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()) {
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()
{
using (Context ctx = new Context()) {
var s = ctx.MkFixedpoint();
BoolSort B = ctx.BoolSort;
Sort BV8 = ctx.MkBitVecSort(8);
FuncDecl edge = ctx.MkFuncDecl("edge", new Sort[]{BV8, BV8}, B);
FuncDecl path = ctx.MkFuncDecl("path", new Sort[]{BV8, BV8}, B);
BitVecExpr x = (BitVecExpr)ctx.MkBound(0,BV8);
BitVecExpr y = (BitVecExpr)ctx.MkBound(1,BV8);
BitVecExpr z = (BitVecExpr)ctx.MkBound(2,BV8);
s.RegisterRelation(edge);
s.RegisterRelation(path);
s.AddRule(ctx.MkImplies((BoolExpr)edge[x,y],(BoolExpr)path[x,y]));
s.AddRule(ctx.MkImplies(ctx.MkAnd((BoolExpr)path[x,y],(BoolExpr)path[y,z]),
(BoolExpr)path[x,z]));
for (uint i = 0; i < 128; ++i) {
s.AddFact(edge, i, i+1);
}
Console.WriteLine(s.Query((BoolExpr)path[ctx.MkBV(0,8),ctx.MkBV(129,8)]));
Console.WriteLine(s.GetAnswer());
Console.WriteLine(s.Query((BoolExpr)path[ctx.MkBV(0,8),ctx.MkBV(128,8)]));
Console.WriteLine(s.GetAnswer());
Console.WriteLine(s.Query((BoolExpr)path[x,ctx.MkBV(20,8)]));
Console.WriteLine(s.GetAnswer());
Console.WriteLine(s.Query(ctx.MkAnd((BoolExpr)path[x,y],
(BoolExpr)path[y,ctx.MkBV(20,8)])));
Console.WriteLine(s.GetAnswer());
}
}
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);
}
}
/// <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 static Expr EeAndGt(String left1, int left2, String right1, int right2)
{
using (Context ctx = new Context())
{
Expr a = ctx.MkConst(left1, ctx.MkIntSort());
Expr b = ctx.MkNumeral(left2, ctx.MkIntSort());
Expr c = ctx.MkConst(right1, ctx.MkIntSort());
Expr d = ctx.MkNumeral(right2, ctx.MkIntSort());
Solver s = ctx.MkSolver();
s.Assert(ctx.MkAnd(ctx.MkEq((ArithExpr)a, (ArithExpr)b), ctx.MkGt((ArithExpr)c, (ArithExpr)d)));
s.Check();
BoolExpr testing = ctx.MkAnd(ctx.MkEq((ArithExpr)a, (ArithExpr)b), ctx.MkGt((ArithExpr)c, (ArithExpr)d));
Model model = Check(ctx, testing, Status.SATISFIABLE);
Expr result2;
Model m2 = s.Model;
foreach (FuncDecl d2 in m2.Decls)
{
result2 = m2.ConstInterp(d2);
return result2;
}
}
return null;
}
public void Run()
{
Dictionary<string, string> settings = new Dictionary<string, string>() { { "AUTO_CONFIG", "true" }, { "MODEL", "true" } };
using (Context ctx = new Context(settings))
{
IntExpr a = ctx.MkIntConst("a");
IntExpr b = ctx.MkIntConst("b");
IntExpr c = ctx.MkIntConst("c");
RealExpr d = ctx.MkRealConst("d");
RealExpr e = ctx.MkRealConst("e");
BoolExpr q = ctx.MkAnd(
ctx.MkGt(a, ctx.MkAdd(b, ctx.MkInt(2))),
ctx.MkEq(a, ctx.MkAdd(ctx.MkMul(ctx.MkInt(2), c), ctx.MkInt(10))),
ctx.MkLe(ctx.MkAdd(c, b), ctx.MkInt(1000)),
ctx.MkGe(d, e));
Solver s = ctx.MkSolver();
s.Assert(q);
Console.WriteLine(s.Check());
Console.WriteLine(s.Model);
}
}
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>() {
{ "AUTO_CONFIG", "true" },
{ "MODEL", "true" } };
using (Context ctx = new Context(cfg))
{
RealExpr x = ctx.MkRealConst("x");
RealExpr y = ctx.MkRealConst("y");
Solver s = ctx.MkSolver();
s.Assert(ctx.MkAnd(ctx.MkEq(ctx.MkAdd(x, ctx.MkReal("10000000000000000000000")), y),
ctx.MkGt(y, ctx.MkReal("20000000000000000"))));
s.Check();
Console.WriteLine(s.Model);
Expr q = ctx.MkAdd(ctx.MkPower(ctx.MkReal(2), ctx.MkReal(1, 2)),
ctx.MkPower(ctx.MkReal(3), ctx.MkReal(1, 2)));
Console.WriteLine(q);
AlgebraicNum an = (AlgebraicNum)q.Simplify();
Console.WriteLine(an);
Console.WriteLine("[" + an.ToLower(10) + "," + an.ToUpper(10) + "]");
Console.WriteLine(an.ToDecimal(10));
}
}
public void Run()
{
Dictionary<string, string> cfg = new Dictionary<string, string>() {
{ "AUTO_CONFIG", "true" } };
using (Context ctx = new Context(cfg))
{
IntExpr[] x = new IntExpr[20];
IntExpr[] y = new IntExpr[20];
for (uint i = 0; i < 20; i++)
{
x[i] = ctx.MkIntConst(string.Format("x_{0}", i));
y[i] = ctx.MkIntConst(string.Format("y_{0}", i));
}
BoolExpr f = ctx.MkAnd(ctx.MkGe(ctx.MkAdd(x), ctx.MkInt(0)),
ctx.MkGe(ctx.MkAdd(y), ctx.MkInt(0)));
Console.WriteLine("now: " + ctx.GetParamValue("PP_MAX_DEPTH"));
ctx.UpdateParamValue("PP_MAX_DEPTH", "1");
Console.WriteLine(f);
ctx.UpdateParamValue("PP_MAX_DEPTH", "100");
ctx.UpdateParamValue("PP_MAX_NUM_LINES", "10");
Console.WriteLine(f);
ctx.UpdateParamValue("PP_MAX_NUM_LINES", "20");
ctx.UpdateParamValue("PP_MAX_WIDTH", "300");
Console.WriteLine(f);
Console.WriteLine("now: " + ctx.GetParamValue("PP_MAX_WIDTH"));
}
}
public BoolExpr DependsOn(Context ctx, BoolExpr pack, BoolExpr[] deps)
{
BoolExpr[] q = new BoolExpr[deps.Length];
for (uint i = 0; i < deps.Length; i++)
q[i] = ctx.MkImplies(pack, deps[i]);
return ctx.MkAnd(q);
}
public void Run()
{
Dictionary<string, string> cfg = new Dictionary<string, string>() {
{ "AUTO_CONFIG", "true" } };
using (Context ctx = new Context(cfg))
{
BitVecExpr x = ctx.MkBVConst("x", 32);
BitVecExpr[] powers = new BitVecExpr[32];
for (uint i = 0; i < 32; i++)
powers[i] = ctx.MkBVSHL(ctx.MkBV(1, 32), ctx.MkBV(i, 32));
BoolExpr step_zero = ctx.MkEq(ctx.MkBVAND(x, ctx.MkBVSub(x, ctx.MkBV(1, 32))), ctx.MkBV(0, 32));
BoolExpr fast = ctx.MkAnd(ctx.MkNot(ctx.MkEq(x, ctx.MkBV(0, 32))),
step_zero);
BoolExpr slow = ctx.MkFalse();
foreach (BitVecExpr p in powers)
slow = ctx.MkOr(slow, ctx.MkEq(x, p));
TestDriver.CheckString(fast, "(and (not (= x #x00000000)) (= (bvand x (bvsub x #x00000001)) #x00000000))");
Solver s = ctx.MkSolver();
s.Assert(ctx.MkNot(ctx.MkEq(fast, slow)));
TestDriver.CheckUNSAT(s.Check());
s = ctx.MkSolver();
s.Assert(ctx.MkNot(step_zero));
TestDriver.CheckSAT(s.Check());
}
}
public void Run()
{
Dictionary<string, string> cfg = new Dictionary<string, string>() {
{ "AUTO_CONFIG", "true" } };
using (Context ctx = new Context(cfg))
{
ArithExpr[] a = new ArithExpr[5];
for (uint x = 0; x < 5; x++)
a[x] = ctx.MkInt(x+1);
foreach (Expr e in a)
Console.WriteLine(e);
ArithExpr[] X = new ArithExpr[5];
for (uint i = 0; i < 5; i++)
X[i] = ctx.MkIntConst(string.Format("x{0}", i));
ArithExpr[] Y = new ArithExpr[5];
for (uint i = 0; i < 5; i++)
Y[i] = ctx.MkIntConst(string.Format("y{0}", i));
foreach (Expr e in X)
Console.WriteLine(e);
ArithExpr[] X_plus_Y = new ArithExpr[5];
for (uint i = 0; i < 5; i++)
X_plus_Y[i] = ctx.MkAdd(X[i], Y[i]);
foreach (Expr e in X_plus_Y)
Console.WriteLine(e);
BoolExpr[] X_gt_Y = new BoolExpr[5];
for (uint i = 0; i < 5; i++)
X_gt_Y[i] = ctx.MkGt(X[i], Y[i]);
foreach (Expr e in X_gt_Y)
Console.WriteLine(e);
Console.WriteLine(ctx.MkAnd(X_gt_Y));
Expr[][] matrix = new Expr[3][];
for (uint i = 0; i < 3; i++) {
matrix[i] = new Expr[3];
for (uint j = 0; j < 3; j++)
matrix[i][j] = ctx.MkIntConst(string.Format("x_{0}_{1}", i + 1, j + 1));
}
foreach(Expr[] row in matrix) {
foreach(Expr e in row)
Console.Write(" " + e);
Console.WriteLine();
}
}
}
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 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))
{
BitVecExpr x = ctx.MkBVConst("x", 32);
BitVecExpr y = ctx.MkBVConst("y", 32);
BitVecExpr zero = ctx.MkBV(0, 32);
BoolExpr trick = ctx.MkBVSLT(ctx.MkBVXOR(x, y), zero);
BoolExpr opposite = ctx.MkOr(ctx.MkAnd(ctx.MkBVSLT(x, zero), ctx.MkBVSGE(y, zero)),
ctx.MkAnd(ctx.MkBVSGE(x, zero), ctx.MkBVSLT(y, zero)));
Solver s = ctx.MkSolver();
s.Assert(ctx.MkNot(ctx.MkEq(trick, opposite)));
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 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);
}
}
public void Run()
{
Dictionary<string, string> cfg = new Dictionary<string, string>() {
{ "AUTO_CONFIG", "true" } };
using (Context ctx = new Context(cfg))
{
Expr x = ctx.MkConst("x", ctx.IntSort);
Console.WriteLine(x == ctx.MkIntConst("x"));
BoolExpr a = (BoolExpr)ctx.MkConst("a", ctx.BoolSort);
BoolExpr b = (BoolExpr)ctx.MkConst("b", ctx.BoolSort);
Console.WriteLine(ctx.MkAnd(a, b));
}
}
public void Run()
{
Dictionary<string, string> cfg = new Dictionary<string, string>() {
{ "AUTO_CONFIG", "true" } };
using (Context ctx = new Context(cfg))
{
BitVecExpr x = ctx.MkBVConst("x", 32);
BitVecExpr y = ctx.MkBVConst("y", 32);
BoolExpr q = ctx.MkAnd(ctx.MkEq(ctx.MkBVAdd(x, y), ctx.MkBV(2, 32)),
ctx.MkBVSGT(x, ctx.MkBV(0, 32)),
ctx.MkBVSGT(y, ctx.MkBV(0, 32)));
Console.WriteLine(q);
Solver s = ctx.MkSolver();
s.Assert(q);
Console.WriteLine(s.Check());
Console.WriteLine(s.Model);
q = ctx.MkEq(ctx.MkBVAND(x, y), ctx.MkBVNeg(y));
Console.WriteLine(q);
s = ctx.MkSolver();
s.Assert(q);
Console.WriteLine(s.Check());
Console.WriteLine(s.Model);
q = ctx.MkBVSLT(x, ctx.MkBV(0, 32));
Console.WriteLine(q);
s = ctx.MkSolver();
s.Assert(q);
Console.WriteLine(s.Check());
Console.WriteLine(s.Model);
q = ctx.MkBVULT(x, ctx.MkBV(0, 32));
Console.WriteLine(q);
s = ctx.MkSolver();
s.Assert(q);
Console.WriteLine(s.Check());
}
}
public void Run()
{
using (Context ctx = new Context()) {
var s = ctx.MkFixedpoint();
BoolSort B = ctx.BoolSort;
Sort BV8 = ctx.MkBitVecSort(8);
FuncDecl f = ctx.MkFuncDecl("f", BV8, B);
FuncDecl g = ctx.MkFuncDecl("g", BV8, B);
BitVecExpr b0 = (BitVecExpr)ctx.MkBound(0,BV8);
s.RegisterRelation(f);
s.RegisterRelation(g);
s.AddRule((BoolExpr)f[b0]);
BitVecExpr mask0 = ctx.MkBV(0xFE,8);
BoolExpr even = ctx.MkEq(b0,ctx.MkBVAND(b0,mask0));
s.AddRule(ctx.MkImplies(ctx.MkAnd((BoolExpr)f[b0],even), (BoolExpr)g[b0]));
Console.WriteLine(s.Query((BoolExpr)g[b0]));
Console.WriteLine(s.GetAnswer());
}
}
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>
/// Shows how to read an SMT1 file.
/// </summary>
static void SMT1FileTest(string filename)
{
Console.Write("SMT File test ");
using (Context ctx = new Context(new Dictionary<string, string>() { { "MODEL", "true" } }))
{
ctx.ParseSMTLIBFile(filename);
BoolExpr a = ctx.MkAnd(ctx.SMTLIBFormulas);
Console.WriteLine("read formula: " + a);
}
}
/// <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>
/// 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());
}
public static void FloatingPointExample2(Context ctx)
{
Console.WriteLine("FloatingPointExample2");
FPSort double_sort = ctx.MkFPSort(11, 53);
FPRMSort rm_sort = ctx.MkFPRoundingModeSort();
FPRMExpr rm = (FPRMExpr)ctx.MkConst(ctx.MkSymbol("rm"), rm_sort);
BitVecExpr x = (BitVecExpr)ctx.MkConst(ctx.MkSymbol("x"), ctx.MkBitVecSort(64));
FPExpr y = (FPExpr)ctx.MkConst(ctx.MkSymbol("y"), double_sort);
FPExpr fp_val = ctx.MkFP(42, double_sort);
BoolExpr c1 = ctx.MkEq(y, fp_val);
BoolExpr c2 = ctx.MkEq(x, ctx.MkFPToBV(rm, y, 64, false));
BoolExpr c3 = ctx.MkEq(x, ctx.MkBV(42, 64));
BoolExpr c4 = ctx.MkEq(ctx.MkNumeral(42, ctx.RealSort), ctx.MkFPToReal(fp_val));
BoolExpr c5 = ctx.MkAnd(c1, c2, c3, c4);
Console.WriteLine("c5 = " + c5);
/* Generic solver */
Solver s = ctx.MkSolver();
s.Assert(c5);
Console.WriteLine(s);
if (s.Check() != Status.SATISFIABLE)
throw new TestFailedException();
Console.WriteLine("OK, model: {0}", s.Model.ToString());
}
public static void FloatingPointExample1(Context ctx)
{
Console.WriteLine("FloatingPointExample1");
FPSort s = ctx.MkFPSort(11, 53);
Console.WriteLine("Sort: {0}", s);
FPNum x = (FPNum)ctx.MkNumeral("-1e1", s); /* -1 * 10^1 = -10 */
FPNum y = (FPNum)ctx.MkNumeral("-10", s); /* -10 */
FPNum z = (FPNum)ctx.MkNumeral("-1.25p3", s); /* -1.25 * 2^3 = -1.25 * 8 = -10 */
Console.WriteLine("x={0}; y={1}; z={2}", x.ToString(), y.ToString(), z.ToString());
BoolExpr a = ctx.MkAnd(ctx.MkFPEq(x, y), ctx.MkFPEq(y, z));
Check(ctx, ctx.MkNot(a), Status.UNSATISFIABLE);
/* nothing is equal to NaN according to floating-point
* equality, so NaN == k should be unsatisfiable. */
FPExpr k = (FPExpr)ctx.MkConst("x", s);
FPExpr nan = ctx.MkFPNaN(s);
/* solver that runs the default tactic for QF_FP. */
Solver slvr = ctx.MkSolver("QF_FP");
slvr.Add(ctx.MkFPEq(nan, k));
if (slvr.Check() != Status.UNSATISFIABLE)
throw new TestFailedException();
Console.WriteLine("OK, unsat:" + Environment.NewLine + slvr);
/* NaN is equal to NaN according to normal equality. */
slvr = ctx.MkSolver("QF_FP");
slvr.Add(ctx.MkEq(nan, nan));
if (slvr.Check() != Status.SATISFIABLE)
throw new TestFailedException();
Console.WriteLine("OK, sat:" + Environment.NewLine + slvr);
/* Let's prove -1e1 * -1.25e3 == +100 */
x = (FPNum)ctx.MkNumeral("-1e1", s);
y = (FPNum)ctx.MkNumeral("-1.25p3", s);
FPExpr x_plus_y = (FPExpr)ctx.MkConst("x_plus_y", s);
FPNum r = (FPNum)ctx.MkNumeral("100", s);
slvr = ctx.MkSolver("QF_FP");
slvr.Add(ctx.MkEq(x_plus_y, ctx.MkFPMul(ctx.MkFPRoundNearestTiesToAway(), x, y)));
slvr.Add(ctx.MkNot(ctx.MkFPEq(x_plus_y, r)));
if (slvr.Check() != Status.UNSATISFIABLE)
throw new TestFailedException();
Console.WriteLine("OK, unsat:" + Environment.NewLine + slvr);
}
/// <summary>
/// Extract unsatisfiable core example with AssertAndTrack
/// </summary>
public static void UnsatCoreAndProofExample2(Context ctx)
{
Console.WriteLine("UnsatCoreAndProofExample2");
Solver solver = ctx.MkSolver();
BoolExpr pa = ctx.MkBoolConst("PredA");
BoolExpr pb = ctx.MkBoolConst("PredB");
BoolExpr pc = ctx.MkBoolConst("PredC");
BoolExpr pd = ctx.MkBoolConst("PredD");
BoolExpr f1 = ctx.MkAnd(new BoolExpr[] { pa, pb, pc });
BoolExpr f2 = ctx.MkAnd(new BoolExpr[] { pa, ctx.MkNot(pb), pc });
BoolExpr f3 = ctx.MkOr(ctx.MkNot(pa), ctx.MkNot(pc));
BoolExpr f4 = pd;
BoolExpr p1 = ctx.MkBoolConst("P1");
BoolExpr p2 = ctx.MkBoolConst("P2");
BoolExpr p3 = ctx.MkBoolConst("P3");
BoolExpr p4 = ctx.MkBoolConst("P4");
solver.AssertAndTrack(f1, p1);
solver.AssertAndTrack(f2, p2);
solver.AssertAndTrack(f3, p3);
solver.AssertAndTrack(f4, p4);
Status result = solver.Check();
if (result == Status.UNSATISFIABLE)
{
Console.WriteLine("unsat");
Console.WriteLine("core: ");
foreach (Expr c in solver.UnsatCore)
{
Console.WriteLine("{0}", c);
}
}
}
/// <summary>
/// Demonstrates how to use the SMTLIB parser.
/// </summary>
public static void ParserExample1(Context ctx)
{
Console.WriteLine("ParserExample1");
ctx.ParseSMTLIBString("(benchmark tst :extrafuns ((x Int) (y Int)) :formula (> x y) :formula (> x 0))");
foreach (BoolExpr f in ctx.SMTLIBFormulas)
Console.WriteLine("formula {0}", f);
Model m = Check(ctx, ctx.MkAnd(ctx.SMTLIBFormulas), Status.SATISFIABLE);
}
public static void and(BoolExpr f1, BoolExpr f2, out BoolExpr e)
{
e = new BoolExpr(ctx.MkAnd(f1.expr, f2.expr));
}
/// <summary>
/// Find a model for <tt>x < y + 1, x > 2</tt>.
/// Then, assert <tt>not(x = y)</tt>, and find another model.
/// </summary>
public static void FindModelExample2(Context ctx)
{
Console.WriteLine("FindModelExample2");
IntExpr x = ctx.MkIntConst("x");
IntExpr y = ctx.MkIntConst("y");
IntExpr one = ctx.MkInt(1);
IntExpr two = ctx.MkInt(2);
ArithExpr y_plus_one = ctx.MkAdd(y, one);
BoolExpr c1 = ctx.MkLt(x, y_plus_one);
BoolExpr c2 = ctx.MkGt(x, two);
BoolExpr q = ctx.MkAnd(c1, c2);
Console.WriteLine("model for: x < y + 1, x > 2");
Model model = Check(ctx, q, Status.SATISFIABLE);
Console.WriteLine("x = {0}, y = {1}",
(model.Evaluate(x)),
(model.Evaluate(y)));
/* assert not(x = y) */
BoolExpr x_eq_y = ctx.MkEq(x, y);
BoolExpr c3 = ctx.MkNot(x_eq_y);
q = ctx.MkAnd(q, c3);
Console.WriteLine("model for: x < y + 1, x > 2, not(x = y)");
model = Check(ctx, q, Status.SATISFIABLE);
Console.WriteLine("x = {0}, y = {1}",
(model.Evaluate(x)),
(model.Evaluate(y)));
}
/// <summary>
/// Extract unsatisfiable core example
/// </summary>
public static void UnsatCoreAndProofExample()
{
Console.WriteLine("UnsatCoreAndProofExample");
Dictionary<string, string> cfg = new Dictionary<string, string>() { { "PROOF_MODE", "2" } };
using (Context ctx = new Context(cfg))
{
Solver solver = ctx.MkSolver();
BoolExpr pa = ctx.MkBoolConst("PredA");
BoolExpr pb = ctx.MkBoolConst("PredB");
BoolExpr pc = ctx.MkBoolConst("PredC");
BoolExpr pd = ctx.MkBoolConst("PredD");
BoolExpr p1 = ctx.MkBoolConst("P1");
BoolExpr p2 = ctx.MkBoolConst("P2");
BoolExpr p3 = ctx.MkBoolConst("P3");
BoolExpr p4 = ctx.MkBoolConst("P4");
BoolExpr[] assumptions = new BoolExpr[] { ctx.MkNot(p1), ctx.MkNot(p2), ctx.MkNot(p3), ctx.MkNot(p4) };
BoolExpr f1 = ctx.MkAnd(new BoolExpr[] { pa, pb, pc });
BoolExpr f2 = ctx.MkAnd(new BoolExpr[] { pa, ctx.MkNot(pb), pc });
BoolExpr f3 = ctx.MkOr(ctx.MkNot(pa), ctx.MkNot(pc));
BoolExpr f4 = pd;
solver.Assert(ctx.MkOr(f1, p1));
solver.Assert(ctx.MkOr(f2, p2));
solver.Assert(ctx.MkOr(f3, p3));
solver.Assert(ctx.MkOr(f4, p4));
Status result = solver.Check(assumptions);
if (result == Status.UNSATISFIABLE)
{
Console.WriteLine("unsat");
Console.WriteLine("proof: {0}", solver.Proof);
Console.WriteLine("core: ");
foreach (Expr c in solver.UnsatCore)
{
Console.WriteLine("{0}", c);
}
}
}
}
