|
public MkBV ( int v, uint size ) : |
||
| v | int | value of the numeral. |
| size | uint | the size of the bit-vector |
| Résultat | ||
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 two = ctx.MkBV(2, 32);
BitVecExpr three = ctx.MkBV(3, 32);
BitVecExpr tf = ctx.MkBV(24, 32);
Solver s = ctx.MkSolver();
s.Assert(ctx.MkEq(ctx.MkBVLSHR(x, two), three));
Console.WriteLine(s.Check());
Console.WriteLine(s.Model);
s = ctx.MkSolver();
s.Assert(ctx.MkEq(ctx.MkBVSHL(x, two), three));
Console.WriteLine(s.Check());
s = ctx.MkSolver();
s.Assert(ctx.MkEq(ctx.MkBVRotateLeft(x, two), three));
Console.WriteLine(s.Check());
Console.WriteLine(s.Model);
s = ctx.MkSolver();
s.Assert(ctx.MkEq(ctx.MkBVSHL(x, two), tf));
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))
{
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()
{
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 (int i = 0; i < 128; ++i) {
s.AddRule((BoolExpr)edge[ctx.MkBV(i,8),ctx.MkBV(i+1,8)]);
}
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()
{
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()
{
Dictionary<string, string> cfg = new Dictionary<string, string>() {
{ "AUTO_CONFIG", "true" } };
using (Context ctx = new Context(cfg))
{
BitVecExpr x = ctx.MkBVConst("x", 16);
BitVecExpr y = ctx.MkBVConst("y", 16);
Params p = ctx.MkParams();
p.Add(":mul2concat", true);
Tactic t = ctx.Then(ctx.UsingParams(ctx.MkTactic("simplify"), p),
ctx.MkTactic("solve-eqs"),
ctx.MkTactic("bit-blast"),
ctx.MkTactic("aig"),
ctx.MkTactic("sat"));
Solver s = ctx.MkSolver(t);
s.Assert(ctx.MkEq(ctx.MkBVAdd(ctx.MkBVMul(x, ctx.MkBV(32, 16)), y), ctx.MkBV(13, 16)));
s.Assert(ctx.MkBVSLT(ctx.MkBVAND(x, y), ctx.MkBV(10, 16)));
s.Assert(ctx.MkBVSGT(y, ctx.MkBV(-100, 16)));
Console.WriteLine(s.Check());
Model m = s.Model;
Console.WriteLine(m);
Console.WriteLine(ctx.MkBVAdd(ctx.MkBVMul(x, ctx.MkBV(32, 16)), y) + " == " + m.Evaluate(ctx.MkBVAdd(ctx.MkBVMul(x, ctx.MkBV(32, 16)), y)));
Console.WriteLine(ctx.MkBVAND(x, y) + " == " + m.Evaluate(ctx.MkBVAND(x, y)) );
}
}
public void Run()
{
Dictionary<string, string> cfg = new Dictionary<string, string>() {
{ "AUTO_CONFIG", "true" } };
Context ctx = new Context(cfg);
BitVecNum b = ctx.MkBV(0xbadc0de, 32);
Console.WriteLine(b.SExpr());
Console.WriteLine(b);
Console.WriteLine(b.Int64);
}
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());
}
}
/// <summary>
/// Simple bit-vector example.
/// </summary>
/// <remarks>
/// This example disproves that x - 10 <= 0 IFF x <= 10 for (32-bit) machine integers
/// </remarks>
public static void BitvectorExample1()
{
var ctx = new Z3.Context();
using var svc = Z3Api.Own(ctx);
var bv_type = ctx.MkBitVecSort(32);
var x = (BitVecExpr)ctx.MkConst("x", bv_type);
var zero = (BitVecNum)ctx.MkNumeral("0", bv_type);
BitVecNum ten = ctx.MkBV(10, 32);
BitVecExpr x_minus_ten = ctx.MkBVSub(x, ten);
/* bvsle is signed less than or equal to */
BoolExpr c1 = ctx.MkBVSLE(x, ten);
BoolExpr c2 = ctx.MkBVSLE(x_minus_ten, zero);
BoolExpr thm = ctx.MkIff(c1, c2);
print("disprove: x - 10 <= 0 IFF x <= 10 for (32-bit) machine integers");
Disprove(ctx, thm);
}
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", 16);
BitVecExpr y = ctx.MkBVConst("y", 16);
Tactic t = ctx.Then(ctx.MkTactic("simplify"), ctx.MkTactic("solve-eqs"), ctx.MkTactic("bit-blast"), ctx.MkTactic("sat"));
Solver s = ctx.MkSolver(t);
s.Assert(ctx.MkEq(ctx.MkBVOR(x, y), ctx.MkBV(13, 16)));
s.Assert(ctx.MkBVSGT(x, y));
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))
{
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))
{
BitVecExpr x = ctx.MkBVConst("x", 16);
BitVecExpr y = ctx.MkBVConst("y", 16);
Console.WriteLine(ctx.MkBVAdd(x, ctx.MkBV(2, 16)));
Console.WriteLine(ctx.MkBVSub(ctx.MkBVAdd(x, y), ctx.MkBV(1, 16)).Simplify());
BitVecExpr a = ctx.MkBV(-1, 16);
BitVecExpr b = ctx.MkBV(65535, 16);
Console.WriteLine(ctx.MkEq(a, b).Simplify());
a = ctx.MkBV(-1, 32);
b = ctx.MkBV(65535, 32);
Console.WriteLine(ctx.MkEq(a, b).Simplify());
}
}
/// <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));
}
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());
}
/// <summary>
/// Demonstrate how to use <code>Push</code>and <code>Pop</code>to
/// control the size of models.
/// </summary>
/// <remarks>Note: this test is specialized to 32-bit bitvectors.</remarks>
public static void CheckSmall(Context ctx, Solver solver, BitVecExpr[] to_minimize)
{
Sort bv32 = ctx.MkBitVecSort(32);
int num_Exprs = to_minimize.Length;
UInt32[] upper = new UInt32[num_Exprs];
UInt32[] lower = new UInt32[num_Exprs];
BitVecExpr[] values = new BitVecExpr[num_Exprs];
for (int i = 0; i < upper.Length; ++i)
{
upper[i] = UInt32.MaxValue;
lower[i] = 0;
}
bool some_work = true;
int last_index = -1;
UInt32 last_upper = 0;
while (some_work)
{
solver.Push();
bool check_is_sat = true;
while (check_is_sat && some_work)
{
// Assert all feasible bounds.
for (int i = 0; i < num_Exprs; ++i)
{
solver.Assert(ctx.MkBVULE(to_minimize[i], ctx.MkBV(upper[i], 32)));
}
check_is_sat = Status.SATISFIABLE == solver.Check();
if (!check_is_sat)
{
if (last_index != -1)
{
lower[last_index] = last_upper + 1;
}
break;
}
Console.WriteLine("{0}", solver.Model);
// narrow the bounds based on the current model.
for (int i = 0; i < num_Exprs; ++i)
{
Expr v = solver.Model.Evaluate(to_minimize[i]);
UInt64 ui = ((BitVecNum)v).UInt64;
if (ui < upper[i])
{
upper[i] = (UInt32)ui;
}
Console.WriteLine("{0} {1} {2}", i, lower[i], upper[i]);
}
// find a new bound to add
some_work = false;
last_index = 0;
for (int i = 0; i < num_Exprs; ++i)
{
if (lower[i] < upper[i])
{
last_upper = (upper[i] + lower[i]) / 2;
last_index = i;
solver.Assert(ctx.MkBVULE(to_minimize[i], ctx.MkBV(last_upper, 32)));
some_work = true;
break;
}
}
}
solver.Pop();
}
}
/// <summary>
/// Simple bit-vector example.
/// </summary>
/// <remarks>
/// This example disproves that x - 10 <= 0 IFF x <= 10 for (32-bit) machine integers
/// </remarks>
public static void BitvectorExample1(Context ctx)
{
Console.WriteLine("BitvectorExample1");
Sort bv_type = ctx.MkBitVecSort(32);
BitVecExpr x = (BitVecExpr)ctx.MkConst("x", bv_type);
BitVecNum zero = (BitVecNum)ctx.MkNumeral("0", bv_type);
BitVecNum ten = ctx.MkBV(10, 32);
BitVecExpr x_minus_ten = ctx.MkBVSub(x, ten);
/* bvsle is signed less than or equal to */
BoolExpr c1 = ctx.MkBVSLE(x, ten);
BoolExpr c2 = ctx.MkBVSLE(x_minus_ten, zero);
BoolExpr thm = ctx.MkIff(c1, c2);
Console.WriteLine("disprove: x - 10 <= 0 IFF x <= 10 for (32-bit) machine integers");
Disprove(ctx, thm);
}
