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sclass OneColorTheoryChecker {
  replace Cell with URecognizer.Cell.
  
  new ProbabilisticScheduler scheduler;
  
  record OneColorTheory(S text, Cell cell, RGB color) {
  }
  
  OneColorTheory makeOneColorTheory(Cell cell) {
    var color = cell.averageColor();

    var theory = new OneColorTheory("Color of every pixel in $cell is $color.", cell, color);
  
    testOneColorTheory(cell, theory);
    ret theory;
  }

  void noteCellColor(Cell cell, OneColorTheory theory) {
    var desc = "Pixel check at " + cell;
    if (theory.hasExampleNamed(desc)) return;
    var strength = doubleRatio(cell.area(), theory.cell.area()); // how much do we have to say about the cell in the theory?
    var p = colorDistanceToProbability(cell.averageColor(), theory.color);
    addExampleToTheory(theory, desc, p, strength);
  }
  
  double colorDistanceToProbability(RGB col1, RGB col2) {
    ret sqr(colorSimilarity(col1, col2));
  }
  
  void testOneColorTheory(Cell cell, OneColorTheory theory) {  
    noteCellColor(cell, theory);
  
    scheduler.at(shouldSplitCell(cell), r {
      for (var split : usefulSplits(cell))
        scheduler.at(split.probability(), r {
          for (var cell : split!)
            testOneColorTheory(cell, theory.branch(description := "recursion to " + cell));
        });
    });
  }
  
  L<WithProbability<Cell[]>> usefulSplits(Cell cell) {
    ret map withProbability1(llNonNulls(cell.split(0), cell.split(1)));
  }
  
  double shouldSplitCell(Cell cell) {
    ret 1.0;
  }
}