/**
* Determines the value of an LTL-FO+ formula using a 3-valued logic. In
* addition to TRUE and FALSE, we add a third value "?". The following rules
* apply:
* <ul>
* <li>¬ ? = ?</li>
* <li>TRUE ∧ ? = ?</li>
* <li>FALSE ∧ ? = FALSE</li>
* <li>TRUE ∨ ? = TRUE</li>
* <li>FALSE ∨ ? = ?</li>
* <li>X φ = G φ = ? no matter φ</li>
* <li>F φ = φ ∨ ?</li>
* <li>φ U ψ = ψ ∨ ?</li>
* <li>∃<sub>p</sub> x: φ = φ(x<sub>1</sub>) ∨ ... ∨
* φ(x<sub>n</sub>) for x<sub>i</sub> in Dom<sub>s</sub>(p)</li>
* <li>∀<sub>p</sub> x: φ = φ(x<sub>1</sub>) ∧ ... ∧
* φ(x<sub>n</sub>) for x<sub>i</sub> in Dom<sub>s</sub>(p)</li>
*
* @param o
* @param m
* TODO
* @return
*/
protected static Outcome isSatisfiedInCurrentState(Operator o, WatcherMessage m)
{
// This method uses getClass to branch on the type of operator
// used; TODO: redesign with method overriding
Outcome oc1, oc2;
Operator o1, o2, o3;
if (o.GetType() == typeof(OperatorNot))
{
o1 = ((OperatorNot)o).getOperand();
oc1 = isSatisfiedInCurrentState(o1, m);
return threeValuedNot(oc1);
}
else if (o.GetType() == typeof(OperatorX) ||
o.GetType() == typeof(OperatorG))
{
// TODO
// assert(false);
return Outcome.INCONCLUSIVE;
}
else if (o.GetType() == typeof(OperatorEquals))
{
o1 = ((OperatorEquals)o).getLeftOperand();
o2 = ((OperatorEquals)o).getRightOperand();
if (o1.GetType () == typeof(ConstantPath))
{
// Left member is a path; we compare that path
// to the right member
HashSet<Atom> dom = m.getDomain((ConstantPath) o1);
foreach (Atom a in dom)
{
// We return true if at least one value at the end
// of the path equals o2
if (a.Equals(o2))
return Outcome.TRUE;
}
return Outcome.FALSE;
}
else
{
// We compare directly the two members
if (o1.Equals(o2))
return Outcome.TRUE;
}
return Outcome.FALSE;
}
else if (o.GetType() == typeof(OperatorAnd))
{
o1 = ((OperatorAnd)o).getLeftOperand();
oc1 = isSatisfiedInCurrentState(o1, m);
o2 = ((OperatorAnd)o).getRightOperand();
oc2 = isSatisfiedInCurrentState(o2, m);
return threeValuedAnd(oc1, oc2);
}
else if (o.GetType() == typeof(OperatorOr))
{
o1 = ((OperatorOr)o).getLeftOperand();
oc1 = isSatisfiedInCurrentState(o1, m);
o2 = ((OperatorOr)o).getRightOperand();
oc2 = isSatisfiedInCurrentState(o2, m);
return threeValuedOr(oc1, oc2);
}
else if (o.GetType() == typeof(OperatorF))
{
o1 = ((OperatorF)o).getOperand();
oc1 = isSatisfiedInCurrentState(o1, m);
return threeValuedOr(oc1, Outcome.INCONCLUSIVE);
}
else if (o.GetType() == typeof(OperatorImplies))
{
o1 = ((OperatorImplies)o).getLeftOperand();
oc1 = isSatisfiedInCurrentState(o1, m);
o2 = ((OperatorImplies)o).getRightOperand();
oc2 = isSatisfiedInCurrentState(o2, m);
return threeValuedOr(threeValuedNot(oc1), oc2);
}
else if (o.GetType() == typeof(OperatorU))
{
o1 = ((OperatorU)o).getLeftOperand();
oc1 = isSatisfiedInCurrentState(o1, m);
o2 = ((OperatorU)o).getRightOperand();
oc2 = isSatisfiedInCurrentState(o2, m);
return threeValuedOr(oc1, threeValuedAnd(oc1, Outcome.INCONCLUSIVE));
}
else if (o.GetType() == typeof(OperatorV))
{
o1 = ((OperatorV)o).getLeftOperand();
oc1 = isSatisfiedInCurrentState(o1, m);
o2 = ((OperatorV)o).getRightOperand();
oc2 = isSatisfiedInCurrentState(o2, m);
return threeValuedAnd(oc1, threeValuedOr(oc2, Outcome.INCONCLUSIVE));
}
else if (o.GetType() == typeof(FOExists))
{
// Iterate over domain
// TODO: supposes that the string qualifier is an atom
Atom p = new Atom(((FOExists)o).getQualifier());
Atom x = ((FOExists)o).getQuantifiedVariable();
HashSet<Atom> s = m.getDomain(p);
oc1 = Outcome.FALSE;
foreach (Atom a in s)
{
o2 = ((FOExists)o).getOperand();
o3 = o2.evaluate(x, a);
oc2 = isSatisfiedInCurrentState(o3, m);
oc1 = threeValuedOr(oc1, oc2);
}
return oc1;
}
else if (o.GetType() == typeof(FOForAll))
{
// Iterate over domain
// TODO: supposes that the string qualifier is an atom
Atom p = new Atom(((FOForAll)o).getQualifier());
Atom x = ((FOForAll)o).getQuantifiedVariable();
HashSet<Atom> s = m.getDomain(p);
oc1 = Outcome.TRUE;
foreach (Atom a in s)
{
o2 = ((FOForAll)o).getOperand();
o3 = o2.evaluate(x, a);
oc2 = isSatisfiedInCurrentState(o3, m);
oc1 = threeValuedAnd(oc1, oc2);
}
return oc1;
}
else if (o.GetType() == typeof(Constant))
{
// TODO: true and false are checked by comparing their
// string representations; there should be a more graceful
// way to check for true and false
if (((Constant)o).getSymbol() == Operator.m_trueAtom.getSymbol())
{
return Outcome.TRUE;
}
else if (((Constant)o).getSymbol() == Operator.m_falseAtom.getSymbol())
{
return Outcome.FALSE;
}
return Outcome.INCONCLUSIVE;
}
return Outcome.INCONCLUSIVE;
}
/**
* Decomposes a watcher's node, given a received message.
*
* @param m
* The message on which to make the decomposition
* @return A Set of WatcherNodes consisting of the resulting decomposition
* for that node. If the left-hand side of the node is empty,
* returns an empty set.
*/
public HashSet<WatcherNode> spawn(WatcherMessage m)
{
// This method uses getClass to branch on the type of operator
// used; TODO: redesign with method overriding
HashSet<WatcherNode> spawnedSet, outSet = new HashSet<WatcherNode>();
WatcherNode wn;
Operator o2, o3;
// Picks a formula and removes it from Gamma
foreach (Operator o in m_gamma)
{
m_gamma.Remove(o);
// Optimization from original algorithm: if formula can readily
// be decided in current state, bypass decomposition
Outcome oc = isSatisfiedInCurrentState(o, m);
if (oc == Outcome.TRUE)
{
// Formula is true: stop decomposition of this formula and
// continue spawning
return spawn(m);
}
else if (oc == Outcome.FALSE)
{
// Formula is false: stop branch and return empty set
return outSet;
}
// Operator OR
else if (o.GetType() == typeof(OperatorOr))
{
// Do for left operand
wn = new WatcherNode(this);
o2 = ((OperatorOr)o).getLeftOperand();
wn.addToGamma(o2);
spawnedSet = wn.spawn(m);
foreach (WatcherNode wn2 in spawnedSet)
{
outSet.Add(wn2);
}
// Do for right operand
wn = new WatcherNode(this);
o2 = ((OperatorOr)o).getRightOperand();
wn.addToGamma(o2);
spawnedSet = wn.spawn(m);
foreach (WatcherNode wn2 in spawnedSet)
{
outSet.Add(wn2);
}
return outSet;
}
// Operator IMPLIES
else if (o.GetType() == typeof(OperatorImplies))
{
// Do for right operand
wn = new WatcherNode(this);
o2 = ((OperatorImplies)o).getRightOperand();
wn.addToGamma(o2);
spawnedSet = wn.spawn(m);
foreach (WatcherNode wn2 in spawnedSet)
{
outSet.Add(wn2);
}
// Do for right operand
wn = new WatcherNode(this);
o2 = ((OperatorImplies)o).getLeftOperand().getNegated();
wn.addToGamma(o2.getNegatedNormalForm());
spawnedSet = wn.spawn(m);
foreach (WatcherNode wn2 in spawnedSet)
{
outSet.Add(wn2);
}
return outSet;
}
// Operator AND
else if (o.GetType() == typeof(OperatorAnd))
{
// Do for left operand
wn = new WatcherNode(this);
o2 = ((OperatorAnd)o).getLeftOperand();
wn.addToGamma(o2);
// Do for left operand
o2 = ((OperatorAnd)o).getRightOperand();
wn.addToGamma(o2);
spawnedSet = wn.spawn(m);
foreach (WatcherNode wn2 in spawnedSet)
{
outSet.Add(wn2);
}
return outSet;
}
// Operator X
else if (o.GetType() == typeof(OperatorX))
{
wn = new WatcherNode(this);
o2 = ((OperatorX)o).getOperand();
wn.addToDelta(o2);
spawnedSet = wn.spawn(m);
foreach (WatcherNode wn2 in spawnedSet)
{
outSet.Add(wn2);
}
return outSet;
}
// Operator G
else if (o.GetType() == typeof(OperatorG))
{
// Do for left operand
wn = new WatcherNode(this);
o2 = ((OperatorG)o).getOperand();
wn.addToGamma(o2);
wn.addToDelta(o);
spawnedSet = wn.spawn(m);
foreach (WatcherNode wn2 in spawnedSet)
{
outSet.Add(wn2);
}
return outSet;
}
// Operator F
else if (o.GetType() == typeof(OperatorF))
{
// Do for left node
wn = new WatcherNode(this);
o2 = ((OperatorF)o).getOperand();
wn.addToGamma(o2);
spawnedSet = wn.spawn(m);
foreach (WatcherNode wn2 in spawnedSet)
{
outSet.Add(wn2);
}
// Do for right node
wn = new WatcherNode(this);
wn.addToDelta(o);
spawnedSet = wn.spawn(m);
foreach (WatcherNode wn2 in spawnedSet)
{
outSet.Add(wn2);
}
return outSet;
}
// Operator U
else if (o.GetType() == typeof(OperatorU))
{
// Do for left node
wn = new WatcherNode(this);
o2 = ((OperatorU)o).getRightOperand();
wn.addToGamma(o2);
spawnedSet = wn.spawn(m);
foreach (WatcherNode wn2 in spawnedSet)
{
outSet.Add(wn2);
}
// Do for right node
wn = new WatcherNode(this);
wn.addToDelta(o);
spawnedSet = wn.spawn(m);
foreach (WatcherNode wn2 in spawnedSet)
{
outSet.Add(wn2);
}
return outSet;
}
// Operator V
else if (o.GetType() == typeof(OperatorV))
{
// Do for left node
wn = new WatcherNode(this);
o2 = ((OperatorV)o).getLeftOperand();
wn.addToGamma(o2);
o2 = ((OperatorV)o).getRightOperand();
wn.addToGamma(o2);
spawnedSet = wn.spawn(m);
foreach (WatcherNode wn2 in spawnedSet)
{
outSet.Add(wn2);
}
// Do for right node
wn = new WatcherNode(this);
o2 = ((OperatorV)o).getRightOperand();
wn.addToGamma(o2);
wn.addToDelta(o);
spawnedSet = wn.spawn(m);
foreach (WatcherNode wn2 in spawnedSet)
{
outSet.Add(wn2);
}
return outSet;
}
// Operator [p=x]
else if (o.GetType() == typeof(FOForAll))
{
// Iterate over domain
wn = new WatcherNode(this);
// TODO: supposes that the string qualifier is an atom
Atom p = new Atom(((FOForAll)o).getQualifier());
Atom x = ((FOForAll)o).getQuantifiedVariable();
HashSet<Atom> s = m.getDomain(p);
foreach (Atom v in s)
{
o2 = ((FOForAll)o).getOperand();
o3 = o2.evaluate(x, v);
wn.addToGamma(o3);
}
spawnedSet = wn.spawn(m);
foreach (WatcherNode wn2 in spawnedSet)
{
outSet.Add(wn2);
}
return outSet;
}
// Operator <p=x>
else if (o.GetType() == typeof(FOExists))
{
// Iterate over domain
// TODO: supposes that the string qualifier is an atom
Atom p = new Atom(((FOExists)o).getQualifier());
Atom x = ((FOExists)o).getQuantifiedVariable();
HashSet<Atom> s = m.getDomain(p);
foreach (Atom v in s)
{
wn = new WatcherNode(this);
o2 = ((FOExists)o).getOperand();
o3 = o2.evaluate(x, v);
wn.addToGamma(o3);
spawnedSet = wn.spawn(m);
foreach (WatcherNode wn2 in spawnedSet)
{
outSet.Add(wn2);
}
}
// TODO (Dominic): Validate this ?
return outSet;
}
// Operator =
else if (o.GetType() == typeof(OperatorEquals))
{
// This should never happen! When down to the evaluation
// of an equality, all variables should be evaluated!
//assert(false);
return outSet;
}
// Operator NOT
else if (o.GetType() == typeof(OperatorNot))
{
// Do for operand
wn = new WatcherNode(this);
o2 = ((OperatorNot)o).getOperand();
if (o2.GetType() != typeof(Constant))
{
// This should not happen! Negations should be pushed
// to atoms
//assert(false);
return outSet;
}
// TODO: true and false are checked by comparing their
// string representations; there should be a more graceful
// way
// to check for true and false
if (((Constant)o).getSymbol() == Operator.m_trueAtom.getSymbol())
{
// Constant TRUE, i.e. evaluates to FALSE: this branch
// does not return anything
// i.e. do nothing
}
else if (((Constant)o).getSymbol() == Operator.m_falseAtom.getSymbol())
{
// Constant FALSE, i.e. evaluates to TRUE: just pass on
// the recursive evaluation
spawnedSet = spawn(m);
foreach (WatcherNode wn2 in spawnedSet)
{
outSet.Add(wn2);
}
return outSet;
}
else
{
// This should never happen! All atoms should evaluate
// down
// to either true or false.
System.Diagnostics.Debug.Assert (false, "Unrecognized operator in watcher node");
return outSet;
}
}
// Constants (true or false)
else if (o.GetType() == typeof(Constant))
{
// TODO: true and false are checked by comparing their
// string representations; there should be a more graceful
// way
// to check for true and false
if (((Constant)o).getSymbol() == Operator.m_trueAtom.getSymbol())
{
// Constant TRUE: just pass on the recursive evaluation
spawnedSet = spawn(m);
foreach (WatcherNode wn2 in spawnedSet)
{
outSet.Add(wn2);
}
}
else if (((Constant)o).getSymbol() == Operator.m_falseAtom.getSymbol())
{
// This branch is stopped: this branch does not return
// anything
// i.e. do nothing
return outSet;
}
else
{
// This should never happen! All atoms should evaluate
// down to either true or false.
//assert(false);
return outSet;
}
}
}
if (m_gamma.Count == 0)
{
// Gamma is empty: return a set with myself
outSet.Add(this);
}
return outSet;
}