static Euler() {
RdfRelation[] rs = new RdfRelation[] {
#if !SILVERLIGHT
new SemWeb.Inference.Relations.MathAbsoluteValueRelation(), new SemWeb.Inference.Relations.MathCosRelation(), new SemWeb.Inference.Relations.MathDegreesRelation(), new SemWeb.Inference.Relations.MathEqualToRelation(),
new SemWeb.Inference.Relations.MathNegationRelation(), new SemWeb.Inference.Relations.MathRoundedRelation(), new SemWeb.Inference.Relations.MathSinRelation(), new SemWeb.Inference.Relations.MathSinhRelation(), new SemWeb.Inference.Relations.MathTanRelation(), new SemWeb.Inference.Relations.MathTanhRelation(),
new SemWeb.Inference.Relations.MathAtan2Relation(), new SemWeb.Inference.Relations.MathDifferenceRelation(), new SemWeb.Inference.Relations.MathExponentiationRelation(), new SemWeb.Inference.Relations.MathIntegerQuotientRelation(),
new SemWeb.Inference.Relations.MathQuotientRelation(), new SemWeb.Inference.Relations.MathRemainderRelation(),
new SemWeb.Inference.Relations.MathSumRelation(), new SemWeb.Inference.Relations.MathProductRelation(),
new SemWeb.Inference.Relations.MathGreaterThanRelation(), new SemWeb.Inference.Relations.MathLessThanRelation(), new SemWeb.Inference.Relations.MathNotGreaterThanRelation(), new SemWeb.Inference.Relations.MathNotLessThanRelation(), new SemWeb.Inference.Relations.MathNotEqualToRelation()
#endif
};
builtInRelations = new Hashtable();
foreach (RdfRelation r in rs)
builtInRelations[r.Uri] = r;
}
static Euler()
{
RdfRelation[] rs = new RdfRelation[] {
#if !SILVERLIGHT
new SemWeb.Inference.Relations.MathAbsoluteValueRelation(), new SemWeb.Inference.Relations.MathCosRelation(), new SemWeb.Inference.Relations.MathDegreesRelation(), new SemWeb.Inference.Relations.MathEqualToRelation(),
new SemWeb.Inference.Relations.MathNegationRelation(), new SemWeb.Inference.Relations.MathRoundedRelation(), new SemWeb.Inference.Relations.MathSinRelation(), new SemWeb.Inference.Relations.MathSinhRelation(), new SemWeb.Inference.Relations.MathTanRelation(), new SemWeb.Inference.Relations.MathTanhRelation(),
new SemWeb.Inference.Relations.MathAtan2Relation(), new SemWeb.Inference.Relations.MathDifferenceRelation(), new SemWeb.Inference.Relations.MathExponentiationRelation(), new SemWeb.Inference.Relations.MathIntegerQuotientRelation(),
new SemWeb.Inference.Relations.MathQuotientRelation(), new SemWeb.Inference.Relations.MathRemainderRelation(),
new SemWeb.Inference.Relations.MathSumRelation(), new SemWeb.Inference.Relations.MathProductRelation(),
new SemWeb.Inference.Relations.MathGreaterThanRelation(), new SemWeb.Inference.Relations.MathLessThanRelation(), new SemWeb.Inference.Relations.MathNotGreaterThanRelation(), new SemWeb.Inference.Relations.MathNotLessThanRelation(), new SemWeb.Inference.Relations.MathNotEqualToRelation()
#endif
};
builtInRelations = new Hashtable();
foreach (RdfRelation r in rs)
{
builtInRelations[r.Uri] = r;
}
}
private static ArrayList prove(Hashtable cases, SelectableSource world, Statement[] goal, int maxNumberOfSteps)
{
// This is the main routine from euler.js.
// cases: Resource (predicate) => IList of Sequent
if (world != null) // cache our queries to the world, if a world is provided
{
world = new SemWeb.Stores.CachedSource(world);
}
StatementMap cached_subproofs = new StatementMap();
// Create the queue and add the first item.
ArrayList queue = new ArrayList();
{
QueueItem start = new QueueItem();
start.env = new Hashtable();
start.rule = new Sequent(Statement.All, goal, null);
start.src = null;
start.ind = 0;
start.parent = null;
start.ground = new ArrayList();
queue.Add(start);
if (Debug)
{
Console.Error.WriteLine("Euler: Queue: " + start);
}
}
// The evidence array holds the results of this proof.
ArrayList evidence = new ArrayList();
// Track how many steps we take to not go over the limit.
int step = 0;
// Process the queue until it's empty or we reach our step limit.
while (queue.Count > 0)
{
// deal with the QueueItem at the top of the queue
QueueItem c = (QueueItem)queue[queue.Count - 1];
queue.RemoveAt(queue.Count - 1);
ArrayList g = new ArrayList(c.ground);
// have we done too much?
step++;
if (maxNumberOfSteps != -1 && step >= maxNumberOfSteps)
{
if (Debug)
{
Console.Error.WriteLine("Euler: Maximum number of steps exceeded. Giving up.");
}
return(null);
}
// if each statement in the body of the sequent has been proved
if (c.ind == c.rule.body.Length)
{
// if this is the top-level sequent being proved; we've found a complete evidence for the goal
if (c.parent == null)
{
EvidenceItem ev = new EvidenceItem();
ev.head = new Statement[c.rule.body.Length];
bool canRepresentHead = true;
for (int i = 0; i < c.rule.body.Length; i++)
{
ev.head[i] = evaluate(c.rule.body[i], c.env);
if (ev.head[i].AnyNull) // can't represent it: literal in subject position, for instance
{
canRepresentHead = false;
}
}
ev.body = c.ground;
ev.env = c.env;
if (Debug)
{
Console.Error.WriteLine("Euler: Found Evidence: " + ev);
}
if (!canRepresentHead)
{
continue;
}
evidence.Add(ev);
// this is a subproof of something; whatever it is a subgroup for can
// be incremented
}
else
{
// if the rule had no body, it was just an axiom and we represent that with Ground
if (c.rule.body.Length != 0)
{
g.Add(new Ground(c.rule, c.env));
}
// advance the parent being proved and put the advanced
// parent into the queue; unify the parent variable assignments
// with this one's
QueueItem r = new QueueItem();
r.rule = c.parent.rule;
r.src = c.parent.src;
r.ind = c.parent.ind;
r.parent = c.parent.parent;
r.env = (Hashtable)c.parent.env.Clone();
r.ground = g;
unify(c.rule.head, c.env, r.rule.body[r.ind], r.env, true);
r.ind++;
queue.Add(r);
if (Debug)
{
Console.Error.WriteLine("Euler: Queue Advancement: " + r);
}
// The number of live children for this parent is decremented since we are
// done with this subproof, but we store the result for later.
if (c.parent.solutions == null)
{
c.parent.solutions = new StatementList();
}
c.parent.solutions.Add(evaluate(r.rule.body[r.ind - 1], r.env));
decrementLife(c.parent, cached_subproofs);
}
// this sequent still has parts of the body left to be proved; try to
// find evidence for the next statement in the body, and if we find
// evidence, queue up that evidence
}
else
{
// this is the next part of the body that we need to try to prove
Statement t = c.rule.body[c.ind];
// Try to process this predicate with a user-provided custom
// function that resolves things like mathematical relations.
// euler.js provides similar functionality, but the system
// of user predicates is completely different here.
RdfRelation b = FindUserPredicate(t.Predicate);
if (b != null)
{
Resource[] args;
Variable[] unifyResult;
Resource value = evaluate(t.Object, c.env);
if (!c.rule.callArgs.ContainsKey(t.Subject))
{
// The array of arguments to this relation is just the subject of the triple itself
args = new Resource[] { evaluate(t.Subject, c.env) };
unifyResult = new Variable[1];
if (t.Subject is Variable)
{
unifyResult[0] = (Variable)t.Subject;
}
}
else
{
// The array of arguments to this relation comes from a pre-grouped arg list.
args = (Resource[])c.rule.callArgs[t.Subject];
unifyResult = new Variable[args.Length];
for (int i = 0; i < args.Length; i++)
{
if (args[i] is Variable)
{
unifyResult[i] = (Variable)args[i];
args[i] = evaluate(args[i], c.env);
}
}
}
// Run the user relation on the array of arguments (subject) and on the object.
if (b.Evaluate(args, ref value))
{
// If it succeeds, we press on.
// The user predicate may update the 'value' variable and the argument
// list array, and so we want to unify any variables in the subject
// or object of this user predicate with the values given to us
// by the user predicate.
Hashtable newenv = (Hashtable)c.env.Clone();
if (t.Object is Variable)
{
unify(value, null, t.Object, newenv, true);
}
for (int i = 0; i < args.Length; i++)
{
if (unifyResult[i] != null)
{
unify(args[i], null, unifyResult[i], newenv, true);
}
}
Statement grnd = evaluate(t, newenv);
if (grnd != Statement.All) // sometimes not representable, like if literal as subject
{
g.Add(new Ground(new Sequent(grnd, new Statement[0], null), new Hashtable()));
}
QueueItem r = new QueueItem();
r.rule = c.rule;
r.src = c.src;
r.ind = c.ind;
r.parent = c.parent;
r.env = newenv;
r.ground = g;
r.ind++;
queue.Add(r);
// Note: Since we are putting something back in for c, we don't touch the life counter on the parent.
}
else
{
// If the predicate fails, decrement the life of the parent.
decrementLife(c.parent, cached_subproofs);
}
continue;
}
// t can be proved either by the use of a rule
// or if t literally exists in the world
Statement t_resolved = evaluate(t, c.env);
// If resolving this statement requires putting a literal in subject or predicate position, we
// can't prove it.
if (t_resolved == Statement.All)
{
decrementLife(c.parent, cached_subproofs);
continue;
}
ArrayList tcases = new ArrayList();
// See if we have already tried to prove this.
if (cached_subproofs.ContainsKey(t_resolved))
{
StatementList cached_solutions = (StatementList)cached_subproofs[t_resolved];
if (cached_solutions == null)
{
if (Debug)
{
Console.Error.WriteLine("Euler: Dropping queue item because we have already failed to prove it: " + t_resolved);
}
}
else
{
foreach (Statement s in cached_solutions)
{
if (Debug)
{
Console.Error.WriteLine("Euler: Using Cached Axiom: " + s);
}
Sequent seq = new Sequent(s);
tcases.Add(seq);
}
}
}
else
{
// get all of the rules that apply to the predicate in question
if (t_resolved.Predicate != null && cases.ContainsKey(t_resolved.Predicate))
{
tcases.AddRange((IList)cases[t_resolved.Predicate]);
}
if (cases.ContainsKey("WILDCARD"))
{
tcases.AddRange((IList)cases["WILDCARD"]);
}
// if t has no unbound variables and we've matched something from
// the axioms, don't bother looking at the world, and don't bother
// proving it any other way than by the axiom.
bool lookAtWorld = true;
foreach (Sequent seq in tcases)
{
if (seq.body.Length == 0 && seq.head == t_resolved)
{
lookAtWorld = false;
tcases.Clear();
tcases.Add(seq);
break;
}
}
// if there is a seprate world, get all of the world
// statements that witness t
if (world != null && lookAtWorld)
{
MemoryStore w = new MemoryStore();
if (Debug)
{
Console.Error.WriteLine("Running " + c);
}
if (Debug)
{
Console.Error.WriteLine("Euler: Ask World: " + t_resolved);
}
world.Select(t_resolved, w);
foreach (Statement s in w)
{
if (Debug)
{
Console.Error.WriteLine("Euler: World Select Response: " + s);
}
Sequent seq = new Sequent(s);
tcases.Add(seq);
}
}
}
// If there is no evidence or potential evidence (i.e. rules)
// for t, then we will dump this QueueItem by not queuing any
// subproofs.
// Otherwise we try each piece of evidence in turn.
foreach (Sequent rl in tcases)
{
ArrayList g2 = (ArrayList)c.ground.Clone();
if (rl.body.Length == 0)
{
g2.Add(new Ground(rl, new Hashtable()));
}
QueueItem r = new QueueItem();
r.rule = rl;
r.src = rl;
r.ind = 0;
r.parent = c;
r.env = new Hashtable();
r.ground = g2;
if (unify(t, c.env, rl.head, r.env, true))
{
QueueItem ep = c; // euler path
while ((ep = ep.parent) != null)
{
if (ep.src == c.src && unify(ep.rule.head, ep.env, c.rule.head, c.env, false))
{
break;
}
}
if (ep == null)
{
// It is better for caching subproofs to work an entire proof out before
// going on, which means we want to put the new queue item at the
// top of the stack.
queue.Add(r);
c.liveChildren++;
if (Debug)
{
Console.Error.WriteLine("Euler: Queue from Axiom: " + r);
}
}
}
}
// If we did not add anything back into the queue for this item, then
// we decrement the life of the parent.
if (c.liveChildren == 0)
{
decrementLife(c.parent, cached_subproofs);
}
}
}
return(evidence);
}
