Ackermann := proc( m :: nonnegint, n :: nonnegint )
  option remember; # optional automatic memoization
  if m = 0 then
    n + 1
  elif m = 1 then
    n + 2
  elif m = 2 then
    2 * n + 3
  elif m = 3 then
    8 * 2^n - 3
  elif n = 0 then
    thisproc( m - 1, 1 )
  else
    thisproc( m - 1, thisproc( m, n - 1 ) )
  end if
end proc: