for rel,target in pairs(Cache[pane.id].links) do
    initialize_cache_if_necessary(target)
    save_links(target)

  for rel,x in pairs(Cache[pane.id].links) do
    process_all(x, function(target)
      initialize_cache_if_necessary(target)
      save_links(target)
    end)

-- links might contain either a single target or a list of them
function process_all(x, fn)
  if type(x) == 'string' then
    fn(x)
  else
    for _,target in ipairs(x) do
      fn(target)
    end
  end
end

-- Most edge types/labels are unique; a node can have only one edge with each type.
-- However there are some exceptions.
-- The opposite of a unique edge (e.g. parent) might be non-unique (e.g. child).
Non_unique_edges = {'side', 'child', 'cross'}

  elseif string.match(column.name, '%S+ of %S+') then
    local rel, start_id = string.match(column.name, '(%S+) of (%S+)')
    initialize_cache_if_necessary(start_id)
    populate_step_column(column, start_id, rel)

  if Cache[pane.id].links[rel] then

  if Cache[pane.id].links[rel] and not array.find(Non_unique_edges, rel) then

  print('connecting up links')
  Cache[pane.id].links[rel] = new_pane.id
  Cache[new_pane.id].links[Opposite[rel]] = pane.id
  if #Surface[Cursor_pane.col] == 1 then

  -- connect up links
  add_edge(pane.id, rel, new_pane.id)
  add_edge(new_pane.id, Opposite[rel], pane.id)
  if #Surface[Cursor_pane.col] == 1 and not array.find(Non_unique_edges, rel) then

  if Cache[pane.id].links[rel] then
    add_error(('%s already has a %s note'):format(pane.id, rel))

  if not can_add_edge(pane.id, rel, Grab_pane.id) then
    return
  end
  if not can_add_edge(Grab_pane.id, Opposite[rel], pane.id) then

  print('connecting up links')
  Cache[pane.id].links[rel] = Grab_pane.id
  Cache[Grab_pane.id].links[Opposite[rel]] = pane.id

  -- connect up links
  add_edge(pane.id, rel, Grab_pane.id)
  add_edge(Grab_pane.id, Opposite[rel], pane.id)

end
-- Can we add an edge called 'rel' from src to target?
-- Precondition: both ids are already in Cache.
function can_add_edge(src, rel, target)
  if array.find(Non_unique_edges, rel) then
    -- check if already present
    for _,id in ipairs(Cache[src].links[rel]) do
      if id == target then
        add_error(('%s is already a %s of %s'):format(target, rel, src))
        return false
      end
    end
  else
    -- check for conflict
    if Cache[src].links[rel] then
      add_error(('%s already has a %s note'):format(src, rel))
      return false
    end
  end
  return true
end
function add_edge(src, rel, target)
  if array.find(Non_unique_edges, rel) then
    if Cache[src].links[rel] == nil then
      Cache[src].links[rel] = {target}
    else
      table.insert(Cache[src].links[rel], target)
    end
  else
    Cache[src].links[rel] = target
  end

  -- TODO: non-unique

  -- TODO: non-unique

    -- TODO: non-unique

  -- TODO: non-unique

  -- TODO: non-unique

  command.open_file_in_next_column(Cache[pane.id].links[rel])

  if array.find(Non_unique_edges, rel) then
    local column = {name=(('%s of %s'):format(rel, pane.id))}
    populate_step_column(column, pane.id, rel)
    add_column_to_right_of_cursor(column)
    plan_draw()
  else
    command.open_file_in_next_column(Cache[pane.id].links[rel])
  end
end
function populate_step_column(column, start_id, rel)
  local n = #Cache[start_id].links[rel]
  for i, id in ipairs(Cache[start_id].links[rel]) do
    local pane = load_pane(id)
    add_title(pane, ('%d/%d'):format(i, n))
    table.insert(column, pane)
  end

  if Opposite[rel] ~= rel then
    populate_unroll_column_asymmetric(column, id, rel)

  if Opposite[rel] == rel then
    add_error(("link type %s is undirected and can't be unrolled"):format(rel))
    return

end
function populate_unroll_column_asymmetric(column, id, rel)

  if array.find(Non_unique_edges, rel) then
    add_error(("link type %s is not unique and can't be unrolled"):format(rel))
    return
  end

    -- TODO: non-unique

  -- TODO: non-unique

  -- TODO: non-unique