public void Run() { using (Context ctx = new Context()) { BoolExpr p = ctx.MkBoolConst("p"); BoolExpr q = ctx.MkBoolConst("q"); Console.WriteLine(ctx.MkAnd(p, q)); Console.WriteLine(ctx.MkOr(p, q)); Console.WriteLine(ctx.MkAnd(p, ctx.MkTrue())); Console.WriteLine(ctx.MkOr(p, ctx.MkFalse())); Console.WriteLine(ctx.MkNot(p)); Console.WriteLine(ctx.MkImplies(p, q)); Console.WriteLine(ctx.MkEq(p, q).Simplify()); Console.WriteLine(ctx.MkEq(p, q)); BoolExpr r = ctx.MkBoolConst("r"); Console.WriteLine(ctx.MkNot(ctx.MkEq(p, ctx.MkNot(ctx.MkEq(q, r))))); Console.WriteLine(ctx.MkNot(ctx.MkEq(ctx.MkNot(ctx.MkEq(p, q)), r))); Console.WriteLine(ctx.MkEq(p, ctx.MkTrue())); Console.WriteLine(ctx.MkEq(p, ctx.MkFalse())); Console.WriteLine(ctx.MkEq(p, ctx.MkTrue()).Simplify()); Console.WriteLine(ctx.MkEq(p, ctx.MkFalse()).Simplify()); Console.WriteLine(ctx.MkEq(p, p).Simplify()); Console.WriteLine(ctx.MkEq(p, q).Simplify()); Console.WriteLine(ctx.MkAnd(p, q, r)); Console.WriteLine(ctx.MkOr(p, q, r)); IntExpr x = ctx.MkIntConst("x"); Console.WriteLine(x is BoolExpr); Console.WriteLine(p is BoolExpr); Console.WriteLine(ctx.MkAnd(p, q) is BoolExpr); Console.WriteLine(p is BoolExpr); Console.WriteLine(ctx.MkAdd(x, ctx.MkInt(1)) is BoolExpr); Console.WriteLine(p.IsAnd); Console.WriteLine(ctx.MkOr(p, q).IsOr); Console.WriteLine(ctx.MkAnd(p, q).IsAnd); Console.WriteLine(x.IsNot); Console.WriteLine(p.IsNot); Console.WriteLine(ctx.MkNot(p)); Console.WriteLine(ctx.MkNot(p).IsDistinct); Console.WriteLine(ctx.MkEq(p, q).IsDistinct); Console.WriteLine(ctx.MkDistinct(p, q).IsDistinct); Console.WriteLine(ctx.MkDistinct(x, ctx.MkAdd(x, ctx.MkInt(1)), ctx.MkAdd(x, ctx.MkInt(2))).IsDistinct); Console.WriteLine(); Console.WriteLine(ctx.MkBool(true)); Console.WriteLine(ctx.MkBool(false)); Console.WriteLine(ctx.BoolSort); Context ctx1 = new Context(); Console.WriteLine(ctx1.MkBool(true)); Console.WriteLine(ctx1.BoolSort); Console.WriteLine(ctx1.MkBool(true).Sort == ctx1.BoolSort); Console.WriteLine(ctx1.MkBool(true).Sort == ctx.BoolSort); Console.WriteLine(ctx1.MkBool(true).Sort != ctx.BoolSort); } }
public void Run() { using (Context ctx = new Context()) { Sort U = ctx.MkUninterpretedSort("U"); Console.WriteLine(U); Expr a = ctx.MkConst("a", U); a = ctx.MkConst("a", U); Expr b = ctx.MkConst("b", U); Expr c = ctx.MkConst("c", U); IntExpr x = ctx.MkIntConst("x"); IntExpr y = ctx.MkIntConst("y"); Console.WriteLine(ctx.MkAnd(ctx.MkEq(a, b), ctx.MkEq(a, c))); Console.WriteLine(U == ctx.IntSort); Sort U2 = ctx.MkUninterpretedSort("U"); Console.WriteLine(U == U2); U2 = ctx.MkUninterpretedSort("U2"); Console.WriteLine(U == U2); Console.WriteLine(ctx.MkDistinct(a, b, c)); FuncDecl f = ctx.MkFuncDecl("f", new Sort[] { U, U }, U); Console.WriteLine(ctx.MkEq(f[a,b], b)); } }
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() { using (Context ctx = new Context()) { BoolExpr p = ctx.MkBoolConst("p"); Console.WriteLine(ctx.MkNot(p)); Console.WriteLine(ctx.MkNot(p)); IntExpr x = ctx.MkIntConst("x"); IntExpr y = ctx.MkIntConst("y"); Console.WriteLine(ctx.MkAdd(x, ctx.MkInt(1))); Console.WriteLine(ctx.MkAdd(ctx.MkInt(1), x)); Console.WriteLine(ctx.MkAdd(x, y)); Console.WriteLine(ctx.MkMul(ctx.MkInt(2), x)); Console.WriteLine(ctx.MkMul(x, ctx.MkInt(2))); Console.WriteLine(ctx.MkMul(x, y)); Console.WriteLine(ctx.MkDiv(x, y)); Console.WriteLine(ctx.MkMod(x, y)); Console.WriteLine(ctx.MkEq(x, y)); Console.WriteLine(ctx.MkDistinct(x, y, x)); Console.WriteLine(ctx.MkNot(ctx.MkEq(x, y))); Console.WriteLine(ctx.MkEq(x, y)); Console.WriteLine(ctx.MkAdd(x, ctx.MkInt(1))); Console.WriteLine(ctx.MkAdd(x, ctx.MkInt(1))); BoolExpr q = ctx.MkBoolConst("q"); Console.WriteLine(ctx.MkNot(p)); Console.WriteLine(ctx.MkNot(p)); Console.WriteLine(ctx.MkAnd(p, q)); Console.WriteLine(ctx.MkAnd(p, q)); Console.WriteLine(ctx.MkEq(x, y)); } }
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" }, { "MODEL", "true" } }; using (Context ctx = new Context(cfg)) { Constructor c_leaf = ctx.MkConstructor("leaf", "is_leaf", new string[] { "val" }, new Sort[] { ctx.IntSort }); Constructor c_node = ctx.MkConstructor("node", "is_node", new string[] { "left", "right" }, new Sort[] { null, null }, new uint[] { 1, 1 }); Constructor[] constr_1 = new Constructor[] { c_leaf, c_node }; Constructor c_nil = ctx.MkConstructor("nil", "is_nil"); Constructor c_cons = ctx.MkConstructor("cons", "is_cons", new string[] { "car", "cdr" }, new Sort[] { null, null }, new uint[] { 0, 1 }); Constructor[] constr_2 = new Constructor[] { c_nil, c_cons }; DatatypeSort[] ts = ctx.MkDatatypeSorts(new string[] { "Tree", "TreeList" }, new Constructor[][] { constr_1, constr_2 }); DatatypeSort Tree = ts[0]; DatatypeSort TreeList = ts[1]; FuncDecl leaf = Tree.Constructors[0]; FuncDecl node = Tree.Constructors[1]; FuncDecl val = Tree.Accessors[0][0]; FuncDecl nil = TreeList.Constructors[0]; FuncDecl cons = TreeList.Constructors[1]; Expr t1 = leaf[ctx.MkInt(10)]; Expr tl1 = cons[t1, nil.Apply()]; Expr t2 = node[tl1, nil.Apply()]; Console.WriteLine(t2); Console.WriteLine(val.Apply(t1).Simplify()); t1 = ctx.MkConst("t1", TreeList); t2 = ctx.MkConst("t2", TreeList); Expr t3 = ctx.MkConst("t3", TreeList); Solver s = ctx.MkSolver(); s.Assert(ctx.MkDistinct(t1, t2, t3)); Console.WriteLine(s.Check()); Console.WriteLine(s.Model); } }
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); } }
/// <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(); } }
/// <summary> /// Show that <code>distinct(a_0, ... , a_n)</code> is /// unsatisfiable when <code>a_i</code>'s are arrays from boolean to /// boolean and n > 4. /// </summary> /// <remarks>This example also shows how to use the <code>distinct</code> construct.</remarks> public static void ArrayExample3(Context ctx) { Console.WriteLine("ArrayExample3"); for (int n = 2; n <= 5; n++) { Console.WriteLine("n = {0}", n); Sort bool_type = ctx.MkBoolSort(); Sort array_type = ctx.MkArraySort(bool_type, bool_type); Expr[] a = new Expr[n]; /* create arrays */ for (int i = 0; i < n; i++) { a[i] = ctx.MkConst(String.Format("array_{0}", i), array_type); } /* assert distinct(a[0], ..., a[n]) */ BoolExpr d = ctx.MkDistinct(a); Console.WriteLine("{0}", (d)); /* context is satisfiable if n < 5 */ Model model = Check(ctx, d, n < 5 ? Status.SATISFIABLE : Status.UNSATISFIABLE); if (n < 5) { for (int i = 0; i < n; i++) { Console.WriteLine("{0} = {1}", a[i], model.Evaluate(a[i])); } } } }