HOL-master/examples/lassie/sempre/src/edu/stanford/nlp/sempre/tables/dpd/DPDParser.java
package edu.stanford.nlp.sempre.tables.dpd;

import java.util.*;

import edu.stanford.nlp.sempre.*;
import edu.stanford.nlp.sempre.tables.DenotationTypeInference;
import edu.stanford.nlp.sempre.tables.InfiniteListValue;
import edu.stanford.nlp.sempre.tables.ScopedValue;
import edu.stanford.nlp.sempre.tables.TableDerivationPruningComputer;
import edu.stanford.nlp.sempre.tables.grow.ApplyFn;
import fig.basic.*;

/**
 * A DPDParser parses utterances like a FloatingParser, but the dynamic programming states
 * also include the *denotation* in addition to (start,end) or depth/size.
 *
 * DPDParser makes 2 passes:
 * - Pass 1: Find the parse paths that lead to the correct final denotation.
 * - Pass 2: Use regular beam search (from FloatingParser), but only restrict
 *   the parse paths to the ones found in Pass 1.
 *
 * @author ppasupat
 */
public class DPDParser extends FloatingParser {
  public static class Options {
    @Option(gloss = "Use the targetValue at test time")
    public boolean cheat = false;
    @Option(gloss = "During training, use FloatingParser instead (don't use DPDParser at all)")
    public boolean useFloatingParserForTrain = false;
    @Option(gloss = "During training, combine the derivation list from FloatingParser")
    public boolean combineFromFloatingParser = false;
    @Option(gloss = "Random object for shuffling the derivation list")
    public Random shuffleRandom = new Random(1);
    @Option(gloss = "Custom maximum depth for DPDParser (default = FloatingParser's maxDepth)")
    public int dpdParserMaxDepth = -1;
    @Option(gloss = "Custom beam size for DPDParser (default = FloatingParser's beamSize)")
    public int dpdParserBeamSize = -1;
    @Option(gloss = "Prune the cells in first pass")
    public int firstPassBeamSize = -1;
    @Option(gloss = "Stop the current pass if the number of (cell, denotation) pairs exceeds this number")
    public int maxNumCellDenotations = 5000000;
    @Option(gloss = "Stop the current pass if it has used more than this amount of time (in seconds)")
    public int maxDPDParsingTime = 600;
    @Option(gloss = "Allowed pruning strategies in first pass (must not depend on actual formulas)")
    public List<String> allowedPrunersInFirstPass = new ArrayList<>(Arrays.asList(
        DefaultDerivationPruningComputer.emptyDenotation,
        DefaultDerivationPruningComputer.nonLambdaError,
        DefaultDerivationPruningComputer.mistypedMerge,
        DefaultDerivationPruningComputer.badSummarizerHead,
        TableDerivationPruningComputer.lambdaDCSError,
        TableDerivationPruningComputer.subsetMerge,
        TableDerivationPruningComputer.sameMark,
        TableDerivationPruningComputer.subsetMerge,
        TableDerivationPruningComputer.aggregateInfinite,
        TableDerivationPruningComputer.aggregateUncomparable
        ));
    @Option(gloss = "Use all pruning strategies if only one formula can produce the denotation")
    public boolean aggressivelyPruneSingleFormulas = true;
    // Debugging flags
    @Option(gloss = "DEBUG: Put the cell name in the canonical utterance of final derivations")
    public boolean putCellNameInCanonicalUtterance = false;
    @Option(gloss = "DEBUG: Dump denotations after each pass")
    public DumpSpec dumpDenotations = DumpSpec.NONE;
    @Option(gloss = "DEBUG: Dump allowed ingredients after the first pass")
    public boolean dumpAllowedIngredients = false;
    @Option(gloss = "DEBUG: Summarize denotations after each pass")
    public boolean summarizeDenotations = false;
    @Option(gloss = "DEBUG: Count the number of useful unique-denotations and cell-denotations")
    public boolean summarizeCountUseful = false;
    @Option(gloss = "DEBUG: Do not do first pass; allow any ingredients in the second pass")
    public boolean ignoreFirstPass = false;
  }
  public static Options opts = new Options();

  public static enum DumpSpec { NONE, UNIQUE, NONERROR, ALL, FORMULA }

  public DPDParser(Spec spec) {
    super(spec);
  }

  @Override
  public ParserState newParserState(Params params, Example ex, boolean computeExpectedCounts) {
    if (computeExpectedCounts) {    // Training
      // Only use floating?
      if (opts.useFloatingParserForTrain)
        return super.newParserState(params, ex, computeExpectedCounts);
      // Use mixture?
      if (opts.combineFromFloatingParser)
        return new DPDParserState(this, params, ex, computeExpectedCounts,
            super.newParserState(params, ex, computeExpectedCounts));
      // Otherwise, just use DPDParser (look at denotation)
      return new DPDParserState(this, params, ex, computeExpectedCounts);
    } else {    // Test
      // Cheat by looking at denotation?
      if (opts.cheat)
        return new DPDParserState(this, params, ex, computeExpectedCounts);
      // Otherwise, don't cheat and just use floating parser
      return super.newParserState(params, ex, computeExpectedCounts);
    }
  }

}

/**
 * Actual parsing logic.
 */
class DPDParserState extends ParserState {

  private final DerivationPruner pruner;
  private final int maxDepth, beamSize;
  private final CatSizeBound catSizeBound;
  private final ParserState backoffParserState;
  private long firstPassParseTime, secondPassParseTime;
  private boolean timeout = false;

  private Map<Rule, Long> ruleTime;

  public DPDParserState(DPDParser parser, Params params, Example ex, boolean computeExpectedCounts) {
    this(parser, params, ex, computeExpectedCounts, null);
  }

  public DPDParserState(DPDParser parser, Params params, Example ex, boolean computeExpectedCounts, ParserState backoff) {
    super(parser, params, ex, computeExpectedCounts);
    pruner = new DerivationPruner(this);
    maxDepth = DPDParser.opts.dpdParserMaxDepth > 0 ? DPDParser.opts.dpdParserMaxDepth : FloatingParser.opts.maxDepth;
    beamSize = DPDParser.opts.dpdParserBeamSize > 0 ? DPDParser.opts.dpdParserBeamSize : Parser.opts.beamSize;
    catSizeBound = new CatSizeBound(maxDepth, parser.grammar);
    backoffParserState = backoff;
  }

  @Override
  protected int getBeamSize() { return beamSize; }

  protected void ensureExecuted(Derivation deriv) {
    deriv.ensureExecuted(parser.executor, ex.context);
    if (!deriv.isFeaturizedAndScored() && currentPass != ParsingPass.FIRST)
      featurizeAndScoreDerivation(deriv);
  }

  // ============================================================
  // Dynamic programming cells
  // ============================================================

  // Pass 1: Just try to reach the correct denotation
  //   state name => denotation => FirstPassData
  private final Map<String, Map<Value, Metadata>> firstPassCells = new HashMap<>();
  // Pass 2: Using results from Pass 1 to prune the possible formulas
  //   state name => denotation => SecondPassData
  private final Map<String, Map<Value, Metadata>> secondPassCells = new HashMap<>();

  enum ParsingPass { FIRST, SECOND, DONE };
  ParsingPass currentPass = ParsingPass.FIRST;

  private Map<String, Map<Value, Metadata>> getCellsForCurrentPass() {
    return currentPass == ParsingPass.FIRST ? firstPassCells : secondPassCells;
  }

  // ============================================================
  // DenotationIngredient
  // ============================================================

  // Represents a possible method for creating a particular denotation in a particular cell.
  class Ingredient {
    public final String parentCell;
    public final Rule rule;
    public final Value child1, child2;
    private final int hashCode;

    public Ingredient(String parentCell, Rule rule, Derivation deriv1, Derivation deriv2) {
      this.parentCell = parentCell;
      this.rule = rule;
      if (deriv1 == null) {
        this.child1 = null;
      } else {
        ensureExecuted(deriv1);
        this.child1 = deriv1.value;
      }
      if (deriv2 == null) {
        this.child2 = null;
      } else {
        ensureExecuted(deriv2);
        this.child2 = deriv2.value;
      }
      hashCode = parentCell.hashCode()
          + ((rule == null) ? 0 : rule.hashCode() * 1729)
          + ((child1 == null) ? 0 : child1.hashCode() * 42)
          + ((child2 == null) ? 0 : child2.hashCode() * 345);
    }

    public Ingredient(String parentCell) {
      this(parentCell, null, null, null);
    }

    @Override
    public boolean equals(Object o) {
      if (!(o instanceof Ingredient)) return false;
      Ingredient that = (Ingredient) o;
      if (!parentCell.equals(that.parentCell)) return false;
      if (rule != that.rule) return false;    // Rules must be the same object
      if ((child1 == null && that.child1 != null) || (child1 != null && !child1.equals(that.child1))) return false;
      if ((child2 == null && that.child2 != null) || (child2 != null && !child2.equals(that.child2))) return false;
      return true;
    }

    @Override
    public int hashCode() { return hashCode; }

    @Override
    public String toString() {
      String cellName = parentCell;
      if (cellName.contains(":")) {
        String[] parts = cellName.split(":");
        assert parts.length == 2;
        cellName = String.format("&%2s:%s", parts[1], parts[0]);
      }
      return new StringBuilder().append("[ ").append(cellName).append(" | ").append(rule)
          .append(" | ").append(child1).append(" | ").append(child2).append(" ]").toString();
    }
  }

  private final Set<Ingredient> allowedIngredients = new HashSet<>();

  // ============================================================
  // BackPointer
  // ============================================================

  // Back pointer for dynamic programming. Points to a child cell.
  class BackPointer {
    public final String cell;
    public final Value value;

    public BackPointer(String cell, Value denotation) {
      this.cell = cell;
      this.value = denotation;
    }

    @Override
    public boolean equals(Object o) {
      if (!(o instanceof BackPointer)) return false;
      BackPointer that = (BackPointer) o;
      return cell.equals(that.cell) && value.equals(that.value);
    }

    @Override
    public int hashCode() {
      return cell.hashCode() * 100 + value.hashCode();
    }

    @Override
    public String toString() {
      return cell + " " + value;
    }

    public boolean isSingleFormula() {
      return getCellsForCurrentPass().get(cell).get(value).singleFormula;
    }
  }

  public BackPointer getBackPointer(String cell, Derivation child) {
    if (cell == null || child == null) return null;
    ensureExecuted(child);
    return new BackPointer(cell, child.value);
  }

  // ============================================================
  // Metadata
  // ============================================================

  // Stores derivations and other data
  class Metadata {
    public final Value value;
    // List of possible parse paths to create this value
    public Set<Ingredient> possibleIngredients = new HashSet<>();
    // Backpointers for backtracking after the first pass
    public Set<BackPointer> backPointers = new HashSet<>();
    // All derivations containing formulas that execute to the denotation.
    // For the FIRST pass, this has only 1 formula.
    // For the SECOND pass, this will eventually be pruned to the beam size.
    public List<Derivation> derivations = new ArrayList<>();
    // Whether there is only one possible formula that executes to the denotation.
    // (only used during the first pass)
    // If so, we can apply any pruning heuristic on the formulas built upon this formula.
    public boolean singleFormula = true;

    public Metadata(Value value) {
      this.value = value;
    }

    public void add(Derivation deriv, Ingredient ingredient, BackPointer bp1, BackPointer bp2) {
      if (currentPass == ParsingPass.FIRST) {
        if (derivations.isEmpty()) {
          if (Parser.opts.verbose >= 3)
            LogInfo.logs("Metadata.add: %s %s", value, deriv);
          derivations.add(deriv);
        } else if (!derivations.get(0).formula.equals(deriv.formula)) {
          singleFormula = false;
        }
        if (Parser.opts.verbose >= 3) {
          LogInfo.logs("possibleIngredients.add: %s", ingredient);
        }
        possibleIngredients.add(ingredient);
        if (bp1 != null) {
          backPointers.add(bp1);
          if (!bp1.isSingleFormula()) singleFormula = false;
        }
        if (bp2 != null) {
          backPointers.add(bp2);
          if (!bp2.isSingleFormula()) singleFormula = false;
        }
      } else if (currentPass == ParsingPass.SECOND) {
        derivations.add(deriv);
        singleFormula = (derivations.size() == 1);
      }
    }
  }

  // ============================================================
  // Add to Chart
  // ============================================================

  private void addToChart(Derivation deriv, Ingredient ingredient,
      BackPointer bp1, BackPointer bp2) {
    if (Parser.opts.verbose >= 3)
      LogInfo.logs("addToChart %s %s: %s", ingredient.parentCell, deriv.value, deriv);
    ensureExecuted(deriv);
    Map<String, Map<Value, Metadata>> cells = getCellsForCurrentPass();
    Map<Value, Metadata> denotationToData = cells.get(ingredient.parentCell);
    if (denotationToData == null)
      cells.put(ingredient.parentCell, denotationToData = new HashMap<>());
    Metadata metadata = denotationToData.get(deriv.value);
    if (metadata == null)
      denotationToData.put(deriv.value, metadata = new Metadata(deriv.value));
    metadata.add(deriv, ingredient, bp1, bp2);
  }

  private String anchoredCell(String cat, int start, int end) {
    return (cat + "[" + start + "," + end + "]").intern();
  }

  private String floatingCell(String cat, int depth) {
    return (cat + ":" + depth).intern();
  }

  // ============================================================
  // Apply Rule
  // ============================================================

  private boolean isRootRule(Rule rule) {
    return Rule.rootCat.equals(rule.lhs);
  }

  private boolean applyRule(Rule rule, int start, int end, int depth,
      String cell1, Derivation child1, String cell2, Derivation child2) {
    if (timeout && !isRootRule(rule)) return false;
    applyRuleActual(rule, start, end, depth, cell1, child1, cell2, child2);
    return true;
  }

  private void applyRuleActual(Rule rule, int start, int end, int depth,
      String cell1, Derivation child1, String cell2, Derivation child2) {
    if (Parser.opts.verbose >= 5)
      LogInfo.logs("applyRule %s [%s:%s] depth=%s, %s %s", rule, start, end, depth, child1, child2);

    Ingredient anchoredIngredient = null, floatingIngredient = null;
    if (depth == -1) {
      anchoredIngredient = new Ingredient(anchoredCell(rule.lhs, start, end), rule, child1, child2);
      floatingIngredient = new Ingredient(floatingCell(rule.lhs, 0), rule, child1, child2);
    } else {
      floatingIngredient = new Ingredient(floatingCell(rule.lhs, depth), rule, child1, child2);
    }
    if (currentPass == ParsingPass.SECOND && !DPDParser.opts.ignoreFirstPass) {
      // Prune invalid ingredient
      if (!allowedIngredients.contains(anchoredIngredient)
          && !allowedIngredients.contains(floatingIngredient)) return;
    }
    BackPointer bp1 = getBackPointer(cell1, child1), bp2 = getBackPointer(cell2, child2);
    boolean singleFormula = (bp1 == null || bp1.isSingleFormula()) && (bp2 == null || bp2.isSingleFormula());

    List<Derivation> children;
    if (child1 == null)  // 0-ary
      children = Collections.emptyList();
    else if (child2 == null) // 1-ary
      children = Collections.singletonList(child1);
    else {
      children = ListUtils.newList(child1, child2);
      // optionally: ensure that specific anchors are only used once (or K times) per final derivation
      // Cannot impose useAnchorsOnce on the first pass without dropping correct derivations!
      if (currentPass != ParsingPass.FIRST) {
        if (FloatingParser.opts.useAnchorsOnce) {
          if (FloatingRuleUtils.derivationAnchorsOverlap(child1, child2))
            return;
        } else if (FloatingParser.opts.useMaxAnchors >= 0) {
          if (FloatingRuleUtils.maxNumAnchorOverlaps(child1, child2)
              > FloatingParser.opts.useMaxAnchors)
            return;
        }
      }
    }

    // Call the semantic function on the children and read the results
    DerivationStream results = rule.sem.call(ex,
        new SemanticFn.CallInfo(rule.lhs, start, end, rule, children));
    while (results.hasNext()) {
      Derivation newDeriv = results.next();
      newDeriv = newDeriv.betaReduction();
      if (DPDParser.opts.aggressivelyPruneSingleFormulas) {
        if (currentPass == ParsingPass.FIRST && singleFormula) {
          if (pruner.isPruned(newDeriv, null)) continue;
        } else {
          if (pruner.isPruned(newDeriv)) continue;
        }
      } else {
        if (pruner.isPruned(newDeriv)) continue;
      }
      if (newDeriv.value instanceof ErrorValue) {
        // Assign canonical error value
        newDeriv.value = new DPDErrorValue(newDeriv, rule, child1, child2);
      }
      if (depth == -1) {
        // Anchored rule
        addToChart(newDeriv, anchoredIngredient, bp1, bp2);
        addToChart(newDeriv, floatingIngredient, bp1, bp2);
      } else {
        // Floating rule
        addToChart(newDeriv, floatingIngredient, bp1, bp2);
      }
    }
  }

  private boolean applyAnchoredRule(Rule rule, int start, int end) {
    return applyRule(rule, start, end, -1, null, null, null, null);
  }
  private boolean applyAnchoredRule(Rule rule, int start, int end,
      String cell1, Derivation child1) {
    return applyRule(rule, start, end, -1, cell1, child1, null, null);
  }
  private boolean applyAnchoredRule(Rule rule, int start, int end,
      String cell1, Derivation child1, String cell2, Derivation child2) {
    return applyRule(rule, start, end, -1, cell1, child1, cell2, child2);
  }

  private boolean applyFloatingRule(Rule rule, int depth) {
    return applyRule(rule, -1, -1, depth, null, null, null, null);
  }
  private boolean applyFloatingRule(Rule rule, int depth,
      String cell1, Derivation child1) {
    return applyRule(rule, -1, -1, depth, cell1, child1, null, null);
  }
  private boolean applyFloatingRule(Rule rule, int depth,
      String cell1, Derivation child1, String cell2, Derivation child2) {
    return applyRule(rule, -1, -1, depth, cell1, child1, cell2, child2);
  }

  // ============================================================
  // Get derivations
  // ============================================================

  private List<Derivation> getDerivations(Object cell) {
    Map<String, Map<Value, Metadata>> cells = getCellsForCurrentPass();
    Map<Value, Metadata> denotationToData = cells.get(cell);
    if (denotationToData == null) return Collections.emptyList();
    List<Derivation> derivations = new ArrayList<>();
    for (Metadata metadata : denotationToData.values()) {
      derivations.addAll(metadata.derivations);
    }
    return derivations;
  }

  /**
   * Return a collection of ChildDerivationsGroup.
   *
   * The rule should be applied on all derivations (or all pairs of derivations) in each ChildDerivationsGroup.
   */
  private Collection<ChildDerivationsGroup> getFilteredDerivations(Rule rule, String cell1, String cell2) {
    List<Derivation> derivations1 = getDerivations(cell1),
        derivations2 = (cell2 == null) ? null : getDerivations(cell2);
    if (!FloatingParser.opts.filterChildDerivations)
      return Collections.singleton(new ChildDerivationsGroup(derivations1, derivations2));
    // Try to filter down the number of partial logical forms
    if (rule.getSem().supportFilteringOnTypeData())
      return rule.getSem().getFilteredDerivations(derivations1, derivations2);
    return Collections.singleton(new ChildDerivationsGroup(derivations1, derivations2));
  }

  private Collection<ChildDerivationsGroup> getFilteredDerivations(Rule rule, String cell) {
    return getFilteredDerivations(rule, cell, null);
  }

  // ============================================================
  // Build Anchored
  // ============================================================

  // Build derivations over span |start|, |end|.
  private void buildAnchored(int start, int end) {
    // Apply unary tokens on spans (rule $A (a))
    for (Rule rule : parser.grammar.getRules()) {
      if (timeout && !isRootRule(rule)) continue;
      if (!rule.isAnchored()) continue;
      if (rule.rhs.size() != 1 || rule.isCatUnary()) continue;
      boolean match = (end - start == 1) && ex.token(start).equals(rule.rhs.get(0));
      if (!match) continue;

      StopWatch stopWatch = new StopWatch().start();
      applyAnchoredRule(rule, start, end);
      ruleTime.put(rule, ruleTime.getOrDefault(rule, 0L) + stopWatch.stop().ms);
    }

    // Apply binaries on spans (rule $A ($B $C)), ...
    for (int mid = start + 1; mid < end; mid++) {
      for (Rule rule : parser.grammar.getRules()) {
        if (timeout && !isRootRule(rule)) continue;
        if (!rule.isAnchored()) continue;
        if (rule.rhs.size() != 2) continue;

        StopWatch stopWatch = new StopWatch().start();
        String rhs1 = rule.rhs.get(0);
        String rhs2 = rule.rhs.get(1);
        boolean match1 = (mid - start == 1) && ex.token(start).equals(rhs1);
        boolean match2 = (end - mid == 1) && ex.token(mid).equals(rhs2);

        if (!Rule.isCat(rhs1) && Rule.isCat(rhs2)) {  // token $Cat
          if (match1) {
            String cell = anchoredCell(rhs2, mid, end);
            List<Derivation> derivations = getDerivations(cell);
            for (Derivation deriv : derivations)
              if (!applyAnchoredRule(rule, start, end, cell, deriv)) break;
          }
        } else if (Rule.isCat(rhs1) && !Rule.isCat(rhs2)) {  // $Cat token
          if (match2) {
            String cell = anchoredCell(rhs1, start, mid);
            List<Derivation> derivations = getDerivations(cell);
            for (Derivation deriv : derivations)
              if (!applyAnchoredRule(rule, start, end, cell, deriv)) break;
          }
        } else if (!Rule.isCat(rhs1) && !Rule.isCat(rhs2)) {  // token token
          if (match1 && match2)
            if (!applyAnchoredRule(rule, start, end)) break;
        } else {  // $Cat $Cat
          String cell1 = anchoredCell(rhs1, start, mid);
          String cell2 = anchoredCell(rhs2, mid, end);
          List<Derivation> derivations1 = getDerivations(cell1);
          List<Derivation> derivations2 = getDerivations(cell2);
          derivLoop:
            for (Derivation deriv1 : derivations1)
              for (Derivation deriv2 : derivations2)
                if (!applyAnchoredRule(rule, start, end, cell1, deriv1, cell2, deriv2)) break derivLoop;
        }
        ruleTime.put(rule, ruleTime.getOrDefault(rule, 0L) + stopWatch.stop().ms);
      }
    }

    // Apply unary categories on spans (rule $A ($B))
    // Important: do this in topologically sorted order and after all the binaries are done.
    for (Rule rule : parser.getCatUnaryRules()) {
      if (timeout && !isRootRule(rule)) continue;
      if (!rule.isAnchored()) continue;

      StopWatch stopWatch = new StopWatch().start();
      String cell = anchoredCell(rule.rhs.get(0), start, end);
      List<Derivation> derivations = getDerivations(cell);
      for (Derivation deriv : derivations) {
        if (!applyAnchoredRule(rule, start, end, cell, deriv)) break;
      }
      ruleTime.put(rule, ruleTime.getOrDefault(rule, 0L) + stopWatch.stop().ms);
    }
  }

  // ============================================================
  // Build Floating
  // ============================================================

  // Build floating derivations of exactly depth |depth|.
  private void buildFloating(int depth) {
    // Build a floating predicate from thin air
    // (rule $A (a)); note that "a" is ignored
    if (depth == 0) {
      for (Rule rule : parser.grammar.getRules()) {
        if (timeout && !isRootRule(rule)) continue;
        if (!rule.isFloating()) continue;
        if (rule.rhs.size() != 1 || rule.isCatUnary()) continue;

        StopWatch stopWatch = new StopWatch().start();
        applyFloatingRule(rule, depth);
        ruleTime.put(rule, ruleTime.getOrDefault(rule, 0L) + stopWatch.stop().ms);
      }
    }

    // Apply unary categories on spans (rule $A ($B))
    for (Rule rule : parser.getCatUnaryRules()) {
      if (timeout && !isRootRule(rule)) continue;
      if (!rule.isFloating()) continue;
      if (catSizeBound.getBound(rule.lhs) < depth) continue;

      StopWatch stopWatch = new StopWatch().start();
      String cell = floatingCell(rule.rhs.get(0), depth - 1);
      derivLoop:
        for (ChildDerivationsGroup group : getFilteredDerivations(rule, cell))
          for (Derivation deriv : group.derivations1)
            if (!applyFloatingRule(rule, depth, cell, deriv)) break derivLoop;
      ruleTime.put(rule, ruleTime.getOrDefault(rule, 0L) + stopWatch.stop().ms);
    }

    // Apply binaries on spans (rule $A ($B $C)), ...
    for (Rule rule : parser.grammar.getRules()) {
      if (timeout && !isRootRule(rule)) continue;
      if (!rule.isFloating()) continue;
      if (rule.rhs.size() != 2) continue;
      if (catSizeBound.getBound(rule.lhs) < depth) continue;

      StopWatch stopWatch = new StopWatch().start();
      String rhs1 = rule.rhs.get(0);
      String rhs2 = rule.rhs.get(1);
      if (!Rule.isCat(rhs1) || !Rule.isCat(rhs2))
        throw new RuntimeException("Floating rules with > 1 arguments cannot have tokens on the RHS: " + rule);

      if (FloatingParser.opts.useSizeInsteadOfDepth) {
        derivLoop:
          for (int depth1 = 0; depth1 < depth; depth1++) {  // sizes must add up to depth-1 (actually size-1)
            int depth2 = depth - 1 - depth1;
            String cell1 = floatingCell(rhs1, depth1);
            String cell2 = floatingCell(rhs2, depth2);
            for (ChildDerivationsGroup group : getFilteredDerivations(rule, cell1, cell2))
              for (Derivation deriv1 : group.derivations1)
                for (Derivation deriv2 : group.derivations2)
                  if (!applyFloatingRule(rule, depth, cell1, deriv1, cell2, deriv2)) break derivLoop;
          }
      } else {
        {
          derivLoop:
            for (int subDepth = 0; subDepth < depth; subDepth++) {  // depth-1 <=depth-1
              String cell1 = floatingCell(rhs1, depth - 1);
              String cell2 = floatingCell(rhs2, subDepth);
              for (ChildDerivationsGroup group : getFilteredDerivations(rule, cell1, cell2))
                for (Derivation deriv1 : group.derivations1)
                  for (Derivation deriv2 : group.derivations2)
                    if (!applyFloatingRule(rule, depth, cell1, deriv1, cell2, deriv2)) break derivLoop;
            }
        }
        {
          derivLoop:
            for (int subDepth = 0; subDepth < depth - 1; subDepth++) {  // <depth-1 depth-1
              String cell1 = floatingCell(rhs1, subDepth);
              String cell2 = floatingCell(rhs2, depth - 1);
              for (ChildDerivationsGroup group : getFilteredDerivations(rule, cell1, cell2))
                for (Derivation deriv1 : group.derivations1)
                  for (Derivation deriv2 : group.derivations2)
                    if (!applyFloatingRule(rule, depth, cell1, deriv1, cell2, deriv2)) break derivLoop;
            }
        }
      }
      ruleTime.put(rule, ruleTime.getOrDefault(rule, 0L) + stopWatch.stop().ms);
    }
  }

  // ============================================================
  // Infer (main entry)
  // ============================================================

  @Override public void infer() {
    LogInfo.begin_track("DPDParser.infer()");
    StopWatch watch;
    // First pass
    if (!DPDParser.opts.ignoreFirstPass) {
      LogInfo.begin_track("First pass");
      StopWatchSet.begin("DPDParser.firstPass");
      watch = new StopWatch().start();
      currentPass = ParsingPass.FIRST;
      ApplyFn.exactScopeHead = false;       // TODO: Make this not specific to ApplyFn
      runParsingPass();
      ApplyFn.exactScopeHead = true;
      if (DPDParser.opts.summarizeCountUseful) countUseful();
      collectPossibleIngredients();
      firstPassParseTime = watch.stop().getCurrTimeLong();
      StopWatchSet.end();
      LogInfo.end_track();
    }
    // Second pass
    LogInfo.begin_track("Second pass");
    StopWatchSet.begin("DPDParser.secondPass");
    watch = new StopWatch().start();
    currentPass = ParsingPass.SECOND;
    runParsingPass();
    secondPassParseTime = watch.stop().getCurrTimeLong();
    StopWatchSet.end();
    LogInfo.end_track();
    // Collect final derivations
    StopWatchSet.begin("DPDParser.final");
    currentPass = ParsingPass.DONE;
    collectFinalDerivations();
    ensureExecuted();
    if (computeExpectedCounts) {
      expectedCounts = new HashMap<>();
      ParserState.computeExpectedCounts(predDerivations, expectedCounts);
    }
    StopWatchSet.end();
    LogInfo.end_track();
  }

  private void runParsingPass() {
    // Create a parsing thread and run for some time
    timeout = false;
    Thread parsingThread = new Thread(new DPDParserParsingThread());
    parsingThread.start();
    try {
      parsingThread.join(DPDParser.opts.maxDPDParsingTime * 1000);
      if (parsingThread.isAlive()) {
        // This will only interrupt first or second passes, not the final candidate collection.
        LogInfo.warnings("Parsing time exceeded %d seconds. Will now interrupt ...", DPDParser.opts.maxDPDParsingTime);
        timeout = true;
        parsingThread.interrupt();
        parsingThread.join();
      }
    } catch (InterruptedException e) {
      e.printStackTrace();
      LogInfo.fails("DPDParser error: %s", e);
    }
    evaluation.add((currentPass == ParsingPass.FIRST ? "first" : "second") + "passTimeout", timeout);
  }

  public class DPDParserParsingThread implements Runnable {
    @Override
    public void run() {
      ruleTime = new HashMap<>();

      Set<String> categories = new HashSet<String>();
      for (Rule rule : parser.grammar.getRules())
        categories.add(rule.lhs);

      // Set the pruner
      if (currentPass == ParsingPass.FIRST) {
        pruner.setCustomAllowedPruningStrategies(DPDParser.opts.allowedPrunersInFirstPass);
      } else {
        pruner.setCustomAllowedPruningStrategies(null);     // All pruners allowed
      }

      // Base case ($TOKEN, $PHRASE, $LEMMA_PHRASE)
      // Denotations are StringValue
      for (Derivation deriv : gatherTokenAndPhraseDerivations()) {
        ensureExecuted(deriv);
        addToChart(deriv, new Ingredient(anchoredCell(deriv.cat, deriv.start, deriv.end)), null, null);
      }

      // Build up anchored derivations
      int numTokens = ex.numTokens();
      for (int len = 1; len <= numTokens; len++) {
        for (int i = 0; i + len <= numTokens; i++)  {
          buildAnchored(i, i + len);
          for (String cat : categories) {
            if (Rule.rootCat.equals(cat)) continue;
            pruneBeam(anchoredCell(cat, i, i + len));
          }
        }
      }

      // Build up floating derivations
      for (int depth = 0; depth <= maxDepth; depth++) {
        if (Parser.opts.verbose >= 1)
          LogInfo.begin_track("(%s) %s = %d", currentPass, FloatingParser.opts.useSizeInsteadOfDepth ? "SIZE" : "DEPTH", depth);
        buildFloating(depth);
        for (String cat : categories) {
          if (Rule.rootCat.equals(cat)) continue;
          pruneBeam(floatingCell(cat, depth));
        }
        if (Parser.opts.verbose >= 1) {
          Map<String, Integer> statistics = countNumCells(getCellsForCurrentPass());
          LogInfo.logs("(%s) %d cells | %d unique-denotations | %d cell-denotations | %d derivations",
              currentPass, statistics.get("Cells"), statistics.get("UniqueDenotations"),
              statistics.get("CellDenotations"), statistics.get("Derivations"));
          LogInfo.end_track();
        }
        int numCellDenotations = getNumCellDenotations(), maxNumCellDenotations = DPDParser.opts.maxNumCellDenotations;
        if (depth != maxDepth && maxNumCellDenotations >= 0 && maxNumCellDenotations < numCellDenotations) {
          LogInfo.logs("Stop parsing: number of (cell, denotation) pairs is %d > %d",
              numCellDenotations, maxNumCellDenotations);
          break;
        }
      }
      if (DPDParser.opts.dumpDenotations != DPDParser.DumpSpec.NONE) dumpDenotations(getCellsForCurrentPass());
      if (DPDParser.opts.summarizeDenotations) classifyUniqueDenotations(getCellsForCurrentPass());
      if (FloatingParser.opts.summarizeRuleTime) summarizeRuleTime();
    }
  }

  // Prune to the beam size
  private void pruneBeam(String cell) {
    if (currentPass == ParsingPass.FIRST && DPDParser.opts.firstPassBeamSize > 0) {
      Map<String, Map<Value, Metadata>> cells = getCellsForCurrentPass();
      Map<Value, Metadata> denotationToData = cells.get(cell);
      if (denotationToData == null || denotationToData.size() <= DPDParser.opts.firstPassBeamSize) return;
      // TODO: Prune based on some criteria
      if (Parser.opts.verbose >= 1)
        LogInfo.logs("Pruning first pass beam: %d => %d", denotationToData.entrySet().size(), DPDParser.opts.firstPassBeamSize);
      List<Map.Entry<Value, Metadata>> pruned = new ArrayList<>(denotationToData.entrySet());
      denotationToData = new HashMap<>();
      for (Map.Entry<Value, Metadata> entry : pruned.subList(0, DPDParser.opts.firstPassBeamSize))
        denotationToData.put(entry.getKey(), entry.getValue());
      cells.put(cell, denotationToData);
    } else if (currentPass == ParsingPass.SECOND) {
      Map<String, Map<Value, Metadata>> cells = getCellsForCurrentPass();
      Map<Value, Metadata> denotationToData = cells.get(cell);
      if (denotationToData == null) return;
      for (Metadata metadata : denotationToData.values()) {
        pruneCell(cell, metadata.derivations);
      }
    }
  }

  // ============================================================
  // Collect ingredients (after FIRST pass)
  // ============================================================

  private void collectPossibleIngredients() {
    if (Parser.opts.verbose >= 4)
      LogInfo.logs("DPDParserState.collectPossibleIngredients()");
    Set<BackPointer> usedBps = new HashSet<>();
    collectPossibleIngredients(anchoredCell(Rule.rootCat, 0, numTokens), usedBps);
    for (int depth = 1; depth <= maxDepth; depth++)
      collectPossibleIngredients(floatingCell(Rule.rootCat, depth), usedBps);
    if (Parser.opts.verbose >= 4 || DPDParser.opts.dumpAllowedIngredients) {
      LogInfo.begin_track("allowedDenotationIngredients");
      Set<String> sorted = new TreeSet<>();
      for (Ingredient ingredient : allowedIngredients)
        sorted.add(ingredient.toString());
      for (String ingredient : sorted)
        LogInfo.logs("%s", ingredient);
      LogInfo.end_track();
    }
  }

  private void collectPossibleIngredients(String cell, Set<BackPointer> usedBps) {
    if (Parser.opts.verbose >= 4)
      LogInfo.logs("DPDParserState.collectPossibleIngredients(%s)", cell);
    Map<Value, Metadata> denotationToMetadata = firstPassCells.get(cell);
    if (denotationToMetadata == null) return;
    for (Value denotation : denotationToMetadata.keySet()) {
      double compatibility = parser.valueEvaluator.getCompatibility(ex.targetValue, denotation);
      if (compatibility != 1) continue;
      if (Parser.opts.verbose >= 2)
        LogInfo.logs("[%f] %s", compatibility, denotationToMetadata.get(denotation).derivations.get(0));
      BackPointer bp = new BackPointer(cell, denotation);
      if (!usedBps.contains(bp))
        collectPossibleIngredients(bp, usedBps, 0);
    }
  }

  private void collectPossibleIngredients(BackPointer bp, Set<BackPointer> usedBps, int depth) {
    if (Parser.opts.verbose >= 4)
      LogInfo.logs("DPDParserState.collectPossibleIngredients(%s)", bp);
    usedBps.add(bp);
    Map<Value, Metadata> denotationToMetadata = firstPassCells.get(bp.cell);
    if (denotationToMetadata == null) return;
    Metadata metadata = denotationToMetadata.get(bp.value);
    if (metadata == null) return;
    allowedIngredients.addAll(metadata.possibleIngredients);
    if (Parser.opts.verbose >= 4)
      LogInfo.logs("Adding %s", metadata.possibleIngredients);
    // Recurse
    for (BackPointer childBp : metadata.backPointers) {
      if (!usedBps.contains(childBp))
        collectPossibleIngredients(childBp, usedBps, depth + 1);
    }
  }

  // ============================================================
  // Collect final derivations (after SECOND pass)
  // ============================================================

  private void collectFinalDerivations() {
    String cellName = anchoredCell(Rule.rootCat, 0, numTokens);
    for (Derivation deriv : getDerivations(cellName)) {
      if (DPDParser.opts.putCellNameInCanonicalUtterance)
        deriv.canonicalUtterance = cellName;
      predDerivations.add(deriv);
    }
    for (int depth = 0; depth <= maxDepth; depth++) {
      cellName = floatingCell(Rule.rootCat, depth);
      for (Derivation deriv : getDerivations(cellName)) {
        if (DPDParser.opts.putCellNameInCanonicalUtterance)
          deriv.canonicalUtterance = cellName;
        predDerivations.add(deriv);
      }
    }
    if (backoffParserState != null) {
      // Also combine derivations from the backoff parser state
      LogInfo.begin_track("Backoff ParserState");
      backoffParserState.infer();
      predDerivations.addAll(backoffParserState.predDerivations);
      // Prevent oracles from always being at the front.
      Collections.shuffle(predDerivations, DPDParser.opts.shuffleRandom);
      LogInfo.end_track();
    }
  }

  // ============================================================
  // Collect statistics
  // ============================================================

  // Collect the statistics and put them into the Evaluation object
  @Override
  protected void setEvaluation() {
    super.setEvaluation();
    // Parse times
    evaluation.add("firstPassParseTime", firstPassParseTime);
    evaluation.add("secondPassParseTime", secondPassParseTime);
    // Number of cells
    for (Map.Entry<String, Integer> entry : countNumCells(firstPassCells).entrySet())
      evaluation.add("firstPass" + entry.getKey(), entry.getValue());
    for (Map.Entry<String, Integer> entry : countNumCells(secondPassCells).entrySet())
      evaluation.add("secondPass" + entry.getKey(), entry.getValue());
    // Number of possible ingredients
    evaluation.add("allowedIngredients", allowedIngredients.size());
  }

  private Map<String, Integer> countNumCells(Map<String, Map<Value, Metadata>> cells) {
    int numAnchored = 0, numFloating = 0, numDenotations = 0,
        numErrorDenotations = 0, numUniqueErrorDenotations = 0, numDerivations = 0;
    Set<Value> uniqueDenotations = new HashSet<>();
    for (Map.Entry<String, Map<Value, Metadata>> entry : cells.entrySet()) {
      if (entry.getKey().contains(",")) numAnchored++; else numFloating++;
      for (Map.Entry<Value, Metadata> subentry : entry.getValue().entrySet()) {
        Value denotation = subentry.getKey();
        numDenotations++;
        uniqueDenotations.add(denotation);
        if (denotation instanceof ErrorValue)
          numErrorDenotations++;
        numDerivations += subentry.getValue().derivations.size();
      }
    }
    for (Value denotation : uniqueDenotations) {
      if (denotation instanceof ErrorValue)
        numUniqueErrorDenotations++;
    }
    Map<String, Integer> statistics = new HashMap<>();
    statistics.put("Cells", cells.size());
    statistics.put("Anchored", numAnchored);
    statistics.put("Floating", numFloating);
    statistics.put("CellDenotations", numDenotations);
    statistics.put("ErrorDenotations", numErrorDenotations);
    statistics.put("UniqueDenotations", uniqueDenotations.size());
    statistics.put("UniqueErrorDenotations", numUniqueErrorDenotations);
    statistics.put("Derivations", numDerivations);
    return statistics;
  }

  private int getNumCellDenotations() {
    int numDenotations = 0;
    for (Map<Value, Metadata> value : getCellsForCurrentPass().values()) {
      numDenotations += value.size();
    }
    return numDenotations;
  }

  // ============================================================
  // Debug: print all denotations in all cells
  // ============================================================

  protected void dumpDenotations(Map<String, Map<Value, Metadata>> cells) {
    Map<String, Formula> denotationToSampleFormula = new TreeMap<>();
    for (Map.Entry<String, Map<Value, Metadata>> entry : cells.entrySet()) {
      String cellName = entry.getKey();
      if (DPDParser.opts.dumpDenotations == DPDParser.DumpSpec.NONERROR && Grammar.isIntermediate(cellName)) continue;
      if (cellName.contains(":")) {
        String[] parts = cellName.split(":");
        assert parts.length == 2;
        cellName = String.format("&%2s:%s", parts[1], parts[0]);
      }
      for (Map.Entry<Value, Metadata> subentry : entry.getValue().entrySet()) {
        Value denotation = subentry.getKey();
        String key = null;
        switch (DPDParser.opts.dumpDenotations) {
          case UNIQUE:
            key = denotation.toString();
            break;
          case NONERROR:
            if (denotation instanceof ErrorValue || denotation instanceof DPDErrorValue) continue;
            key = cellName + " | " + denotation;
            break;
          case ALL:
            key = cellName + " | " + denotation;
            break;
          default:
            throw new RuntimeException("Unknown dump option: " + DPDParser.opts.dumpDenotations);
        }
        if (!denotationToSampleFormula.containsKey(key))
          denotationToSampleFormula.put(key, subentry.getValue().derivations.get(0).formula);
      }
    }
    LogInfo.begin_track("%s DENOTATIONS", DPDParser.opts.dumpDenotations);
    for (Map.Entry<String, Formula> entry : denotationToSampleFormula.entrySet())
      LogInfo.logs("%s | %s", entry.getKey(), entry.getValue());
    LogInfo.end_track();
  }

  // ============================================================
  // Debug: classify unique-denotations by attributes
  // ============================================================

  protected void classifyUniqueDenotations(Map<String, Map<Value, Metadata>> cells) {
    Set<String> denotations = new HashSet<>();
    Map<String, Integer> attributeCounter = new TreeMap<>();
    for (Map.Entry<String, Map<Value, Metadata>> entry : cells.entrySet()) {
      for (Map.Entry<Value, Metadata> subentry : entry.getValue().entrySet()) {
        Value denotation = subentry.getKey();
        String key = denotation.toString();
        if (denotations.contains(key)) continue;
        MapUtils.incr(attributeCounter, getDenotationAttributes(denotation));
        denotations.add(key);
      }
    }
    LogInfo.begin_track("Denotation Classification");
    for (Map.Entry<String, Integer> entry : attributeCounter.entrySet()) {
      LogInfo.logs("%7d (%6.2f%%) : %s", entry.getValue(),
          entry.getValue() * 100.0 / denotations.size(), entry.getKey());
    }
    LogInfo.end_track();
  }

  protected String getDenotationAttributes(Value denotation) {
    StringBuilder sb = new StringBuilder();
    if (denotation instanceof ListValue || denotation instanceof InfiniteListValue) {
      sb.append("L");
      if (denotation instanceof InfiniteListValue) {
        sb.append("|size=Inf");
        sb.append("|type=").append(DenotationTypeInference.getValueType(denotation));
      } else {
        // Size
        List<Value> values = ((ListValue) denotation).values;
        if (values.size() == 0)      sb.append("|size=0");
        else if (values.size() == 1) sb.append("|size=1");
        else                         sb.append("|size=many");
        // Type
        if (!values.isEmpty())
          sb.append("|type=").append(DenotationTypeInference.getValueType(denotation));
      }
    } else if (denotation instanceof ScopedValue) {
      sb.append("S");
      try {
        ListValue head = (ListValue) ((ScopedValue) denotation).head;
        PairListValue relation = (PairListValue) ((ScopedValue) denotation).relation;
        // Head
        if (head.values.size() == 1) sb.append("|hsize=1");
        else                         sb.append("|hsize=many");
        sb.append("|htype=").append(DenotationTypeInference.getKeyType(denotation));
        // Relation
        int relationSize = 0;
        for (Pair<Value, Value> pair : relation.pairs) {
          if (pair.getSecond() instanceof ListValue) {
            relationSize = Math.max(relationSize, ((ListValue) pair.getSecond()).values.size());
          } else if (pair.getSecond() instanceof InfiniteListValue) {
            relationSize = Integer.MAX_VALUE;
          } else {
            throw new RuntimeException();
          }
        }
        if (relationSize == 0)      sb.append("|vsize=0");
        else if (relationSize == 1) sb.append("|vsize=1");
        else if (relationSize == Integer.MAX_VALUE) sb.append("|vsize=Inf");
        else                        sb.append("|vsize=many");
        sb.append("|vtype=").append(DenotationTypeInference.getValueType(denotation));
      } catch (Exception e) {
        sb.append("|???=").append(e);
      }
    } else {
      // Currently PairListValue and ErrorValue, which don't appear in grow grammar,
      // are not handled explicitly.
      sb.append("X=" + denotation.getClass().getSimpleName());
    }
    return sb.toString();
  }

  // ============================================================
  // Debug: count the number of useful unique-denotations and cell-denotations
  // ============================================================

  private void countUseful() {
    Set<String> allUniqueDenotations = new HashSet<>(), usefulUniqueDenotations = new HashSet<>(),
        allCellDenotations = new HashSet<>(), usefulCellDenotations = new HashSet<>();
    Set<BackPointer> usedBps = new HashSet<>();
    // All cells and denotations
    for (Map.Entry<String, Map<Value, Metadata>> entry : firstPassCells.entrySet()) {
      for (Value value : entry.getValue().keySet()) {
        // Unique-denotations
        String denotation = value.toString();
        allUniqueDenotations.add(denotation);
        // Cell-denotations
        String cellDenotation = entry.getKey() + " | " + denotation;
        allCellDenotations.add(cellDenotation);
      }
    }
    // Useful unique-denotations and cell-denotations
    findUseful(anchoredCell(Rule.rootCat, 0, numTokens), usedBps, usefulUniqueDenotations, usefulCellDenotations);
    for (int depth = 1; depth <= maxDepth; depth++)
      findUseful(floatingCell(Rule.rootCat, depth), usedBps, usefulUniqueDenotations, usefulCellDenotations);
    // Summarize
    LogInfo.begin_track("countUseful %s", ex.id);
    LogInfo.logs("uniqueDenotations: %d / %d (%.3f%%)", usefulUniqueDenotations.size(), allUniqueDenotations.size(),
        usefulUniqueDenotations.size() * 100.0 / allUniqueDenotations.size());
    LogInfo.logs("cellDenotations: %d / %d (%.3f%%)", usefulCellDenotations.size(), allCellDenotations.size(),
        usefulCellDenotations.size() * 100.0 / allCellDenotations.size());
    LogInfo.end_track();
  }

  private void findUseful(String cell, Set<BackPointer> usedBps,
      Set<String> usefulUniqueDenotations, Set<String> usefulCellDenotations) {
    Map<Value, Metadata> denotationToMetadata = firstPassCells.get(cell);
    if (denotationToMetadata == null) return;
    for (Value denotation : denotationToMetadata.keySet()) {
      BackPointer bp = new BackPointer(cell, denotation);
      findUseful(bp, usedBps, usefulUniqueDenotations, usefulCellDenotations);
    }
  }

  private void findUseful(BackPointer bp, Set<BackPointer> usedBps,
      Set<String> usefulUniqueDenotations, Set<String> usefulCellDenotations) {
    usedBps.add(bp);
    // Unique-denotations
    String denotation = bp.value.toString();
    usefulUniqueDenotations.add(denotation);
    // Cell-denotations
    String cellDenotation = bp.cell + " | " + denotation;
    usefulCellDenotations.add(cellDenotation);
    // Recurse
    Map<Value, Metadata> denotationToMetadata = firstPassCells.get(bp.cell);
    if (denotationToMetadata == null) return;
    Metadata metadata = denotationToMetadata.get(bp.value);
    if (metadata == null) return;
    for (BackPointer childBp : metadata.backPointers) {
      if (!usedBps.contains(childBp))
        findUseful(childBp, usedBps, usefulUniqueDenotations, usefulCellDenotations);
    }
  }

  // ============================================================
  // Debug: summarize the time used in each rule
  // ============================================================

  private void summarizeRuleTime() {
    List<Map.Entry<Rule, Long>> entries = new ArrayList<>(ruleTime.entrySet());
    entries.sort(new ValueComparator<>(true));
    LogInfo.begin_track("(%s) Rule time", currentPass);
    for (Map.Entry<Rule, Long> entry : entries) {
      LogInfo.logs("%9d : %s", entry.getValue(), entry.getKey());
    }
    LogInfo.end_track();
  }
}
