C# Context.MkForall方法代码示例

 /// <summary>
 /// Generates a slightly randomized expression.
 /// </summary>
 static BoolExpr MkRandomExpr(Context ctx, System.Random rng)
 {
     int limit = 1073741823;
         Sort i = ctx.IntSort;
         Sort b = ctx.BoolSort;
         Symbol sr1 = ctx.MkSymbol(rng.Next(0, limit));
         Symbol sr2 = ctx.MkSymbol(rng.Next(0, limit));
         Symbol sr3 = ctx.MkSymbol(rng.Next(0, limit));
         FuncDecl r1 = ctx.MkFuncDecl(sr1, i, b);
         FuncDecl r2 = ctx.MkFuncDecl(sr2, i, b);
         FuncDecl r3 = ctx.MkFuncDecl(sr3, i, b);
         Symbol s = ctx.MkSymbol(rng.Next(0, limit));
         Expr x = ctx.MkConst(s, i);
         BoolExpr r1x = (BoolExpr)ctx.MkApp(r1, x);
         BoolExpr r2x = (BoolExpr)ctx.MkApp(r2, x);
         BoolExpr r3x = (BoolExpr)ctx.MkApp(r3, x);
         Expr[] vars = { x };
         BoolExpr rl1 = ctx.MkForall(vars, ctx.MkImplies(r1x, r2x));
         BoolExpr rl2 = ctx.MkForall(vars, ctx.MkImplies(r2x, r1x));
         BoolExpr rl3 = (BoolExpr)ctx.MkApp(r1, ctx.MkInt(3));
         BoolExpr q = (BoolExpr)ctx.MkApp(r3, ctx.MkInt(2));
         BoolExpr a1 = ctx.MkNot(q);
         BoolExpr q1 = ctx.MkExists(vars, ctx.MkAnd(r3x, r2x));
         BoolExpr q2 = ctx.MkExists(vars, ctx.MkAnd(r3x, r1x));
         BoolExpr[] all = { a1, q1, q2 };
         return ctx.MkAnd(all);
 }

    public void Run()
    {
        Dictionary<string, string> cfg = new Dictionary<string, string>() { };

        using (Context ctx = new Context(cfg))
        {
            FuncDecl f = ctx.MkFuncDecl("f", ctx.IntSort, ctx.IntSort);
            FuncDecl g = ctx.MkFuncDecl("g", ctx.IntSort, ctx.IntSort);

            IntExpr a = ctx.MkIntConst("a");
            IntExpr b = ctx.MkIntConst("b");
            IntExpr c = ctx.MkIntConst("c");

            IntExpr x = ctx.MkIntConst("x");

            Solver s = ctx.MkSolver();
            Params p = ctx.MkParams();
            p.Add("AUTO_CONFIG", false);
            p.Add("MBQI", false);
            s.Parameters = p;

            s.Assert(ctx.MkForall(new Expr[] { x }, ctx.MkEq(f[g[x]], x), 1, new Pattern[] { ctx.MkPattern(f[g[x]]) }));
            s.Assert(ctx.MkEq(a, g[b]));
            s.Assert(ctx.MkEq(b, c));
            s.Assert(ctx.MkDistinct(f[a], c));

            Console.WriteLine(s);
            Console.WriteLine(s.Check());
        }
    }

    public void Run()
    {
        Dictionary<string, string> cfg = new Dictionary<string, string>() {
            { "AUTO_CONFIG", "true" } };

        using (Context ctx = new Context(cfg))
        {
            Sort A = ctx.MkUninterpretedSort("A");
            Sort B = ctx.MkUninterpretedSort("B");

            FuncDecl f = ctx.MkFuncDecl("f", A, B);

            Expr a1 = ctx.MkConst("a1", A);
            Expr a2 = ctx.MkConst("a2", A);
            Expr b = ctx.MkConst("b", B);
            Expr x = ctx.MkConst("x", A);
            Expr y = ctx.MkConst("y", A);

            Solver s = ctx.MkSolver();

            s.Assert(ctx.MkNot(ctx.MkEq(a1, a2)));
            s.Assert(ctx.MkEq(f[a1], b));
            s.Assert(ctx.MkEq(f[a2], b));
            s.Assert(ctx.MkForall(new Expr[] { x, y }, ctx.MkImplies(ctx.MkEq(f[x], f[y]),
                                                                     ctx.MkEq(x, y)),
                                                       1,
                                                       new Pattern[] { ctx.MkPattern(f[x], f[y]) }));
            Console.WriteLine(s);
            Console.WriteLine(s.Check());
        }
    }

    public void Run()
    {
        Dictionary<string, string> cfg = new Dictionary<string, string>() {
            { "AUTO_CONFIG", "true" } };

        using (Context ctx = new Context(cfg))
        {
            FuncDecl f = ctx.MkFuncDecl("f", new Sort[] { ctx.IntSort, ctx.IntSort }, ctx.IntSort);
            IntExpr x = ctx.MkIntConst("x");
            IntExpr y = ctx.MkIntConst("y");

            Console.WriteLine(ctx.MkForall(new Expr[] { x, y }, ctx.MkEq(f[x, y], ctx.MkInt(0))));
            Console.WriteLine(ctx.MkExists(new Expr[] { x }, ctx.MkGe((ArithExpr)f[x, x], ctx.MkInt(0))));

            IntExpr a = ctx.MkIntConst("a");
            IntExpr b = ctx.MkIntConst("b");

            Solver s = ctx.MkSolver();
            s.Assert(ctx.MkForall(new Expr[] { x }, ctx.MkEq(f[x, x], ctx.MkInt(0))));
            s.Assert(ctx.MkEq(f[a, b], ctx.MkInt(1)));
            Console.WriteLine(s.Check());
            Console.WriteLine(s.Model);
        }
    }

    public void Run()
    {
        using (Context ctx = new Context())
        {
            FuncDecl f = ctx.MkFuncDecl("f", new Sort[] { ctx.IntSort, ctx.RealSort }, ctx.IntSort);

            try
            {
                Console.WriteLine(f.Domain[3]);
            }
            catch (IndexOutOfRangeException ex)
            {
                Console.WriteLine("failed: " + ex.Message);
            }

            IntExpr x = ctx.MkIntConst("x");

            Console.WriteLine(f[ctx.MkInt(1), ctx.MkReal(1)]);
            Console.WriteLine(f[ctx.MkInt(1), ctx.MkReal(1)].Sort);
            Console.WriteLine(f[ctx.MkInt(1), ctx.MkReal(1)].NumArgs);
            foreach (Expr e in f[ctx.MkAdd(x, ctx.MkInt(1)), ctx.MkReal(1)].Args)
            Console.WriteLine(e);
            Console.WriteLine(f[ctx.MkAdd(x, ctx.MkInt(1)), ctx.MkReal(1)].Args[0]);
            Console.WriteLine(f[ctx.MkAdd(x, ctx.MkInt(1)), ctx.MkReal(1)].Args[0].Equals(ctx.MkAdd(x, ctx.MkInt(1))));
            Console.WriteLine(f[ctx.MkAdd(x, ctx.MkInt(1)), ctx.MkReal(1)].FuncDecl[ctx.MkInt(2), ctx.MkInt2Real((IntExpr)ctx.MkAdd(x, ctx.MkInt(1)))]);

            Console.WriteLine(ctx.MkInt(1).IsExpr);
            Console.WriteLine(ctx.MkAdd(x, ctx.MkInt(1)).IsExpr);
            Console.WriteLine(ctx.MkForall(new Expr[] { x }, ctx.MkGt(x, ctx.MkInt(0))).IsExpr);
            Console.WriteLine(ctx.MkInt(1).IsConst);
            Console.WriteLine(x.IsConst);
            Console.WriteLine(ctx.MkAdd(x, ctx.MkInt(1)).IsConst);
            Console.WriteLine(ctx.MkForall(new Expr[] { x }, ctx.MkGt(x, ctx.MkInt(0))).IsConst);

            Console.WriteLine(ctx.MkForall(new Expr[] { x }, ctx.MkGt(x, ctx.MkInt(0))).Body.Args[0]);
            Console.WriteLine(ctx.MkForall(new Expr[] { x }, ctx.MkGt(x, ctx.MkInt(0))).Body.Args[0].IsExpr);
            Console.WriteLine(ctx.MkForall(new Expr[] { x }, ctx.MkGt(x, ctx.MkInt(0))).Body.Args[0].IsConst);
            Console.WriteLine(ctx.MkForall(new Expr[] { x }, ctx.MkGt(x, ctx.MkInt(0))).Body.Args[0].IsVar);
            Console.WriteLine(x.IsVar);
            Console.WriteLine(ctx.MkITE(ctx.MkTrue(), x, ctx.MkAdd(x, ctx.MkInt(1))));

            Context ctx1 = new Context();
            Console.WriteLine(ctx1.MkITE(ctx1.MkTrue(), x.Translate(ctx1), ctx.MkAdd(x, ctx.MkInt(1)).Translate(ctx1)));
            Console.WriteLine(ctx.MkITE(ctx.MkTrue(), ctx.MkInt(1), ctx.MkInt(1)));

            Console.WriteLine(ctx.MkDistinct(x, ctx.MkAdd(x, ctx.MkInt(1)), ctx.MkAdd(x, ctx.MkInt(2))));

            Console.WriteLine(ctx1.MkAnd(ctx1.MkDistinct(x.Translate(ctx1), ctx1.MkInt(1)),
                                         ctx1.MkGt((IntExpr)x.Translate(ctx1), ctx1.MkInt(0))));

        }
    }

    public void Run()
    {
        Dictionary<string, string> cfg = new Dictionary<string, string>() {
            { "AUTO_CONFIG", "true" } };

        using (Context ctx = new Context(cfg))
        {
            FuncDecl f = ctx.MkFuncDecl("f", new Sort[] { ctx.IntSort, ctx.IntSort }, ctx.IntSort);
            IntExpr x = ctx.MkIntConst("x");
            IntExpr y = ctx.MkIntConst("y");

            Quantifier qf = ctx.MkForall(new Expr[] { x, y }, ctx.MkEq(f[x, y], ctx.MkInt(0)));
            Console.WriteLine(qf.Body);

            Expr v1 = qf.Body.Args[0].Args[0];
            Console.WriteLine(v1);
            Console.WriteLine(v1 == ctx.MkBound(1, ctx.IntSort));
        }
    }

        //Constructor
        public Z3Context()
        {
            //Initialize Config and Context
            _config = new Config();
            _config.SetParamValue("MODEL", "true"); // corresponds to /m switch
            _config.SetParamValue("MACRO_FINDER", "true");
            _context = new Context(_config);

            //Setup custom conversion method BoolToInt (boolean -> integer)----------------------------------------------------------------
            FuncDecl boolToInt = _context.MkFuncDecl("BoolToInt", _context.MkBoolSort(), _context.MkIntSort());
            Term i = _context.MkConst("i", _context.MkBoolSort());
            Term fDef = _context.MkIte(_context.MkEq(i, _context.MkTrue()), _context.MkIntNumeral(1), _context.MkIntNumeral(0)); // x == true => 1, x == false => 0
            Term fStatement = _context.MkForall(0, new Term[] { i }, null, _context.MkEq(_context.MkApp(boolToInt, i), fDef));
            _context.AssertCnstr(fStatement);

            //
            _functions.Add("BoolToInt", new Z3Function(boolToInt));
            //-----------------------------------------------------------------------------------------------------------------------------
        }

    public void Run()
    {
        Dictionary<string, string> cfg = new Dictionary<string, string>() {
            { "AUTO_CONFIG", "true" } };

        using (Context ctx = new Context(cfg))
        {
            Sort T = ctx.MkUninterpretedSort("Type");
            FuncDecl subtype = ctx.MkFuncDecl("subtype", new Sort[] { T, T }, ctx.BoolSort);
            FuncDecl array_of = ctx.MkFuncDecl("array_of", T, T);
            Expr root = ctx.MkConst("root", T);

            Expr x = ctx.MkConst("x", T);
            Expr y = ctx.MkConst("y", T);
            Expr z = ctx.MkConst("z", T);

            BoolExpr[] axioms = new BoolExpr[] {
                ctx.MkForall(new Expr[] { x }, subtype[x, x]),
                ctx.MkForall(new Expr[] { x, y , z }, ctx.MkImplies(ctx.MkAnd((BoolExpr)subtype[x,y], (BoolExpr)subtype[y,z]), (BoolExpr)subtype[x,z])),
                ctx.MkForall(new Expr[] { x, y }, ctx.MkImplies(ctx.MkAnd((BoolExpr)subtype[x, y], (BoolExpr)subtype[y,x]), ctx.MkEq(x, y))),
                ctx.MkForall(new Expr[] { x, y, z }, ctx.MkImplies(ctx.MkAnd((BoolExpr)subtype[x,y],(BoolExpr)subtype[x,z]),
                                                                   ctx.MkOr((BoolExpr)subtype[y,z], (BoolExpr)subtype[z,y]))),
                ctx.MkForall(new Expr[] { x, y }, ctx.MkImplies((BoolExpr)subtype[x,y], (BoolExpr)subtype[array_of[x], array_of[y]])),
                ctx.MkForall(new Expr[] { x }, (BoolExpr) subtype[root, x])
            };

            Solver s = ctx.MkSolver();
            s.Assert(axioms);
            Console.WriteLine(s);
            Console.WriteLine(s.Check());
            Expr[] universe = s.Model.SortUniverse(T);
            foreach (var e in universe)
                Console.WriteLine(e);
            Console.WriteLine(s.Model);
        }
    }

        static void QuantifierExample2(Context ctx)
        {

            Console.WriteLine("QuantifierExample2");

            Expr q1, q2;
            FuncDecl f = ctx.MkFuncDecl("f", ctx.IntSort, ctx.IntSort);
            FuncDecl g = ctx.MkFuncDecl("g", ctx.IntSort, ctx.IntSort);

            // Quantifier with Exprs as the bound variables.
            {
                Expr x = ctx.MkConst("x", ctx.IntSort);
                Expr y = ctx.MkConst("y", ctx.IntSort);
                Expr f_x = ctx.MkApp(f, x);
                Expr f_y = ctx.MkApp(f, y);
                Expr g_y = ctx.MkApp(g, y);
                Pattern[] pats = new Pattern[] { ctx.MkPattern(new Expr[] { f_x, g_y }) };
                Expr[] no_pats = new Expr[] { f_y };
                Expr[] bound = new Expr[2] { x, y };
                Expr body = ctx.MkAnd(ctx.MkEq(f_x, f_y), ctx.MkEq(f_y, g_y));

                q1 = ctx.MkForall(bound, body, 1, null, no_pats, ctx.MkSymbol("q"), ctx.MkSymbol("sk"));

                Console.WriteLine("{0}", q1);
            }

            // Quantifier with de-Brujin indices.
            {
                Expr x = ctx.MkBound(1, ctx.IntSort);
                Expr y = ctx.MkBound(0, ctx.IntSort);
                Expr f_x = ctx.MkApp(f, x);
                Expr f_y = ctx.MkApp(f, y);
                Expr g_y = ctx.MkApp(g, y);
                Pattern[] pats = new Pattern[] { ctx.MkPattern(new Expr[] { f_x, g_y }) };
                Expr[] no_pats = new Expr[] { f_y };
                Symbol[] names = new Symbol[] { ctx.MkSymbol("x"), ctx.MkSymbol("y") };
                Sort[] sorts = new Sort[] { ctx.IntSort, ctx.IntSort };
                Expr body = ctx.MkAnd(ctx.MkEq(f_x, f_y), ctx.MkEq(f_y, g_y));

                q2 = ctx.MkForall(sorts, names, body, 1,
                                         null, // pats,
                                         no_pats,
                                         ctx.MkSymbol("q"),
                                         ctx.MkSymbol("sk")
                                        );
                Console.WriteLine("{0}", q2);
            }

            Console.WriteLine("{0}", (q1.Equals(q2)));
        }

        /// <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>
        /// Create axiom: function f is injective in the i-th argument.
        /// </summary>
        /// <remarks>
        /// The following axiom is produced:
        /// <c>
        /// forall (x_0, ..., x_n) finv(f(x_0, ..., x_i, ..., x_{n-1})) = x_i
        /// </c>
        /// Where, <code>finv</code>is a fresh function declaration.
        /// </summary>
        public static BoolExpr InjAxiom(Context ctx, FuncDecl f, int i)
        {
            Sort[] domain = f.Domain;
            uint sz = f.DomainSize;

            if (i >= sz)
            {
                Console.WriteLine("failed to create inj axiom");
                return null;
            }

            /* declare the i-th inverse of f: finv */
            Sort finv_domain = f.Range;
            Sort finv_range = domain[i];
            FuncDecl finv = ctx.MkFuncDecl("f_fresh", finv_domain, finv_range);

            /* allocate temporary arrays */
            Expr[] xs = new Expr[sz];
            Symbol[] names = new Symbol[sz];
            Sort[] types = new Sort[sz];

            /* fill types, names and xs */

            for (uint j = 0; j < sz; j++)
            {
                types[j] = domain[j];
                names[j] = ctx.MkSymbol(String.Format("x_{0}", j));
                xs[j] = ctx.MkBound(j, types[j]);
            }
            Expr x_i = xs[i];

            /* create f(x_0, ..., x_i, ..., x_{n-1}) */
            Expr fxs = f[xs];

            /* create f_inv(f(x_0, ..., x_i, ..., x_{n-1})) */
            Expr finv_fxs = finv[fxs];

            /* create finv(f(x_0, ..., x_i, ..., x_{n-1})) = x_i */
            Expr eq = ctx.MkEq(finv_fxs, x_i);

            /* use f(x_0, ..., x_i, ..., x_{n-1}) as the pattern for the quantifier */
            Pattern p = ctx.MkPattern(new Expr[] { fxs });

            /* create & assert quantifier */
            BoolExpr q = ctx.MkForall(
                types, /* types of quantified variables */
                names, /* names of quantified variables */
                eq,
                1,
                new Pattern[] { p } /* patterns */);

            return q;
        }

 public override BoolExpr toZ3Bool(Context ctx)
 {
     var qf = quantified_variables.Select(x => x.toZ3(ctx)).ToArray();
     if (this.quantifier == Quantifier.Exists)
         return ctx.MkExists(qf, inner.toZ3Bool(ctx));
     else if (this.quantifier == Quantifier.Forall)
         return ctx.MkForall(qf, inner.toZ3Bool(ctx));
     else
         throw new ArgumentException();
 }

        private BoolExpr[] GenerateAllConstraints(Context context, Environment environment, IReadOnlyList<LambdaExpression> lambdaExpressions)
        {
            var constraints = new List<BoolExpr>();

            foreach (LambdaExpression lambdaExpression in lambdaExpressions)
            {
                var forAllParameters = new Dictionary<string, Expr>();
                foreach (ParameterExpression parameter in lambdaExpression.Parameters)
                {
                    Sort typeSort;
                    if (!environment.Types.TryGetValue(parameter.Type, out typeSort))
                    {
                        throw new NotSupportedException("This type was not registered through objectTheorem.CreateInstance<T> :" + parameter.Type);
                    }

                    forAllParameters.Add(parameter.Name, context.MkConst(parameter.Type.ToString(), typeSort));
                }

                var generator = new LambdaExpressionToConstraintGenerator(context, environment);
                generator.LambdaParameterConstants = forAllParameters;
                Expr forAllBody = generator.Visit(lambdaExpression);

                var forAll = context.MkForall(forAllParameters.Values.ToArray(), forAllBody);

                constraints.Add(forAll);
            }

            return constraints.ToArray();
        }