translate InFix notation into PostFix notation.

result.txt

>ghci Translate.hs
GHCi, version 7.8.3: http://www.haskell.org/ghc/  :? for help
Loading package ghc-prim ... linking ... done.
Loading package integer-gmp ... linking ... done.
Loading package base ... linking ... done.
[1 of 1] Compiling Translate        ( Translate.hs, interpreted )
Ok, modules loaded: Translate.
*Translate> translate "1 + 2 * 3 ^ 4"
Loading package array-0.5.0.0 ... linking ... done.
Loading package deepseq-1.3.0.2 ... linking ... done.
Loading package containers-0.5.5.1 ... linking ... done.
"1 2 3 4 ^ * +"
*Translate> translate "1 + 2 * 3 + 4"
"1 2 3 * + 4 +"
*Translate> translate "1 + 2 * 3 * 4"
"1 2 3 * 4 * +"
*Translate> translate "1 + 2 * 3 / 4"
"1 2 3 * 4 / +"
*Translate>

Translate.hs

module Translate
( toPostFix 
, translate
) where 

import Data.Char
import qualified Data.Map as Map

-- ("operator",priority)
operators = Map.fromList [ ("+",1)
	    		 , ("-",1)
			 , ("*",2)
			 , ("/",2)
			 , ("^",3)
			 ]

type Stack = [String]

translate :: String -> String 
translate src = unwords . toPostFix [] $ words src

-- Translate from InFix to PostFix
toPostFix :: Stack -> [String] -> [String]
toPostFix [] [] = []

toPostFix [] (token:lestToken) 
  | Nothing /= priToken = toPostFix [token] lestToken
  | True == isNum token = token : ( toPostFix [] lestToken ) 
  | otherwise = error "token parse error #1"
    where priToken = Map.lookup token operators

toPostFix (op:stk) [] = op : toPostFix stk []

toPostFix (op:stk) (token:lestToken)
  | Nothing /= priToken && ( priOp >= priToken ) = op : toPostFix (stk) (token:lestToken)
  | Nothing /= priToken && ( priOp < priToken  ) = toPostFix (token:op:stk) lestToken
  | True == isNum token   = token : ( toPostFix (op:stk) lestToken )
  | otherwise = error "token parse error #2"
    where priOp    = Map.lookup op operators
    	  priToken = Map.lookup token operators
 

isNum :: String -> Bool
isNum src = src == filter (\x -> isDigit x ) src