Closures & Recursion

[Stefan Brantschen <sbr@...>]

Newbie question: I ran into the question how to use closures with  
recursion -- consider this snippet:

local function visited (x)
-- Check and register if a table 'x' has been visited
  local vis = {}
  return function (x)
  for _, v in pairs(vis) do
    if x == v then return true
  end
  v[#v+1] = x
  return false
end

function visit (x)
-- Visit potentially recursive and circular structures.
  local cv = visited()
  if type(x) == "string" then
    -- do something
  elseif type(x) = ... -- more types to ensure end of recursion
    -- do something
  elseif type(x) == "table" then
    if not cv(x) then
      for _, v in pairs(x) do
        visit (x)
      end
    end
  end
end

The issue with this code is of course that each recursion call will  
create a new closure ('local cv = visited()') and hence all this does  
not work as intended.

What is the Correct Way to go with LUA in this case (of course  
without creating globals to keep visited table -- if possible)?

Thanks and regards
- Stefan