/*++
Copyright (c) 2012 Microsoft Corporation
Module Name:
Program.java
Abstract:
Z3 Java API: Example program
Author:
Christoph Wintersteiger (cwinter) 2012-11-27
Notes:
--*/
import java.util.*;
import com.microsoft.z3.*;
class JavaExample
{
@SuppressWarnings("serial")
class TestFailedException extends Exception
{
public TestFailedException()
{
super("Check FAILED");
}
};
// / Create axiom: function f is injective in the i-th argument.
// / <remarks>
// / The following axiom is produced:
// / <code>
// / forall (x_0, ..., x_n) finv(f(x_0, ..., x_i, ..., x_{n-1})) = x_i
// / </code>
// / Where, <code>finv</code>is a fresh function declaration.
public BoolExpr injAxiom(Context ctx, FuncDecl f, int i)
{
Sort[] domain = f.getDomain();
int sz = f.getDomainSize();
if (i >= sz)
{
System.out.println("failed to create inj axiom");
return null;
}
/* declare the i-th inverse of f: finv */
Sort finv_domain = f.getRange();
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 (int j = 0; j < sz; j++)
{
types[j] = domain[j];
names[j] = ctx.mkSymbol("x_" + Integer.toString(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.apply(xs);
/* create f_inv(f(x_0, ..., x_i, ..., x_{n-1})) */
Expr finv_fxs = finv.apply(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(fxs);
/* create & assert quantifier */
BoolExpr q = ctx.mkForall(types, /* types of quantified variables */
names, /* names of quantified variables */
eq, 1, new Pattern[] { p } /* patterns */, null, null, null);
return q;
}
// / Create axiom: function f is injective in the i-th argument.
// / <remarks>
// / The following axiom is produced:
// / <code>
// / forall (x_0, ..., x_n) finv(f(x_0, ..., x_i, ..., x_{n-1})) = x_i
// / </code>
// / Where, <code>finv</code>is a fresh function declaration.
public BoolExpr injAxiomAbs(Context ctx, FuncDecl f, int i)
{
Sort[] domain = f.getDomain();
int sz = f.getDomainSize();
if (i >= sz)
{
System.out.println("failed to create inj axiom");
return null;
}
/* declare the i-th inverse of f: finv */
Sort finv_domain = f.getRange();
Sort finv_range = domain[i];
FuncDecl finv = ctx.mkFuncDecl("f_fresh", finv_domain, finv_range);
/* allocate temporary arrays */
Expr[] xs = new Expr[sz];
/* fill types, names and xs */
for (int j = 0; j < sz; j++)
{
xs[j] = ctx.mkConst("x_" + Integer.toString(j), domain[j]);
}
Expr x_i = xs[i];
/* create f(x_0, ..., x_i, ..., x_{n-1}) */
Expr fxs = f.apply(xs);
/* create f_inv(f(x_0, ..., x_i, ..., x_{n-1})) */
Expr finv_fxs = finv.apply(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(fxs);
/* create & assert quantifier */
BoolExpr q = ctx.mkForall(xs, /* types of quantified variables */
eq, /* names of quantified variables */
1, new Pattern[] { p } /* patterns */, null, null, null);
return q;
}
// / Assert the axiom: function f is commutative.
// / <remarks>
// / This example uses the SMT-LIB parser to simplify the axiom
// construction.
// / </remarks>
private BoolExpr commAxiom(Context ctx, FuncDecl f) throws Exception
{
Sort t = f.getRange();
Sort[] dom = f.getDomain();
if (dom.length != 2 || !t.equals(dom[0]) || !t.equals(dom[1]))
{
System.out.println(Integer.toString(dom.length) + " "
+ dom[0].toString() + " " + dom[1].toString() + " "
+ t.toString());
throw new Exception(
"function must be binary, and argument types must be equal to return type");
}
String bench = "(assert (forall (x " + t.getName()
+ ") (y " + t.getName() + ") (= (" + f.getName() + " x y) ("
+ f.getName() + " y x))))";
return ctx.parseSMTLIB2String(bench, new Symbol[] { t.getName() },
new Sort[] { t }, new Symbol[] { f.getName() },
new FuncDecl[] { f })[0];
}
// / "Hello world" example: create a Z3 logical context, and delete it.
public void simpleExample()
{
System.out.println("SimpleExample");
Log.append("SimpleExample");
{
Context ctx = new Context();
/* do something with the context */
/* be kind to dispose manually and not wait for the GC. */
ctx.close();
}
}
Model check(Context ctx, BoolExpr f, Status sat) throws TestFailedException
{
Solver s = ctx.mkSolver();
s.add(f);
if (s.check() != sat)
throw new TestFailedException();
if (sat == Status.SATISFIABLE)
return s.getModel();
else
return null;
}
void solveTactical(Context ctx, Tactic t, Goal g, Status sat)
throws TestFailedException
{
Solver s = ctx.mkSolver(t);
System.out.println("\nTactical solver: " + s);
for (BoolExpr a : g.getFormulas())
s.add(a);
System.out.println("Solver: " + s);
if (s.check() != sat)
throw new TestFailedException();
}
ApplyResult applyTactic(Context ctx, Tactic t, Goal g)
{
System.out.println("\nGoal: " + g);
ApplyResult res = t.apply(g);
System.out.println("Application result: " + res);
Status q = Status.UNKNOWN;
for (Goal sg : res.getSubgoals())
if (sg.isDecidedSat())
q = Status.SATISFIABLE;
else if (sg.isDecidedUnsat())
q = Status.UNSATISFIABLE;
switch (q)
{
case UNKNOWN:
System.out.println("Tactic result: Undecided");
break;
case SATISFIABLE:
System.out.println("Tactic result: SAT");
break;
case UNSATISFIABLE:
System.out.println("Tactic result: UNSAT");
break;
}
return res;
}
void prove(Context ctx, BoolExpr f, boolean useMBQI) throws TestFailedException
{
BoolExpr[] assumptions = new BoolExpr[0];
prove(ctx, f, useMBQI, assumptions);
}
void prove(Context ctx, BoolExpr f, boolean useMBQI,
BoolExpr... assumptions) throws TestFailedException
{
System.out.println("Proving: " + f);
Solver s = ctx.mkSolver();
Params p = ctx.mkParams();
p.add("mbqi", useMBQI);
s.setParameters(p);
for (BoolExpr a : assumptions)
s.add(a);
s.add(ctx.mkNot(f));
Status q = s.check();
switch (q)
{
case UNKNOWN:
System.out.println("Unknown because: " + s.getReasonUnknown());
break;
case SATISFIABLE:
throw new TestFailedException();
case UNSATISFIABLE:
System.out.println("OK, proof: " + s.getProof());
break;
}
}
void disprove(Context ctx, BoolExpr f, boolean useMBQI)
throws TestFailedException
{
BoolExpr[] a = {};
disprove(ctx, f, useMBQI, a);
}
void disprove(Context ctx, BoolExpr f, boolean useMBQI,
BoolExpr... assumptions) throws TestFailedException
{
System.out.println("Disproving: " + f);
Solver s = ctx.mkSolver();
Params p = ctx.mkParams();
p.add("mbqi", useMBQI);
s.setParameters(p);
for (BoolExpr a : assumptions)
s.add(a);
s.add(ctx.mkNot(f));
Status q = s.check();
switch (q)
{
case UNKNOWN:
System.out.println("Unknown because: " + s.getReasonUnknown());
break;
case SATISFIABLE:
System.out.println("OK, model: " + s.getModel());
break;
case UNSATISFIABLE:
throw new TestFailedException();
}
}
void modelConverterTest(Context ctx) throws TestFailedException
{
System.out.println("ModelConverterTest");
ArithExpr xr = (ArithExpr) ctx.mkConst(ctx.mkSymbol("x"),
ctx.mkRealSort());
ArithExpr yr = (ArithExpr) ctx.mkConst(ctx.mkSymbol("y"),
ctx.mkRealSort());
Goal g4 = ctx.mkGoal(true, false, false);
g4.add(ctx.mkGt(xr, ctx.mkReal(10, 1)));
g4.add(ctx.mkEq(yr, ctx.mkAdd(xr, ctx.mkReal(1, 1))));
g4.add(ctx.mkGt(yr, ctx.mkReal(1, 1)));
ApplyResult ar = applyTactic(ctx, ctx.mkTactic("simplify"), g4);
if (ar.getNumSubgoals() == 1
&& (ar.getSubgoals()[0].isDecidedSat() || ar.getSubgoals()[0]
.isDecidedUnsat()))
throw new TestFailedException();
ar = applyTactic(ctx, ctx.andThen(ctx.mkTactic("simplify"),
ctx.mkTactic("solve-eqs")), g4);
if (ar.getNumSubgoals() == 1
&& (ar.getSubgoals()[0].isDecidedSat() || ar.getSubgoals()[0]
.isDecidedUnsat()))
throw new TestFailedException();
Solver s = ctx.mkSolver();
for (BoolExpr e : ar.getSubgoals()[0].getFormulas())
s.add(e);
Status q = s.check();
System.out.println("Solver says: " + q);
System.out.println("Model: \n" + s.getModel());
if (q != Status.SATISFIABLE)
throw new TestFailedException();
}
// / A simple array example.
void arrayExample1(Context ctx) throws TestFailedException
{
System.out.println("ArrayExample1");
Log.append("ArrayExample1");
Goal g = ctx.mkGoal(true, false, false);
ArraySort asort = ctx.mkArraySort(ctx.getIntSort(),
ctx.mkBitVecSort(32));
ArrayExpr aex = (ArrayExpr) ctx.mkConst(ctx.mkSymbol("MyArray"), asort);
Expr sel = ctx.mkSelect(aex, ctx.mkInt(0));
g.add(ctx.mkEq(sel, ctx.mkBV(42, 32)));
Symbol xs = ctx.mkSymbol("x");
IntExpr xc = (IntExpr) ctx.mkConst(xs, ctx.getIntSort());
Symbol fname = ctx.mkSymbol("f");
Sort[] domain = { ctx.getIntSort() };
FuncDecl fd = ctx.mkFuncDecl(fname, domain, ctx.getIntSort());
Expr[] fargs = { ctx.mkConst(xs, ctx.getIntSort()) };
IntExpr fapp = (IntExpr) ctx.mkApp(fd, fargs);
g.add(ctx.mkEq(ctx.mkAdd(xc, fapp), ctx.mkInt(123)));
Solver s = ctx.mkSolver();
for (BoolExpr a : g.getFormulas())
s.add(a);
System.out.println("Solver: " + s);
Status q = s.check();
System.out.println("Status: " + q);
if (q != Status.SATISFIABLE)
throw new TestFailedException();
System.out.println("Model = " + s.getModel());
System.out.println("Interpretation of MyArray:\n"
+ s.getModel().getFuncInterp(aex.getFuncDecl()));
System.out.println("Interpretation of x:\n"
+ s.getModel().getConstInterp(xc));
System.out.println("Interpretation of f:\n"
+ s.getModel().getFuncInterp(fd));
System.out.println("Interpretation of MyArray as Term:\n"
+ s.getModel().getFuncInterp(aex.getFuncDecl()));
}
// / Prove <tt>store(a1, i1, v1) = store(a2, i2, v2) implies (i1 = i3 or i2
// = i3 or select(a1, i3) = select(a2, i3))</tt>.
// / <remarks>This example demonstrates how to use the array
// theory.</remarks>
public void arrayExample2(Context ctx) throws TestFailedException
{
System.out.println("ArrayExample2");
Log.append("ArrayExample2");
Sort int_type = ctx.getIntSort();
Sort array_type = ctx.mkArraySort(int_type, int_type);
ArrayExpr a1 = (ArrayExpr) ctx.mkConst("a1", array_type);
ArrayExpr a2 = ctx.mkArrayConst("a2", int_type, int_type);
Expr i1 = ctx.mkConst("i1", int_type);
Expr i2 = ctx.mkConst("i2", int_type);
Expr i3 = ctx.mkConst("i3", int_type);
Expr v1 = ctx.mkConst("v1", int_type);
Expr v2 = ctx.mkConst("v2", int_type);
Expr st1 = ctx.mkStore(a1, i1, v1);
Expr st2 = ctx.mkStore(a2, i2, v2);
Expr sel1 = ctx.mkSelect(a1, i3);
Expr sel2 = ctx.mkSelect(a2, i3);
/* create antecedent */
BoolExpr antecedent = ctx.mkEq(st1, st2);
/*
* create consequent: i1 = i3 or i2 = i3 or select(a1, i3) = select(a2,
* i3)
*/
BoolExpr consequent = ctx.mkOr(ctx.mkEq(i1, i3), ctx.mkEq(i2, i3),
ctx.mkEq(sel1, sel2));
/*
* prove store(a1, i1, v1) = store(a2, i2, v2) implies (i1 = i3 or i2 =
* i3 or select(a1, i3) = select(a2, i3))
*/
BoolExpr thm = ctx.mkImplies(antecedent, consequent);
System.out
.println("prove: store(a1, i1, v1) = store(a2, i2, v2) implies (i1 = i3 or i2 = i3 or select(a1, i3) = select(a2, i3))");
System.out.println(thm);
prove(ctx, thm, false);
}
// / Show that <code>distinct(a_0, ... , a_n)</code> is
// / unsatisfiable when <code>a_i</code>'s are arrays from boolean to
// / boolean and n > 4.
// / <remarks>This example also shows how to use the <code>distinct</code>
// construct.</remarks>
public void arrayExample3(Context ctx) throws TestFailedException
{
System.out.println("ArrayExample3");
Log.append("ArrayExample2");
for (int n = 2; n <= 5; n++)
{
System.out.println("n = " + Integer.toString(n));
Sort bool_type = ctx.mkBoolSort();
Sort array_type = ctx.mkArraySort(bool_type, bool_type);
Expr[] a = new Expr[n];
/* create arrays */
for (int i = 0; i < n; i++)
{
a[i] = ctx.mkConst("array_" + Integer.toString(i), array_type);
}
/* assert distinct(a[0], ..., a[n]) */
BoolExpr d = ctx.mkDistinct(a);
System.out.println(d);
/* context is satisfiable if n < 5 */
Model model = check(ctx, d, n < 5 ? Status.SATISFIABLE
: Status.UNSATISFIABLE);
if (n < 5)
{
for (int i = 0; i < n; i++)
{
System.out.println(a[i].toString() + " = "
+ model.evaluate(a[i], false));
}
}
}
}
// / Sudoku solving example.
void sudokuExample(Context ctx) throws TestFailedException
{
System.out.println("SudokuExample");
Log.append("SudokuExample");
// 9x9 matrix of integer variables
IntExpr[][] X = new IntExpr[9][];
for (int i = 0; i < 9; i++)
{
X[i] = new IntExpr[9];
for (int j = 0; j < 9; j++)
X[i][j] = (IntExpr) ctx.mkConst(
ctx.mkSymbol("x_" + (i + 1) + "_" + (j + 1)),
ctx.getIntSort());
}
// each cell contains a value in {1, ..., 9}
BoolExpr[][] cells_c = new BoolExpr[9][];
for (int i = 0; i < 9; i++)
{
cells_c[i] = new BoolExpr[9];
for (int 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 (int 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 (int j = 0; j < 9; j++) {
IntExpr[] col = new IntExpr[9];
for (int i = 0; i < 9; i++) {
col[i] = X[i][j];
}
cols_c[j] = ctx.mkDistinct(col);
}
// each 3x3 square contains a digit at most once
BoolExpr[][] sq_c = new BoolExpr[3][];
for (int i0 = 0; i0 < 3; i0++)
{
sq_c[i0] = new BoolExpr[3];
for (int j0 = 0; j0 < 3; j0++)
{
IntExpr[] square = new IntExpr[9];
for (int i = 0; i < 3; i++)
for (int 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();
for (BoolExpr[] t : 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);
for (BoolExpr[] t : 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 (int i = 0; i < 9; i++)
for (int j = 0; j < 9; j++)
if (0 != instance[i][j])
instance_c = ctx.mkAnd(
instance_c,
ctx.mkEq(X[i][j], ctx.mkInt(instance[i][j])));
Solver s = ctx.mkSolver();
s.add(sudoku_c);
s.add(instance_c);
if (s.check() == Status.SATISFIABLE)
{
Model m = s.getModel();
Expr[][] R = new Expr[9][9];
for (int i = 0; i < 9; i++)
for (int j = 0; j < 9; j++)
R[i][j] = m.evaluate(X[i][j], false);
System.out.println("Sudoku solution:");
for (int i = 0; i < 9; i++)
{
for (int j = 0; j < 9; j++)
System.out.print(" " + R[i][j]);
System.out.println();
}
} else
{
System.out.println("Failed to solve sudoku");
throw new TestFailedException();
}
}
// / A basic example of how to use quantifiers.
void quantifierExample1(Context ctx)
{
System.out.println("QuantifierExample");
Log.append("QuantifierExample");
IntSort[] types = new IntSort[3];
IntExpr[] xs = new IntExpr[3];
Symbol[] names = new Symbol[3];
IntExpr[] vars = new IntExpr[3];
for (int j = 0; j < 3; j++)
{
types[j] = ctx.getIntSort();
names[j] = ctx.mkSymbol("x_" + Integer.toString(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"));
System.out.println("Quantifier X: " + x.toString());
Expr y = ctx.mkForall(xs, body_const, 1, null, null,
ctx.mkSymbol("Q2"), ctx.mkSymbol("skid2"));
System.out.println("Quantifier Y: " + y.toString());
}
void quantifierExample2(Context ctx)
{
System.out.println("QuantifierExample2");
Log.append("QuantifierExample2");
Expr q1, q2;
FuncDecl f = ctx.mkFuncDecl("f", ctx.getIntSort(), ctx.getIntSort());
FuncDecl g = ctx.mkFuncDecl("g", ctx.getIntSort(), ctx.getIntSort());
// Quantifier with Exprs as the bound variables.
{
Expr x = ctx.mkConst("x", ctx.getIntSort());
Expr y = ctx.mkConst("y", ctx.getIntSort());
Expr f_x = ctx.mkApp(f, x);
Expr f_y = ctx.mkApp(f, y);
Expr g_y = ctx.mkApp(g, y);
@SuppressWarnings("unused")
Pattern[] pats = new Pattern[] { ctx.mkPattern(f_x, g_y) };
Expr[] no_pats = new Expr[] { f_y };
Expr[] bound = new Expr[] { 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"));
System.out.println(q1);
}
// Quantifier with de-Bruijn indices.
{
Expr x = ctx.mkBound(1, ctx.getIntSort());
Expr y = ctx.mkBound(0, ctx.getIntSort());
Expr f_x = ctx.mkApp(f, x);
Expr f_y = ctx.mkApp(f, y);
Expr g_y = ctx.mkApp(g, y);
@SuppressWarnings("unused")
Pattern[] pats = new Pattern[] { ctx.mkPattern(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.getIntSort(), ctx.getIntSort() };
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"));
System.out.println(q2);
}
System.out.println(q1.equals(q2));
}
// / 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"/>
public void quantifierExample3(Context ctx) throws TestFailedException
{
System.out.println("QuantifierExample3");
Log.append("QuantifierExample3");
/*
* 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.getIntSort();
FuncDecl f = ctx.mkFuncDecl("f", new Sort[] { I, I }, I);
/* f is injective in the second argument. */
BoolExpr inj = injAxiom(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);
}
// / 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"/>
public void quantifierExample4(Context ctx) throws TestFailedException
{
System.out.println("QuantifierExample4");
Log.append("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.getIntSort();
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);
}
// / Some basic tests.
void basicTests(Context ctx) throws TestFailedException
{
System.out.println("BasicTests");
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, false, false);
g.add(trivial_eq);
g.add(nontrivial_eq);
System.out.println("Goal: " + g);
Solver solver = ctx.mkSolver();
for (BoolExpr a : g.getFormulas())
solver.add(a);
if (solver.check() != Status.SATISFIABLE)
throw new TestFailedException();
ApplyResult ar = applyTactic(ctx, ctx.mkTactic("simplify"), g);
if (ar.getNumSubgoals() == 1
&& (ar.getSubgoals()[0].isDecidedSat() || ar.getSubgoals()[0]
.isDecidedUnsat()))
throw new TestFailedException();
ar = applyTactic(ctx, ctx.mkTactic("smt"), g);
if (ar.getNumSubgoals() != 1 || !ar.getSubgoals()[0].isDecidedSat())
throw new TestFailedException();
g.add(ctx.mkEq(ctx.mkNumeral(1, ctx.mkBitVecSort(32)),
ctx.mkNumeral(2, ctx.mkBitVecSort(32))));
ar = applyTactic(ctx, ctx.mkTactic("smt"), g);
if (ar.getNumSubgoals() != 1 || !ar.getSubgoals()[0].isDecidedUnsat())
throw new TestFailedException();
Goal g2 = ctx.mkGoal(true, true, false);
ar = applyTactic(ctx, ctx.mkTactic("smt"), g2);
if (ar.getNumSubgoals() != 1 || !ar.getSubgoals()[0].isDecidedSat())
throw new TestFailedException();
g2 = ctx.mkGoal(true, true, false);
g2.add(ctx.mkFalse());
ar = applyTactic(ctx, ctx.mkTactic("smt"), g2);
if (ar.getNumSubgoals() != 1 || !ar.getSubgoals()[0].isDecidedUnsat())
throw new TestFailedException();
Goal g3 = ctx.mkGoal(true, true, false);
Expr xc = ctx.mkConst(ctx.mkSymbol("x"), ctx.getIntSort());
Expr yc = ctx.mkConst(ctx.mkSymbol("y"), ctx.getIntSort());
g3.add(ctx.mkEq(xc, ctx.mkNumeral(1, ctx.getIntSort())));
g3.add(ctx.mkEq(yc, ctx.mkNumeral(2, ctx.getIntSort())));
BoolExpr constr = ctx.mkEq(xc, yc);
g3.add(constr);
ar = applyTactic(ctx, ctx.mkTactic("smt"), g3);
if (ar.getNumSubgoals() != 1 || !ar.getSubgoals()[0].isDecidedUnsat())
throw new TestFailedException();
modelConverterTest(ctx);
// Real num/den test.
RatNum rn = ctx.mkReal(42, 43);
Expr inum = rn.getNumerator();
Expr iden = rn.getDenominator();
System.out.println("Numerator: " + inum + " Denominator: " + iden);
if (!inum.toString().equals("42") || !iden.toString().equals("43"))
throw new TestFailedException();
if (!rn.toDecimalString(3).toString().equals("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).getBigInteger().toString().equals(bn))
throw new TestFailedException();
if (!ctx.mkBV(bn, 128).getBigInteger().toString().equals(bn))
throw new TestFailedException();
if (ctx.mkBV(bn, 32).getBigInteger().toString().equals(bn))
throw new TestFailedException();
// Error handling test.
try
{
@SuppressWarnings("unused")
IntExpr i = ctx.mkInt("1/2");
throw new TestFailedException(); // unreachable
} catch (Z3Exception e)
{
}
}
// / Some basic expression casting tests.
void castingTest(Context ctx) throws TestFailedException
{
System.out.println("CastingTest");
Sort[] domain = { ctx.getBoolSort(), ctx.getBoolSort() };
FuncDecl f = ctx.mkFuncDecl("f", domain, ctx.getBoolSort());
AST upcast = ctx.mkFuncDecl(ctx.mkSymbol("q"), domain,
ctx.getBoolSort());
try
{
@SuppressWarnings("unused")
FuncDecl downcast = (FuncDecl) f; // OK
} catch (ClassCastException e)
{
throw new TestFailedException();
}
try
{
@SuppressWarnings("unused")
Expr uc = (Expr) upcast;
throw new TestFailedException(); // should not be reachable!
} catch (ClassCastException e)
{
}
Symbol s = ctx.mkSymbol(42);
IntSymbol si = (s.getClass() == IntSymbol.class) ? (IntSymbol) s : null;
if (si == null)
throw new TestFailedException();
try
{
@SuppressWarnings("unused")
IntSymbol si2 = (IntSymbol) s;
} catch (ClassCastException e)
{
throw new TestFailedException();
}
s = ctx.mkSymbol("abc");
StringSymbol ss = (s.getClass() == StringSymbol.class) ? (StringSymbol) s
: null;
if (ss == null)
throw new TestFailedException();
try
{
@SuppressWarnings("unused")
StringSymbol ss2 = (StringSymbol) s;
} catch (ClassCastException e)
{
throw new TestFailedException();
}
try
{
@SuppressWarnings("unused")
IntSymbol si2 = (IntSymbol) s;
throw new TestFailedException(); // unreachable
} catch (Exception e)
{
}
Sort srt = ctx.mkBitVecSort(32);
BitVecSort bvs = null;
try
{
bvs = (BitVecSort) srt;
} catch (ClassCastException e)
{
throw new TestFailedException();
}
if (bvs.getSize() != 32)
throw new TestFailedException();
Expr q = ctx.mkAdd(ctx.mkInt(1), ctx.mkInt(2));
Expr q2 = q.getArgs()[1];
Sort qs = q2.getSort();
if (qs.getClass() != IntSort.class)
throw new TestFailedException();
try
{
@SuppressWarnings("unused")
IntSort isrt = (IntSort) qs;
} catch (ClassCastException e)
{
throw new TestFailedException();
}
AST a = ctx.mkInt(42);
try
{
Expr.class.cast(a);
} catch (ClassCastException e)
{
throw new TestFailedException();
}
try
{
ArithExpr.class.cast(a);
} catch (ClassCastException e)
{
throw new TestFailedException();
}
try
{
IntExpr.class.cast(a);
} catch (ClassCastException e)
{
throw new TestFailedException();
}
try
{
IntNum.class.cast(a);
} catch (ClassCastException e)
{
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();
for (Expr[] ea : earr)
for (Expr e : ea)
{
try
{
Expr ns = ctx.mkNot((BoolExpr) e);
@SuppressWarnings("unused")
BoolExpr ens = (BoolExpr) ns;
} catch (ClassCastException ex)
{
throw new TestFailedException();
}
}
}
// / Shows how to read an SMT2 file.
void smt2FileTest(String filename)
{
Date before = new Date();
System.out.println("SMT2 File test ");
System.gc();
{
HashMap<String, String> cfg = new HashMap<String, String>();
cfg.put("model", "true");
Context ctx = new Context(cfg);
BoolExpr a = ctx.mkAnd(ctx.parseSMTLIB2File(filename, null, null, null, null));
long t_diff = ((new Date()).getTime() - before.getTime()) / 1000;
System.out.println("SMT2 file read time: " + t_diff + " sec");
// Iterate over the formula.
LinkedList<Expr> q = new LinkedList<Expr>();
q.add(a);
int cnt = 0;
while (q.size() > 0)
{
AST cur = (AST) q.removeFirst();
cnt++;
if (cur.getClass() == Expr.class)
if (!(cur.isVar()))
for (Expr c : ((Expr) cur).getArgs())
q.add(c);
}
System.out.println(cnt + " ASTs");
}
long t_diff = ((new Date()).getTime() - before.getTime()) / 1000;
System.out.println("SMT2 file test took " + t_diff + " sec");
}
// / Shows how to use Solver(logic)
// / @param ctx
void logicExample(Context ctx) throws TestFailedException
{
System.out.println("LogicTest");
Log.append("LogicTest");
com.microsoft.z3.Global.ToggleWarningMessages(true);
BitVecSort bvs = ctx.mkBitVecSort(32);
Expr x = ctx.mkConst("x", bvs);
Expr y = ctx.mkConst("y", bvs);
BoolExpr eq = ctx.mkEq(x, y);
// Use a solver for QF_BV
Solver s = ctx.mkSolver("QF_BV");
s.add(eq);
Status res = s.check();
System.out.println("solver result: " + res);
// Or perhaps a tactic for QF_BV
Goal g = ctx.mkGoal(true, false, false);
g.add(eq);
Tactic t = ctx.mkTactic("qfbv");
ApplyResult ar = t.apply(g);
System.out.println("tactic result: " + ar);
if (ar.getNumSubgoals() != 1 || !ar.getSubgoals()[0].isDecidedSat())
throw new TestFailedException();
}
// / Demonstrates how to use the ParOr tactic.
void parOrExample(Context ctx) throws TestFailedException
{
System.out.println("ParOrExample");
Log.append("ParOrExample");
BitVecSort bvs = ctx.mkBitVecSort(32);
Expr x = ctx.mkConst("x", bvs);
Expr y = ctx.mkConst("y", bvs);
BoolExpr q = ctx.mkEq(x, y);
Goal g = ctx.mkGoal(true, false, false);
g.add(q);
Tactic t1 = ctx.mkTactic("qfbv");
Tactic t2 = ctx.mkTactic("qfbv");
Tactic p = ctx.parOr(t1, t2);
ApplyResult ar = p.apply(g);
if (ar.getNumSubgoals() != 1 || !ar.getSubgoals()[0].isDecidedSat())
throw new TestFailedException();
}
void bigIntCheck(Context ctx, RatNum r)
{
System.out.println("Num: " + r.getBigIntNumerator());
System.out.println("Den: " + r.getBigIntDenominator());
}
// / Find a model for <code>x xor y</code>.
public void findModelExample1(Context ctx) throws TestFailedException
{
System.out.println("FindModelExample1");
Log.append("FindModelExample1");
BoolExpr x = ctx.mkBoolConst("x");
BoolExpr y = ctx.mkBoolConst("y");
BoolExpr x_xor_y = ctx.mkXor(x, y);
Model model = check(ctx, x_xor_y, Status.SATISFIABLE);
System.out.println("x = " + model.evaluate(x, false) + ", y = "
+ model.evaluate(y, false));
}
// / Find a model for <tt>x < y + 1, x > 2</tt>.
// / Then, assert <tt>not(x = y)</tt>, and find another model.
public void findModelExample2(Context ctx) throws TestFailedException
{
System.out.println("FindModelExample2");
Log.append("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);
System.out.println("model for: x < y + 1, x > 2");
Model model = check(ctx, q, Status.SATISFIABLE);
System.out.println("x = " + model.evaluate(x, false) + ", y ="
+ model.evaluate(y, false));
/* assert not(x = y) */
BoolExpr x_eq_y = ctx.mkEq(x, y);
BoolExpr c3 = ctx.mkNot(x_eq_y);
q = ctx.mkAnd(q, c3);
System.out.println("model for: x < y + 1, x > 2, not(x = y)");
model = check(ctx, q, Status.SATISFIABLE);
System.out.println("x = " + model.evaluate(x, false) + ", y = "
+ model.evaluate(y, false));
}
// / Prove <tt>x = y implies g(x) = g(y)</tt>, and
// / disprove <tt>x = y implies g(g(x)) = g(y)</tt>.
// / <remarks>This function demonstrates how to create uninterpreted
// / types and functions.</remarks>
public void proveExample1(Context ctx) throws TestFailedException
{
System.out.println("ProveExample1");
Log.append("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.apply(x);
Expr gy = g.apply(y);
/* assert x = y */
BoolExpr eq = ctx.mkEq(x, y);
/* prove g(x) = g(y) */
BoolExpr f = ctx.mkEq(gx, gy);
System.out.println("prove: x = y implies g(x) = g(y)");
prove(ctx, ctx.mkImplies(eq, f), false);
/* create g(g(x)) */
Expr ggx = g.apply(gx);
/* disprove g(g(x)) = g(y) */
f = ctx.mkEq(ggx, gy);
System.out.println("disprove: x = y implies g(g(x)) = g(y)");
disprove(ctx, ctx.mkImplies(eq, f), false);
/* Print the model using the custom model printer */
Model m = check(ctx, ctx.mkNot(f), Status.SATISFIABLE);
System.out.println(m);
}
// / Prove <tt>not(g(g(x) - g(y)) = g(z)), x + z <= y <= x implies z < 0
// </tt>.
// / Then, show that <tt>z < -1</tt> is not implied.
// / <remarks>This example demonstrates how to combine uninterpreted
// functions
// / and arithmetic.</remarks>
public void proveExample2(Context ctx) throws TestFailedException
{
System.out.println("ProveExample2");
Log.append("ProveExample2");
/* declare function g */
Sort I = ctx.getIntSort();
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);
System.out
.println("prove: not(g(g(x) - g(y)) = g(z)), x + z <= y <= x implies z < 0");
prove(ctx, f, false, c1, c2, c3);
/* disprove z < -1 */
IntExpr minus_one = ctx.mkInt(-1);
f = ctx.mkLt(z, minus_one);
System.out
.println("disprove: not(g(g(x) - g(y)) = g(z)), x + z <= y <= x implies z < -1");
disprove(ctx, f, false, c1, c2, c3);
}
// / Show how push & pop can be used to create "backtracking" points.
// / <remarks>This example also demonstrates how big numbers can be
// / created in ctx.</remarks>
public void pushPopExample1(Context ctx) throws TestFailedException
{
System.out.println("PushPopExample1");
Log.append("PushPopExample1");
/* create a big number */
IntSort int_type = ctx.getIntSort();
IntExpr big_number = ctx
.mkInt("1000000000000000000000000000000000000000000000000000000");
/* create number 3 */
IntExpr three = (IntExpr) ctx.mkNumeral("3", int_type);
/* create x */
IntExpr x = ctx.mkIntConst("x");
Solver solver = ctx.mkSolver();
/* assert x >= "big number" */
BoolExpr c1 = ctx.mkGe(x, big_number);
System.out.println("assert: x >= 'big number'");
solver.add(c1);
/* create a backtracking point */
System.out.println("push");
solver.push();
/* assert x <= 3 */
BoolExpr c2 = ctx.mkLe(x, three);
System.out.println("assert: x <= 3");
solver.add(c2);
/* context is inconsistent at this point */
if (solver.check() != Status.UNSATISFIABLE)
throw new TestFailedException();
/*
* backtrack: the constraint x <= 3 will be removed, since it was
* asserted after the last ctx.Push.
*/
System.out.println("pop");
solver.pop(1);
/* the context is consistent again. */
if (solver.check() != Status.SATISFIABLE)
throw new TestFailedException();
/* new constraints can be asserted... */
/* create y */
IntExpr y = ctx.mkIntConst("y");
/* assert y > x */
BoolExpr c3 = ctx.mkGt(y, x);
System.out.println("assert: y > x");
solver.add(c3);
/* the context is still consistent. */
if (solver.check() != Status.SATISFIABLE)
throw new TestFailedException();
}
// / Tuples.
// / <remarks>Check that the projection of a tuple
// / returns the corresponding element.</remarks>
public void tupleExample(Context ctx) throws TestFailedException
{
System.out.println("TupleExample");
Log.append("TupleExample");
Sort int_type = ctx.getIntSort();
TupleSort tuple = ctx.mkTupleSort(ctx.mkSymbol("mk_tuple"), // name of
// tuple
// constructor
new Symbol[] { ctx.mkSymbol("first"), ctx.mkSymbol("second") }, // names
// of
// projection
// operators
new Sort[] { int_type, int_type } // types of projection
// operators
);
FuncDecl first = tuple.getFieldDecls()[0]; // declarations are for
// projections
@SuppressWarnings("unused")
FuncDecl second = tuple.getFieldDecls()[1];
Expr x = ctx.mkConst("x", int_type);
Expr y = ctx.mkConst("y", int_type);
Expr n1 = tuple.mkDecl().apply(x, y);
Expr n2 = first.apply(n1);
BoolExpr n3 = ctx.mkEq(x, n2);
System.out.println("Tuple example: " + n3);
prove(ctx, n3, false);
}
// / Simple bit-vector example.
// / <remarks>
// / This example disproves that x - 10 <= 0 IFF x <= 10 for (32-bit)
// machine integers
// / </remarks>
public void bitvectorExample1(Context ctx) throws TestFailedException
{
System.out.println("BitvectorExample1");
Log.append("BitvectorExample1");
BitVecSort 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);
System.out
.println("disprove: x - 10 <= 0 IFF x <= 10 for (32-bit) machine integers");
disprove(ctx, thm, false);
}
// / Find x and y such that: x ^ y - 103 == x * y
public void bitvectorExample2(Context ctx) throws TestFailedException
{
System.out.println("BitvectorExample2");
Log.append("BitvectorExample2");
/* construct x ^ y - 103 == x * y */
BitVecSort bv_type = ctx.mkBitVecSort(32);
BitVecExpr x = ctx.mkBVConst("x", 32);
BitVecExpr y = ctx.mkBVConst("y", 32);
BitVecExpr x_xor_y = ctx.mkBVXOR(x, y);
BitVecExpr c103 = (BitVecNum) ctx.mkNumeral("103", bv_type);
BitVecExpr lhs = ctx.mkBVSub(x_xor_y, c103);
BitVecExpr rhs = ctx.mkBVMul(x, y);
BoolExpr ctr = ctx.mkEq(lhs, rhs);
System.out
.println("find values of x and y, such that x ^ y - 103 == x * y");
/* find a model (i.e., values for x an y that satisfy the constraint */
Model m = check(ctx, ctr, Status.SATISFIABLE);
System.out.println(m);
}
// / Demonstrates how to use the SMTLIB parser.
public void parserExample1(Context ctx) throws TestFailedException
{
System.out.println("ParserExample1");
Log.append("ParserExample1");
BoolExpr f = ctx.parseSMTLIB2String(
"(declare-const x Int) (declare-const y Int) (assert (and (> x y) (> x 0)))",
null, null, null, null)[0];
System.out.println("formula " + f);
@SuppressWarnings("unused")
Model m = check(ctx, f, Status.SATISFIABLE);
}
// / Demonstrates how to initialize the parser symbol table.
public void parserExample2(Context ctx) throws TestFailedException
{
System.out.println("ParserExample2");
Log.append("ParserExample2");
Symbol[] declNames = { ctx.mkSymbol("a"), ctx.mkSymbol("b") };
FuncDecl a = ctx.mkConstDecl(declNames[0], ctx.mkIntSort());
FuncDecl b = ctx.mkConstDecl(declNames[1], ctx.mkIntSort());
FuncDecl[] decls = new FuncDecl[] { a, b };
BoolExpr f = ctx.parseSMTLIB2String("(assert (> a b))", null, null,
declNames, decls)[0];
System.out.println("formula: " + f);
check(ctx, f, Status.SATISFIABLE);
}
// / Demonstrates how to initialize the parser symbol table.
public void parserExample3(Context ctx) throws Exception
{
System.out.println("ParserExample3");
Log.append("ParserExample3");
/* declare function g */
Sort I = ctx.mkIntSort();
FuncDecl g = ctx.mkFuncDecl("g", new Sort[] { I, I }, I);
BoolExpr ca = commAxiom(ctx, g);
BoolExpr thm = ctx.parseSMTLIB2String(
"(declare-fun (Int Int) Int) (assert (forall ((x Int) (y Int)) (=> (= x y) (= (gg x 0) (gg 0 y)))))",
null, null, new Symbol[] { ctx.mkSymbol("gg") },
new FuncDecl[] { g })[0];
System.out.println("formula: " + thm);
prove(ctx, thm, false, ca);
}
// / Demonstrates how to handle parser errors using Z3 error handling
// support.
// / <remarks></remarks>
public void parserExample5(Context ctx)
{
System.out.println("ParserExample5");
try
{
ctx.parseSMTLIB2String(
/*
* the following string has a parsing error: missing
* parenthesis
*/
"(declare-const x Int (declare-const y Int)) (assert (> x y))",
null, null, null, null);
} catch (Z3Exception e)
{
System.out.println("Z3 error: " + e);
}
}
// / Create an ite-Expr (if-then-else Exprs).
public void iteExample(Context ctx)
{
System.out.println("ITEExample");
Log.append("ITEExample");
BoolExpr f = ctx.mkFalse();
Expr one = ctx.mkInt(1);
Expr zero = ctx.mkInt(0);
Expr ite = ctx.mkITE(f, one, zero);
System.out.println("Expr: " + ite);
}
// / Create an enumeration data type.
public void enumExample(Context ctx) throws TestFailedException
{
System.out.println("EnumExample");
Log.append("EnumExample");
Symbol name = ctx.mkSymbol("fruit");
EnumSort fruit = ctx.mkEnumSort(name, ctx.mkSymbol("apple"),
ctx.mkSymbol("banana"), ctx.mkSymbol("orange"));
System.out.println((fruit.getConsts()[0]));
System.out.println((fruit.getConsts()[1]));
System.out.println((fruit.getConsts()[2]));
System.out.println((fruit.getTesterDecls()[0]));
System.out.println((fruit.getTesterDecls()[1]));
System.out.println((fruit.getTesterDecls()[2]));
Expr apple = fruit.getConsts()[0];
Expr banana = fruit.getConsts()[1];
Expr orange = fruit.getConsts()[2];
/* Apples are different from oranges */
prove(ctx, ctx.mkNot(ctx.mkEq(apple, orange)), false);
/* Apples pass the apple test */
prove(ctx, (BoolExpr) ctx.mkApp(fruit.getTesterDecls()[0], apple),
false);
/* Oranges fail the apple test */
disprove(ctx, (BoolExpr) ctx.mkApp(fruit.getTesterDecls()[0], orange),
false);
prove(ctx,
(BoolExpr) ctx.mkNot((BoolExpr) ctx.mkApp(
fruit.getTesterDecls()[0], orange)), false);
Expr fruity = ctx.mkConst("fruity", fruit);
/* If something is fruity, then it is an apple, banana, or orange */
prove(ctx,
ctx.mkOr(ctx.mkEq(fruity, apple), ctx.mkEq(fruity, banana),
ctx.mkEq(fruity, orange)), false);
}
// / Create a list datatype.
public void listExample(Context ctx) throws TestFailedException
{
System.out.println("ListExample");
Log.append("ListExample");
Sort int_ty;
ListSort int_list;
Expr nil, l1, l2, x, y, u, v;
BoolExpr fml, fml1;
int_ty = ctx.mkIntSort();
int_list = ctx.mkListSort(ctx.mkSymbol("int_list"), int_ty);
nil = ctx.mkConst(int_list.getNilDecl());
l1 = ctx.mkApp(int_list.getConsDecl(), ctx.mkInt(1), nil);
l2 = ctx.mkApp(int_list.getConsDecl(), ctx.mkInt(2), nil);
/* nil != cons(1, nil) */
prove(ctx, ctx.mkNot(ctx.mkEq(nil, l1)), false);
/* cons(2,nil) != cons(1, nil) */
prove(ctx, ctx.mkNot(ctx.mkEq(l1, l2)), false);
/* cons(x,nil) = cons(y, nil) => x = y */
x = ctx.mkConst("x", int_ty);
y = ctx.mkConst("y", int_ty);
l1 = ctx.mkApp(int_list.getConsDecl(), x, nil);
l2 = ctx.mkApp(int_list.getConsDecl(), y, nil);
prove(ctx, ctx.mkImplies(ctx.mkEq(l1, l2), ctx.mkEq(x, y)), false);
/* cons(x,u) = cons(x, v) => u = v */
u = ctx.mkConst("u", int_list);
v = ctx.mkConst("v", int_list);
l1 = ctx.mkApp(int_list.getConsDecl(), x, u);
l2 = ctx.mkApp(int_list.getConsDecl(), y, v);
prove(ctx, ctx.mkImplies(ctx.mkEq(l1, l2), ctx.mkEq(u, v)), false);
prove(ctx, ctx.mkImplies(ctx.mkEq(l1, l2), ctx.mkEq(x, y)), false);
/* is_nil(u) or is_cons(u) */
prove(ctx, ctx.mkOr((BoolExpr) ctx.mkApp(int_list.getIsNilDecl(), u),
(BoolExpr) ctx.mkApp(int_list.getIsConsDecl(), u)), false);
/* occurs check u != cons(x,u) */
prove(ctx, ctx.mkNot(ctx.mkEq(u, l1)), false);
/* destructors: is_cons(u) => u = cons(head(u),tail(u)) */
fml1 = ctx.mkEq(
u,
ctx.mkApp(int_list.getConsDecl(),
ctx.mkApp(int_list.getHeadDecl(), u),
ctx.mkApp(int_list.getTailDecl(), u)));
fml = ctx.mkImplies((BoolExpr) ctx.mkApp(int_list.getIsConsDecl(), u),
fml1);
System.out.println("Formula " + fml);
prove(ctx, fml, false);
disprove(ctx, fml1, false);
}
// / Create a binary tree datatype.
public void treeExample(Context ctx) throws TestFailedException
{
System.out.println("TreeExample");
Log.append("TreeExample");
Sort cell;
FuncDecl nil_decl, is_nil_decl, cons_decl, is_cons_decl, car_decl, cdr_decl;
Expr nil, l1, l2, x, y, u, v;
BoolExpr fml, fml1;
String[] head_tail = new String[] { "car", "cdr" };
Sort[] sorts = new Sort[] { null, null };
int[] sort_refs = new int[] { 0, 0 };
Constructor nil_con, cons_con;
nil_con = ctx.mkConstructor("nil", "is_nil", null, null, null);
cons_con = ctx.mkConstructor("cons", "is_cons", head_tail, sorts,
sort_refs);
Constructor[] constructors = new Constructor[] { nil_con, cons_con };
cell = ctx.mkDatatypeSort("cell", constructors);
nil_decl = nil_con.ConstructorDecl();
is_nil_decl = nil_con.getTesterDecl();
cons_decl = cons_con.ConstructorDecl();
is_cons_decl = cons_con.getTesterDecl();
FuncDecl[] cons_accessors = cons_con.getAccessorDecls();
car_decl = cons_accessors[0];
cdr_decl = cons_accessors[1];
nil = ctx.mkConst(nil_decl);
l1 = ctx.mkApp(cons_decl, nil, nil);
l2 = ctx.mkApp(cons_decl, l1, nil);
/* nil != cons(nil, nil) */
prove(ctx, ctx.mkNot(ctx.mkEq(nil, l1)), false);
/* cons(x,u) = cons(x, v) => u = v */
u = ctx.mkConst("u", cell);
v = ctx.mkConst("v", cell);
x = ctx.mkConst("x", cell);
y = ctx.mkConst("y", cell);
l1 = ctx.mkApp(cons_decl, x, u);
l2 = ctx.mkApp(cons_decl, y, v);
prove(ctx, ctx.mkImplies(ctx.mkEq(l1, l2), ctx.mkEq(u, v)), false);
prove(ctx, ctx.mkImplies(ctx.mkEq(l1, l2), ctx.mkEq(x, y)), false);
/* is_nil(u) or is_cons(u) */
prove(ctx,
ctx.mkOr((BoolExpr) ctx.mkApp(is_nil_decl, u),
(BoolExpr) ctx.mkApp(is_cons_decl, u)), false);
/* occurs check u != cons(x,u) */
prove(ctx, ctx.mkNot(ctx.mkEq(u, l1)), false);
/* destructors: is_cons(u) => u = cons(car(u),cdr(u)) */
fml1 = ctx.mkEq(
u,
ctx.mkApp(cons_decl, ctx.mkApp(car_decl, u),
ctx.mkApp(cdr_decl, u)));
fml = ctx.mkImplies((BoolExpr) ctx.mkApp(is_cons_decl, u), fml1);
System.out.println("Formula " + fml);
prove(ctx, fml, false);
disprove(ctx, fml1, false);
}
// / Create a forest of trees.
// / <remarks>
// / forest ::= nil | cons(tree, forest)
// / tree ::= nil | cons(forest, forest)
// / </remarks>
public void forestExample(Context ctx) throws TestFailedException
{
System.out.println("ForestExample");
Log.append("ForestExample");
Sort tree, forest;
@SuppressWarnings("unused")
FuncDecl nil1_decl, is_nil1_decl, cons1_decl, is_cons1_decl, car1_decl, cdr1_decl;
@SuppressWarnings("unused")
FuncDecl nil2_decl, is_nil2_decl, cons2_decl, is_cons2_decl, car2_decl, cdr2_decl;
@SuppressWarnings("unused")
Expr nil1, nil2, t1, t2, t3, t4, f1, f2, f3, l1, l2, x, y, u, v;
//
// Declare the names of the accessors for cons.
// Then declare the sorts of the accessors.
// For this example, all sorts refer to the new types 'forest' and
// 'tree'
// being declared, so we pass in null for both sorts1 and sorts2.
// On the other hand, the sort_refs arrays contain the indices of the
// two new sorts being declared. The first element in sort1_refs
// points to 'tree', which has index 1, the second element in sort1_refs
// array
// points to 'forest', which has index 0.
//
Symbol[] head_tail1 = new Symbol[] { ctx.mkSymbol("head"),
ctx.mkSymbol("tail") };
Sort[] sorts1 = new Sort[] { null, null };
int[] sort1_refs = new int[] { 1, 0 }; // the first item points to a
// tree, the second to a forest
Symbol[] head_tail2 = new Symbol[] { ctx.mkSymbol("car"),
ctx.mkSymbol("cdr") };
Sort[] sorts2 = new Sort[] { null, null };
int[] sort2_refs = new int[] { 0, 0 }; // both items point to the forest
// datatype.
Constructor nil1_con, cons1_con, nil2_con, cons2_con;
Constructor[] constructors1 = new Constructor[2], constructors2 = new Constructor[2];
Symbol[] sort_names = { ctx.mkSymbol("forest"), ctx.mkSymbol("tree") };
/* build a forest */
nil1_con = ctx.mkConstructor(ctx.mkSymbol("nil"),
ctx.mkSymbol("is_nil"), null, null, null);
cons1_con = ctx.mkConstructor(ctx.mkSymbol("cons1"),
ctx.mkSymbol("is_cons1"), head_tail1, sorts1, sort1_refs);
constructors1[0] = nil1_con;
constructors1[1] = cons1_con;
/* build a tree */
nil2_con = ctx.mkConstructor(ctx.mkSymbol("nil2"),
ctx.mkSymbol("is_nil2"), null, null, null);
cons2_con = ctx.mkConstructor(ctx.mkSymbol("cons2"),
ctx.mkSymbol("is_cons2"), head_tail2, sorts2, sort2_refs);
constructors2[0] = nil2_con;
constructors2[1] = cons2_con;
Constructor[][] clists = new Constructor[][] { constructors1,
constructors2 };
Sort[] sorts = ctx.mkDatatypeSorts(sort_names, clists);
forest = sorts[0];
tree = sorts[1];
//
// Now that the datatype has been created.
// Query the constructors for the constructor
// functions, testers, and field accessors.
//
nil1_decl = nil1_con.ConstructorDecl();
is_nil1_decl = nil1_con.getTesterDecl();
cons1_decl = cons1_con.ConstructorDecl();
is_cons1_decl = cons1_con.getTesterDecl();
FuncDecl[] cons1_accessors = cons1_con.getAccessorDecls();
car1_decl = cons1_accessors[0];
cdr1_decl = cons1_accessors[1];
nil2_decl = nil2_con.ConstructorDecl();
is_nil2_decl = nil2_con.getTesterDecl();
cons2_decl = cons2_con.ConstructorDecl();
is_cons2_decl = cons2_con.getTesterDecl();
FuncDecl[] cons2_accessors = cons2_con.getAccessorDecls();
car2_decl = cons2_accessors[0];
cdr2_decl = cons2_accessors[1];
nil1 = ctx.mkConst(nil1_decl);
nil2 = ctx.mkConst(nil2_decl);
f1 = ctx.mkApp(cons1_decl, nil2, nil1);
t1 = ctx.mkApp(cons2_decl, nil1, nil1);
t2 = ctx.mkApp(cons2_decl, f1, nil1);
t3 = ctx.mkApp(cons2_decl, f1, f1);
t4 = ctx.mkApp(cons2_decl, nil1, f1);
f2 = ctx.mkApp(cons1_decl, t1, nil1);
f3 = ctx.mkApp(cons1_decl, t1, f1);
/* nil != cons(nil,nil) */
prove(ctx, ctx.mkNot(ctx.mkEq(nil1, f1)), false);
prove(ctx, ctx.mkNot(ctx.mkEq(nil2, t1)), false);
/* cons(x,u) = cons(x, v) => u = v */
u = ctx.mkConst("u", forest);
v = ctx.mkConst("v", forest);
x = ctx.mkConst("x", tree);
y = ctx.mkConst("y", tree);
l1 = ctx.mkApp(cons1_decl, x, u);
l2 = ctx.mkApp(cons1_decl, y, v);
prove(ctx, ctx.mkImplies(ctx.mkEq(l1, l2), ctx.mkEq(u, v)), false);
prove(ctx, ctx.mkImplies(ctx.mkEq(l1, l2), ctx.mkEq(x, y)), false);
/* is_nil(u) or is_cons(u) */
prove(ctx,
ctx.mkOr((BoolExpr) ctx.mkApp(is_nil1_decl, u),
(BoolExpr) ctx.mkApp(is_cons1_decl, u)), false);
/* occurs check u != cons(x,u) */
prove(ctx, ctx.mkNot(ctx.mkEq(u, l1)), false);
}
// / Demonstrate how to use #Eval.
public void evalExample1(Context ctx)
{
System.out.println("EvalExample1");
Log.append("EvalExample1");
IntExpr x = ctx.mkIntConst("x");
IntExpr y = ctx.mkIntConst("y");
IntExpr two = ctx.mkInt(2);
Solver solver = ctx.mkSolver();
/* assert x < y */
solver.add(ctx.mkLt(x, y));
/* assert x > 2 */
solver.add(ctx.mkGt(x, two));
/* find model for the constraints above */
Model model = null;
if (Status.SATISFIABLE == solver.check())
{
model = solver.getModel();
System.out.println(model);
System.out.println("\nevaluating x+y");
Expr v = model.evaluate(ctx.mkAdd(x, y), false);
if (v != null)
{
System.out.println("result = " + (v));
} else
{
System.out.println("Failed to evaluate: x+y");
}
} else
{
System.out.println("BUG, the constraints are not satisfiable.");
}
}
// / Demonstrate how to use #Eval on tuples.
public void evalExample2(Context ctx)
{
System.out.println("EvalExample2");
Log.append("EvalExample2");
Sort int_type = ctx.getIntSort();
TupleSort tuple = ctx.mkTupleSort(ctx.mkSymbol("mk_tuple"), // name of
// tuple
// constructor
new Symbol[] { ctx.mkSymbol("first"), ctx.mkSymbol("second") }, // names
// of
// projection
// operators
new Sort[] { int_type, int_type } // types of projection
// operators
);
FuncDecl first = tuple.getFieldDecls()[0]; // declarations are for
// projections
FuncDecl second = tuple.getFieldDecls()[1];
Expr tup1 = ctx.mkConst("t1", tuple);
Expr tup2 = ctx.mkConst("t2", tuple);
Solver solver = ctx.mkSolver();
/* assert tup1 != tup2 */
solver.add(ctx.mkNot(ctx.mkEq(tup1, tup2)));
/* assert first tup1 = first tup2 */
solver.add(ctx.mkEq(ctx.mkApp(first, tup1), ctx.mkApp(first, tup2)));
/* find model for the constraints above */
Model model = null;
if (Status.SATISFIABLE == solver.check())
{
model = solver.getModel();
System.out.println(model);
System.out.println("evaluating tup1 "
+ (model.evaluate(tup1, false)));
System.out.println("evaluating tup2 "
+ (model.evaluate(tup2, false)));
System.out.println("evaluating second(tup2) "
+ (model.evaluate(ctx.mkApp(second, tup2), false)));
} else
{
System.out.println("BUG, the constraints are satisfiable.");
}
}
// / Demonstrate how to use <code>Push</code>and <code>Pop</code>to
// / control the size of models.
// / <remarks>Note: this test is specialized to 32-bit bitvectors.</remarks>
public void checkSmall(Context ctx, Solver solver, BitVecExpr... to_minimize)
{
int num_Exprs = to_minimize.length;
int[] upper = new int[num_Exprs];
int[] lower = new int[num_Exprs];
for (int i = 0; i < upper.length; ++i)
{
upper[i] = Integer.MAX_VALUE;
lower[i] = 0;
}
boolean some_work = true;
int last_index = -1;
int last_upper = 0;
while (some_work)
{
solver.push();
boolean check_is_sat = true;
while (check_is_sat && some_work)
{
// Assert all feasible bounds.
for (int i = 0; i < num_Exprs; ++i)
{
solver.add(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;
}
System.out.println(solver.getModel());
// narrow the bounds based on the current model.
for (int i = 0; i < num_Exprs; ++i)
{
Expr v = solver.getModel().evaluate(to_minimize[i], false);
int ui = ((BitVecNum) v).getInt();
if (ui < upper[i])
{
upper[i] = (int) ui;
}
System.out.println(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.add(ctx.mkBVULE(to_minimize[i],
ctx.mkBV(last_upper, 32)));
some_work = true;
break;
}
}
}
solver.pop();
}
}
// / Reduced-size model generation example.
public void findSmallModelExample(Context ctx)
{
System.out.println("FindSmallModelExample");
Log.append("FindSmallModelExample");
BitVecExpr x = ctx.mkBVConst("x", 32);
BitVecExpr y = ctx.mkBVConst("y", 32);
BitVecExpr z = ctx.mkBVConst("z", 32);
Solver solver = ctx.mkSolver();
solver.add(ctx.mkBVULE(x, ctx.mkBVAdd(y, z)));
checkSmall(ctx, solver, x, y, z);
}
// / Simplifier example.
public void simplifierExample(Context ctx)
{
System.out.println("SimplifierExample");
Log.append("SimplifierExample");
IntExpr x = ctx.mkIntConst("x");
IntExpr y = ctx.mkIntConst("y");
IntExpr z = ctx.mkIntConst("z");
@SuppressWarnings("unused")
IntExpr u = ctx.mkIntConst("u");
Expr t1 = ctx.mkAdd(x, ctx.mkSub(y, ctx.mkAdd(x, z)));
Expr t2 = t1.simplify();
System.out.println((t1) + " -> " + (t2));
}
// / Extract unsatisfiable core example
public void unsatCoreAndProofExample(Context ctx)
{
System.out.println("UnsatCoreAndProofExample");
Log.append("UnsatCoreAndProofExample");
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(pa, pb, pc);
BoolExpr f2 = ctx.mkAnd(pa, ctx.mkNot(pb), pc);
BoolExpr f3 = ctx.mkOr(ctx.mkNot(pa), ctx.mkNot(pc));
BoolExpr f4 = pd;
solver.add(ctx.mkOr(f1, p1));
solver.add(ctx.mkOr(f2, p2));
solver.add(ctx.mkOr(f3, p3));
solver.add(ctx.mkOr(f4, p4));
Status result = solver.check(assumptions);
if (result == Status.UNSATISFIABLE)
{
System.out.println("unsat");
System.out.println("proof: " + solver.getProof());
System.out.println("core: ");
for (Expr c : solver.getUnsatCore())
{
System.out.println(c);
}
}
}
/// Extract unsatisfiable core example with AssertAndTrack
public void unsatCoreAndProofExample2(Context ctx)
{
System.out.println("UnsatCoreAndProofExample2");
Log.append("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)
{
System.out.println("unsat");
System.out.println("core: ");
for (Expr c : solver.getUnsatCore())
{
System.out.println(c);
}
}
}
public void finiteDomainExample(Context ctx)
{
System.out.println("FiniteDomainExample");
Log.append("FiniteDomainExample");
FiniteDomainSort s = ctx.mkFiniteDomainSort("S", 10);
FiniteDomainSort t = ctx.mkFiniteDomainSort("T", 10);
FiniteDomainNum s1 = (FiniteDomainNum)ctx.mkNumeral(1, s);
FiniteDomainNum t1 = (FiniteDomainNum)ctx.mkNumeral(1, t);
System.out.println(s);
System.out.println(t);
System.out.println(s1);
System.out.println(t1);
System.out.println(s1.getInt());
System.out.println(t1.getInt());
// But you cannot mix numerals of different sorts
// even if the size of their domains are the same:
// System.out.println(ctx.mkEq(s1, t1));
}
public void floatingPointExample1(Context ctx) throws TestFailedException
{
System.out.println("FloatingPointExample1");
Log.append("FloatingPointExample1");
FPSort s = ctx.mkFPSort(11, 53);
System.out.println("Sort: " + 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 */
System.out.println("x=" + x.toString() +
"; y=" + y.toString() +
"; z=" + 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();
System.out.println("OK, unsat:" + System.getProperty("line.separator") + 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();
System.out.println("OK, sat:" + System.getProperty("line.separator") + 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();
System.out.println("OK, unsat:" + System.getProperty("line.separator") + slvr);
}
public void floatingPointExample2(Context ctx) throws TestFailedException
{
System.out.println("FloatingPointExample2");
Log.append("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.getRealSort()), ctx.mkFPToReal(fp_val));
BoolExpr c5 = ctx.mkAnd(c1, c2, c3, c4);
System.out.println("c5 = " + c5);
/* Generic solver */
Solver s = ctx.mkSolver();
s.add(c5);
if (s.check() != Status.SATISFIABLE)
throw new TestFailedException();
System.out.println("OK, model: " + s.getModel().toString());
}
public void optimizeExample(Context ctx)
{
System.out.println("Opt");
Optimize opt = ctx.mkOptimize();
// Set constraints.
IntExpr xExp = ctx.mkIntConst("x");
IntExpr yExp = ctx.mkIntConst("y");
opt.Add(ctx.mkEq(ctx.mkAdd(xExp, yExp), ctx.mkInt(10)),
ctx.mkGe(xExp, ctx.mkInt(0)),
ctx.mkGe(yExp, ctx.mkInt(0)));
// Set objectives.
Optimize.Handle mx = opt.MkMaximize(xExp);
Optimize.Handle my = opt.MkMaximize(yExp);
System.out.println(opt.Check());
System.out.println(mx);
System.out.println(my);
}
public void translationExample() {
Context ctx1 = new Context();
Context ctx2 = new Context();
Sort s1 = ctx1.getIntSort();
Sort s2 = ctx2.getIntSort();
Sort s3 = s1.translate(ctx2);
System.out.println(s1 == s2);
System.out.println(s1.equals(s2));
System.out.println(s2.equals(s3));
System.out.println(s1.equals(s3));
Expr e1 = ctx1.mkIntConst("e1");
Expr e2 = ctx2.mkIntConst("e1");
Expr e3 = e1.translate(ctx2);
System.out.println(e1 == e2);
System.out.println(e1.equals(e2));
System.out.println(e2.equals(e3));
System.out.println(e1.equals(e3));
}
public void stringExample() {
System.out.println("String example");
Context ctx = new Context();
Expr a = ctx.mkToRe(ctx.mkString("abcd"));
Expr b = ctx.mkFullRe(ctx.mkReSort(ctx.mkStringSort()));
System.out.println(a);
System.out.println(b);
System.out.println(a.getSort());
System.out.println(b.getSort());
Expr c = ctx.mkConcat(ctx.mkToRe(ctx.mkString("abc")),
ctx.mkFullRe(ctx.mkReSort(ctx.mkStringSort())),
ctx.mkEmptyRe(ctx.mkReSort(ctx.mkStringSort())),
ctx.mkAllcharRe(ctx.mkReSort(ctx.mkStringSort())),
ctx.mkToRe(ctx.mkString("d")));
System.out.println(c);
}
public static void main(String[] args)
{
JavaExample p = new JavaExample();
try
{
com.microsoft.z3.Global.ToggleWarningMessages(true);
Log.open("test.log");
System.out.print("Z3 Major Version: ");
System.out.println(Version.getMajor());
System.out.print("Z3 Full Version: ");
System.out.println(Version.getString());
System.out.print("Z3 Full Version String: ");
System.out.println(Version.getFullVersion());
p.stringExample();
p.simpleExample();
{ // These examples need model generation turned on.
HashMap<String, String> cfg = new HashMap<String, String>();
cfg.put("model", "true");
Context ctx = new Context(cfg);
p.optimizeExample(ctx);
p.basicTests(ctx);
p.castingTest(ctx);
p.sudokuExample(ctx);
p.quantifierExample1(ctx);
p.quantifierExample2(ctx);
p.logicExample(ctx);
p.parOrExample(ctx);
p.findModelExample1(ctx);
p.findModelExample2(ctx);
p.pushPopExample1(ctx);
p.arrayExample1(ctx);
p.arrayExample3(ctx);
p.bitvectorExample1(ctx);
p.bitvectorExample2(ctx);
p.parserExample1(ctx);
p.parserExample2(ctx);
p.parserExample5(ctx);
p.iteExample(ctx);
p.evalExample1(ctx);
p.evalExample2(ctx);
p.findSmallModelExample(ctx);
p.simplifierExample(ctx);
p.finiteDomainExample(ctx);
p.floatingPointExample1(ctx);
// core dumps: p.floatingPointExample2(ctx);
}
{ // These examples need proof generation turned on.
HashMap<String, String> cfg = new HashMap<String, String>();
cfg.put("proof", "true");
Context ctx = new Context(cfg);
p.proveExample1(ctx);
p.proveExample2(ctx);
p.arrayExample2(ctx);
p.tupleExample(ctx);
// throws p.parserExample3(ctx);
p.enumExample(ctx);
p.listExample(ctx);
p.treeExample(ctx);
p.forestExample(ctx);
p.unsatCoreAndProofExample(ctx);
p.unsatCoreAndProofExample2(ctx);
}
{ // These examples need proof generation turned on and auto-config
// set to false.
HashMap<String, String> cfg = new HashMap<String, String>();
cfg.put("proof", "true");
cfg.put("auto-config", "false");
Context ctx = new Context(cfg);
p.quantifierExample3(ctx);
p.quantifierExample4(ctx);
}
p.translationExample();
Log.close();
if (Log.isOpen())
System.out.println("Log is still open!");
} catch (Z3Exception ex)
{
System.out.println("Z3 Managed Exception: " + ex.getMessage());
System.out.println("Stack trace: ");
ex.printStackTrace(System.out);
} catch (TestFailedException ex)
{
System.out.println("TEST CASE FAILED: " + ex.getMessage());
System.out.println("Stack trace: ");
ex.printStackTrace(System.out);
} catch (Exception ex)
{
System.out.println("Unknown Exception: " + ex.getMessage());
System.out.println("Stack trace: ");
ex.printStackTrace(System.out);
}
}
}