/**
* translate boogie statement to prover expression
*
* @param s
* @return
*/
protected ProverExpr statement2ProverExpr(Statement s) {
if (s instanceof AssignStatement) {
AssignStatement st = (AssignStatement) s;
if (st.getLeft() instanceof SimpleHeapAccess || st.getLeft() instanceof ArrayReadExpression) {
return arrayWrite2ProverExpr(st.getLeft(), expression2ProverExpr(st.getRight()));
} else {
return theoremProver.mkEq(
expression2ProverExpr(st.getLeft()), expression2ProverExpr(st.getRight()));
}
} else if (s instanceof AssumeStatement) {
AssumeStatement st = (AssumeStatement) s;
return guardExpression2ProverExpr(st.getExpression());
} else if (s instanceof AssertStatement) {
AssertStatement st = (AssertStatement) s;
return guardExpression2ProverExpr(st.getExpression());
} else if (s instanceof InvokeStatement) {
InvokeStatement st = (InvokeStatement) s;
if (st.getReturnTargets().size() > 1) {
Log.error("A method with too many return parameters! Should have been removed in SSA");
return null;
}
ProverFun fun = procedure2ProverExpr(st.getInvokedProcedure());
Log.error(
"This should not happen as calls are removed by SSA: "
+ fun.toString()); // TODO: proper error handling?
// This can never happen.
LinkedList<ProverExpr> args = new LinkedList<ProverExpr>();
for (Expression e : st.getArguments()) {
args.add(expression2ProverExpr(e));
}
ProverExpr ret = fun.mkExpr((ProverExpr[]) args.toArray(new ProverExpr[args.size()]));
if (st.getReturnTargets().size() > 0) {
ProverExpr lhs = expression2ProverExpr(st.getReturnTargets().get(0));
if (st.getReturnTargets().get(0) instanceof SimpleHeapAccess
|| st.getReturnTargets().get(0) instanceof ArrayReadExpression) {
ret = arrayWrite2ProverExpr(st.getReturnTargets().get(0), ret);
// ((NAryExpression)lhs).addArgument(ret);
// ret = VCExpressionGenerator.binOp(TmpConstants.Eq,
// ((NAryExpression)lhs).getArgument(0),lhs);
} else {
ret = theoremProver.mkEq(lhs, ret);
}
}
return ret;
} else if (s instanceof ExpressionStatement) {
ExpressionStatement es = (ExpressionStatement) s;
return expression2ProverExpr(es.getExpression());
} else {
Log.error("Unmatched Statement " + s.toString());
return null;
}
}
/**
* Translates a guard in an axiom to a prover expression
*
* @param exp
* @return
*/
private ProverExpr guardExpression2ProverExpr(Expression exp) {
if (exp instanceof BinOpExpression) {
/*
* TODO: this case should only occur for inlined axioms. The current
* type system is a bit messed up as it does not really allow
* boolean types in the Boogie program. If we do a major revision,
* we should definitely take care of this
*/
return expression2ProverExpr(exp);
} else if (exp instanceof IteExpression) {
return expression2ProverExpr(exp);
} else {
return theoremProver.mkEq(expression2ProverExpr(exp), theoremProver.mkLiteral(1));
}
}
/**
* @param arrexp
* @param rhs
* @return
*/
private ProverExpr arrayWrite2ProverExpr(Expression arrexp, ProverExpr rhs) {
if (arrexp instanceof SimpleHeapAccess || arrexp instanceof ArrayReadExpression) {
/*
* This is needed here only for one purpose: a[x] = 5 in Boogie is
* translated to a__i[x__j] = 5 in SSA-Boogie but in the VC we have
* to write (= a__i (store a__(i-1) x__j 5), so we need to be able
* to access the previous incarnation of array typed variables
* Probably, we should settle this already during SSA and introduce
* uninterpreted procedures for store and select
*/
Expression base;
LinkedList<Expression> args = new LinkedList<Expression>();
if (arrexp instanceof SimpleHeapAccess) {
SimpleHeapAccess exp = (SimpleHeapAccess) arrexp;
base = exp.getHeapVariable();
args.add(exp.getBaseExpression());
args.add(exp.getFieldExpression());
} else {
ArrayReadExpression exp = (ArrayReadExpression) arrexp;
base = exp.getBaseExpression();
args.add(exp.getIndexExpression());
}
ProverExpr newbase = expression2ProverExpr(base);
ProverExpr lhs =
arrayExpression2ProverExpr(base, args, rhs, new HashMap<Variable, ProverExpr>());
return theoremProver.mkEq(newbase, lhs);
}
Log.error("CRAAAAAAAAAASH");
return null;
}
/**
* Checks the formula
*
* @return Result of the prover
*/
protected ProverResult checkSat() {
// build query info
QueryInfo qi = new QueryInfo();
qi.setTime(0);
qi.setSize(numberOfConjuncts);
methodInfo.getQueries().add(qi);
StopWatch sw = StopWatch.getInstanceAndStart();
ProverResult res = ProverResult.Error;
// check formula
if (z3_output) {
z3_stream.append("(check-sat)"); // not needed actually
// call Z3 via JNI and map result
String formula = z3_stream.toString();
Log.info(formula);
int result = z3.check(formula);
if (-1 == result) res = ProverResult.Unsat;
else if (1 == result) res = ProverResult.Sat;
} else {
res = theoremProver.checkSat(true);
}
// measure time
qi.setTime(sw.stop());
// log time
Log.info(
String.format(" Query #%d: %s", methodInfo.getQueries().size(), qi.getFormattedTime()));
return res;
}
private ProverFun procedure2ProverExpr(BoogieProcedure proc) {
HashMap<Variable, ProverExpr> localbound = new HashMap<Variable, ProverExpr>();
if (!usedFunctions.containsKey(proc)) {
LinkedList<ProverType> args = new LinkedList<ProverType>();
int idx = 0;
for (Variable v : proc.getParameterList()) {
ProverExpr arg = theoremProver.mkBoundVariable(idx++, type2ProverSort(v.getType()));
args.add(arg.getType());
localbound.put(v, arg);
}
ProverFun vcf = null;
ProverType[] arr = args.toArray(new ProverType[args.size()]);
if (proc.isPure()
&& proc.getRootBlock() != null
&& proc.getRootBlock().getStatements().size() == 1) {
// TODO: this is a hack:
// we assume that this case only occurs for prelude functions
// which have only one statement
// this will not work in any other case
Statement stmt = proc.getRootBlock().getStatements().get(0);
ProverExpr b = null;
if (stmt instanceof ExpressionStatement) {
ExpressionStatement es = (ExpressionStatement) stmt;
b = expression2ProverExpr(es.getExpression(), localbound);
} else {
throw new RuntimeException("procedure2ProverExpr failed");
}
vcf = theoremProver.mkDefinedFunction(getProverFriendlyName(proc.getName()), arr, b);
} else {
vcf =
theoremProver.mkUnintFunction(
getProverFriendlyName(proc.getName()),
arr,
type2ProverSort(proc.getReturnVariable().getType()));
// TODO: uninterpreted functions?
}
usedFunctions.put(proc, vcf);
}
return usedFunctions.get(proc);
}
/**
* @param base
* @param indices
* @param rhs is null if we have Select operation, otherwise it is the value E on the right hand
* side of an assignment a[x]=E.
* @param boundvars
* @return This is needed here only for one purpose: a[x] = 5 in Boogie is translated to
* a__i[x__j] = 5 in SSA-Boogie but in the VC we have to write (= a__i (store a__(i-1) x__j
* 5), so we need to be able to access the previous incarnation of array typed variables
* Probably, we should settle this already during SSA and introduce uninterpreted procedures
* for store and select.
*/
private ProverExpr arrayExpression2ProverExpr(
Expression base,
LinkedList<Expression> indices,
ProverExpr rhs,
HashMap<Variable, ProverExpr> boundvars) {
LinkedList<ProverExpr> args = new LinkedList<ProverExpr>();
if (rhs != null) {
if (base instanceof SSAVariable) {
SSAVariable var = (SSAVariable) base;
SSAVariable tmp = null;
for (Variable v : proc.getVarIncarnationMap().get(((SSAVariable) base).getOriginalVar())) {
if (v instanceof SSAVariable) {
if (((SSAVariable) v).getIncarnation() == ((SSAVariable) base).getIncarnation() - 1) {
tmp = (SSAVariable) v;
break;
}
}
}
if (tmp == null) {
tmp = new SSAVariable(var.getOriginalVar(), var.getIncarnation() - 1);
proc.getVarIncarnationMap().get(((SSAVariable) base).getOriginalVar()).addFirst(tmp);
}
base = tmp;
} else {
Log.error(
"org.joogie.vcgen.VCGeneration.arrayaccess2VCExpression: this case has not been considered ... Joogie will crash!");
}
}
ProverExpr arr = expression2ProverExpr(base, boundvars);
for (Expression idx : indices) {
args.add(expression2ProverExpr(idx, boundvars));
}
if (rhs != null)
return theoremProver.mkStore(
arr, (ProverExpr[]) (args.toArray(new ProverExpr[args.size()])), rhs);
else
return theoremProver.mkSelect(
arr, (ProverExpr[]) (args.toArray(new ProverExpr[args.size()])));
}
/** send an axiom to the prover */
protected void addAssertion(ProverExpr pexp) {
/*
* if (z3_firstquery) { z3_stream.append(z3_printSMT2Declarations());
* z3_firstquery = false; } z3_stream.append(z3_proverExpr2SMT2(pexp));
* System.err.println(z3_stream.toString());
*/
theoremProver.addAssertion(pexp);
/*
* if (z3_output) { if (z3_firstquery) {
* z3_stream.append(z3_printSMT2Declarations()); z3_firstquery = false;
* } z3_stream.append(z3_proverExpr2SMT2(pexp)); }
*/
}
/**
* Translates a BoogieType to a Prover Type
*
* @param t
* @return
*/
private ProverType type2ProverSort(BoogieType t) {
if (t.getName().compareTo("int") == 0) {
return theoremProver.getIntType();
} else if (t.getName().compareTo("bool") == 0) {
return theoremProver.getBooleanType();
} else if (t.getName().compareTo("$stringsizetype") == 0) {
ProverType[] argTypes = {theoremProver.getIntType()};
return theoremProver.getArrayType(argTypes, theoremProver.getIntType());
} else if (t instanceof BoogieFieldType) {
return theoremProver.getIntType();
} else if (t instanceof BoogieArrayType) {
ProverType[] argTypes = {theoremProver.getIntType()};
return theoremProver.getArrayType(
argTypes, type2ProverSort(((BoogieArrayType) t).getNestedType()));
} else if (t instanceof HeapType) {
ProverType[] argTypes = {theoremProver.getIntType(), theoremProver.getIntType()};
return theoremProver.getArrayType(argTypes, theoremProver.getIntType());
} else if (t instanceof BoogieObjectType) {
return theoremProver.getIntType();
}
// TODO: not tested!
return theoremProver.getIntType();
}
/**
* generates a prover expression from an expression e
*
* @param e
* @param boundvars
* @return
*/
private ProverExpr expression2ProverExpr(Expression e, HashMap<Variable, ProverExpr> boundvars) {
try {
if (e instanceof ArrayReadExpression) {
ArrayReadExpression exp = (ArrayReadExpression) e;
return arrayExpression2ProverExpr(
exp.getBaseExpression(),
new LinkedList<Expression>(Arrays.asList(new Expression[] {exp.getIndexExpression()})),
null,
boundvars);
} else if (e instanceof InvokeExpression) {
InvokeExpression exp = (InvokeExpression) e;
ProverFun fun = procedure2ProverExpr(exp.getInvokedProcedure());
LinkedList<ProverExpr> args = new LinkedList<ProverExpr>();
for (Expression e2 : exp.getArguments()) {
args.add(expression2ProverExpr(e2, boundvars));
}
return fun.mkExpr((ProverExpr[]) args.toArray(new ProverExpr[args.size()]));
} else if (e instanceof SimpleHeapAccess) {
SimpleHeapAccess exp = (SimpleHeapAccess) e;
return arrayExpression2ProverExpr(
exp.getHeapVariable(),
new LinkedList<Expression>(
Arrays.asList(
new Expression[] {exp.getBaseExpression(), exp.getFieldExpression()})),
null,
boundvars);
} else if (e instanceof TypeExpression) {
TypeExpression exp = (TypeExpression) e;
return expression2ProverExpr(exp.getTypeVariable(), boundvars);
} else if (e instanceof Variable) {
Variable exp = (Variable) e;
if (boundvars.containsKey(exp)) {
return boundvars.get(exp);
}
if (!usedVariable.containsKey(exp)) {
ProverExpr pe =
theoremProver.mkVariable(
getProverFriendlyName(exp.getName()), type2ProverSort(exp.getType()));
usedVariable.put(exp, pe);
}
return usedVariable.get(exp);
} else if (e instanceof UboundedIntConstant) {
UboundedIntConstant exp = (UboundedIntConstant) e;
return theoremProver.mkLiteral(BigInteger.valueOf(exp.getValue()));
} else if (e instanceof Constant) {
Log.error("DEBUG-ERROR, there should not be any constant but Integers! VC will be wrong!");
return expression2ProverExpr(BoogieProgram.v().getNullReference(), boundvars);
} else if (e instanceof QuantifiedExpression) {
// TODO: right now, Quantifiers can only be used in Axioms
QuantifiedExpression qe = (QuantifiedExpression) e;
HashMap<Variable, ProverExpr> bvars = new HashMap<Variable, ProverExpr>(boundvars);
// LinkedList<ProverExpr> localBound = new
// LinkedList<ProverExpr>();
int idx = 0;
for (Variable v : qe.getBoundVariables()) {
ProverExpr boundvar = theoremProver.mkBoundVariable(idx++, type2ProverSort(v.getType()));
bvars.put(v, boundvar);
// localBound.add(boundvar);
}
ProverExpr boundExp = expression2ProverExpr(qe.getExpression(), bvars);
if (qe.getQuantifier() == Quantifier.ForAll) {
return theoremProver.mkAll(boundExp, theoremProver.getBooleanType());
} else {
return theoremProver.mkEx(boundExp, theoremProver.getBooleanType());
}
} else if (e instanceof BinOpExpression) {
BinOpExpression be = (BinOpExpression) e;
ProverExpr left = (expression2ProverExpr(be.getLhs(), boundvars));
ProverExpr right = (expression2ProverExpr(be.getRhs(), boundvars));
switch (be.getOp()) {
case Eq:
{
return theoremProver.mkEq(left, right);
}
case Lt:
{
return theoremProver.mkLt(left, right);
}
case Le:
{
return theoremProver.mkLeq(left, right);
}
case Gt:
{
return theoremProver.mkGt(left, right);
}
case Ge:
{
return theoremProver.mkGeq(left, right);
}
case Neq:
{
return theoremProver.mkNot(theoremProver.mkEq(left, right));
}
case Implies:
{
return theoremProver.mkOr(theoremProver.mkNot(left), right);
}
case LAnd:
{
return theoremProver.mkAnd(left, right);
}
case LOr:
{
return theoremProver.mkOr(left, right);
}
case Plus:
{
return theoremProver.mkPlus(left, right);
}
case Minus:
{
return theoremProver.mkMinus(left, right);
}
case Mul:
{
return theoremProver.mkMult(left, right);
}
default:
{
throw new RuntimeException("Unmatched binop: " + be.getOp().toString());
// TODO: a proper exception might be nice.
// However, this case can only occur if we screw up the
// implementation
}
}
} else if (e instanceof IteExpression) {
IteExpression ite = (IteExpression) e;
ProverExpr condE = expression2ProverExpr(ite.getCond(), boundvars);
ProverExpr thenE = expression2ProverExpr(ite.getThen(), boundvars);
ProverExpr elseE = expression2ProverExpr(ite.getElse(), boundvars);
return theoremProver.mkIte(condE, thenE, elseE);
} else {
Log.error("Unmatched Expression " + e.toString());
return null;
}
} catch (Exception exc) {
Log.error("expression2ProverExpr failed: " + exc.toString());
Log.error("Called on expression: " + e.toString());
if (e instanceof BinOpExpression) {
BinOpExpression boe = (BinOpExpression) e;
Log.error(boe.getLhs().getType().toString() + " and " + boe.getRhs().getType());
}
return null;
}
}
protected ProverExpr makeHelperVar(String name) {
z3_helperVars.add(name);
return theoremProver.mkVariable(name, theoremProver.getBooleanType());
}
/** pop the top frame from the prover stack */
protected void popProverStack() {
theoremProver.pop();
if (z3_output) {
z3_stream.append("(pop)");
}
}
/** push a new frame on the prover stack */
protected void pushProverStack() {
theoremProver.push();
if (z3_output) {
z3_stream.append("(push)");
}
}
