mirror of
https://github.com/Z3Prover/z3
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2167 lines
80 KiB
Java
2167 lines
80 KiB
Java
/*++
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Copyright (c) 2012 Microsoft Corporation
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Module Name:
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Program.java
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Abstract:
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Z3 Java API: Example program
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Author:
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Christoph Wintersteiger (cwinter) 2012-11-27
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Notes:
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--*/
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import com.microsoft.z3.*;
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import java.util.*;
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import java.util.stream.Collectors;
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import java.util.stream.IntStream;
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import java.util.stream.Stream;
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import static java.util.stream.Stream.concat;
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class JavaGenericExample
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{
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@SuppressWarnings("serial")
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static class TestFailedException extends Exception
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{
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public TestFailedException()
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{
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super("Check FAILED");
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}
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}
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// / Create axiom: function f is injective in the i-th argument.
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// / <remarks>
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// / The following axiom is produced:
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// / <code>
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// / forall (x_0, ..., x_n) finv(f(x_0, ..., x_i, ..., x_{n-1})) = x_i
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// / </code>
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// / Where, <code>finv</code>is a fresh function declaration.
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public <R extends Sort> BoolExpr injAxiom(Context ctx, FuncDecl<R> f, int i)
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{
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Sort[] domain = f.getDomain();
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int sz = f.getDomainSize();
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if (i >= sz)
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{
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System.out.println("failed to create inj axiom");
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return null;
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}
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/* declare the i-th inverse of f: finv */
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Sort finv_domain = f.getRange();
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Sort finv_range = domain[i];
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FuncDecl<Sort> finv = ctx.mkFuncDecl("f_fresh", finv_domain, finv_range);
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/* allocate temporary arrays */
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/* fill types, names and xs */
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Sort[] types = domain.clone();
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List<Expr<Sort>> xs = IntStream.range(0, sz).mapToObj(j -> ctx.mkBound(j, types[j])).collect(Collectors.toList());
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Symbol[] names = IntStream.range(0, sz).mapToObj(j -> ctx.mkSymbol(String.format("x_%d", j))).toArray(Symbol[]::new);
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Expr<Sort> x_i = xs.get(i);
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/* create f(x_0, ..., x_i, ..., x_{n-1}) */
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Expr<R> fxs = f.apply(xs.toArray(new Expr[0]));
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/* create f_inv(f(x_0, ..., x_i, ..., x_{n-1})) */
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Expr<Sort> finv_fxs = finv.apply(fxs);
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/* create finv(f(x_0, ..., x_i, ..., x_{n-1})) = x_i */
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BoolExpr eq = ctx.mkEq(finv_fxs, x_i);
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/* use f(x_0, ..., x_i, ..., x_{n-1}) as the pattern for the quantifier */
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Pattern p = ctx.mkPattern(fxs);
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/* create & assert quantifier */
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return ctx.mkForall(types, /* types of quantified variables */
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names, /* names of quantified variables */
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eq, 1, new Pattern[] { p } /* patterns */, null, null, null);
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}
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// / Create axiom: function f is injective in the i-th argument.
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// / <remarks>
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// / The following axiom is produced:
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// / <code>
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// / forall (x_0, ..., x_n) finv(f(x_0, ..., x_i, ..., x_{n-1})) = x_i
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// / </code>
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// / Where, <code>finv</code>is a fresh function declaration.
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public <R extends Sort> BoolExpr injAxiomAbs(Context ctx, FuncDecl<R> f, int i)
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{
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Sort[] domain = f.getDomain();
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int sz = f.getDomainSize();
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if (i >= sz)
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{
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System.out.println("failed to create inj axiom");
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return null;
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}
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/* declare the i-th inverse of f: finv */
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R finv_domain = f.getRange();
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Sort finv_range = domain[i];
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FuncDecl<Sort> finv = ctx.mkFuncDecl("f_fresh", finv_domain, finv_range);
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/* allocate temporary arrays */
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List<Expr<Sort>> xs = IntStream.range(0, sz).mapToObj(j -> ctx.mkConst(String.format("x_%d", j), domain[j])).collect(Collectors.toList());
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/* fill types, names and xs */
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Expr<Sort> x_i = xs.get(i);
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/* create f(x_0, ..., x_i, ..., x_{n-1}) */
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Expr<R> fxs = f.apply(xs.toArray(new Expr[0]));
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/* create f_inv(f(x_0, ..., x_i, ..., x_{n-1})) */
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Expr<Sort> finv_fxs = finv.apply(fxs);
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/* create finv(f(x_0, ..., x_i, ..., x_{n-1})) = x_i */
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BoolExpr eq = ctx.mkEq(finv_fxs, x_i);
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/* use f(x_0, ..., x_i, ..., x_{n-1}) as the pattern for the quantifier */
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Pattern p = ctx.mkPattern(fxs);
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/* create & assert quantifier */
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return ctx.mkForall(xs.toArray(new Expr[0]), /* types of quantified variables */
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eq, /* names of quantified variables */
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1, new Pattern[] { p } /* patterns */, null, null, null);
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}
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// / Assert the axiom: function f is commutative.
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// / <remarks>
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// / This example uses the SMT-LIB parser to simplify the axiom
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// construction.
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// / </remarks>
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private <R extends Sort> BoolExpr commAxiom(Context ctx, FuncDecl<R> f) throws Exception
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{
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R t = f.getRange();
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Sort[] dom = f.getDomain();
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if (dom.length != 2 || !t.equals(dom[0]) || !t.equals(dom[1]))
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{
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System.out.printf("%d %s %s %s%n", dom.length, dom[0], dom[1], t);
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throw new Exception("function must be binary, and argument types must be equal to return type");
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}
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String bench = String.format("(assert (forall (x %s) (y %s) (= (%s x y) (%s y x))))", t.getName(), t.getName(), f.getName(), f.getName());
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return ctx.parseSMTLIB2String(bench, new Symbol[] { t.getName() },
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new Sort[] { t }, new Symbol[] { f.getName() },
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new FuncDecl[] { f })[0];
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}
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// / "Hello world" example: create a Z3 logical context, and delete it.
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public void simpleExample()
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{
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System.out.println("SimpleExample");
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Log.append("SimpleExample");
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{
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Context ctx = new Context();
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/* do something with the context */
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/* be kind to dispose manually and not wait for the GC. */
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ctx.close();
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}
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}
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@SuppressWarnings("unchecked")
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Model check(Context ctx, Expr<BoolSort> f, Status sat) throws TestFailedException
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{
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Solver s = ctx.mkSolver();
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s.add(f);
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if (s.check() != sat)
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throw new TestFailedException();
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if (sat == Status.SATISFIABLE)
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return s.getModel();
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else
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return null;
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}
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void solveTactical(Context ctx, Tactic t, Goal g, Status sat)
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throws TestFailedException
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{
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Solver s = ctx.mkSolver(t);
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System.out.printf("%nTactical solver: %s%n", s);
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s.add(g.getFormulas());
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System.out.printf("Solver: %s%n", s);
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if (s.check() != sat)
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throw new TestFailedException();
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}
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ApplyResult applyTactic(Context ctx, Tactic t, Goal g)
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{
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System.out.printf("%nGoal: %s%n", g);
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ApplyResult res = t.apply(g);
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System.out.printf("Application result: %s%n", res);
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Status q = Status.UNKNOWN;
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for (Goal sg : res.getSubgoals())
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if (sg.isDecidedSat())
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q = Status.SATISFIABLE;
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else if (sg.isDecidedUnsat())
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q = Status.UNSATISFIABLE;
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switch (q)
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{
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case UNKNOWN:
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System.out.println("Tactic result: Undecided");
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break;
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case SATISFIABLE:
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System.out.println("Tactic result: SAT");
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break;
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case UNSATISFIABLE:
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System.out.println("Tactic result: UNSAT");
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break;
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}
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return res;
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}
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void prove(Context ctx, Expr<BoolSort> f, boolean useMBQI) throws TestFailedException
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{
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BoolExpr[] assumptions = new BoolExpr[0];
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prove(ctx, f, useMBQI, assumptions);
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}
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@SafeVarargs
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final void prove(Context ctx, Expr<BoolSort> f, boolean useMBQI,
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Expr<BoolSort>... assumptions) throws TestFailedException
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{
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System.out.printf("Proving: %s%n", f);
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Solver s = ctx.mkSolver();
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Params p = ctx.mkParams();
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p.add("mbqi", useMBQI);
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s.setParameters(p);
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s.add(assumptions);
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s.add(ctx.mkNot(f));
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Status q = s.check();
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switch (q)
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{
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case UNKNOWN:
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System.out.printf("Unknown because: %s%n", s.getReasonUnknown());
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break;
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case SATISFIABLE:
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throw new TestFailedException();
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case UNSATISFIABLE:
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System.out.printf("OK, proof: %s%n", s.getProof());
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break;
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}
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}
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void disprove(Context ctx, Expr<BoolSort> f, boolean useMBQI)
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throws TestFailedException
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{
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BoolExpr[] a = {};
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disprove(ctx, f, useMBQI, a);
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}
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@SafeVarargs
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final void disprove(Context ctx, Expr<BoolSort> f, boolean useMBQI,
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Expr<BoolSort>... assumptions) throws TestFailedException
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{
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System.out.printf("Disproving: %s%n", f);
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Solver s = ctx.mkSolver();
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Params p = ctx.mkParams();
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p.add("mbqi", useMBQI);
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s.setParameters(p);
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s.add(assumptions);
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s.add(ctx.mkNot(f));
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Status q = s.check();
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switch (q)
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{
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case UNKNOWN:
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System.out.printf("Unknown because: %s%n", s.getReasonUnknown());
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break;
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case SATISFIABLE:
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System.out.printf("OK, model: %s%n", s.getModel());
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break;
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case UNSATISFIABLE:
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throw new TestFailedException();
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}
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}
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@SuppressWarnings("unchecked")
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void modelConverterTest(Context ctx) throws TestFailedException
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{
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System.out.println("ModelConverterTest");
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Expr<RealSort> xr = ctx.mkConst(ctx.mkSymbol("x"), ctx.mkRealSort());
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Expr<RealSort> yr = ctx.mkConst(ctx.mkSymbol("y"), ctx.mkRealSort());
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Goal g4 = ctx.mkGoal(true, false, false);
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g4.add(ctx.mkGt(xr, ctx.mkReal(10, 1)));
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g4.add(ctx.mkEq(yr, ctx.mkAdd(xr, ctx.mkReal(1, 1))));
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g4.add(ctx.mkGt(yr, ctx.mkReal(1, 1)));
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ApplyResult ar = applyTactic(ctx, ctx.mkTactic("simplify"), g4);
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if (ar.getNumSubgoals() == 1
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&& (ar.getSubgoals()[0].isDecidedSat() || ar.getSubgoals()[0]
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.isDecidedUnsat()))
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throw new TestFailedException();
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ar = applyTactic(ctx, ctx.andThen(ctx.mkTactic("simplify"),
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ctx.mkTactic("solve-eqs")), g4);
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if (ar.getNumSubgoals() == 1
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&& (ar.getSubgoals()[0].isDecidedSat() || ar.getSubgoals()[0]
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.isDecidedUnsat()))
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throw new TestFailedException();
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Solver s = ctx.mkSolver();
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for (BoolExpr e : ar.getSubgoals()[0].getFormulas())
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s.add(e);
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Status q = s.check();
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System.out.printf("Solver says: %s%n", q);
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System.out.printf("Model: %n%s%n", s.getModel());
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if (q != Status.SATISFIABLE)
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throw new TestFailedException();
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}
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// / A simple array example.
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@SuppressWarnings("unchecked")
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void arrayExample1(Context ctx) throws TestFailedException
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{
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System.out.println("ArrayExample1");
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Log.append("ArrayExample1");
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Goal g = ctx.mkGoal(true, false, false);
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ArraySort<IntSort, BitVecSort> asort = ctx.mkArraySort(ctx.getIntSort(),
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ctx.mkBitVecSort(32));
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Expr<ArraySort<IntSort, BitVecSort>> aex = ctx.mkConst(ctx.mkSymbol("MyArray"), asort);
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Expr<BitVecSort> sel = ctx.mkSelect(aex, ctx.mkInt(0));
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g.add(ctx.mkEq(sel, ctx.mkBV(42, 32)));
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Symbol xs = ctx.mkSymbol("x");
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IntExpr xc = (IntExpr) ctx.mkConst(xs, ctx.getIntSort());
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Symbol fname = ctx.mkSymbol("f");
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Sort[] domain = { ctx.getIntSort() };
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FuncDecl<IntSort> fd = ctx.mkFuncDecl(fname, domain, ctx.getIntSort());
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Expr<?>[] fargs = { ctx.mkConst(xs, ctx.getIntSort()) };
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Expr<IntSort> fapp = ctx.mkApp(fd, fargs);
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g.add(ctx.mkEq(ctx.mkAdd(xc, fapp), ctx.mkInt(123)));
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Solver s = ctx.mkSolver();
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for (BoolExpr a : g.getFormulas())
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s.add(a);
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System.out.printf("Solver: %s%n", s);
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Status q = s.check();
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System.out.printf("Status: %s%n", q);
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if (q != Status.SATISFIABLE)
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throw new TestFailedException();
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System.out.printf("Model = %s%n", s.getModel());
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System.out.printf("Interpretation of MyArray:%n%s%n", s.getModel().getFuncInterp(aex.getFuncDecl()));
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System.out.printf("Interpretation of x:%n%s%n", s.getModel().getConstInterp(xc));
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System.out.printf("Interpretation of f:%n%s%n", s.getModel().getFuncInterp(fd));
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System.out.printf("Interpretation of MyArray as Term:%n%s%n", s.getModel().getFuncInterp(aex.getFuncDecl()));
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}
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// / Prove <tt>store(a1, i1, v1) = store(a2, i2, v2) implies (i1 = i3 or i2
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// = i3 or select(a1, i3) = select(a2, i3))</tt>.
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// / <remarks>This example demonstrates how to use the array
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// theory.</remarks>
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public void arrayExample2(Context ctx) throws TestFailedException
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{
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System.out.println("ArrayExample2");
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Log.append("ArrayExample2");
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IntSort int_type = ctx.getIntSort();
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ArraySort<IntSort, IntSort> array_type = ctx.mkArraySort(int_type, int_type);
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Expr<ArraySort<IntSort, IntSort>> a1 = ctx.mkConst("a1", array_type);
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ArrayExpr<IntSort, IntSort> a2 = ctx.mkArrayConst("a2", int_type, int_type);
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Expr<IntSort> i1 = ctx.mkConst("i1", int_type);
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Expr<IntSort> i2 = ctx.mkConst("i2", int_type);
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Expr<IntSort> i3 = ctx.mkConst("i3", int_type);
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Expr<IntSort> v1 = ctx.mkConst("v1", int_type);
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Expr<IntSort> v2 = ctx.mkConst("v2", int_type);
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ArrayExpr<IntSort, IntSort> st1 = ctx.mkStore(a1, i1, v1);
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ArrayExpr<IntSort, IntSort> st2 = ctx.mkStore(a2, i2, v2);
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Expr<IntSort> sel1 = ctx.mkSelect(a1, i3);
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Expr<IntSort> sel2 = ctx.mkSelect(a2, i3);
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/* create antecedent */
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BoolExpr antecedent = ctx.mkEq(st1, st2);
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/*
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* create consequent: i1 = i3 or i2 = i3 or select(a1, i3) = select(a2,
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* i3)
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*/
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BoolExpr consequent = ctx.mkOr(ctx.mkEq(i1, i3), ctx.mkEq(i2, i3), ctx.mkEq(sel1, sel2));
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/*
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* prove store(a1, i1, v1) = store(a2, i2, v2) implies (i1 = i3 or i2 =
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* i3 or select(a1, i3) = select(a2, i3))
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*/
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BoolExpr thm = ctx.mkImplies(antecedent, consequent);
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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))");
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System.out.println(thm);
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prove(ctx, thm, false);
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}
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// / Show that <code>distinct(a_0, ... , a_n)</code> is
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// / unsatisfiable when <code>a_i</code>'s are arrays from boolean to
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// / boolean and n > 4.
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// / <remarks>This example also shows how to use the <code>distinct</code>
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// construct.</remarks>
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@SuppressWarnings("unchecked")
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public void arrayExample3(Context ctx) throws TestFailedException
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{
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System.out.println("ArrayExample3");
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Log.append("ArrayExample2");
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for (int n = 2; n <= 5; n++)
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{
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System.out.printf("n = %d%n", n);
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BoolSort bool_type = ctx.mkBoolSort();
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ArraySort<BoolSort, BoolSort> array_type = ctx.mkArraySort(bool_type, bool_type);
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List<Expr<ArraySort<BoolSort, BoolSort>>> a = IntStream.range(0, n).mapToObj(i -> ctx.mkConst(String.format("array_%d", i), array_type)).collect(Collectors.toList());
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/* create arrays */
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/* assert distinct(a[0], ..., a[n]) */
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BoolExpr d = ctx.mkDistinct(a.toArray(new Expr[0]));
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System.out.println(d);
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/* context is satisfiable if n < 5 */
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Model model = check(ctx, d, n < 5 ? Status.SATISFIABLE : Status.UNSATISFIABLE);
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if (n < 5)
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{
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for (int i = 0; i < n; i++)
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{
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System.out.printf("%s = %s%n", a.get(i), model.evaluate(a.get(i), false));
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}
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}
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}
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}
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// / Sudoku solving example.
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@SuppressWarnings({"unchecked", "CodeBlock2Expr"})
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void sudokuExample(Context ctx) throws TestFailedException
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{
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System.out.println("SudokuExample");
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Log.append("SudokuExample");
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// 9x9 matrix of integer variables
|
|
List<List<Expr<IntSort>>> X = IntStream.range(0, 9).mapToObj(i -> IntStream.range(0, 9).mapToObj(j ->
|
|
ctx.mkConst(ctx.mkSymbol(String.format("x_%d_%d", i + 1, j + 1)), ctx.getIntSort()))
|
|
.collect(Collectors.toList())).collect(Collectors.toList());
|
|
|
|
// each cell contains a value in {1, ..., 9}
|
|
List<List<BoolExpr>> cells_c = X.stream().map(r -> r.stream().map(c ->
|
|
ctx.mkAnd(ctx.mkLe(ctx.mkInt(1), c), ctx.mkLe(c, ctx.mkInt(9))))
|
|
.collect(Collectors.toList())).collect(Collectors.toList());
|
|
|
|
// each row contains a digit at most once
|
|
List<BoolExpr> rows_c = new ArrayList<>();
|
|
for (int i1 = 0; i1 < 9; i1++) {
|
|
BoolExpr boolExpr = ctx.mkDistinct(X.get(i1).toArray(new Expr[0]));
|
|
rows_c.add(boolExpr);
|
|
}
|
|
|
|
// each column contains a digit at most once
|
|
List<BoolExpr> cols_c = new ArrayList<>();
|
|
for (int idx = 0; idx < 9; idx++) {
|
|
int j1 = idx;
|
|
BoolExpr boolExpr = ctx.mkDistinct(X.stream().map(r -> r.get(j1)).toArray(Expr[]::new));
|
|
cols_c.add(boolExpr);
|
|
}
|
|
|
|
// each 3x3 square contains a digit at most once
|
|
List<List<BoolExpr>> sq_c = new ArrayList<>();
|
|
for (int i0 = 0; i0 < 3; i0++) {
|
|
List<BoolExpr> collect = new ArrayList<>();
|
|
for (int j0 = 0; j0 < 3; j0++) {
|
|
List<Expr<IntSort>> list = new ArrayList<>();
|
|
for (int i = 0; i < 3; i++) {
|
|
for (int j = 0; j < 3; j++) {
|
|
Expr<IntSort> intSortExpr = X.get(3 * i0 + i).get(3 * j0 + j);
|
|
list.add(intSortExpr);
|
|
}
|
|
}
|
|
BoolExpr boolExpr = ctx.mkDistinct(list.toArray(new Expr[0]));
|
|
collect.add(boolExpr);
|
|
}
|
|
sq_c.add(collect);
|
|
}
|
|
|
|
Stream<BoolExpr> sudoku_s = cells_c.stream().flatMap(Collection::stream);
|
|
sudoku_s = concat(sudoku_s, rows_c.stream());
|
|
sudoku_s = concat(sudoku_s, cols_c.stream());
|
|
sudoku_s = concat(sudoku_s, sq_c.stream().flatMap(Collection::stream));
|
|
BoolExpr sudoku_c = ctx.mkAnd(sudoku_s.toArray(BoolExpr[]::new));
|
|
|
|
// 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 }
|
|
};
|
|
|
|
// assert the variables we know
|
|
BoolExpr instance_c = ctx.mkAnd(IntStream.range(0, 9).boxed().flatMap(i -> IntStream.range(0, 9).filter(j -> instance[i][j] != 0).mapToObj(j -> ctx.mkEq(X.get(i).get(j), ctx.mkInt(instance[i][j])))).toArray(Expr[]::new));
|
|
|
|
Solver s = ctx.mkSolver();
|
|
s.add(sudoku_c);
|
|
s.add(instance_c);
|
|
|
|
if (s.check() == Status.SATISFIABLE)
|
|
{
|
|
Model m = s.getModel();
|
|
List<List<Expr<IntSort>>> R = X.stream().map(r -> r.stream().map(c -> m.eval(c, false)).collect(Collectors.toList())).collect(Collectors.toList());
|
|
System.out.println("Sudoku solution:");
|
|
R.forEach(r -> System.out.println(r.stream().map(Objects::toString).collect(Collectors.joining(" "))));
|
|
} else
|
|
{
|
|
System.out.println("Failed to solve sudoku");
|
|
throw new TestFailedException();
|
|
}
|
|
}
|
|
|
|
// / A basic example of how to use quantifiers.
|
|
|
|
@SuppressWarnings("unchecked")
|
|
void quantifierExample1(Context ctx)
|
|
{
|
|
System.out.println("QuantifierExample");
|
|
Log.append("QuantifierExample");
|
|
|
|
IntSort[] types = new IntSort[3];
|
|
Arrays.fill(types, ctx.getIntSort());
|
|
Symbol[] names = IntStream.range(0, 3).mapToObj(j -> ctx.mkSymbol(String.format("x_%d", j))).toArray(Symbol[]::new);
|
|
List<Expr<IntSort>> xs = IntStream.range(0, 3).mapToObj(j -> ctx.mkConst(names[j], types[j])).collect(Collectors.toList());
|
|
List<Expr<IntSort>> vars = IntStream.range(0, 3).mapToObj(j -> ctx.mkBound(2 - j, types[j])).collect(Collectors.toList());
|
|
|
|
BoolExpr body_vars = ctx.mkAnd(
|
|
ctx.mkEq(ctx.mkAdd(vars.get(0), ctx.mkInt(1)), ctx.mkInt(2)),
|
|
ctx.mkEq(ctx.mkAdd(vars.get(1), ctx.mkInt(2)),
|
|
ctx.mkAdd(vars.get(2), ctx.mkInt(3))));
|
|
|
|
BoolExpr body_const = ctx.mkAnd(
|
|
ctx.mkEq(ctx.mkAdd(xs.get(0), ctx.mkInt(1)), ctx.mkInt(2)),
|
|
ctx.mkEq(ctx.mkAdd(xs.get(1), ctx.mkInt(2)),
|
|
ctx.mkAdd(xs.get(2), ctx.mkInt(3))));
|
|
|
|
Quantifier x = ctx.mkForall(types, names, body_vars, 1, null, null,
|
|
ctx.mkSymbol("Q1"), ctx.mkSymbol("skid1"));
|
|
System.out.printf("Quantifier X: %s%n", x.toString());
|
|
|
|
Quantifier y = ctx.mkForall(xs.toArray(new Expr[0]), body_const, 1, null, null,
|
|
ctx.mkSymbol("Q2"), ctx.mkSymbol("skid2"));
|
|
System.out.printf("Quantifier Y: %s%n", y.toString());
|
|
}
|
|
|
|
void quantifierExample2(Context ctx)
|
|
{
|
|
|
|
System.out.println("QuantifierExample2");
|
|
Log.append("QuantifierExample2");
|
|
|
|
Quantifier q1, q2;
|
|
FuncDecl<IntSort> f = ctx.mkFuncDecl("f", ctx.getIntSort(), ctx.getIntSort());
|
|
FuncDecl<IntSort> g = ctx.mkFuncDecl("g", ctx.getIntSort(), ctx.getIntSort());
|
|
|
|
// Quantifier with Exprs as the bound variables.
|
|
{
|
|
Expr<IntSort> x = ctx.mkConst("x", ctx.getIntSort());
|
|
Expr<IntSort> y = ctx.mkConst("y", ctx.getIntSort());
|
|
Expr<IntSort> f_x = ctx.mkApp(f, x);
|
|
Expr<IntSort> f_y = ctx.mkApp(f, y);
|
|
Expr<IntSort> 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 };
|
|
BoolExpr 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<IntSort> x = ctx.mkBound(1, ctx.getIntSort());
|
|
Expr<IntSort> y = ctx.mkBound(0, ctx.getIntSort());
|
|
Expr<IntSort> f_x = ctx.mkApp(f, x);
|
|
Expr<IntSort> f_y = ctx.mkApp(f, y);
|
|
Expr<IntSort> 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() };
|
|
BoolExpr 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 */
|
|
IntSort I = ctx.getIntSort();
|
|
FuncDecl<IntSort> 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 */
|
|
IntExpr x = ctx.mkIntConst("x");
|
|
IntExpr y = ctx.mkIntConst("y");
|
|
IntExpr v = ctx.mkIntConst("v");
|
|
IntExpr w = ctx.mkIntConst("w");
|
|
Expr<IntSort> fxy = ctx.mkApp(f, x, y);
|
|
Expr<IntSort> 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 */
|
|
IntSort I = ctx.getIntSort();
|
|
FuncDecl<IntSort> 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 */
|
|
IntExpr x = ctx.mkIntConst("x");
|
|
IntExpr y = ctx.mkIntConst("y");
|
|
IntExpr v = ctx.mkIntConst("v");
|
|
IntExpr w = ctx.mkIntConst("w");
|
|
Expr<IntSort> fxy = ctx.mkApp(f, x, y);
|
|
Expr<IntSort> 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");
|
|
|
|
BoolSort bs = ctx.mkBoolSort();
|
|
|
|
Sort[] domain = { bs, bs };
|
|
FuncDecl<BoolSort> f = ctx.mkFuncDecl(fname, domain, bs);
|
|
Expr<BoolSort> fapp = ctx.mkApp(f, ctx.mkConst(x, bs), ctx.mkConst(y, bs));
|
|
|
|
Expr<?>[] fargs2 = { ctx.mkFreshConst("cp", bs) };
|
|
Sort[] domain2 = { bs };
|
|
Expr<BoolSort> 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.printf("Goal: %s%n", g);
|
|
|
|
Solver solver = ctx.mkSolver();
|
|
|
|
solver.add(g.getFormulas());
|
|
|
|
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<IntSort> xc = ctx.mkConst(ctx.mkSymbol("x"), ctx.getIntSort());
|
|
Expr<IntSort> 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);
|
|
IntNum inum = rn.getNumerator();
|
|
IntNum iden = rn.getDenominator();
|
|
System.out.printf("Numerator: %s Denominator: %s%n", inum, iden);
|
|
if (!inum.toString().equals("42") || !iden.toString().equals("43"))
|
|
throw new TestFailedException();
|
|
|
|
if (!rn.toDecimalString(3).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 ignored)
|
|
{
|
|
}
|
|
|
|
// Coercing type change in Z3
|
|
Expr<IntSort> integerDivision = ctx.mkDiv(ctx.mkInt(1), ctx.mkInt(2));
|
|
System.out.printf("%s -> %s%n", integerDivision, integerDivision.simplify()); // (div 1 2) -> 0
|
|
|
|
Expr<RealSort> realDivision = ctx.mkDiv(ctx.mkReal(1), ctx.mkReal(2));
|
|
System.out.printf("%s -> %s%n", realDivision, realDivision.simplify()); // (/ 1.0 2.0) -> 1/2
|
|
|
|
Expr<ArithSort> mixedDivision1 = ctx.mkDiv(ctx.mkReal(1), ctx.mkInt(2));
|
|
Expr<ArithSort> tmp = mixedDivision1;
|
|
// the return type is a Expr<ArithSort> here but since we know it is a
|
|
// real view it as such.
|
|
Expr<RealSort> mixedDivision2 = mixedDivision1.distillSort(RealSort.class);
|
|
System.out.printf("%s -> %s%n", mixedDivision2, mixedDivision2.simplify()); // (/ 1.0 (to_real 2)) -> 1/2
|
|
|
|
// empty distillSort
|
|
mixedDivision1.distillSort(ArithSort.class);
|
|
|
|
try {
|
|
mixedDivision1.distillSort(IntSort.class);
|
|
throw new TestFailedException(); // unreachable
|
|
} catch (Z3Exception exception) {
|
|
System.out.println(exception); // com.microsoft.z3.Z3Exception: Cannot cast expression of sort
|
|
// com.microsoft.z3.RealSort to com.microsoft.z3.IntSort.
|
|
}
|
|
|
|
Expr<BoolSort> eq1 = ctx.mkEq(realDivision, integerDivision);
|
|
System.out.printf("%s -> %s%n", eq1, eq1.simplify()); // (= (/ 1.0 2.0) (to_real (div 1 2))) -> false
|
|
|
|
Expr<BoolSort> eq2 = ctx.mkEq(realDivision, mixedDivision2);
|
|
System.out.printf("%s -> %s%n", eq2, eq2.simplify()); // (= (/ 1.0 2.0) (/ 1.0 (to_real 2))) -> true
|
|
}
|
|
|
|
// / Shows how to use Solver(logic)
|
|
|
|
// / @param ctx
|
|
void logicExample(Context ctx) throws TestFailedException
|
|
{
|
|
System.out.println("LogicTest");
|
|
Log.append("LogicTest");
|
|
|
|
Global.ToggleWarningMessages(true);
|
|
|
|
BitVecSort bvs = ctx.mkBitVecSort(32);
|
|
Expr<BitVecSort> x = ctx.mkConst("x", bvs);
|
|
Expr<BitVecSort> 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.printf("solver result: %s%n", 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.printf("tactic result: %s%n", 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<BitVecSort> x = ctx.mkConst("x", bvs);
|
|
Expr<BitVecSort> 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.printf("Num: %s%n", r.getBigIntNumerator());
|
|
System.out.printf("Den: %s%n", 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.printf("x = %s, y = %s%n", model.evaluate(x, false), 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");
|
|
IntNum one = ctx.mkInt(1);
|
|
IntNum two = ctx.mkInt(2);
|
|
|
|
ArithExpr<IntSort> 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.printf("x = %s, y =%s%n", model.evaluate(x, false), 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.printf("x = %s, y = %s%n", model.evaluate(x, false), 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. */
|
|
UninterpretedSort U = ctx.mkUninterpretedSort(ctx.mkSymbol("U"));
|
|
|
|
/* declare function g */
|
|
FuncDecl<UninterpretedSort> g = ctx.mkFuncDecl("g", U, U);
|
|
|
|
/* create x and y */
|
|
Expr<UninterpretedSort> x = ctx.mkConst("x", U);
|
|
Expr<UninterpretedSort> y = ctx.mkConst("y", U);
|
|
/* create g(x), g(y) */
|
|
Expr<UninterpretedSort> gx = g.apply(x);
|
|
Expr<UninterpretedSort> 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<UninterpretedSort> 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 */
|
|
IntSort I = ctx.getIntSort();
|
|
|
|
FuncDecl<IntSort> 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<IntSort> gx = ctx.mkApp(g, x);
|
|
Expr<IntSort> gy = ctx.mkApp(g, y);
|
|
Expr<IntSort> gz = ctx.mkApp(g, z);
|
|
|
|
/* create zero */
|
|
IntNum zero = ctx.mkInt(0);
|
|
|
|
/* assert not(g(g(x) - g(y)) = g(z)) */
|
|
ArithExpr<IntSort> gx_gy = ctx.mkSub(gx, gy);
|
|
Expr<IntSort> ggx_gy = ctx.mkApp(g, gx_gy);
|
|
BoolExpr eq = ctx.mkEq(ggx_gy, gz);
|
|
BoolExpr c1 = ctx.mkNot(eq);
|
|
|
|
/* assert x + z <= y */
|
|
ArithExpr<IntSort> 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 */
|
|
IntNum 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();
|
|
IntNum 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");
|
|
|
|
IntSort 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
|
|
);
|
|
// have to cast here because it is not possible to type a member of an array of mixed generics
|
|
@SuppressWarnings("unchecked")
|
|
FuncDecl<IntSort> first = (FuncDecl<IntSort>) tuple.getFieldDecls()[0]; // declarations are for
|
|
// projections
|
|
@SuppressWarnings("unused")
|
|
FuncDecl<?> second = tuple.getFieldDecls()[1];
|
|
Expr<IntSort> x = ctx.mkConst("x", int_type);
|
|
Expr<IntSort> y = ctx.mkConst("y", int_type);
|
|
Expr<TupleSort> n1 = tuple.mkDecl().apply(x, y);
|
|
Expr<IntSort> n2 = first.apply(n1);
|
|
BoolExpr n3 = ctx.mkEq(x, n2);
|
|
System.out.printf("Tuple example: %s%n", 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);
|
|
Expr<BitVecSort> x = ctx.mkConst("x", bv_type);
|
|
Expr<BitVecSort> zero = 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);
|
|
Expr<BitVecSort> c103 = 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.printf("formula %s%n", 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<IntSort> a = ctx.mkConstDecl(declNames[0], ctx.mkIntSort());
|
|
FuncDecl<IntSort> 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.printf("formula: %s%n", 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 */
|
|
IntSort I = ctx.mkIntSort();
|
|
FuncDecl<IntSort> 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.printf("formula: %s%n", 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.printf("Z3 error: %s%n", 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();
|
|
IntNum one = ctx.mkInt(1);
|
|
IntNum zero = ctx.mkInt(0);
|
|
Expr<IntSort> ite = ctx.mkITE(f, one, zero);
|
|
|
|
System.out.printf("Expr: %s%n", ite);
|
|
}
|
|
|
|
// / Create an enumeration data type.
|
|
|
|
public <T extends Sort> void enumExampleTyped(Context ctx) throws TestFailedException
|
|
{
|
|
System.out.println("EnumExample");
|
|
Log.append("EnumExample");
|
|
|
|
Symbol name = ctx.mkSymbol("fruit");
|
|
|
|
EnumSort<T> fruit = ctx.mkEnumSort(name, ctx.mkSymbol("apple"),
|
|
ctx.mkSymbol("banana"), ctx.mkSymbol("orange"));
|
|
|
|
// helper function for consistent typing: https://docs.oracle.com/javase/tutorial/java/generics/capture.html
|
|
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<EnumSort<T>> apple = fruit.getConsts()[0];
|
|
Expr<EnumSort<T>> banana = fruit.getConsts()[1];
|
|
Expr<EnumSort<T>> 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, ctx.mkApp(fruit.getTesterDecls()[0], apple),
|
|
false);
|
|
|
|
/* Oranges fail the apple test */
|
|
disprove(ctx, ctx.mkApp(fruit.getTesterDecls()[0], orange), false);
|
|
prove(ctx, ctx.mkNot(ctx.mkApp(fruit.getTesterDecls()[0], orange)), false);
|
|
|
|
Expr<EnumSort<T>> 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);
|
|
}
|
|
|
|
// while you can do this untyped, it's safer to have a helper function -- this will prevent you from
|
|
// mixing up your enum types
|
|
public void enumExampleUntyped(Context ctx) throws TestFailedException
|
|
{
|
|
System.out.println("EnumExample");
|
|
Log.append("EnumExample");
|
|
|
|
Symbol name = ctx.mkSymbol("fruit2");
|
|
|
|
EnumSort<Object> fruit = ctx.mkEnumSort(name, ctx.mkSymbol("apple2"),
|
|
ctx.mkSymbol("banana2"), ctx.mkSymbol("orange2"));
|
|
|
|
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<EnumSort<Object>> apple = fruit.getConsts()[0];
|
|
Expr<EnumSort<Object>> banana = fruit.getConsts()[1];
|
|
Expr<EnumSort<Object>> 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, ctx.mkApp(fruit.getTesterDecls()[0], apple),
|
|
false);
|
|
|
|
/* Oranges fail the apple test */
|
|
disprove(ctx, ctx.mkApp(fruit.getTesterDecls()[0], orange), false);
|
|
prove(ctx, ctx.mkNot(ctx.mkApp(fruit.getTesterDecls()[0], orange)), false);
|
|
|
|
Expr<EnumSort<Object>> 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.
|
|
|
|
@SuppressWarnings("unchecked")
|
|
public void listExample(Context ctx) throws TestFailedException
|
|
{
|
|
System.out.println("ListExample");
|
|
Log.append("ListExample");
|
|
|
|
IntSort int_ty = ctx.mkIntSort();
|
|
|
|
ListSort<IntSort> int_list = ctx.mkListSort(ctx.mkSymbol("int_list"), int_ty);
|
|
|
|
Expr<ListSort<IntSort>> nil = ctx.mkConst(int_list.getNilDecl());
|
|
Expr<ListSort<IntSort>> l1 = ctx.mkApp(int_list.getConsDecl(), ctx.mkInt(1), nil);
|
|
Expr<ListSort<IntSort>> 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 */
|
|
Expr<IntSort> x = ctx.mkConst("x", int_ty);
|
|
Expr<IntSort> 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 */
|
|
Expr<ListSort<IntSort>> u = ctx.mkConst("u", int_list);
|
|
Expr<ListSort<IntSort>> 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(ctx.mkApp(int_list.getIsNilDecl(), u), 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)) */
|
|
BoolExpr fml1 = ctx.mkEq(u, ctx.mkApp(int_list.getConsDecl(),
|
|
ctx.mkApp(int_list.getHeadDecl(), u),
|
|
ctx.mkApp(int_list.getTailDecl(), u)));
|
|
BoolExpr fml = ctx.mkImplies(ctx.mkApp(int_list.getIsConsDecl(), u), fml1);
|
|
System.out.printf("Formula %s%n", fml);
|
|
|
|
prove(ctx, fml, false);
|
|
|
|
disprove(ctx, fml1, false);
|
|
}
|
|
|
|
// / Create a binary tree datatype.
|
|
|
|
@SuppressWarnings("unchecked")
|
|
public <Tree> void treeExample(Context ctx) throws TestFailedException
|
|
{
|
|
System.out.println("TreeExample");
|
|
Log.append("TreeExample");
|
|
|
|
String[] head_tail = new String[] { "car", "cdr" };
|
|
Sort[] sorts = new Sort[] { null, null };
|
|
int[] sort_refs = new int[] { 0, 0 };
|
|
Constructor<Tree> 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<Tree>[] constructors = new Constructor[] { nil_con, cons_con };
|
|
|
|
DatatypeSort<Tree> cell = ctx.mkDatatypeSort("cell", constructors);
|
|
|
|
FuncDecl<DatatypeSort<Tree>> nil_decl = nil_con.ConstructorDecl();
|
|
FuncDecl<BoolSort> is_nil_decl = nil_con.getTesterDecl();
|
|
FuncDecl<DatatypeSort<Tree>> cons_decl = cons_con.ConstructorDecl();
|
|
FuncDecl<BoolSort> is_cons_decl = cons_con.getTesterDecl();
|
|
FuncDecl<?>[] cons_accessors = cons_con.getAccessorDecls();
|
|
FuncDecl<?> car_decl = cons_accessors[0];
|
|
FuncDecl<?> cdr_decl = cons_accessors[1];
|
|
|
|
Expr<DatatypeSort<Tree>> nil = ctx.mkConst(nil_decl);
|
|
Expr<DatatypeSort<Tree>> l1 = ctx.mkApp(cons_decl, nil, nil);
|
|
Expr<DatatypeSort<Tree>> 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 */
|
|
Expr<DatatypeSort<Tree>> u = ctx.mkConst("u", cell);
|
|
Expr<DatatypeSort<Tree>> v = ctx.mkConst("v", cell);
|
|
Expr<DatatypeSort<Tree>> x = ctx.mkConst("x", cell);
|
|
Expr<DatatypeSort<Tree>> 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(ctx.mkApp(is_nil_decl, u), 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)) */
|
|
BoolExpr fml1 = ctx.mkEq(u, ctx.mkApp(cons_decl, ctx.mkApp(car_decl, u), ctx.mkApp(cdr_decl, u)));
|
|
BoolExpr fml = ctx.mkImplies(ctx.mkApp(is_cons_decl, u), fml1);
|
|
System.out.printf("Formula %s%n", 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>
|
|
@SuppressWarnings({"unchecked", "unused", "UnusedAssignment"})
|
|
public <Tree, Forest> void forestExample(Context ctx) throws TestFailedException
|
|
{
|
|
System.out.println("ForestExample");
|
|
Log.append("ForestExample");
|
|
|
|
DatatypeSort<Forest> forest;
|
|
DatatypeSort<Tree> tree;
|
|
FuncDecl<DatatypeSort<Forest>> nil1_decl, cons1_decl, cdr1_decl, car2_decl, cdr2_decl;
|
|
FuncDecl<DatatypeSort<Tree>> car1_decl, nil2_decl, cons2_decl;
|
|
FuncDecl<BoolSort> is_nil1_decl, is_nil2_decl, is_cons1_decl, is_cons2_decl;
|
|
|
|
//
|
|
// 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<Forest> nil1_con, cons1_con;
|
|
Constructor<Tree> nil2_con, cons2_con;
|
|
Constructor<Forest>[] constructors1 = new Constructor[2];
|
|
Constructor<Tree>[] constructors2 = new Constructor[2];
|
|
Symbol[] sort_names = { ctx.mkSymbol("forest"), ctx.mkSymbol("tree") };
|
|
|
|
/* build a forest */
|
|
nil1_con = ctx.mkConstructor(ctx.mkSymbol("nil1"),
|
|
ctx.mkSymbol("is_nil1"), 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<Object>[][] clists = new Constructor[][] { constructors1,
|
|
constructors2 };
|
|
|
|
Sort[] sorts = ctx.mkDatatypeSorts(sort_names, clists);
|
|
forest = (DatatypeSort<Forest>) sorts[0];
|
|
tree = (DatatypeSort<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 = (FuncDecl<DatatypeSort<Tree>>) cons1_accessors[0];
|
|
cdr1_decl = (FuncDecl<DatatypeSort<Forest>>) 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 = (FuncDecl<DatatypeSort<Forest>>) cons2_accessors[0];
|
|
cdr2_decl = (FuncDecl<DatatypeSort<Forest>>) cons2_accessors[1];
|
|
|
|
Expr<DatatypeSort<Forest>> nil1 = ctx.mkConst(nil1_decl);
|
|
Expr<DatatypeSort<Tree>> nil2 = ctx.mkConst(nil2_decl);
|
|
Expr<DatatypeSort<Forest>> f1 = ctx.mkApp(cons1_decl, nil2, nil1);
|
|
Expr<DatatypeSort<Tree>> t1 = ctx.mkApp(cons2_decl, nil1, nil1);
|
|
Expr<DatatypeSort<Tree>> t2 = ctx.mkApp(cons2_decl, f1, nil1);
|
|
Expr<DatatypeSort<Tree>> t3 = ctx.mkApp(cons2_decl, f1, f1);
|
|
Expr<DatatypeSort<Tree>> t4 = ctx.mkApp(cons2_decl, nil1, f1);
|
|
Expr<DatatypeSort<Forest>> f2 = ctx.mkApp(cons1_decl, t1, nil1);
|
|
Expr<DatatypeSort<Forest>> 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 */
|
|
Expr<DatatypeSort<Forest>> u = ctx.mkConst("u", forest);
|
|
Expr<DatatypeSort<Forest>> v = ctx.mkConst("v", forest);
|
|
Expr<DatatypeSort<Tree>> x = ctx.mkConst("x", tree);
|
|
Expr<DatatypeSort<Tree>> y = ctx.mkConst("y", tree);
|
|
Expr<DatatypeSort<Forest>> l1 = ctx.mkApp(cons1_decl, x, u);
|
|
Expr<DatatypeSort<Forest>> 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(ctx.mkApp(is_nil1_decl, u), 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");
|
|
IntNum 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<IntSort> v = model.evaluate(ctx.mkAdd(x, y), false);
|
|
if (v != null)
|
|
{
|
|
System.out.printf("result = %s%n", v);
|
|
} else
|
|
{
|
|
System.out.println("Failed to evaluate: x+y");
|
|
}
|
|
} else
|
|
{
|
|
System.out.println("BUG, the constraints are satisfiable.");
|
|
}
|
|
}
|
|
|
|
// / Demonstrate how to use #Eval on tuples.
|
|
|
|
@SuppressWarnings("unchecked")
|
|
public void evalExample2(Context ctx)
|
|
{
|
|
System.out.println("EvalExample2");
|
|
Log.append("EvalExample2");
|
|
|
|
IntSort 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<IntSort> first = (FuncDecl<IntSort>) tuple.getFieldDecls()[0]; // declarations are for
|
|
// projections
|
|
FuncDecl<IntSort> second = (FuncDecl<IntSort>) tuple.getFieldDecls()[1];
|
|
Expr<TupleSort> tup1 = ctx.mkConst("t1", tuple);
|
|
Expr<TupleSort> 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.printf("evaluating tup1 %s%n", model.evaluate(tup1, false));
|
|
System.out.printf("evaluating tup2 %s%n", model.evaluate(tup2, false));
|
|
System.out.printf("evaluating second(tup2) %s%n", 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 (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<BitVecSort> v = solver.getModel().evaluate(to_minimize[i], false);
|
|
// we still have to cast because we want to use a method in BitVecNum
|
|
// however, we cannot cast to a type which doesn't match the generic, e.g. IntNum
|
|
int ui = ((BitVecNum) v).getInt();
|
|
if (ui < upper[i])
|
|
{
|
|
upper[i] = ui;
|
|
}
|
|
System.out.printf("%d %d %d%n", 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.
|
|
|
|
@SuppressWarnings("unchecked")
|
|
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");
|
|
|
|
ArithExpr<IntSort> t1 = ctx.mkAdd(x, ctx.mkSub(y, ctx.mkAdd(x, z)));
|
|
Expr<IntSort> t2 = t1.simplify();
|
|
System.out.printf("%s -> %s%n", 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.printf("proof: %s%n", 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 <S, T> void finiteDomainExample(Context ctx)
|
|
{
|
|
System.out.println("FiniteDomainExample");
|
|
Log.append("FiniteDomainExample");
|
|
|
|
FiniteDomainSort<S> s = ctx.mkFiniteDomainSort("S", 10);
|
|
FiniteDomainSort<T> t = ctx.mkFiniteDomainSort("T", 10);
|
|
FiniteDomainNum<S> s1 = (FiniteDomainNum<S>) ctx.mkNumeral(1, s);
|
|
FiniteDomainNum<T> t1 = (FiniteDomainNum<T>) 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.printf("Sort: %s%n", 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.printf("x=%s; y=%s; z=%s%n", x.toString(), y.toString(), 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.printf("OK, unsat:%n%s%n", 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.printf("OK, sat:%n%s%n", 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.printf("OK, unsat:%n%s%n", 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.printf("c5 = %s%n", c5);
|
|
|
|
/* Generic solver */
|
|
Solver s = ctx.mkSolver();
|
|
s.add(c5);
|
|
|
|
if (s.check() != Status.SATISFIABLE)
|
|
throw new TestFailedException();
|
|
|
|
System.out.printf("OK, model: %s%n", s.getModel());
|
|
}
|
|
|
|
@SuppressWarnings("unchecked")
|
|
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<IntSort> mx = opt.MkMaximize(xExp);
|
|
Optimize.Handle<IntSort> 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));
|
|
|
|
IntExpr e1 = ctx1.mkIntConst("e1");
|
|
IntExpr e2 = ctx2.mkIntConst("e1");
|
|
Expr<IntSort> 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 static void main(String[] args)
|
|
{
|
|
JavaGenericExample p = new JavaGenericExample();
|
|
try
|
|
{
|
|
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.simpleExample();
|
|
|
|
{ // These examples need model generation turned on.
|
|
HashMap<String, String> cfg = new HashMap<>();
|
|
cfg.put("model", "true");
|
|
Context ctx = new Context(cfg);
|
|
|
|
p.optimizeExample(ctx);
|
|
p.basicTests(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<>();
|
|
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.enumExampleTyped(ctx);
|
|
p.enumExampleUntyped(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<>();
|
|
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.printf("Z3 Managed Exception: %s%n", ex.getMessage());
|
|
System.out.println("Stack trace: ");
|
|
ex.printStackTrace(System.out);
|
|
} catch (TestFailedException ex)
|
|
{
|
|
System.out.printf("TEST CASE FAILED: %s%n", ex.getMessage());
|
|
System.out.println("Stack trace: ");
|
|
ex.printStackTrace(System.out);
|
|
} catch (Exception ex)
|
|
{
|
|
System.out.printf("Unknown Exception: %s%n", ex.getMessage());
|
|
System.out.println("Stack trace: ");
|
|
ex.printStackTrace(System.out);
|
|
}
|
|
}
|
|
}
|