Task

Create a stack-based evaluator for an expression in   reverse Polish notation (RPN)   that also shows the changes in the stack as each individual token is processed as a table.



 Assume an input of a correct, space separated, string of tokens of an RPN expression
 Test with the RPN expression generated from the   Parsing/Shunting-yard algorithm   task: 

         3 4 2 * 1 5 - 2 3 ^ ^ / + 

 Print or display the output here


Notes

    ^    means exponentiation in the expression above.
    /    means division.


See also

   Parsing/Shunting-yard algorithm for a method of generating an RPN from an infix expression.
   Several solutions to 24 game/Solve make use of RPN evaluators (although tracing how they work is not a part of that task).
   Parsing/RPN to infix conversion.
   Arithmetic evaluation.


let reduce op = function
  | b::a::r -> (op a b)::r
  | _ -> failwith "invalid expression"
 
let interprete s = function
  | "+" -> "add",    reduce ( + ) s
  | "-" -> "subtr",  reduce ( - ) s
  | "*" -> "mult",   reduce ( * ) s
  | "/" -> "divide", reduce ( / ) s
  | "^" -> "exp",    reduce ( ** ) s
  | str -> "push", (System.Double.Parse str) :: s
 
let interp_and_show s inp =
  let op,s'' = interprete s inp
  printf "%5s%8s " inp op
  List.iter (printf " %-6.3F") (List.rev s'')
  printf "\n";
  s''
 
let eval str =
  printfn "Token  Action  Stack";
  let ss = str.ToString().Split() |> Array.toList
  List.fold interp_and_show [] ss