/// <summary>
/// Finds the minimal elements, in the partial order induced by unification, of the partial model facts.
/// The number of minimal elements gives a lower bound on the number of distinct facts that must appear in an valid model.
/// </summary>
private void BuildPartialModelLowerBounds()
{
//// Step 1. Bin facts by head symbol.
Term pattern;
LinkedList <Term> gbin;
Map <Term, MutableTuple <bool> > ngbin;
var grdBins = new Map <Symbol, LinkedList <Term> >(Symbol.Compare);
//// A term maps to true if it is deleted from the bin.
var ngBins = new Map <Symbol, Map <Term, MutableTuple <bool> > >(Symbol.Compare);
foreach (var f in Facts.Facts)
{
pattern = MkPattern(f);
if (pattern == f)
{
Contract.Assert(pattern.Groundness == Groundness.Ground);
if (!grdBins.TryFindValue(f.Symbol, out gbin))
{
gbin = new LinkedList <Term>();
grdBins.Add(f.Symbol, gbin);
}
gbin.AddLast(f);
}
else
{
Contract.Assert(pattern.Groundness == Groundness.Variable);
if (!ngBins.TryFindValue(f.Symbol, out ngbin))
{
ngbin = new Map <Term, MutableTuple <bool> >(Term.Compare);
ngBins.Add(f.Symbol, ngbin);
}
if (!ngbin.ContainsKey(pattern))
{
ngbin.Add(pattern, new MutableTuple <bool>(false));
}
}
}
//// Step 2. Any non-ground fact that matches with a ground fact is not minimal.
Matcher matcher;
foreach (var kv in ngBins)
{
ngbin = kv.Value;
if (!grdBins.TryFindValue(kv.Key, out gbin))
{
continue;
}
foreach (var p in ngbin)
{
matcher = new Matcher(p.Key);
foreach (var g in gbin)
{
if (matcher.TryMatch(g))
{
p.Value.Item1 = true;
break;
}
}
}
PruneBin(ngbin);
}
//// Step 3. Iteratively compute the minimal elements until a fixpoint is reached.
Term mgu;
bool changed;
LinkedList <Term> newGLBs;
foreach (var kv in ngBins)
{
ngbin = kv.Value;
changed = true;
while (changed)
{
changed = false;
newGLBs = null;
foreach (var p1 in ngbin)
{
foreach (var p2 in ngbin.GetEnumerable(p1.Key))
{
if (p1.Key == p2.Key)
{
continue;
}
else if (Unifier.IsUnifiable(p1.Key, p2.Key, x => MkNormalizedVar(Facts.Index, x), out mgu))
{
if (mgu != p1.Key)
{
p1.Value.Item1 = true;
}
if (mgu != p2.Key)
{
p2.Value.Item1 = true;
}
if (mgu != p1.Key && mgu != p2.Key && !ngbin.ContainsKey(mgu))
{
changed = true;
if (newGLBs == null)
{
newGLBs = new LinkedList <Term>();
}
newGLBs.AddLast(mgu);
}
}
}
}
PruneBin(ngbin, newGLBs);
}
}
//// Step 4. Create lower bounds
Cardinality card;
foreach (var kv in ngBins)
{
grdBins.TryFindValue(kv.Key, out gbin);
if (gbin == null)
{
card = new Cardinality(new BigInteger(kv.Value.Count));
}
else
{
card = new Cardinality(new BigInteger(kv.Value.Count) + new BigInteger(gbin.Count));
}
AddConstraint(varMap[(UserSymbol)kv.Key].Item3 >= new CardCnst(card));
}
foreach (var kv in grdBins)
{
if (ngBins.ContainsKey(kv.Key))
{
continue;
}
AddConstraint(varMap[(UserSymbol)kv.Key].Item3 >= new CardCnst(new Cardinality(new BigInteger(kv.Value.Count))));
}
}