Parsing/RPN to infix conversion

You are encouraged to solve this task according to the task description, using any language you may know.
Task

Create a program that takes an RPN representation of an expression formatted as a space separated sequence of tokens and generates the equivalent expression in infix notation.

 Assume an input of a correct, space separated, string of tokens
 Generate a space separated output string representing the same expression in infix notation
 Show how the major datastructure of your algorithm changes with each new token parsed.
 Test with the following input RPN strings then print and display the output here.


 RPN input 
 sample output


 3 4 2 * 1 5 - 2 3 ^ ^ / +
 3 + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3


 1 2 + 3 4 + ^ 5 6 + ^
 ( ( 1 + 2 ) ^ ( 3 + 4 ) ) ^ ( 5 + 6 )

 Operator precedence and operator associativity is given in this table:


 operator 
 precedence 
 associativity 
 operation


  ^  
 4 
 right 
 exponentiation


  *  
 3 
 left 
 multiplication


  /  
 3 
 left 
 division


  +  
 2 
 left 
 addition


  -  
 2 
 left 
 subtraction



See also

   Parsing/Shunting-yard algorithm   for a method of generating an RPN from an infix expression.
   Parsing/RPN calculator algorithm   for a method of calculating a final value from this output RPN expression.
   Postfix to infix   from the RubyQuiz site.


 
   type Priority is range 1..4;
   type Infix is record
      Precedence : Priority;
      Expression : Unbounded_String;
   end record;
   package Expression_Stack is new Generic_Stack (Infix);
   use Expression_Stack;
 
   function Convert (RPN : String) return String is
      Arguments : Stack;
      procedure Pop
                (  Operation   : Character;
                   Precedence  : Priority;
                   Association : Priority
                )  is
         Right, Left : Infix;
         Result      : Infix;
      begin
         Pop (Right, Arguments);
         Pop (Left,  Arguments);
         Result.Precedence := Association;
         if Left.Precedence < Precedence then
            Append (Result.Expression, '(');
            Append (Result.Expression, Left.Expression);
            Append (Result.Expression, ')');
         else  
            Append (Result.Expression, Left.Expression);
         end if;
         Append (Result.Expression, ' ');
         Append (Result.Expression, Operation);
         Append (Result.Expression, ' ');
         if Right.Precedence < Precedence then
            Append (Result.Expression, '(');
            Append (Result.Expression, Right.Expression);
            Append (Result.Expression, ')');
         else  
            Append (Result.Expression, Right.Expression);
         end if;
         Push (Result, Arguments);
      end Pop;
      Pointer : Integer := RPN'First;
   begin
      while Pointer <= RPN'Last loop
         case RPN (Pointer) is
            when ' ' =>
               Pointer := Pointer + 1;
            when '0'..'9' =>
               declare
                  Start : constant Integer := Pointer;
               begin
                  loop
                     Pointer := Pointer + 1;
                     exit when Pointer > RPN'Last
                       or else RPN (Pointer) not in '0'..'9';
                  end loop;
                  Push
                  (  (  4,
                        To_Unbounded_String (RPN (Start..Pointer - 1))
                     ),
                     Arguments
                  );
               end;
            when '+' | '-' =>
               Pop (RPN (Pointer), 1, 1);
               Pointer := Pointer + 1;
            when '*' | '/' =>
               Pop (RPN (Pointer), 2, 2);
               Pointer := Pointer + 1;
            when '^' =>
               Pop (RPN (Pointer), 4, 3);
               Pointer := Pointer + 1;
            when others =>
               raise Constraint_Error with "Syntax";
         end case;
      end loop;
      declare
         Result : Infix;
      begin
         Pop (Result, Arguments);
         return To_String (Result.Expression);
      end;
   end Convert;
 