public ConjunctionDomain(string baseDomain, Template left, Template right, ref Z3Context z3Context, string str, int constantRange)
{
this.str = str;
args = new List<ICEDomain>();
args.Add(ICEDomainFactory.GetInstance(baseDomain, left, ref z3Context, str + "_1", constantRange));
args.Add(ICEDomainFactory.GetInstance(baseDomain, right, ref z3Context, str + "_2", constantRange));
}
string str; // is "b1" for functionname == "b1"
#endregion Fields
#region Constructors
public ConjunctionDomain(string baseDomain, int numConjuncts, ref Z3Context z3Context, string str, int constantRange)
{
Debug.Assert(numConjuncts > 0);
args = new List<ICEDomain>();
this.str = str;
for (int i = 0; i < numConjuncts; i++)
{
if (baseDomain == "Intervals")
{
this.args.Add(new ICEIntervals(ref z3Context, this.str + "_" + i.ToString(), constantRange) as ICEDomain);
}
else if (baseDomain == "Octagons")
{
this.args.Add(new ICEOctagons(ref z3Context, this.str + "_" + i.ToString(), constantRange) as ICEDomain);
}
else throw new ICEHoudiniInternalError("Domain not found");
}
}
public Term constructSMTConstraint(List<Model.Element> states, ref Z3Context z3Context)
{
//Debug.Assert(states.Count == 1);
List<Term> terms = new List<Term>();
for (int i = 0; i < this.args.Count; i++)
{
terms.Add(this.args.ElementAt(i).constructSMTConstraint(states, ref z3Context));
}
return z3Context.context.MkAnd(terms.ToArray());
}
public static ICEDomain GetInstance(string domainName, ref Z3Context z3Context, string str, int constantRange)
{
if (domainName == "Intervals")
{
return new ICEIntervals(ref z3Context, str, constantRange) as ICEDomain;
}
else if (domainName == "Octagons")
{
return new ICEOctagons(ref z3Context, str, constantRange) as ICEDomain;
}
int pos = domainName.IndexOf("(");
if (pos <= 0)
{
Console.WriteLine("Domain {0} not found", domainName);
Console.WriteLine("Supported domains are:");
Console.WriteLine(" {Intervals}");
throw new ICEHoudiniInternalError("Domain not found");
}
else{
string baseDomain = domainName.Substring(0, pos);
string templateString = domainName.Substring(pos);
TemplateParser.initialize(templateString);
Template t = TemplateParser.Parse();
return GetInstance(baseDomain, t, ref z3Context, str, constantRange);
}
}
public static ICEDomain GetInstance(string baseDomain, Template t, ref Z3Context z3Context, string str, int constantRange)
{
if (t.op == TemplateOperator.None)
{
if (t.value == 1)
{
if (baseDomain == "Intervals")
{
return new ICEIntervals(ref z3Context, str, constantRange);
}
else if (baseDomain == "Octagons")
{
return new ICEOctagons(ref z3Context, str, constantRange);
}
else throw new ICEHoudiniInternalError("Domain not found");
}
else
{
return new ConjunctionDomain(baseDomain, t.value, ref z3Context, str, constantRange);
}
}
if (t.op == TemplateOperator.ConjunctionOp)
{
return new ConjunctionDomain(baseDomain, t.left, t.right, ref z3Context, str, constantRange);
}
Debug.Assert(t.op == TemplateOperator.DisjunctionOp);
return new DisjunctionDomain(baseDomain, t.left, t.right, ref z3Context, str, constantRange);
}
public Term constructSMTConstraint(List<Model.Element> states, ref Z3Context z3Context)
{
Context context = z3Context.context;
Term termHasFirst = context.MkConst(this.str + "_hf", z3Context.boolSort);
Term termHasSecond = context.MkConst(this.str + "_hs", z3Context.boolSort);
Term termSign1 = context.MkConst(this.str + "_s1", z3Context.boolSort);
Term termSign2 = context.MkConst(this.str + "_s2", z3Context.boolSort);
Term termVar1 = context.MkConst(this.str + "_v1", z3Context.intSort);
Term termVar2 = context.MkConst(this.str + "_v2", z3Context.intSort);
Term termOp = context.MkConst(this.str + "_op", z3Context.boolSort);
Term termConstant = context.MkConst(this.str + "_c", z3Context.intSort);
if(!this.numVarsInitialized)
{
this.numVars = states.Count;
this.numVarsInitialized = true;
// assert 0 <= var1, var2 <= numVars-1
context.AssertCnstr(context.MkLe(context.MkNumeral(0, z3Context.intSort), termVar1));
context.AssertCnstr(context.MkLe(termVar1, context.MkNumeral(this.numVars-1, z3Context.intSort)));
context.AssertCnstr(context.MkLe(context.MkNumeral(0, z3Context.intSort), termVar2));
context.AssertCnstr(context.MkLe(termVar2, context.MkNumeral(this.numVars-1, z3Context.intSort)));
if(this.numVars > 1)
{
context.AssertCnstr(context.MkNot(context.MkEq(termVar1, termVar2)));
}
else
{
Debug.Assert(this.numVars == 1);
context.AssertCnstr(context.MkNot(termHasSecond));
}
}
else
{
Debug.Assert(states.Count == this.numVars);
}
Term firstVal = context.MkNumeral(0, z3Context.intSort);
for(int i = this.numVars-1; i >= 0; i--)
{
var state = states[i] as Model.Integer;
if (state == null)
throw new ICEHoudiniInternalError("Incorrect type, expected int");
var intval = state.AsInt();
firstVal = context.MkIte(context.MkEq(termVar1, context.MkNumeral(i, z3Context.intSort)), context.MkNumeral(intval, z3Context.intSort), firstVal);
}
firstVal = context.MkIte(termSign1, firstVal, context.MkUnaryMinus(firstVal));
firstVal = context.MkIte(termHasFirst, firstVal, context.MkNumeral(0, z3Context.intSort));
Term secondVal = context.MkNumeral(0, z3Context.intSort);
if(this.numVars > 1) {
for(int i = this.numVars-1; i >= 0; i--)
{
var state = states[i] as Model.Integer;
if (state == null)
throw new ICEHoudiniInternalError("Incorrect type, expected int");
var intval = state.AsInt();
secondVal = context.MkIte(context.MkEq(termVar2, context.MkNumeral(i, z3Context.intSort)), context.MkNumeral(intval, z3Context.intSort), secondVal);
}
secondVal = context.MkIte(termSign2, secondVal, context.MkUnaryMinus(secondVal));
secondVal = context.MkIte(termHasSecond, secondVal, context.MkNumeral(0, z3Context.intSort));
}
// else hasSecond = false and secondVal = 0 in this case already
Term lhs = context.MkAdd(firstVal, secondVal);
return context.MkIte(termOp, context.MkEq(lhs, termConstant), context.MkLe(lhs, termConstant));
}
public bool initializeFromModel(Z3.Model model, ref Z3Context z3Context)
{
Debug.Assert(model != null);
Context context = z3Context.context;
Term termHasFirst = context.MkConst(this.str + "_hf", z3Context.boolSort);
Term termHasSecond = context.MkConst(this.str + "_hs", z3Context.boolSort);
Term termSign1 = context.MkConst(this.str + "_s1", z3Context.boolSort);
Term termSign2 = context.MkConst(this.str + "_s2", z3Context.boolSort);
Term termVar1 = context.MkConst(this.str + "_v1", z3Context.intSort);
Term termVar2 = context.MkConst(this.str + "_v2", z3Context.intSort);
Term termOp = context.MkConst(this.str + "_op", z3Context.boolSort);
Term termConstant = context.MkConst(this.str + "_c", z3Context.intSort);
bool ret = false;
bool hf = context.GetBoolValue(model.Eval(termHasFirst)).getBool();
bool hs = context.GetBoolValue(model.Eval(termHasSecond)).getBool();
bool s1 = context.GetBoolValue(model.Eval(termSign1)).getBool();
bool s2 = context.GetBoolValue(model.Eval(termSign2)).getBool();
int v1 = context.GetNumeralInt(model.Eval(termVar1));
int v2 = context.GetNumeralInt(model.Eval(termVar2));
bool op = context.GetBoolValue(model.Eval(termOp)).getBool();
int c = context.GetNumeralInt(model.Eval(termConstant));
if (this.hasFirst != hf)
{
ret = true;
goto init;
}
if (!this.hasFirst && !hf)
{
bool oldVal = this.op ? 0 == this.constant : 0 <= this.constant;
bool newVal = op ? 0 == c : 0 <= c;
if (oldVal != newVal)
{
ret = true;
}
goto init;
}
// hf && this.hasFirst
if (this.sign1 != s1 || this.var1 != v1)
{
ret = true;
goto init;
}
if (this.hasSecond != hs)
{
ret = true;
goto init;
}
if (this.hasSecond && hs)
{
if (this.sign2 != s2 || this.var2 != v2)
{
ret = true;
goto init;
}
}
if (this.op != op || this.constant != c)
{
ret = true;
goto init;
}
init:
this.hasFirst = hf;
this.hasSecond = hs;
this.sign1 = s1;
this.sign2 = s2;
this.var1 = v1;
this.var2 = v2;
this.op = op;
this.constant = c;
return ret;
}
public bool initializeFromModel(Z3.Model model, ref Z3Context z3Context)
{
Debug.Assert(model != null);
Context context = z3Context.context;
Term termUpperLimit = context.MkConst(this.str + "_ul", z3Context.intSort);
Term termLowerLimit = context.MkConst(this.str + "_ll", z3Context.intSort);
Term termHasUpperLimit = context.MkConst(this.str + "_hul", z3Context.boolSort);
Term termHasLowerLimit = context.MkConst(this.str + "_hll", z3Context.boolSort);
bool ret = false;
int ul = context.GetNumeralInt(model.Eval(termUpperLimit));
int ll = context.GetNumeralInt(model.Eval(termLowerLimit));
bool hul = context.GetBoolValue(model.Eval(termHasUpperLimit)).getBool();
bool hll = context.GetBoolValue(model.Eval(termHasLowerLimit)).getBool();
if((hasUpperLimit != hul) || (hasUpperLimit && hul && (upperLimit != ul)))
ret = true;
if ((hasLowerLimit != hll) || (hasLowerLimit && hll && (lowerLimit != ll)))
ret = true;
upperLimit = ul;
lowerLimit = ll;
hasUpperLimit = hul;
hasLowerLimit = hll;
return ret;
}
public ICEOctagons(ref Z3Context z3Context, string str, int constantRange)
{
// Initialize the invariant function with "true".
this.hasFirst = false;
this.hasSecond = false;
this.sign1 = false;
this.sign2 = false;
this.var1 = 0;
this.var2 = 0;
this.numVars = 0;
this.numVarsInitialized = false; // will be initialized after the first counter-example is processed.
this.op = true;
this.constant = 0;
this.str = str;
// enter the variables in the z3Context
Context context = z3Context.context;
Term termHasFirst = context.MkConst(this.str + "_hf", z3Context.boolSort);
Term termHasSecond = context.MkConst(this.str + "_hs", z3Context.boolSort);
Term termSign1 = context.MkConst(this.str + "_s1", z3Context.boolSort);
Term termSign2 = context.MkConst(this.str + "_s2", z3Context.boolSort);
Term termVar1 = context.MkConst(this.str + "_v1", z3Context.intSort);
Term termVar2 = context.MkConst(this.str + "_v2", z3Context.intSort);
Term termOp = context.MkConst(this.str + "_op", z3Context.boolSort);
Term termConstant = context.MkConst(this.str + "_c", z3Context.intSort);
// assert -constantRange <= constant <= constantRange
context.AssertCnstr(context.MkLe(context.MkNumeral(-1*constantRange, z3Context.intSort), termConstant));
context.AssertCnstr(context.MkLe(termConstant, context.MkNumeral(constantRange, z3Context.intSort)));
// assert hasSecond => hasFirst
context.AssertCnstr(context.MkImplies(termHasSecond, termHasFirst));
// assert 0 <= var1, var2 <= numVars-1 when the first counter-example is processed.
}
int upperLimit; // \in [-10,10]
#endregion Fields
#region Constructors
public ICEIntervals(ref Z3Context z3Context, string str, int constantRange)
{
// Initialize the invariant function with "true".
this.upperLimit = 0;
this.lowerLimit = 0;
this.hasUpperLimit = false;
this.hasLowerLimit = false;
//this.sampleID = 0;
this.str = str;
// enter the variables in the z3Context
Context context = z3Context.context;
Term termUpperLimit = context.MkConst(this.str + "_ul", z3Context.intSort);
Term termLowerLimit = context.MkConst(this.str + "_ll", z3Context.intSort);
Term termHasUpperLimit = context.MkConst(this.str + "_hul", z3Context.boolSort);
Term termHasLowerLimit = context.MkConst(this.str + "_hll", z3Context.boolSort);
// assert -constantRange <= lowerLimit <= upperLimit <= constantRange
context.AssertCnstr(context.MkLe(context.MkNumeral(-1*constantRange, z3Context.intSort), termLowerLimit));
context.AssertCnstr(context.MkLe(termLowerLimit, termUpperLimit));
context.AssertCnstr(context.MkLe(termUpperLimit, context.MkNumeral(constantRange, z3Context.intSort)));
}
public Term constructSMTConstraint(List<Model.Element> states, ref Z3Context z3Context)
{
Debug.Assert(states.Count == 1);
var state = states[0] as Model.Integer;
if (state == null)
throw new ICEHoudiniInternalError("Incorrect type, expected int");
var intval = state.AsInt();
Context context = z3Context.context;
Term termUpperLimit = context.MkConst(this.str + "_ul", z3Context.intSort);
Term termLowerLimit = context.MkConst(this.str + "_ll", z3Context.intSort);
Term termHasUpperLimit = context.MkConst(this.str + "_hul", z3Context.boolSort);
Term termHasLowerLimit = context.MkConst(this.str + "_hll", z3Context.boolSort);
Term c1_id = context.MkImplies(termHasLowerLimit, context.MkLe(termLowerLimit, context.MkNumeral(intval, z3Context.intSort)));
Term c2_id = context.MkImplies(termHasUpperLimit, context.MkLe(context.MkNumeral(intval, z3Context.intSort), termUpperLimit));
return context.MkAnd(c1_id, c2_id);
}
public bool initializeFromModel(Z3.Model model, ref Z3Context z3Context)
{
Debug.Assert(model != null);
bool ret = false;
if (this.arg1.initializeFromModel(model, ref z3Context))
ret = true;
if (this.arg2.initializeFromModel(model, ref z3Context))
ret = true;
return ret;
}
public Term constructSMTConstraint(List<Model.Element> states, ref Z3Context z3Context)
{
return z3Context.context.MkOr(arg1.constructSMTConstraint(states, ref z3Context), arg2.constructSMTConstraint(states, ref z3Context));
}
public DisjunctionDomain(string baseDomain, Template left, Template right, ref Z3Context z3Context, string str, int constantRange)
{
this.str = str;
this.arg1 = ICEDomainFactory.GetInstance(baseDomain, left, ref z3Context, str + "_1", constantRange);
this.arg2 = ICEDomainFactory.GetInstance(baseDomain, right, ref z3Context, str + "_2", constantRange);
}
private ICEOutcome LearnInvFromTemplate(Dictionary<string, int> impl2Priority, Template t, int range, out VCGenOutcome overallOutcome)
{
overallOutcome = null;
// create a new z3 context
if (z3Context != null)
{
z3Context.context.Dispose();
z3Context.config.Dispose();
}
z3Context = new Z3Context();
foreach (var func in existentialFunctions.Values)
{
// initialize function to an "Octagons" instance with the given template "t".
function2Value[func.Name] = ICEDomainFactory.GetInstance("Octagons", t, ref z3Context, func.Name, range);
}
// add counterexamples into the z3Context. These are obtained from the earlier iterations of the template.
foreach (var cex in counterExamples)
{
AddCounterExampleToZ3Context(cex);
}
var worklist = new SortedSet<Tuple<int, string>>();
name2Impl.Keys.Iter(k => worklist.Add(Tuple.Create(impl2Priority[k], k)));
while (worklist.Any())
{
var impl = worklist.First().Item2;
worklist.Remove(worklist.First());
#region vcgen
var gen = prover.VCExprGen;
var terms = new List<Expr>();
foreach (var tup in impl2FuncCalls[impl])
{
var controlVar = tup.Item2;
var exprVars = tup.Item3;
var varList = new List<Expr>();
exprVars.Args.OfType<Expr>().Iter(v => varList.Add(v));
var args = new List<Expr>();
controlVar.InParams.Iter(v => args.Add(Expr.Ident(v)));
Expr term = Expr.Eq(new NAryExpr(Token.NoToken, new FunctionCall(controlVar), args),
function2Value[tup.Item1].Gamma(varList));
if (controlVar.InParams.Count != 0)
{
term = new ForallExpr(Token.NoToken, new List<Variable>(controlVar.InParams.ToArray()),
new Trigger(Token.NoToken, true, new List<Expr> { new NAryExpr(Token.NoToken, new FunctionCall(controlVar), args) }),
term);
}
terms.Add(term);
}
var env = BinaryTreeAnd(terms, 0, terms.Count - 1);
env.Typecheck(new TypecheckingContext((IErrorSink)null));
var envVC = prover.Context.BoogieExprTranslator.Translate(env);
var vc = gen.Implies(envVC, impl2VC[impl]);
if (CommandLineOptions.Clo.Trace)
{
Console.WriteLine("Verifying {0}: ", impl);
//Console.WriteLine("env: {0}", envVC);
var envFuncs = new HashSet<string>();
impl2FuncCalls[impl].Iter(tup => envFuncs.Add(tup.Item1));
envFuncs.Iter(f => PrintFunction(existentialFunctions[f]));
}
#endregion vcgen
VCExpr finalVC;
#region bound_value_of_cexs
#if false
finalVC = vc;
#else
int bound = 1000000;
terms.Clear();
foreach (var tup in impl2FuncCalls[impl])
{
var exprVars = tup.Item3;
var varList = new List<Expr>();
exprVars.Args.OfType<Expr>().Where(v => v.Type.IsInt).Iter(v => varList.Add(v));
foreach (var variable in varList)
{
terms.Add(Expr.Le(variable, Expr.Literal(bound)));
terms.Add(Expr.Ge(variable, Expr.Literal(-1 * bound)));
//terms.Add(Expr.Ge(variable, Expr.Literal(0)));
}
}
var boundcex = BinaryTreeAnd(terms, 0, terms.Count - 1);
boundcex.Typecheck(new TypecheckingContext((IErrorSink)null));
var boundcexVC = prover.Context.BoogieExprTranslator.Translate(boundcex);
finalVC = gen.Implies(boundcexVC, vc);
#endif
#endregion bound_value_of_cexs
var handler = impl2ErrorHandler[impl].Item1;
var collector = impl2ErrorHandler[impl].Item2;
collector.Reset(impl);
VCisValid = true; // set to false if control reaches HandleCounterExample
realErrorEncountered = false;
newSamplesAdded = false;
var start = DateTime.Now;
prover.Push();
prover.Assert(gen.Not(finalVC), true);
prover.FlushAxiomsToTheoremProver();
prover.Check();
ProverInterface.Outcome proverOutcome = prover.CheckOutcomeCore(handler);
//prover.BeginCheck(impl, vc, handler);
//ProverInterface.Outcome proverOutcome = prover.CheckOutcomeCore(handler);
var inc = (DateTime.Now - start);
proverTime += inc;
numProverQueries++;
if (CommandLineOptions.Clo.Trace)
Console.WriteLine("Prover Time taken = " + inc.TotalSeconds.ToString());
if (proverOutcome == ProverInterface.Outcome.TimeOut || proverOutcome == ProverInterface.Outcome.OutOfMemory)
{
Console.WriteLine("Z3 Prover for implementation {0} times out or runs out of memory !", impl);
z3Context.context.Dispose();
z3Context.config.Dispose();
overallOutcome = new VCGenOutcome(proverOutcome, new List<Counterexample>());
return ICEOutcome.Timeout;
}
if (CommandLineOptions.Clo.Trace)
Console.WriteLine(!VCisValid ? "SAT" : "UNSAT");
if (!VCisValid)
{
if (realErrorEncountered)
{
overallOutcome = new VCGenOutcome(ProverInterface.Outcome.Invalid, collector.real_errors);
return ICEOutcome.ErrorFound;
}
Debug.Assert(newSamplesAdded);
HashSet<string> funcsChanged;
if (!learn(out funcsChanged))
{
// learner timed out or there is no valid conjecture in the current given template
overallOutcome = new VCGenOutcome(ProverInterface.Outcome.Invalid, collector.conjecture_errors);
prover.Pop();
return ICEOutcome.InvariantNotFound;
}
// propagate dependent guys back into the worklist, including self
var deps = new HashSet<string>();
deps.Add(impl);
funcsChanged.Iter(f => deps.UnionWith(function2implAssumed[f]));
funcsChanged.Iter(f => deps.UnionWith(function2implAsserted[f]));
deps.Iter(s => worklist.Add(Tuple.Create(impl2Priority[s], s)));
}
prover.Pop();
}
// The program was verified with the current template!
overallOutcome = new VCGenOutcome(ProverInterface.Outcome.Valid, new List<Counterexample>());
return ICEOutcome.InvariantFound;
}
public bool initializeFromModel(Z3.Model model, ref Z3Context z3Context)
{
Debug.Assert(model != null);
bool ret = false;
for (int i = 0; i < args.Count; i++)
{
if (this.args.ElementAt(i).initializeFromModel(model, ref z3Context))
ret = true;
}
return ret;
}
