|
public MkFuncDecl ( |
||
| name | ||
| domain | Microsoft.Z3.Sort | |
| range | Microsoft.Z3.Sort | |
| return | ||
/// <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()
{
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()
{
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);
FuncDecl finv = ctx.MkFuncDecl("finv", B, A);
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 }, ctx.MkEq(finv[f[x]], x)));
Console.WriteLine(s);
Console.WriteLine(s.Check());
}
}
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");
Expr x = ctx.MkConst("x", A);
Expr y = ctx.MkConst("y", A);
FuncDecl f = ctx.MkFuncDecl("f", A, A);
Solver s = ctx.MkSolver();
s.Assert(ctx.MkEq(f[f[x]], x),
ctx.MkEq(f[x], y),
ctx.MkNot(ctx.MkEq(x, y)));
Console.WriteLine(s.Check());
Model m = s.Model;
Console.WriteLine(m);
Console.WriteLine("interpretation assigned to A: ");
foreach (Expr a in m.SortUniverse(A))
Console.WriteLine(a);
}
}
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()
{
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())
{
Sort U = ctx.MkUninterpretedSort("U");
FuncDecl f = ctx.MkFuncDecl("f", U, U);
Expr a = ctx.MkConst("a", U);
Expr b = ctx.MkConst("b", U);
Expr c = ctx.MkConst("c", U);
Solver s = ctx.MkSolver();
s.Assert(ctx.MkEq(f[f[a]], b),
ctx.MkNot(ctx.MkEq(f[b], c)),
ctx.MkEq(f[c], c));
Console.WriteLine(s.Check());
Model m = s.Model;
foreach (FuncDecl d in m.Decls)
if (d.DomainSize == 0)
Console.WriteLine(d.Name + " -> " + m.ConstInterp(d));
else
Console.WriteLine(d.Name + " -> " + m.FuncInterp(d));
Console.WriteLine(m.NumSorts);
Console.WriteLine(m.Sorts[0]);
foreach(Sort srt in m.Sorts)
Console.WriteLine(srt);
foreach (Expr v in m.SortUniverse(U))
Console.WriteLine(v);
}
}
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");
FuncDecl x_d = x.FuncDecl;
Console.WriteLine("is_expr(x_d): " + x_d.IsExpr);
Console.WriteLine("is_func_decl(x_d): " + x_d.IsFuncDecl);
Console.WriteLine("x_d.Name: " + x_d.Name);
Console.WriteLine("x_d.Range: " + x_d.Range);
Console.WriteLine("x_d.Arity: " + x_d.Arity);
Console.WriteLine("x_d() == x: " + (x_d.Apply() == x));
FuncDecl f = ctx.MkFuncDecl("f", new Sort[] { ctx.IntSort, ctx.RealSort }, ctx.BoolSort);
Console.WriteLine("f.Name: " + f.Name);
Console.WriteLine("f.Range: " + f.Range);
Console.WriteLine("f.Arity: " + f.Arity);
for (uint i = 0; i < f.Arity; i++)
Console.WriteLine("domain(" + i + "): " + f.Domain[i]);
Console.WriteLine(f[x, ctx.MkInt2Real(x)]);
Console.WriteLine(f[x, ctx.MkInt2Real(x)].FuncDecl == f);
}
}
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()) {
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());
}
}
internal static FuncDecl GetOrAddMemberAccessFunction(Context context, Environment environment, MemberInfo memberInfo)
{
FuncDecl memberFunc;
if (!environment.Members.TryGetValue(memberInfo, out memberFunc))
{
Sort memberTypeSort;
if (!environment.Types.TryGetValue(memberInfo.DeclaringType, out memberTypeSort))
{
throw new KeyNotFoundException(memberInfo.DeclaringType + " could not be found at environment.Types");
}
Sort memberReturnTypeEnumSort;
var propertyType = ((PropertyInfo)memberInfo).PropertyType;
if (propertyType == typeof(bool))
memberReturnTypeEnumSort = context.MkBoolSort();
else if (propertyType == typeof(int))
memberReturnTypeEnumSort = context.MkIntSort();
else if (propertyType == typeof(long))
memberReturnTypeEnumSort = context.MkRealSort();
else if (propertyType == typeof(string))
memberReturnTypeEnumSort = environment.PossibleStringValues;
else
{
if (propertyType.IsGenericType && propertyType.GetGenericTypeDefinition() == typeof(IEnumerable<>))
{
var listItemType = propertyType.GenericTypeArguments[0];
var listSort = context.MkSetSort(environment.Types[listItemType]);
memberReturnTypeEnumSort = listSort;
// TODO: add TryGetValue
environment.Types.Add(propertyType, listSort);
}
else if (propertyType.IsEnum)
{
EnumSort enumSort = context.MkEnumSort(propertyType.Name, Enum.GetNames(propertyType));
memberReturnTypeEnumSort = enumSort;
// TODO: add TryGetValue
environment.Types.Add(propertyType, enumSort);
}
else
{
// TODO throw exception if type is not supported
memberReturnTypeEnumSort = environment.Types[propertyType];
}
}
memberFunc = context.MkFuncDecl(memberInfo.Name, memberTypeSort, memberReturnTypeEnumSort);
environment.Members.Add(memberInfo, memberFunc);
}
return memberFunc;
}
/// <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 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()
{
using (Context ctx = new Context()) {
Symbol s1 = ctx.MkSymbol(1);
Symbol s2 = ctx.MkSymbol(1);
Symbol s3 = ctx.MkSymbol(2);
Sort[] domain = new Sort[0];
Sort range = ctx.IntSort;
TestDriver.CheckAssertion("a1", s1 == s2);
TestDriver.CheckAssertion("a2", s1 != s3);
TestDriver.CheckAssertion("a3", ctx.MkSymbol("x") != s1);
TestDriver.CheckAssertion("a4", ctx.MkSymbol("x") == ctx.MkSymbol("x"));
TestDriver.CheckAssertion("a5", ctx.MkFuncDecl("f", domain, range) == ctx.MkFuncDecl("f", domain, range));
TestDriver.CheckAssertion("a6", ctx.MkFuncDecl("f", domain, range) != ctx.MkFuncDecl("g", domain, range));
TestDriver.CheckAssertion("a7", ctx.MkUninterpretedSort("s") == ctx.MkUninterpretedSort("s"));
TestDriver.CheckAssertion("a8", ctx.MkUninterpretedSort("s") != ctx.MkUninterpretedSort("t"));
TestDriver.CheckAssertion("a9", ctx.MkUninterpretedSort("s") != ctx.IntSort);
TestDriver.CheckAssertion("a10", ctx.MkConst("x", range) == ctx.MkConst("x", range));
TestDriver.CheckAssertion("a11", ctx.MkConst("x", range) == ctx.MkConst(ctx.MkSymbol("x"), range));
TestDriver.CheckAssertion("a12", ctx.MkConst("x", range) != ctx.MkConst("y", range));
}
}
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");
FuncDecl f = ctx.MkFuncDecl("f", new Sort[] { ctx.IntSort, ctx.IntSort }, ctx.IntSort);
FuncDecl g = ctx.MkFuncDecl("g", new Sort[] { ctx.IntSort }, ctx.IntSort);
Expr n = f[f[g[x], g[g[x]]], g[g[y]]];
Console.WriteLine(n);
Expr nn = n.Substitute(new Expr[] { g[g[x]], g[y] },
new Expr[] { y, ctx.MkAdd(x, ctx.MkInt(1)) } );
Console.WriteLine(nn);
Console.WriteLine(n.Substitute(g[g[x]], y));
}
}
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 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 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()
{
using (Context ctx = new Context())
{
ArrayExpr a = ctx.MkArrayConst("a", ctx.IntSort, ctx.IntSort);
FuncDecl f = ctx.MkFuncDecl("f", ctx.IntSort, ctx.IntSort);
ArrayExpr m = ctx.MkMap(f, a);
Console.WriteLine(m);
Console.WriteLine(m.IsArrayMap);
Console.WriteLine(a.IsArrayMap);
Console.WriteLine(m.IsSelect);
Console.WriteLine(ctx.MkSelect(m, ctx.MkInt(0)).IsSelect);
Console.WriteLine(ctx.MkStore(m, ctx.MkInt(0), ctx.MkInt(1)).IsStore);
Console.WriteLine(ctx.MkStore(m, ctx.MkInt(0), ctx.MkInt(1)));
Console.WriteLine(m.IsStore);
Console.WriteLine(m.FuncDecl);
Console.WriteLine(m.FuncDecl.Parameters[0].FuncDecl);
Console.WriteLine(m.FuncDecl.Parameters[0].FuncDecl[ctx.MkInt(0)]);
Console.WriteLine(ctx.MkSelect(m, ctx.MkInt(10)));
}
}
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);
}
}
/// <summary>
/// Prove <tt>x = y implies g(x) = g(y)</tt>, and
/// disprove <tt>x = y implies g(g(x)) = g(y)</tt>.
/// </summary>
/// <remarks>This function demonstrates how to create uninterpreted
/// types and functions.</remarks>
public static void ProveExample1(Context ctx)
{
Console.WriteLine("ProveExample1");
/* create uninterpreted type. */
Sort U = ctx.MkUninterpretedSort(ctx.MkSymbol("U"));
/* declare function g */
FuncDecl g = ctx.MkFuncDecl("g", U, U);
/* create x and y */
Expr x = ctx.MkConst("x", U);
Expr y = ctx.MkConst("y", U);
/* create g(x), g(y) */
Expr gx = g[x];
Expr gy = g[y];
/* assert x = y */
BoolExpr eq = ctx.MkEq(x, y);
/* prove g(x) = g(y) */
BoolExpr f = ctx.MkEq(gx, gy);
Console.WriteLine("prove: x = y implies g(x) = g(y)");
Prove(ctx, ctx.MkImplies(eq, f));
/* create g(g(x)) */
Expr ggx = g[gx];
/* disprove g(g(x)) = g(y) */
f = ctx.MkEq(ggx, gy);
Console.WriteLine("disprove: x = y implies g(g(x)) = g(y)");
Disprove(ctx, ctx.MkImplies(eq, f));
/* Print the model using the custom model printer */
Model m = Check(ctx, ctx.MkNot(f), Status.SATISFIABLE);
Console.WriteLine(m);
}
/// <summary>
/// Some basic expression casting tests.
/// </summary>
static void CastingTest(Context ctx)
{
Console.WriteLine("CastingTest");
Sort[] domain = { ctx.BoolSort, ctx.BoolSort };
FuncDecl f = ctx.MkFuncDecl("f", domain, ctx.BoolSort);
AST upcast = ctx.MkFuncDecl(ctx.MkSymbol("q"), domain, ctx.BoolSort);
try
{
FuncDecl downcast = (FuncDecl)f; // OK
}
catch (InvalidCastException)
{
throw new TestFailedException();
}
try
{
Expr uc = (Expr)upcast;
throw new TestFailedException(); // should not be reachable!
}
catch (InvalidCastException)
{
}
Symbol s = ctx.MkSymbol(42);
IntSymbol si = s as IntSymbol;
if (si == null) throw new TestFailedException();
try
{
IntSymbol si2 = (IntSymbol)s;
}
catch (InvalidCastException)
{
throw new TestFailedException();
}
s = ctx.MkSymbol("abc");
StringSymbol ss = s as StringSymbol;
if (ss == null) throw new TestFailedException();
try
{
StringSymbol ss2 = (StringSymbol)s;
}
catch (InvalidCastException)
{
throw new TestFailedException();
}
try
{
IntSymbol si2 = (IntSymbol)s;
throw new TestFailedException(); // unreachable
}
catch
{
}
Sort srt = ctx.MkBitVecSort(32);
BitVecSort bvs = null;
try
{
bvs = (BitVecSort)srt;
}
catch (InvalidCastException)
{
throw new TestFailedException();
}
if (bvs.Size != 32)
throw new TestFailedException();
Expr q = ctx.MkAdd(ctx.MkInt(1), ctx.MkInt(2));
Expr q2 = q.Args[1];
Sort qs = q2.Sort;
if (qs as IntSort == null)
throw new TestFailedException();
try
{
IntSort isrt = (IntSort)qs;
}
catch (InvalidCastException)
{
throw new TestFailedException();
}
AST a = ctx.MkInt(42);
Expr ae = a as Expr;
if (ae == null) throw new TestFailedException();
ArithExpr aae = a as ArithExpr;
if (aae == null) throw new TestFailedException();
IntExpr aie = a as IntExpr;
if (aie == null) throw new TestFailedException();
IntNum ain = a as IntNum;
if (ain == null) throw new TestFailedException();
Expr[][] earr = new Expr[2][];
earr[0] = new Expr[2];
earr[1] = new Expr[2];
earr[0][0] = ctx.MkTrue();
earr[0][1] = ctx.MkTrue();
earr[1][0] = ctx.MkFalse();
earr[1][1] = ctx.MkFalse();
foreach (Expr[] ea in earr)
foreach (Expr e in ea)
{
try
{
Expr ns = ctx.MkNot((BoolExpr)e);
BoolExpr ens = (BoolExpr)ns;
}
catch (InvalidCastException)
{
throw new TestFailedException();
}
}
}
public void Run()
{
using (Context ctx = new Context())
{
this.ctx = ctx;
ctx.UpdateParamValue("DL_GENERATE_EXPLANATIONS", "true");
red_car = new Car(false, 2, 2, 3, "red");
cars = new Car[]{
new Car(true, 0, 3, 0, "yellow"),
new Car(false, 3, 3, 0, "blue"),
new Car(false, 5, 2, 0, "brown"),
new Car(false, 0, 2, 1, "lgreen"),
new Car(true, 1, 2, 1, "light blue"),
new Car(true, 2, 2, 1, "pink"),
new Car(true, 2, 2, 4, "dark green"),
red_car,
new Car(true, 3, 2, 3, "purple"),
new Car(false, 5, 2, 3, "light yellow"),
new Car(true, 4, 2, 0, "orange"),
new Car(false, 4, 2, 4, "black"),
new Car(true, 5, 3, 1, "light purple")
};
this.num_cars = cars.Length;
this.B = ctx.MkBoolSort();
this.bv3 = ctx.MkBitVecSort(3);
List<Sort> domain = new List<Sort>();
foreach (var c in cars) domain.Add(bv3);
this.state = ctx.MkFuncDecl("state", domain.ToArray(), B);
this.fp = ctx.MkFixedpoint();
this.fp.RegisterRelation(state);
// Initial state:
Expr[] args = new Expr[num_cars];
for (int i = 0; i < num_cars; ++i) args[i] = num(cars[i].start);
fp.AddRule((BoolExpr)state[args]);
// Transitions:
for (int pos = 0; pos < num_cars; ++pos)
{
Car car = cars[pos];
for (int i = 0; i < dimension; ++i)
if (car.is_vertical)
{
move_down(i, pos, car);
move_up(i, pos, car);
}
else
{
move_left(i, pos, car);
move_right(i, pos, car);
}
}
// Print the current context:
Console.WriteLine("{0}", fp);
// Prepare the query:
for (int i = 0; i < num_cars; ++i) args[i] = (cars[i] == red_car) ? num(4) : bound(i);
BoolExpr goal = (BoolExpr)state[args];
fp.Query(goal);
// Extract a path:
get_instructions(fp.GetAnswer());
}
}
/// <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>
/// Prove that <tt>f(x, y) = f(w, v) implies y = v</tt> when
/// <code>f</code> is injective in the second argument. <seealso cref="inj_axiom"/>
/// </summary>
public static void QuantifierExample4(Context ctx)
{
Console.WriteLine("QuantifierExample4");
/* If quantified formulas are asserted in a logical context, then
the model produced by Z3 should be viewed as a potential model. */
/* declare function f */
Sort I = ctx.IntSort;
FuncDecl f = ctx.MkFuncDecl("f", new Sort[] { I, I }, I);
/* f is injective in the second argument. */
BoolExpr inj = InjAxiomAbs(ctx, f, 1);
/* create x, y, v, w, fxy, fwv */
Expr x = ctx.MkIntConst("x");
Expr y = ctx.MkIntConst("y");
Expr v = ctx.MkIntConst("v");
Expr w = ctx.MkIntConst("w");
Expr fxy = ctx.MkApp(f, x, y);
Expr fwv = ctx.MkApp(f, w, v);
/* f(x, y) = f(w, v) */
BoolExpr p1 = ctx.MkEq(fxy, fwv);
/* prove f(x, y) = f(w, v) implies y = v */
BoolExpr p2 = ctx.MkEq(y, v);
Prove(ctx, p2, false, inj, p1);
/* disprove f(x, y) = f(w, v) implies x = w */
BoolExpr p3 = ctx.MkEq(x, w);
Disprove(ctx, p3, false, inj, p1);
}
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>
/// Demonstrates how to initialize the parser symbol table.
/// </summary>
public static void ParserExample3(Context ctx)
{
Console.WriteLine("ParserExample3");
/* declare function g */
Sort I = ctx.MkIntSort();
FuncDecl g = ctx.MkFuncDecl("g", new Sort[] { I, I }, I);
BoolExpr ca = CommAxiom(ctx, g);
ctx.ParseSMTLIBString("(benchmark tst :formula (forall (x Int) (y Int) (implies (= x y) (= (gg x 0) (gg 0 y)))))",
null, null,
new Symbol[] { ctx.MkSymbol("gg") },
new FuncDecl[] { g });
BoolExpr thm = ctx.SMTLIBFormulas[0];
Console.WriteLine("formula: {0}", thm);
Prove(ctx, thm, false, ca);
}
/// <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));
}