
RatNum rn = ctx.MkReal(42, 43);
Expr inum = rn.Numerator;
Expr iden = rn.Denominator;
Console.WriteLine("Numerator: " + inum + " Denominator: " + iden);
if (inum.ToString() != "42" || iden.ToString() != "43")
throw new TestFailedException();
if (rn.ToDecimalString(3) != "0.976?")
throw new TestFailedException();
BigIntCheck(ctx, ctx.MkReal("-1231231232/234234333"));
BigIntCheck(ctx, ctx.MkReal("-123123234234234234231232/234234333"));
BigIntCheck(ctx, ctx.MkReal("-234234333"));
BigIntCheck(ctx, ctx.MkReal("234234333/2"));
string bn = "1234567890987654321";
if (ctx.MkInt(bn).BigInteger.ToString() != bn)
throw new TestFailedException();
if (ctx.MkBV(bn, 128).BigInteger.ToString() != bn)
throw new TestFailedException();
if (ctx.MkBV(bn, 32).BigInteger.ToString() == bn)
throw new TestFailedException();
// Error handling test.
try
{
IntExpr i = ctx.MkInt("1/2");
throw new TestFailedException(); // unreachable
}
catch (Z3Exception)
{
}
}
/// <summary>
/// A simple array example.
/// </summary>
/// <param name="ctx"></param>
static void ArrayExample1(Context ctx)
{
Console.WriteLine("ArrayExample1");
Goal g = ctx.MkGoal(true);
ArraySort asort = ctx.MkArraySort(ctx.IntSort, ctx.MkBitVecSort(32));
ArrayExpr aex = (ArrayExpr)ctx.MkConst(ctx.MkSymbol("MyArray"), asort);
Expr sel = ctx.MkSelect(aex, ctx.MkInt(0));
g.Assert(ctx.MkEq(sel, ctx.MkBV(42, 32)));
Symbol xs = ctx.MkSymbol("x");
IntExpr xc = (IntExpr)ctx.MkConst(xs, ctx.IntSort);
Symbol fname = ctx.MkSymbol("f");
Sort[] domain = { ctx.IntSort };
FuncDecl fd = ctx.MkFuncDecl(fname, domain, ctx.IntSort);
Expr[] fargs = { ctx.MkConst(xs, ctx.IntSort) };
IntExpr fapp = (IntExpr)ctx.MkApp(fd, fargs);
g.Assert(ctx.MkEq(ctx.MkAdd(xc, fapp), ctx.MkInt(123)));
Solver s = ctx.MkSolver();
foreach (BoolExpr a in g.Formulas)
s.Assert(a);
Console.WriteLine("Solver: " + s);
Status q = s.Check();
Console.WriteLine("Status: " + q);
if (q != Status.SATISFIABLE)
throw new TestFailedException();
Console.WriteLine("Model = " + s.Model);
Console.WriteLine("Interpretation of MyArray:\n" + s.Model.FuncInterp(aex.FuncDecl));
Console.WriteLine("Interpretation of x:\n" + s.Model.ConstInterp(xc));
Console.WriteLine("Interpretation of f:\n" + s.Model.FuncInterp(fd));
Console.WriteLine("Interpretation of MyArray as Term:\n" + s.Model.FuncInterp(aex.FuncDecl));
}
static void ModelConverterTest(Context ctx)
{
Console.WriteLine("ModelConverterTest");
ArithExpr xr = (ArithExpr)ctx.MkConst(ctx.MkSymbol("x"), ctx.MkRealSort());
ArithExpr yr = (ArithExpr)ctx.MkConst(ctx.MkSymbol("y"), ctx.MkRealSort());
Goal g4 = ctx.MkGoal(true);
g4.Assert(ctx.MkGt(xr, ctx.MkReal(10, 1)));
g4.Assert(ctx.MkEq(yr, ctx.MkAdd(xr, ctx.MkReal(1, 1))));
g4.Assert(ctx.MkGt(yr, ctx.MkReal(1, 1)));
ApplyResult ar = ApplyTactic(ctx, ctx.MkTactic("simplify"), g4);
if (ar.NumSubgoals == 1 && (ar.Subgoals[0].IsDecidedSat || ar.Subgoals[0].IsDecidedUnsat))
throw new TestFailedException();
ar = ApplyTactic(ctx, ctx.AndThen(ctx.MkTactic("simplify"), ctx.MkTactic("solve-eqs")), g4);
if (ar.NumSubgoals == 1 && (ar.Subgoals[0].IsDecidedSat || ar.Subgoals[0].IsDecidedUnsat))
throw new TestFailedException();
Solver s = ctx.MkSolver();
foreach (BoolExpr e in ar.Subgoals[0].Formulas)
s.Assert(e);
Status q = s.Check();
Console.WriteLine("Solver says: " + q);
Console.WriteLine("Model: \n" + s.Model);
Console.WriteLine("Converted Model: \n" + ar.ConvertModel(0, s.Model));
if (q != Status.SATISFIABLE)
throw new TestFailedException();
}
/// <summary>
/// Demonstrates how to use the ParOr tactic.
/// </summary>
static void ParOrExample(Context ctx)
{
Console.WriteLine("ParOrExample");
BitVecSort bvs = ctx.MkBitVecSort(32);
Expr x = ctx.MkConst("x", bvs);
Expr y = ctx.MkConst("y", bvs);
BoolExpr q = ctx.MkEq(x, y);
Goal g = ctx.MkGoal(true);
g.Assert(q);
Tactic t1 = ctx.MkTactic("qfbv");
Tactic t2 = ctx.MkTactic("qfbv");
Tactic p = ctx.ParOr(t1, t2);
ApplyResult ar = p.Apply(g);
if (ar.NumSubgoals != 1 || !ar.Subgoals[0].IsDecidedSat)
throw new TestFailedException();
}
/// <summary>
/// Shows how to use Solver(logic)
/// </summary>
/// <param name="ctx"></param>
static void LogicExample(Context ctx)
{
Console.WriteLine("LogicTest");
Microsoft.Z3.Global.ToggleWarningMessages(true);
BitVecSort bvs = ctx.MkBitVecSort(32);
Expr x = ctx.MkConst("x", bvs);
Expr y = ctx.MkConst("y", bvs);
BoolExpr eq = ctx.MkEq(x, y);
// Use a solver for QF_BV
Solver s = ctx.MkSolver("QF_BV");
s.Assert(eq);
Status res = s.Check();
Console.WriteLine("solver result: " + res);
// Or perhaps a tactic for QF_BV
Goal g = ctx.MkGoal(true);
g.Assert(eq);
Tactic t = ctx.MkTactic("qfbv");
ApplyResult ar = t.Apply(g);
Console.WriteLine("tactic result: " + ar);
if (ar.NumSubgoals != 1 || !ar.Subgoals[0].IsDecidedSat)
throw new TestFailedException();
}
