protected override Dictionary <VCExprVar, Polarity> VisitAfterBinding(VCExprQuantifier node, Polarity arg)
{
var result = node.Body.Accept(this, arg);
foreach (var x in node.BoundVars)
{
result.Remove(x);
}
return(result);
}
public override bool Visit(VCExprQuantifier node, bool arg)
{
Contract.Requires(node != null);
foreach (VCExprVar v in node.BoundVars)
{
Contract.Assert(v != null);
RegisterType(v.Type);
}
return(base.Visit(node, arg));
}
/////////////////////////////////////////////////////////////////////////////////////
public bool Visit(VCExprQuantifier node, LineariserOptions options)
{
//Contract.Requires(node != null);
//Contract.Requires(options != null);
AssertAsFormula(node.Quan.ToString(), options);
Contract.Assert(node.TypeParameters.Count == 0);
Namer.PushScope(); try {
string kind = node.Quan == Quantifier.ALL ? "!" : "?";
wr.Write("{0} [", kind);
for (int i = 0; i < node.BoundVars.Count; i++)
{
VCExprVar var = node.BoundVars[i];
Contract.Assert(var != null);
// ensure that the variable name starts with ?
string printedName = Namer.GetLocalName(var, "V" + MakeIdPrintable(var.Name));
Contract.Assert(printedName != null);
Contract.Assert(printedName[0] == 'V');
if (i > 0)
{
wr.Write(",");
}
wr.Write("{0}", printedName);
}
wr.Write("] : (");
/* if (options.QuantifierIds) {
* // only needed for Z3
* VCQuantifierInfos! infos = node.Infos;
* if (infos.qid != null) {
* wr.Write("(QID ");
* wr.Write(infos.qid);
* wr.Write(") ");
* }
* if (0 <= infos.uniqueId) {
* wr.Write("(SKOLEMID ");
* wr.Write(infos.uniqueId);
* wr.Write(") ");
* }
* } */
Linearise(node.Body, options);
// WriteTriggers(node.Triggers, options);
wr.Write(")");
return(true);
} finally {
Namer.PopScope();
}
}
private void InstantiateQuantifier(VCExprQuantifier quantifierExpr)
{
var boundVariableToLabels = quantifierExpr.Info.instantiationLabels;
var boundVariableToExprs = boundVariableToLabels.Keys.ToDictionary(
boundVariable => boundVariable,
boundVariable =>
boundVariableToLabels[boundVariable]
.SelectMany(label =>
accLabelToInstances.ContainsKey(label) ? accLabelToInstances[label] : new HashSet <VCExpr>()).ToHashSet());
ConstructInstances(quantifierExpr, boundVariableToExprs, 0, new List <VCExpr>());
}
public override Dictionary <VCExprVar, Polarity> Visit(VCExprQuantifier node, Polarity arg)
{
var result = base.Visit(node, arg);
if (arg != Polarity.Unknown && !result.Keys.Intersect(BoundTermVars).Any())
{
if ((arg == Polarity.Positive) == (node.Quan == Quantifier.EX))
{
quantifiers.Add(node);
}
}
return(result);
}
private VCExpr AugmentWithInstances(VCExprQuantifier quantifierExpr)
{
if (quantifierExpr.Quan == Quantifier.ALL)
{
return(vcExprGen.And(quantifierExpr,
vcExprGen.NAry(VCExpressionGenerator.AndOp,
quantifierInstantiationInfo[quantifierExpr].instances.Values.ToList())));
}
else
{
return(vcExprGen.Or(quantifierExpr,
vcExprGen.NAry(VCExpressionGenerator.OrOp,
quantifierInstantiationInfo[quantifierExpr].instances.Values.ToList())));
}
}
private void ConstructInstances(VCExprQuantifier quantifierExpr,
Dictionary <VCExprVar, HashSet <VCExpr> > boundVariableToExprs, int n, List <VCExpr> instance)
{
if (quantifierExpr.BoundVars.Count == n)
{
InstantiateQuantifierAtInstance(quantifierExpr, instance);
return;
}
var boundVariable = quantifierExpr.BoundVars[n];
foreach (var expr in boundVariableToExprs[boundVariable])
{
instance.Add(expr);
ConstructInstances(quantifierExpr, boundVariableToExprs, n + 1, instance);
instance.RemoveAt(n);
}
}
public VCExpr BindQuantifier(VCExprQuantifier node)
{
if (node.TypeParameters.Count > 0)
{
return(node);
}
var boundVariableToLabels = node.Info.instantiationLabels;
if (boundVariableToLabels.Count < node.BoundVars.Count ||
boundVariableToLabels.Any(kv => kv.Value.Count == 0))
{
return(node);
}
var v = new VCExprVar($"{quantifierBindingNamePrefix}{quantifierBinding.Count}", Type.Bool);
quantifierBinding[v] = node;
quantifierInstantiationInfo[node] = new QuantifierInstantiationInfo(boundVariableToLabels);
return(v);
}
private void InstantiateQuantifierAtInstance(VCExprQuantifier quantifierExpr, List <VCExpr> instance)
{
var quantifierInstantiationInfo = this.quantifierInstantiationInfo[quantifierExpr];
if (quantifierInstantiationInfo.instances.ContainsKey(instance))
{
return;
}
var subst = new VCExprSubstitution(
Enumerable.Range(0, quantifierExpr.BoundVars.Count).ToDictionary(
x => quantifierExpr.BoundVars[x],
x => instance[x]), new Dictionary <TypeVariable, Type>());
var substituter = new SubstitutingVCExprVisitor(vcExprGen);
var instantiation = substituter.Mutate(quantifierExpr.Body, subst);
quantifierInstantiationInfo.instances[new List <VCExpr>(instance)] =
Skolemizer.Skolemize(this, quantifierExpr.Quan == Quantifier.ALL ? Polarity.Positive : Polarity.Negative,
instantiation);
}
private VCExpr PerformSkolemization(VCExprQuantifier node, bool arg)
{
var oldToNew = node.BoundVars.ToDictionary(v => v, v => (VCExpr)qiEngine.FreshSkolemConstant(v));
foreach (var x in node.BoundVars)
{
bound.Add(x, oldToNew[x]);
}
var retExpr = (VCExprQuantifier)base.Visit(node, arg);
retExpr.Info.instantiationExprs.Iter(kv =>
{
kv.Value.Iter(expr => { qiEngine.AddTerm(kv.Key, expr.Accept(this, arg)); });
});
foreach (var x in node.BoundVars)
{
bound.Remove(x);
}
return(retExpr.Body);
}
private VCExpr HandleQuantifier(VCExprQuantifier node, List <VCExprVar /*!*/> /*!*/ newBoundVars, VariableBindings bindings)
{
Contract.Requires(bindings != null);
Contract.Requires(node != null);
Contract.Requires(cce.NonNullElements(newBoundVars));
Contract.Ensures(Contract.Result <VCExpr>() != null);
List <VCTrigger /*!*/> /*!*/ newTriggers = MutateTriggers(node.Triggers, bindings);
Contract.Assert(cce.NonNullElements(newTriggers));
VCExpr /*!*/ newBody = Mutate(node.Body, bindings);
Contract.Assert(newBody != null);
newBody = AxBuilder.Cast(newBody, Type.Bool);
if (newBoundVars.Count == 0) // might happen that no bound variables are left
{
return(newBody);
}
return(Gen.Quantify(node.Quan, new List <TypeVariable /*!*/>(), newBoundVars,
newTriggers, node.Infos, newBody));
}
////////////////////////////////////////////////////////////////////////////
public override VCExpr Visit(VCExprQuantifier node, VariableBindings oldBindings)
{
Contract.Requires(oldBindings != null);
Contract.Requires(node != null);
Contract.Ensures(Contract.Result <VCExpr>() != null);
VariableBindings /*!*/
bindings = oldBindings.Clone();
// bound term variables are replaced with bound term variables
// typed in a simpler way
List <VCExprVar /*!*/> /*!*/
newBoundVars =
BoundVarsAfterErasure(node.BoundVars, bindings);
// type variables are replaced with ordinary quantified variables
GenBoundVarsForTypeParams(node.TypeParameters, newBoundVars, bindings);
VCExpr /*!*/
newNode = HandleQuantifier(node, newBoundVars, bindings);
Contract.Assert(newNode != null);
if (!(newNode is VCExprQuantifier) || !IsUniversalQuantifier(node))
{
return(newNode);
}
VariableBindings /*!*/
bindings2;
if (!RedoQuantifier(node, (VCExprQuantifier)newNode, node.BoundVars, oldBindings,
out bindings2, out newBoundVars))
{
return(newNode);
}
GenBoundVarsForTypeParams(node.TypeParameters, newBoundVars, bindings2);
return(HandleQuantifier(node, newBoundVars, bindings2));
}
public override VCExpr Visit(VCExprQuantifier node, FlattenerState state)
{
Contract.Requires(node != null);
Contract.Ensures(Contract.Result <VCExpr>() != null);
if (state.InTerm)
{
return(GetVarFor(node));
}
// we only flatten within the matrix of the quantified formula,
// not within the triggers (since SMT-solvers do not seem to
// appreciate triggers with let-binders)
VCExpr newBody = Mutate(node.Body, state);
// Check whether any of the extracted terms contain variables
// bound by this quantifier. In this case, we have to add
// let-binders and remove the extracted terms
bool cont = true;
while (cont)
{
List <VCExprLetBinding /*!*/> /*!*/
localBindings =
RemoveBindingsWithVars(node.BoundVars, node.TypeParameters);
Contract.Assert(cce.NonNullElements(localBindings));
if (localBindings.Count > 0)
{
newBody = AddBindings(localBindings, newBody, state);
}
else
{
cont = false;
}
}
return(Gen.Quantify(node.Quan, node.TypeParameters, node.BoundVars, node.Triggers, node.Infos, newBody));
}
/////////////////////////////////////////////////////////////////////////////////////
public bool Visit(VCExprQuantifier node, LineariserOptions options)
{
//Contract.Requires(options != null);
//Contract.Requires(node != null);
AssertAsFormula(node.Quan.ToString(), options);
Contract.Assert(node.TypeParameters.Count == 0);
Namer.PushScope();
try {
string kind = node.Quan == Quantifier.ALL ? "FORALL" : "EXISTS";
wr.Write("({0} (", kind);
for (int i = 0; i < node.BoundVars.Count; i++)
{
VCExprVar var = node.BoundVars[i];
Contract.Assert(var != null);
string printedName = Namer.GetLocalName(var, var.Name);
Contract.Assert(printedName != null);
if (i != 0)
{
wr.Write(" ");
}
WriteId(printedName);
if (options.UseTypes)
{
wr.Write(" :TYPE {0}", TypeToString(var.Type));
}
}
wr.Write(") ");
WriteTriggers(node.Triggers, options);
if (options.QuantifierIds)
{
// only needed for Z3
VCQuantifierInfos infos = node.Infos;
Contract.Assert(infos != null);
if (infos.qid != null)
{
wr.Write("(QID ");
wr.Write(infos.qid);
wr.Write(") ");
}
if (0 <= infos.uniqueId)
{
wr.Write("(SKOLEMID ");
wr.Write(infos.uniqueId);
wr.Write(") ");
}
}
if (options.UseWeights)
{
int weight = QKeyValue.FindIntAttribute(node.Infos.attributes, "weight", 1);
if (weight != 1)
{
wr.Write("(WEIGHT ");
wr.Write(weight);
wr.Write(") ");
}
}
Linearise(node.Body, options);
wr.Write(")");
return(true);
} finally {
Namer.PopScope();
}
}
/////////////////////////////////////////////////////////////////////////////////////
public bool Visit(VCExprQuantifier node, LineariserOptions options)
{
Contract.Assert(node.TypeParameters.Count == 0);
UnderQuantifier++;
Namer.PushScope(); try {
string kind = node.Quan == Quantifier.ALL ? "forall" : "exists";
wr.Write("({0} (", kind);
for (int i = 0; i < node.BoundVars.Count; i++)
{
VCExprVar var = node.BoundVars[i];
Contract.Assert(var != null);
string printedName = Namer.GetQuotedLocalName(var, var.Name);
Contract.Assert(printedName != null);
wr.Write("({0} {1}) ", printedName, TypeToString(var.Type));
}
wr.Write(") ");
VCQuantifierInfos infos = node.Infos;
var weight = QKeyValue.FindIntAttribute(infos.attributes, "weight", 1);
if (!ProverOptions.UseWeights)
{
weight = 1;
}
var hasAttrs = node.Triggers.Count > 0 || infos.qid != null || weight != 1 || infos.uniqueId != -1;
if (hasAttrs)
{
wr.Write("(! ");
}
Linearise(node.Body, options);
if (hasAttrs)
{
wr.Write("\n");
if (infos.qid != null)
{
wr.Write(" :qid {0}\n", SMTLibNamer.QuoteId(infos.qid));
}
if (weight != 1)
{
wr.Write(" :weight {0}\n", weight);
}
if (infos.uniqueId != -1)
{
wr.Write(" :skolemid |{0}|\n", infos.uniqueId);
}
WriteTriggers(node.Triggers, options);
wr.Write(")");
}
wr.Write(")");
return(true);
} finally {
UnderQuantifier--;
Namer.PopScope();
}
}
public Term Visit(VCExprQuantifier node, bool arg)
{
throw new ProofGenUnexpectedStateException(GetType(),
"only expect variables and function operations in extractors");
}
public bool Visit(VCExprQuantifier node, TextWriter wr)
{
//Contract.Requires(wr != null);
//Contract.Requires(node != null);
string /*!*/ quan = node.Quan == Quantifier.ALL ? "Forall" : "Exists";
Contract.Assert(quan != null);
wr.Write("({0} ", quan);
if (node.TypeParameters.Count > 0)
{
wr.Write("<");
string /*!*/ sep = "";
foreach (TypeVariable /*!*/ v in node.TypeParameters)
{
Contract.Assert(v != null);
wr.Write(sep);
sep = ", ";
wr.Write("{0}", v.Name);
}
wr.Write("> ");
}
if (node.BoundVars.Count > 0)
{
string /*!*/ sep = "";
foreach (VCExprVar /*!*/ v in node.BoundVars)
{
Contract.Assert(v != null);
wr.Write(sep);
sep = ", ";
Print(v, wr);
}
wr.Write(" ");
}
wr.Write(":: ");
if (node.Triggers.Count > 0)
{
wr.Write("{0} ", "{");
string /*!*/ sep = "";
foreach (VCTrigger /*!*/ t in node.Triggers)
{
Contract.Assert(t != null);
wr.Write(sep);
sep = ", ";
string /*!*/ sep2 = "";
foreach (VCExpr /*!*/ e in t.Exprs)
{
Contract.Assert(e != null);
wr.Write(sep2);
sep2 = "+";
Print(e, wr);
}
}
wr.Write(" {0} ", "}");
}
Print(node.Body, wr);
wr.Write(")");
return(true);
}
private VCExpr HandleQuantifier(VCExprQuantifier node, List<VCExprVar/*!*/>/*!*/ newBoundVars, VariableBindings bindings){
Contract.Requires(bindings != null);
Contract.Requires(node != null);
Contract.Requires(cce.NonNullElements(newBoundVars));
Contract.Ensures(Contract.Result<VCExpr>() != null);
List<VCTrigger/*!*/>/*!*/ newTriggers = MutateTriggers(node.Triggers, bindings);
Contract.Assert(cce.NonNullElements(newTriggers));
VCExpr/*!*/ newBody = Mutate(node.Body, bindings);
Contract.Assert(newBody != null);
newBody = AxBuilder.Cast(newBody, Type.Bool);
if (newBoundVars.Count == 0) // might happen that no bound variables are left
return newBody;
return Gen.Quantify(node.Quan, new List<TypeVariable/*!*/>(), newBoundVars,
newTriggers, node.Infos, newBody);
}
////////////////////////////////////////////////////////////////////////////
public override VCExpr Visit(VCExprQuantifier node, VariableBindings oldBindings) {
Contract.Requires(oldBindings != null);
Contract.Requires(node != null);
Contract.Ensures(Contract.Result<VCExpr>() != null);
VariableBindings/*!*/ bindings = oldBindings.Clone();
// bound term variables are replaced with bound term variables
// typed in a simpler way
List<VCExprVar/*!*/>/*!*/ newBoundVars =
BoundVarsAfterErasure(node.BoundVars, bindings);
// type variables are replaced with ordinary quantified variables
GenBoundVarsForTypeParams(node.TypeParameters, newBoundVars, bindings);
VCExpr/*!*/ newNode = HandleQuantifier(node, newBoundVars, bindings);
Contract.Assert(newNode != null);
if (!(newNode is VCExprQuantifier) || !IsUniversalQuantifier(node))
return newNode;
VariableBindings/*!*/ bindings2;
if (!RedoQuantifier(node, (VCExprQuantifier)newNode, node.BoundVars, oldBindings,
out bindings2, out newBoundVars))
return newNode;
GenBoundVarsForTypeParams(node.TypeParameters, newBoundVars, bindings2);
return HandleQuantifier(node, newBoundVars, bindings2);
}
private VCExpr HandleQuantifier(VCExprQuantifier node, List<VCExprVar/*!*/>/*!*/ occurringVars/*!*/, List<VCExprVar/*!*/>/*!*/ newBoundVars, VariableBindings bindings)
{
Contract.Requires(bindings != null);
Contract.Requires(node != null);
Contract.Requires(cce.NonNullElements(occurringVars/*!*/));
Contract.Requires(cce.NonNullElements(newBoundVars));
Contract.Ensures(Contract.Result<VCExpr>() != null);
List<VCExprLetBinding/*!*/>/*!*/ typeVarBindings =
AxBuilderPremisses.GenTypeParamBindings(node.TypeParameters, occurringVars, bindings, true);
Contract.Assert(typeVarBindings != null);
// Check whether some of the type parameters could not be
// determined from the bound variable types. In this case, we
// quantify explicitly over these variables
if (typeVarBindings.Count < node.TypeParameters.Count) {
foreach (TypeVariable/*!*/ var in node.TypeParameters) {
Contract.Assert(var != null);
if (typeVarBindings.All(b => !b.V.Equals(var)))
newBoundVars.Add((VCExprVar)bindings.TypeVariableBindings[var]);
}
}
// the lists of old and new bound variables for which type
// antecedents are to be generated
List<VCExprVar/*!*/>/*!*/ varsWithTypeSpecs = new List<VCExprVar/*!*/>();
List<VCExprVar/*!*/>/*!*/ newVarsWithTypeSpecs = new List<VCExprVar/*!*/>();
if (!IsUniversalQuantifier(node) ||
CommandLineOptions.Clo.TypeEncodingMethod
== CommandLineOptions.TypeEncoding.Predicates) {
foreach (VCExprVar/*!*/ oldVar in occurringVars) {
Contract.Assert(oldVar != null);
varsWithTypeSpecs.Add(oldVar);
newVarsWithTypeSpecs.Add(bindings.VCExprVarBindings[oldVar]);
}
} // else, no type antecedents are created for any variables
List<VCTrigger/*!*/>/*!*/ furtherTriggers;
VCExpr/*!*/ typePremisses =
GenTypePremisses(varsWithTypeSpecs, newVarsWithTypeSpecs,
bindings.TypeVariableBindings,
typeVarBindings, out furtherTriggers);
Contract.Assert(cce.NonNullElements(furtherTriggers));
Contract.Assert(typePremisses != null);
List<VCTrigger/*!*/>/*!*/ newTriggers = MutateTriggers(node.Triggers, bindings);
Contract.Assert(cce.NonNullElements(newTriggers));
newTriggers.AddRange(furtherTriggers);
newTriggers = AddLets2Triggers(newTriggers, typeVarBindings);
VCExpr/*!*/ newBody = Mutate(node.Body, bindings);
Contract.Assert(newBody != null);
// assemble the new quantified formula
if (CommandLineOptions.Clo.TypeEncodingMethod
== CommandLineOptions.TypeEncoding.None) {
typePremisses = VCExpressionGenerator.True;
}
VCExpr/*!*/ bodyWithPremisses =
AxBuilderPremisses.AddTypePremisses(typeVarBindings, typePremisses,
node.Quan == Quantifier.ALL,
AxBuilder.Cast(newBody, Type.Bool));
Contract.Assert(bodyWithPremisses != null);
if (newBoundVars.Count == 0) // might happen that no bound variables are left
return bodyWithPremisses;
foreach (VCExprVar/*!*/ v in newBoundVars) {
Contract.Assert(v != null);
if (v.Type == AxBuilderPremisses.U) {
newTriggers.Add(Gen.Trigger(false, AxBuilderPremisses.Cast(v, Type.Int)));
newTriggers.Add(Gen.Trigger(false, AxBuilderPremisses.Cast(v, Type.Bool)));
}
}
return Gen.Quantify(node.Quan, new List<TypeVariable/*!*/>(), newBoundVars,
newTriggers, node.Infos, bodyWithPremisses);
}
////////////////////////////////////////////////////////////////////////////
public override VCExpr Visit(VCExprQuantifier node, VariableBindings oldBindings)
{
Contract.Requires(oldBindings != null);
Contract.Requires(node != null);
Contract.Ensures(Contract.Result<VCExpr>() != null);
VariableBindings bindings = oldBindings.Clone();
// determine the bound vars that actually occur in the body or
// in any of the triggers (if some variables do not occur, we
// need to take special care of type parameters that only occur
// in the types of such variables)
FreeVariableCollector coll = new FreeVariableCollector();
coll.Collect(node.Body);
foreach (VCTrigger trigger in node.Triggers) {
if (trigger.Pos)
foreach (VCExpr/*!*/ e in trigger.Exprs) {
Contract.Assert(e != null);
coll.Collect(e);
}
}
List<VCExprVar/*!*/> occurringVars = new List<VCExprVar/*!*/>(node.BoundVars.Count);
foreach (VCExprVar var in node.BoundVars)
if (coll.FreeTermVars.ContainsKey(var))
occurringVars.Add(var);
occurringVars.TrimExcess();
// bound term variables are replaced with bound term variables typed in
// a simpler way
List<VCExprVar/*!*/>/*!*/ newBoundVars =
BoundVarsAfterErasure(occurringVars, bindings);
Contract.Assert(cce.NonNullElements(newBoundVars));
VCExpr/*!*/ newNode = HandleQuantifier(node, occurringVars,
newBoundVars, bindings);
Contract.Assert(newNode != null);
if (!(newNode is VCExprQuantifier) || !IsUniversalQuantifier(node))
return newNode;
VariableBindings bindings2;
if (!RedoQuantifier(node, (VCExprQuantifier)newNode, occurringVars, oldBindings,
out bindings2, out newBoundVars))
return newNode;
return HandleQuantifier(node, occurringVars,
newBoundVars, bindings2);
}
