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	your solution doesn't work when a function is the index of a table
neither when a string with a space (for instance) in it is the index.
	You can solve this by eliminating the 'asIndex' parameter and
forcing the characters '[' and ']' at the left side of the assignment.
I also take the liberty to change your repeat-until loop to a while-do-end
to eliminate a redundant test inside (if k ~= nil ...).

function asText(obj)
   visitRef = {}
   visitRef.n = 0

   asTxRecur = function(obj)
      if type(obj) == "table" then
         if visitRef[obj] then
            return "@"..visitRef[obj]
         visitRef.n = visitRef.n +1
         visitRef[obj] = visitRef.n

         local begBrac, endBrac = "{", "}"
         local t = begBrac
         local k, v = next(obj, nil)
         while k do
            if t > begBrac then
               t = t..", "
            t = t.."["..asTxRecur(k).."]="..asTxRecur(v)
            k, v = next(obj, k)
         return t..endBrac
         if type(obj) == "string" then
            return '"'..obj..'"'
            return tostring(obj)
   end -- asTxRecur

   return asTxRecur(obj)
end -- asText

	Also, you couldn't distinguish two different tables with the same
contents.  As you are numbering each table you write, you can change 'begBrac'
to "{@"..visitRef.n and you will be printing each table with a number.
After that you can write every reference to each table (despite it is a
circular reference) with its number and the mentioned difference will be
	I made a function like that (about a year or two), but as my
problem doesn't have circular references I have never tried to resolve it.
On the other side, I made some effort to indent tables.  If you are interested
in it, I'm merging both functions and can send you a copy.