MkGoal() public method

Creates a new Goal.
Note that the Context must have been created with proof generation support if proofs is set to true here.
public MkGoal ( bool models = true, bool unsatCores = false, bool proofs = false ) : Goal
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.
return Goal
Example #1
0
    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]);
        }
    }
Example #2
0
    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]);
        }
    }
Example #3
0
    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]);
        }
    }
Example #4
0
    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);
        }
    }
Example #5
0
    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]);

        }
    }
Example #6
0
    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));
        }
    }
Example #7
0
    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");
        }
    }
Example #8
0
    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));
        }
    }
Example #9
0
    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);

        }
    }
Example #10
0
        /// <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)
            {
            }
        }
Example #11
0
        /// <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));
        }
Example #12
0
        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();
        }
Example #13
0
        /// <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();
        }
Example #14
0
        /// <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();
        }