|
public MkForall ( |
||
| boundConstants | ||
| body | ||
| weight | uint | |
| patterns | ||
| noPatterns | ||
| quantifierID | ||
| skolemID | ||
| Résultat | ||
/// <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()
{
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");
Sort B = ctx.MkUninterpretedSort("B");
FuncDecl f = ctx.MkFuncDecl("f", A, B);
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, y }, ctx.MkImplies(ctx.MkEq(f[x], f[y]),
ctx.MkEq(x, y)),
1,
new Pattern[] { ctx.MkPattern(f[x], f[y]) }));
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))
{
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);
}
}
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))
{
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()
{
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);
}
}
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>
/// 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());
}
/// <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 override BoolExpr toZ3Bool(Context ctx)
{
var qf = quantified_variables.Select(x => x.toZ3(ctx)).ToArray();
if (this.quantifier == Quantifier.Exists)
return ctx.MkExists(qf, inner.toZ3Bool(ctx));
else if (this.quantifier == Quantifier.Forall)
return ctx.MkForall(qf, inner.toZ3Bool(ctx));
else
throw new ArgumentException();
}
private BoolExpr[] GenerateAllConstraints(Context context, Environment environment, IReadOnlyList<LambdaExpression> lambdaExpressions)
{
var constraints = new List<BoolExpr>();
foreach (LambdaExpression lambdaExpression in lambdaExpressions)
{
var forAllParameters = new Dictionary<string, Expr>();
foreach (ParameterExpression parameter in lambdaExpression.Parameters)
{
Sort typeSort;
if (!environment.Types.TryGetValue(parameter.Type, out typeSort))
{
throw new NotSupportedException("This type was not registered through objectTheorem.CreateInstance<T> :" + parameter.Type);
}
forAllParameters.Add(parameter.Name, context.MkConst(parameter.Type.ToString(), typeSort));
}
var generator = new LambdaExpressionToConstraintGenerator(context, environment);
generator.LambdaParameterConstants = forAllParameters;
Expr forAllBody = generator.Visit(lambdaExpression);
var forAll = context.MkForall(forAllParameters.Values.ToArray(), forAllBody);
constraints.Add(forAll);
}
return constraints.ToArray();
}
