program that converts a postfix expression to infix, using a pushdown stack

You want a program to convert something like

   ( 3 ( 4 2 + ) 5 * )

to

   ( ( 3 * ( 4 + 2 ) ) * 5 )

Suppose you have a list of tokens ('(', numbers, operators, ')')
as the programs input.  The algorithm is:


if [token is '('] then
  push '(' on the stack

else if [token is number] then
  push number on the stack

else if [token is operator] then
  while
    pop off two elements a,b
    if top element on stack is '(' then
      pop off the '('
      push back on "(a operator b)"   
      break while
    else 
      push back on "(a operator b)"
  end while

else if [token is ')'] then
  discard