private Proof TryRule(Sequent sequent, InferenceRule rule)
{
RuleType?prevRule = currentRule;
currentRule = rule.type;
FormulaMapping mapping = null;
if (!MapFormulas(rule.conclusion, sequent.conclusion, null, ref mapping))
{
throw new ArgumentException("The given rule should have been applicable to the conclusion");
}
Proof proof = new Proof();
RuleStep step = new RuleStep(1, sequent.conclusion, rule.type);
if (MatchPremises(rule, mapping, ref proof, ref step))
{
proof.AddRuleStep(step);
}
else
{
proof = null;
}
currentRule = prevRule;
return(proof);
}
private Proof TryProve(ISymbol requiredPremise, InferenceRule rule, FormulaMapping mapping, int premiseIndex, ref RuleStep step)
{
ISymbol lastOEPremise = currentOEPremise;
if (rule.type == RuleType.OR_Elimination)
{
currentOEPremise = rule.premises[0].ApplyMapping(mapping);
}
SolverVisitor solverVisitor = new SolverVisitor(this);
requiredPremise.Accept(solverVisitor);
if (rule.type == RuleType.OR_Elimination)
{
currentOEPremise = lastOEPremise;
}
if (solverVisitor.Result != null)
{
Proof proof = solverVisitor.Result;
step.AddReferredStep(proof.ProofSteps[^ 1]);
private bool MatchPremises(InferenceRule rule, FormulaMapping mapping, ref Proof proof, ref RuleStep step, int premiseIndex = 0)
{
if (premiseIndex >= rule.premises.Count)
{
return(true);
}
ISymbol premise = rule.premises[premiseIndex];
List <MappingResult> nonRootMappings = new List <MappingResult>();
for (int i = 0; i < truths.Count; i++)
{
IProofStep truth = truths[i];
foreach (MappingResult mappingResult in FindFormulaMappings(premise, truth.Conclusion, mapping))
{
if (mappingResult.isRoot)
{
step.AddReferredStep(truth);
if (MatchPremises(rule, mappingResult.mapping, ref proof, ref step, premiseIndex + 1))
{
break;
}
step.PopReferredStep();
}
else
{
// Do non-root options later for efficiency
nonRootMappings.Add(mappingResult);
}
}
if (step.referredSteps.Count >= rule.premises.Count)
{
return(true);
}
}
foreach (MappingResult mappingResult in nonRootMappings)
{
Proof newProof = TryProve(mappingResult.formula, rule, mappingResult.mapping, premiseIndex, ref step);
if (newProof != null)
{
proof.AddStepsFromProof(newProof);
return(true);
}
if (step.referredSteps.Count >= rule.premises.Count)
{
return(true);
}
}
if (mapping.Count >= rule.maxFormulaIndex)
{
RuleType lastUnreferredRuleBefore = lastUnreferredRule;
if (rule.type == RuleType.Double_Negation_Elimination && lastUnreferredRule == RuleType.Double_Negation_Elimination)
{
return(false);
}
lastUnreferredRule = rule.type;
ISymbol mappedPremise = premise.ApplyMapping(mapping);
Proof newProof = TryProve(mappedPremise, rule, mapping, premiseIndex, ref step);
if (newProof != null)
{
proof.AddStepsFromProof(newProof);
return(true);
}
lastUnreferredRule = lastUnreferredRuleBefore;
}
// Proof is impossible (invalid)
return(false);
}