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()
{
Dictionary<string, string> cfg = new Dictionary<string, string>() {
{ "AUTO_CONFIG", "true" } };
using (Context ctx = new Context(cfg))
{
IntExpr dog = ctx.MkIntConst("dog");
IntExpr cat = ctx.MkIntConst("cat");
IntExpr mouse = ctx.MkIntConst("mouse");
Solver s = ctx.MkSolver();
s.Assert(ctx.MkGe(dog, ctx.MkInt(1)));
s.Assert(ctx.MkGe(cat, ctx.MkInt(1)));
s.Assert(ctx.MkGe(mouse, ctx.MkInt(1)));
s.Assert(ctx.MkEq(ctx.MkAdd(dog, cat, mouse), ctx.MkInt(100)));
s.Assert(ctx.MkEq(ctx.MkAdd(ctx.MkMul(ctx.MkInt(1500), dog),
ctx.MkMul(ctx.MkInt(100), cat),
ctx.MkMul(ctx.MkInt(25), mouse)),
ctx.MkInt(10000)));
Console.WriteLine(s.Check());
Console.WriteLine(s.Model);
}
}
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()
{
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()
{
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 void Run()
{
using (Context ctx = new Context())
{
RealExpr x = ctx.MkRealConst("x");
RealExpr y = ctx.MkRealConst("y");
RealExpr z = ctx.MkRealConst("z");
FuncDecl f = ctx.MkFuncDecl("f", ctx.RealSort, ctx.RealSort);
Solver s = ctx.MkSolver();
s.Assert(ctx.MkGt(x, ctx.MkReal(10)),
ctx.MkEq(y, ctx.MkAdd(x, ctx.MkReal(3))),
ctx.MkLt(y, ctx.MkReal(15)),
ctx.MkGt((RealExpr)f[x], ctx.MkReal(2)),
ctx.MkNot(ctx.MkEq(f[y], f[x])));
Console.WriteLine(s.Check());
Model m = s.Model;
foreach (FuncDecl fd in m.Decls)
Console.Write(" " + fd.Name);
Console.WriteLine();
foreach (FuncDecl fd in m.Decls)
{
if (fd.DomainSize == 0)
Console.WriteLine(fd.Name + " -> " + m.ConstInterp(fd));
else
Console.WriteLine(fd.Name + " -> " + m.FuncInterp(fd));
}
Console.WriteLine(m.Evaluate(ctx.MkAdd(z, ctx.MkReal(1))));
Console.WriteLine(m.Evaluate(ctx.MkAdd(z, ctx.MkReal(1)), true));
Console.WriteLine(m.Evaluate(z));
FuncInterp fi = m.FuncInterp(f);
Console.WriteLine(fi.Else);
Console.WriteLine(fi.NumEntries);
Console.WriteLine(fi.Entries[0]);
Console.WriteLine(fi.Entries[0].NumArgs);
Console.WriteLine(fi.Entries[0].Args[0]);
Console.WriteLine(fi.Entries[0].Value);
ArrayExpr a = ctx.MkArrayConst("a", ctx.RealSort, ctx.RealSort);
s.Assert(ctx.MkGt((RealExpr)ctx.MkSelect(a, x), ctx.MkReal(10)),
ctx.MkGt((RealExpr)ctx.MkSelect(a, y), ctx.MkReal(20)));
Console.WriteLine(s);
Console.WriteLine(s.Check());
Console.WriteLine(s.Model);
Console.WriteLine(s.Model.Evaluate(a));
Console.WriteLine(s.Model.FuncInterp(a.FuncDecl));
}
}
public void Run()
{
using (Context ctx = new Context())
{
Expr a1 = ctx.MkAdd(ctx.MkRealConst("x"), ctx.MkReal(1));
Expr a2 = ctx.MkAdd(ctx.MkRealConst("x"), ctx.MkReal(1));
Console.WriteLine(a1.GetHashCode() == a2.GetHashCode());
Expr a3 = ctx.MkAdd(ctx.MkRealConst("x"), ctx.MkReal(2));
Console.WriteLine(a3.GetHashCode() == a1.GetHashCode());
}
}
public void Run()
{
Dictionary<string, string> cfg = new Dictionary<string, string>() {
{ "AUTO_CONFIG", "true" } };
using (Context ctx = new Context(cfg))
{
IntExpr x = ctx.MkIntConst("x");
Console.WriteLine(ctx.MkAdd(x, ctx.MkInt(1)).GetHashCode() == ctx.MkAdd(ctx.MkInt(1), x).GetHashCode());
Console.WriteLine(x.Sort.GetHashCode() == ctx.IntSort.GetHashCode());
}
}
public void Run()
{
Dictionary<string, string> cfg = new Dictionary<string, string>() {
{ "AUTO_CONFIG", "true" } };
using (Context ctx = new Context(cfg))
{
IntExpr x = ctx.MkIntConst("x");
RealExpr y = ctx.MkRealConst("y");
Console.WriteLine((ctx.MkAdd(x, ctx.MkInt(1))).Sort);
Console.WriteLine((ctx.MkAdd(y, ctx.MkReal(1))).Sort);
Console.WriteLine((ctx.MkGe(x, ctx.MkInt(2))).Sort);
}
}
public void Run()
{
Dictionary<string, string> cfg = new Dictionary<string, string>() {
{ "AUTO_CONFIG", "true" } };
using (Context ctx = new Context(cfg))
{
IntExpr x = ctx.MkIntConst("x");
IntExpr y = ctx.MkIntConst("y");
Console.WriteLine(ctx.MkAdd(x, y).FuncDecl.DeclKind == Z3_decl_kind.Z3_OP_ADD);
Console.WriteLine(ctx.MkAdd(x, y).FuncDecl.DeclKind == Z3_decl_kind.Z3_OP_SUB);
}
}
public void Run()
{
Dictionary<string, string> cfg = new Dictionary<string, string>() {
{ "AUTO_CONFIG", "true" } };
Context ctx = new Context(cfg);
RealExpr x = ctx.MkRealConst("x");
RealExpr y = ctx.MkRealConst("y");
Console.WriteLine(ctx.MkPower(ctx.MkAdd(x, y), ctx.MkReal(3)));
Console.WriteLine(ctx.MkPower(x, ctx.MkAdd(y, ctx.MkReal(3))));
}
public void Run()
{
Dictionary<string, string> cfg = new Dictionary<string, string>() {
{ "AUTO_CONFIG", "true" } };
using (Context ctx = new Context(cfg))
{
RealExpr d = ctx.MkRealConst("d");
RealExpr a = ctx.MkRealConst("a");
RealExpr t = ctx.MkRealConst("t");
RealExpr v_i = ctx.MkRealConst("v_i");
RealExpr v_f = ctx.MkRealConst("v_f");
BoolExpr[] equations = new BoolExpr[] {
ctx.MkEq(d, ctx.MkAdd(ctx.MkMul(v_i, t),
ctx.MkDiv(ctx.MkMul(a, ctx.MkPower(t, ctx.MkReal(2))),
ctx.MkReal(2)))),
ctx.MkEq(v_f, ctx.MkAdd(v_i, ctx.MkMul(a, t)))
};
Console.WriteLine("Kinematic equations: ");
foreach (BoolExpr e in equations)
Console.WriteLine(e);
BoolExpr[] problem = new BoolExpr[] {
ctx.MkEq(v_i, ctx.MkReal(0)),
ctx.MkEq(t, ctx.MkReal("4.10")),
ctx.MkEq(a, ctx.MkReal(6))
};
Console.WriteLine("Problem: ");
foreach (BoolExpr p in problem)
Console.WriteLine(p);
Solver s = ctx.MkSolver();
s.Assert(equations);
s.Assert(problem);
if (s.Check() != Status.SATISFIABLE)
throw new Exception("BUG");
Console.WriteLine("Solution: ");
Console.WriteLine(s.Model);
Console.WriteLine("Decimal Solution: ");
foreach (FuncDecl f in s.Model.ConstDecls)
Console.WriteLine(f.Name + " = " + ((RatNum)s.Model.ConstInterp(f)).ToDecimalString(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[5];
for (uint i = 0; i < 5; i++)
X[i] = ctx.MkIntConst(string.Format("x_{0}", i));
RealExpr[] Y = new RealExpr[5];
for (uint i = 0; i < 5; i++)
Y[i] = ctx.MkRealConst(string.Format("y_{0}", i));
BoolExpr[] P = new BoolExpr[5];
for (uint i = 0; i < 5; i++)
P[i] = ctx.MkBoolConst(string.Format("p_{0}", i));
foreach (Expr x in X)
Console.WriteLine(x);
foreach (Expr x in Y)
Console.WriteLine(x);
foreach (Expr x in P)
Console.WriteLine(x);
foreach (ArithExpr y in Y)
Console.WriteLine(ctx.MkPower(y, ctx.MkReal(2)));
ArithExpr[] Yp = new ArithExpr[Y.Length];
for (uint i = 0; i < Y.Length; i++)
Yp[i] = ctx.MkPower(Y[i], ctx.MkReal(2));
Console.WriteLine(ctx.MkAdd(Yp));
}
}
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]);
}
}
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");
Params ps = ctx.MkParams();
ps.Add(":som", true);
Expr q = ctx.MkPower(ctx.MkAdd(x, y), ctx.MkReal(3));
q = q.Simplify(ps);
Console.WriteLine(ps);
Console.WriteLine(q);
ps = ctx.MkParams();
ps.Add(":mul-to-power", true);
q = q.Simplify(ps);
Console.WriteLine(ps);
Console.WriteLine(q);
}
}
public void Run()
{
Dictionary<string, string> cfg = new Dictionary<string, string>() {
{ "AUTO_CONFIG", "true" } };
using (Context ctx = new Context(cfg))
{
IntExpr x = ctx.MkIntConst("x");
IntExpr y = ctx.MkIntConst("y");
Solver s = ctx.MkSolver();
Console.WriteLine(s);
s.Assert(ctx.MkGt(x, ctx.MkInt(10)), ctx.MkEq(y, ctx.MkAdd(x, ctx.MkInt(2))));
Console.WriteLine(s);
Console.WriteLine("solving s");
Console.WriteLine(s.Check());
Console.WriteLine("creating new scope");
s.Push();
s.Assert(ctx.MkLt(y, ctx.MkInt(11)));
Console.WriteLine(s);
Console.WriteLine("solving updated constraints");
Console.WriteLine(s.Check());
Console.WriteLine("restoring");
s.Pop();
Console.WriteLine(s);
Console.WriteLine("solving restored constraints");
Console.WriteLine(s.Check());
}
}
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);
}
}
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()
{
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");
Solver s = ctx.MkSolver();
s.Assert(ctx.MkGt(x, ctx.MkReal(1)),
ctx.MkGt(y, ctx.MkReal(1)),
ctx.MkOr(ctx.MkGt(ctx.MkAdd(x, y), ctx.MkReal(1)),
ctx.MkLt(ctx.MkSub(x, y), ctx.MkReal(2))));
Console.WriteLine("asserted constraints: ");
foreach (var c in s.Assertions)
Console.WriteLine(c);
Console.WriteLine(s.Check());
Console.WriteLine(s.Statistics);
Console.WriteLine("stats for last check: ");
foreach (Statistics.Entry e in s.Statistics.Entries)
Console.WriteLine(e);
}
}
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]);
}
}
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]);
}
}
public void Run()
{
using (Context ctx = new Context())
{
IntExpr x = ctx.MkIntConst("x");
Console.WriteLine(ctx.MkAdd(x, ctx.MkInt(1)));
}
}
public void Run()
{
Dictionary<string, string> cfg = new Dictionary<string, string>() {
{ "AUTO_CONFIG", "true" } };
Context ctx = new Context(cfg);
RealExpr x = ctx.MkRealConst("x");
RealExpr y = ctx.MkRealConst("y");
RealExpr z = ctx.MkRealConst("z");
RatNum two = ctx.MkReal(2);
Console.WriteLine(ctx.MkAdd(ctx.MkSub(ctx.MkMul(x, y), ctx.MkPower(y, two)), ctx.MkPower(z, two)));
Console.WriteLine(ctx.MkSub(ctx.MkAdd(ctx.MkMul(x, y), ctx.MkPower(y, two)), ctx.MkPower(z, two)));
Console.WriteLine(ctx.MkMul(ctx.MkAdd(x, y), z));
}
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))
{
Params p = ctx.MkParams();
p.Add(":arith-lhs", true);
p.Add(":som", true);
Solver s = ctx.Then(ctx.With(ctx.MkTactic("simplify"), p),
ctx.MkTactic("normalize-bounds"),
ctx.MkTactic("lia2pb"),
ctx.MkTactic("pb2bv"),
ctx.MkTactic("bit-blast"),
ctx.MkTactic("sat")).Solver;
IntExpr x = ctx.MkIntConst("x");
IntExpr y = ctx.MkIntConst("y");
IntExpr z = ctx.MkIntConst("z");
s.Assert(new BoolExpr[] { ctx.MkGt(x, ctx.MkInt(0)),
ctx.MkLt(x, ctx.MkInt(10)),
ctx.MkGt(y, ctx.MkInt(0)),
ctx.MkLt(y, ctx.MkInt(10)),
ctx.MkGt(z, ctx.MkInt(0)),
ctx.MkLt(z, ctx.MkInt(10)),
ctx.MkEq(ctx.MkAdd(ctx.MkMul(ctx.MkInt(3), y),
ctx.MkMul(ctx.MkInt(2), x)), z) });
Console.WriteLine(s.Check());
Console.WriteLine(s.Model);
s.Reset();
s.Assert(ctx.MkEq(ctx.MkAdd(ctx.MkMul(ctx.MkInt(3), y),
ctx.MkMul(ctx.MkInt(2), x)), z));
Console.WriteLine(s.Check());
}
}
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");
IntExpr y = ctx.MkIntConst("y");
RealExpr a, b, c;
a = ctx.MkRealConst("a");
b = ctx.MkRealConst("b");
c = ctx.MkRealConst("c");
IntExpr s, r;
s = ctx.MkIntConst("s");
r = ctx.MkIntConst("r");
TestDriver.CheckString(ctx.MkAdd(x, ctx.MkInt2Real(y), ctx.MkReal(1), ctx.MkAdd(a, ctx.MkInt2Real(s))),
"(+ x (to_real y) 1.0 a (to_real s))");
TestDriver.CheckString(ctx.MkAdd(ctx.MkInt2Real(y), c), "(+ (to_real y) c)");
}
}
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]);
}
}
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));
}
}
public static void ProveExample2(Context ctx)
{
Console.WriteLine("ProveExample2");
/* declare function g */
Sort I = ctx.IntSort;
FuncDecl g = ctx.MkFuncDecl("g", I, I);
/* create x, y, and z */
IntExpr x = ctx.MkIntConst("x");
IntExpr y = ctx.MkIntConst("y");
IntExpr z = ctx.MkIntConst("z");
/* create gx, gy, gz */
Expr gx = ctx.MkApp(g, x);
Expr gy = ctx.MkApp(g, y);
Expr gz = ctx.MkApp(g, z);
/* create zero */
IntExpr zero = ctx.MkInt(0);
/* assert not(g(g(x) - g(y)) = g(z)) */
ArithExpr gx_gy = ctx.MkSub((IntExpr)gx, (IntExpr)gy);
Expr ggx_gy = ctx.MkApp(g, gx_gy);
BoolExpr eq = ctx.MkEq(ggx_gy, gz);
BoolExpr c1 = ctx.MkNot(eq);
/* assert x + z <= y */
ArithExpr x_plus_z = ctx.MkAdd(x, z);
BoolExpr c2 = ctx.MkLe(x_plus_z, y);
/* assert y <= x */
BoolExpr c3 = ctx.MkLe(y, x);
/* prove z < 0 */
BoolExpr f = ctx.MkLt(z, zero);
Console.WriteLine("prove: not(g(g(x) - g(y)) = g(z)), x + z <= y <= x implies z < 0");
Prove(ctx, f, c1, c2, c3);
/* disprove z < -1 */
IntExpr minus_one = ctx.MkInt(-1);
f = ctx.MkLt(z, minus_one);
Console.WriteLine("disprove: not(g(g(x) - g(y)) = g(z)), x + z <= y <= x implies z < -1");
Disprove(ctx, f, c1, c2, c3);
}
public static void add(IntExpr f1, IntExpr f2, out IntExpr e)
{
e = new IntExpr(ctx.MkAdd(f1.expr, f2.expr));
}
