//
// Given, the list of generated, interesting problems, validate (for soundness) the fact that the original book problem was generated.
// Do so by constructing a goal-based isomorphism partitioning and check that there exists a problem with the same given set.
//
private void Validate(List<GeometryTutorLib.ProblemAnalyzer.Problem<GeometryTutorLib.Hypergraph.EdgeAnnotation>> problems, ProofProblemFigureStatisticsAggregator figureStats)
{
GeometryTutorLib.ProblemAnalyzer.QueryFeatureVector query = GeometryTutorLib.ProblemAnalyzer.QueryFeatureVector.ConstructGoalIsomorphismQueryVector();
GeometryTutorLib.ProblemAnalyzer.PartitionedProblemSpace goalBasedPartitions = new GeometryTutorLib.ProblemAnalyzer.PartitionedProblemSpace(graph, query);
goalBasedPartitions.ConstructPartitions(problems);
// Validate that we have generated all of the original problems from the text.
List<GeometryTutorLib.ProblemAnalyzer.Problem<GeometryTutorLib.Hypergraph.EdgeAnnotation>> generatedBookProblems = goalBasedPartitions.ValidateOriginalProblems(givens, goals);
figureStats.totalBookProblemsGenerated = generatedBookProblems.Count;
if (GeometryTutorLib.Utilities.PROBLEM_GEN_DEBUG)
{
goalBasedPartitions.DumpPartitions();
}
if (GeometryTutorLib.Utilities.BACKWARD_PROBLEM_GEN_DEBUG)
{
Debug.WriteLine("\nAll " + generatedBookProblems.Count + " Book-specified problems: \n");
foreach (GeometryTutorLib.ProblemAnalyzer.Problem<GeometryTutorLib.Hypergraph.EdgeAnnotation> bookProb in generatedBookProblems)
{
Debug.WriteLine(bookProb.ConstructProblemAndSolution(graph));
}
}
figureStats.goalPartitionSummary = goalBasedPartitions.GetGoalBasedPartitionSummary();
}
// Returns: <number of interesting problems, number of original problems generated>
public ProofProblemFigureStatisticsAggregator AnalyzeFigure()
{
ProofProblemFigureStatisticsAggregator figureStats = new ProofProblemFigureStatisticsAggregator();
// For statistical analysis, count the number of each particular type of implicit facts.
CountIntrisicProperties(figureStats);
// Start timing
figureStats.stopwatch.Start();
// Precompute all coordinate-based interesting relations (problem goal nodes)
// These become the basis for the template-based problem generation (these are the goals)
Precompute();
// Handle givens that strengthen the intrinsic parts of the figure; modifies if needed
givens = DoGivensStrengthenFigure();
// Use a worklist technique to instantiate nodes to construct the hypergraph for this figure
ConstructHypergraph();
// Create the integer-based hypergraph representation
ConstructPebblingHypergraph();
// Pebble that hypergraph
Pebble();
// Analyze paths in the hypergraph to generate the pair of <forward problems, backward problems> (precomputed nodes are goals)
KeyValuePair <List <GeometryTutorLib.ProblemAnalyzer.Problem <GeometryTutorLib.Hypergraph.EdgeAnnotation> >,
List <GeometryTutorLib.ProblemAnalyzer.Problem <GeometryTutorLib.Hypergraph.EdgeAnnotation> > > problems = GenerateTemplateProblems();
// Combine the problems together into one list
List <GeometryTutorLib.ProblemAnalyzer.Problem <GeometryTutorLib.Hypergraph.EdgeAnnotation> > candidateProbs = new List <GeometryTutorLib.ProblemAnalyzer.Problem <GeometryTutorLib.Hypergraph.EdgeAnnotation> >();
candidateProbs.AddRange(problems.Key);
//candidateProbs.AddRange(problems.Value); // converse
figureStats.totalBackwardProblemsGenerated = problems.Value.Count;
figureStats.totalProblemsGenerated = candidateProbs.Count;
// Determine which, if any, of the problems are interesting (using definition that 100% of the givens are used)
interestingCalculator = new GeometryTutorLib.ProblemAnalyzer.InterestingProblemCalculator(graph, figure, givens, goals);
List <GeometryTutorLib.ProblemAnalyzer.Problem <GeometryTutorLib.Hypergraph.EdgeAnnotation> > interestingProblems = interestingCalculator.DetermineInterestingProblems(candidateProbs);
figureStats.totalInterestingProblems = interestingProblems.Count;
// Explicit number of facts: hypergraph size - figure facts
figureStats.totalExplicitFacts = graph.vertices.Count - figure.Count;
// Validate that the original book problems were generated.
Validate(interestingProblems, figureStats);
// Stop timing before we generate all of the statistics
figureStats.stopwatch.Stop();
List <GeometryTutorLib.ProblemAnalyzer.Problem <GeometryTutorLib.Hypergraph.EdgeAnnotation> > strictlyInteresting = GetStrictlyInteresting(interestingProblems);
// Construct partitions based on different queries
// GenerateStatistics(interestingProblems, figureStats, strictlyInteresting);
//
// Is this figure complete? That is, do the assumptions define the figure completely?
//
figureStats.isComplete = templateProblemGenerator.DefinesFigure(precomputer.GetPrecomputedRelations(), precomputer.GetStrengthenedClauses());
// Debug.WriteLine("Explicit Complete: " + figureStats.isComplete);
// Construct the K-goal problems
// CalculateKnonStrictCardinalities(interestingCalculator, interestingProblems, figureStats);
return(figureStats);
}
// Returns: <number of interesting problems, number of original problems generated>
public ProofProblemFigureStatisticsAggregator AnalyzeFigure()
{
ProofProblemFigureStatisticsAggregator figureStats = new ProofProblemFigureStatisticsAggregator();
// For statistical analysis, count the number of each particular type of implicit facts.
CountIntrisicProperties(figureStats);
// Start timing
figureStats.stopwatch.Start();
// Precompute all coordinate-based interesting relations (problem goal nodes)
// These become the basis for the template-based problem generation (these are the goals)
Precompute();
// Handle givens that strengthen the intrinsic parts of the figure; modifies if needed
givens = DoGivensStrengthenFigure();
// Use a worklist technique to instantiate nodes to construct the hypergraph for this figure
ConstructHypergraph();
// Create the integer-based hypergraph representation
ConstructPebblingHypergraph();
// Pebble that hypergraph
Pebble();
// Analyze paths in the hypergraph to generate the pair of <forward problems, backward problems> (precomputed nodes are goals)
KeyValuePair<List<GeometryTutorLib.ProblemAnalyzer.Problem<GeometryTutorLib.Hypergraph.EdgeAnnotation>>,
List<GeometryTutorLib.ProblemAnalyzer.Problem<GeometryTutorLib.Hypergraph.EdgeAnnotation>>> problems = GenerateTemplateProblems();
// Combine the problems together into one list
List<GeometryTutorLib.ProblemAnalyzer.Problem<GeometryTutorLib.Hypergraph.EdgeAnnotation>> candidateProbs = new List<GeometryTutorLib.ProblemAnalyzer.Problem<GeometryTutorLib.Hypergraph.EdgeAnnotation>>();
candidateProbs.AddRange(problems.Key);
//candidateProbs.AddRange(problems.Value); // converse
figureStats.totalBackwardProblemsGenerated = problems.Value.Count;
figureStats.totalProblemsGenerated = candidateProbs.Count;
// Determine which, if any, of the problems are interesting (using definition that 100% of the givens are used)
interestingCalculator = new GeometryTutorLib.ProblemAnalyzer.InterestingProblemCalculator(graph, figure, givens, goals);
List<GeometryTutorLib.ProblemAnalyzer.Problem<GeometryTutorLib.Hypergraph.EdgeAnnotation>> interestingProblems = interestingCalculator.DetermineInterestingProblems(candidateProbs);
figureStats.totalInterestingProblems = interestingProblems.Count;
// Explicit number of facts: hypergraph size - figure facts
figureStats.totalExplicitFacts = graph.vertices.Count - figure.Count;
// Validate that the original book problems were generated.
Validate(interestingProblems, figureStats);
// Stop timing before we generate all of the statistics
figureStats.stopwatch.Stop();
List<GeometryTutorLib.ProblemAnalyzer.Problem<GeometryTutorLib.Hypergraph.EdgeAnnotation>> strictlyInteresting = GetStrictlyInteresting(interestingProblems);
// Construct partitions based on different queries
// GenerateStatistics(interestingProblems, figureStats, strictlyInteresting);
//
// Is this figure complete? That is, do the assumptions define the figure completely?
//
figureStats.isComplete = templateProblemGenerator.DefinesFigure(precomputer.GetPrecomputedRelations(), precomputer.GetStrengthenedClauses());
// Debug.WriteLine("Explicit Complete: " + figureStats.isComplete);
// Construct the K-goal problems
// CalculateKnonStrictCardinalities(interestingCalculator, interestingProblems, figureStats);
return figureStats;
}
//
// Given, the list of generated, interesting problems, validate (for soundness) the fact that the original book problem was generated.
// Do so by constructing a goal-based isomorphism partitioning and check that there exists a problem with the same given set.
//
private void Validate(List <GeometryTutorLib.ProblemAnalyzer.Problem <GeometryTutorLib.Hypergraph.EdgeAnnotation> > problems, ProofProblemFigureStatisticsAggregator figureStats)
{
GeometryTutorLib.ProblemAnalyzer.QueryFeatureVector query = GeometryTutorLib.ProblemAnalyzer.QueryFeatureVector.ConstructGoalIsomorphismQueryVector();
GeometryTutorLib.ProblemAnalyzer.PartitionedProblemSpace goalBasedPartitions = new GeometryTutorLib.ProblemAnalyzer.PartitionedProblemSpace(graph, query);
goalBasedPartitions.ConstructPartitions(problems);
// Validate that we have generated all of the original problems from the text.
List <GeometryTutorLib.ProblemAnalyzer.Problem <GeometryTutorLib.Hypergraph.EdgeAnnotation> > generatedBookProblems = goalBasedPartitions.ValidateOriginalProblems(givens, goals);
figureStats.totalBookProblemsGenerated = generatedBookProblems.Count;
if (GeometryTutorLib.Utilities.PROBLEM_GEN_DEBUG)
{
goalBasedPartitions.DumpPartitions();
}
if (GeometryTutorLib.Utilities.BACKWARD_PROBLEM_GEN_DEBUG)
{
Debug.WriteLine("\nAll " + generatedBookProblems.Count + " Book-specified problems: \n");
foreach (GeometryTutorLib.ProblemAnalyzer.Problem <GeometryTutorLib.Hypergraph.EdgeAnnotation> bookProb in generatedBookProblems)
{
Debug.WriteLine(bookProb.ConstructProblemAndSolution(graph));
}
}
figureStats.goalPartitionSummary = goalBasedPartitions.GetGoalBasedPartitionSummary();
}