static O analyzeBitMap_idToText; // func(long) -> S

// Looks only at the values
static void analyzeBitMap(MultiMap<Long, Long> bitMap) {
  analyzeBitMap(values(bitMap.data));
}

static void analyzeBitMap(Collection<L<Long>> bitMap) {
  if (bitMap.isEmpty()) ret;
  
  new HashSet<Long> allSeen;
  for (L<Long> l : bitMap)
    allSeen.addAll(l);
  printStruct(+allSeen);
  MultiMap<Long, Long> implies = fullSelfMap(allSeen);
  MultiMap<Long, Long> eq = fullSelfMap(allSeen);
  
  for (L<Long> l : bitMap) {
    HashSet<Long> set = new HashSet(l);
    for (Long a : cloneList(implies.keySet())) {
      bool ax = set.contains(a);
      for (Long b : cloneList(implies.get(a))) {
        bool bx = set.contains(b);
        if (ax && !bx)
          implies.remove(a, b);
      }
    }
    
    for (Long a : cloneList(eq.keySet())) {
      bool ax = set.contains(a);
      for (Long b : cloneList(eq.get(a))) {
        bool bx = set.contains(b);
        if (ax != bx)
          eq.remove(a, b);
      }
    }
  }
  
  printStruct(+implies);
  //printStruct(+eq);
  
  L<L<Long>> clusters = multiMapToClusters(eq);
  for i over clusters:
    print("Cluster \* i+1 */: " + struct(mapIfFunctionNotNull(analyzeBitMap_idToText, clusters.get(i))));
}

static MultiMap<Long, Long> fullSelfMap(Collection<Long> l) {
  new MultiMap<Long, Long> mm;
  for (Long x : l) mm.putAll(x, l);
  ret mm;
}

static L<L<Long>> multiMapToClusters(MultiMap<Long, Long> mm) {
  // a cluster is a list of concepts.
  // first, make trivial clusters (one per item).
  
  Map<Long, L<Long>> clusters = new TreeMap<Long, L<Long>>();
  for (Long a : mm.keySet()) {
    if (!clusters.containsKey(a))
      clusters.put(a, ll(a));
  }
  
  // then, merge the clusters.
  
  for (Long a : mm.keySet())
    for (Long b : mm.get(a)) {
      L<Long> c1 = clusters.get(a);
      L<Long> c2 = clusters.get(b);
      if (c1 != c2) // different clusters, need to merge!
        mergeClusters(clusters, c1, c2);
    }
  
  ret asList(new HashSet<L<Long>>(clusters.values()));
}

static void mergeClusters(Map<Long, L<Long>> clusters, L<Long> c1, L<Long> c2) {
  for (Long x : c2) {
    clusters.put(x, c1);
    c1.add(x);
  }
}