function add (a)
  local sum = 0
  for i = 1, #a do sum = sum + a[i] end
  return sum
  end

function addfile (filename) 
  local sum = 0 
  for line in io.lines(filename) do 
    sum = sum + line 
  end 
  return sum 
  end

function bt (init, stop, step, assign)
  local t = {}
  for i = init, stop, step do t[i] = assign(i) end
  return t
  end