Solve given make 10 problem

make10.hs

{-
Example:
$ ./make10 7 6 9 5
(6,Plus,9,Divide,5,Plus,7)
(9,Plus,6,Divide,5,Plus,7)
-}

import System.Environment
import Control.Monad
import Data.List
import Data.Ratio

data Operator = Plus | Minus | Multiple | Divide deriving (Show, Eq)
type Expression = (Int, Operator, Int, Operator, Int, Operator, Int)

make10 :: [Int] -> [Expression]
make10 xs = do
    x <- xs
    y <- xs \\ [x]
    z <- xs \\ [x, y]
    w <- xs \\ [x,y,z]
    o1 <- [Plus, Minus, Multiple, Divide]
    o2 <- [Plus, Minus, Multiple, Divide]
    o3 <- [Plus, Minus, Multiple, Divide]
    return $ (x, o1, y, o2, z, o3, w)

apply :: Operator -> Ratio Integer -> Ratio Integer -> Ratio Integer
apply Plus     x y = x + y
apply Minus    x y = x - y
apply Multiple x y = x * y
apply Divide   x y = x / y

calc :: Expression -> Maybe Int
calc (x, o1, y, o2, z, o3, w) =
    let rx = toRational x
        ry = toRational y
        rz = toRational z
        rw = toRational w
        a1 = apply o1
        a2 = apply o2
        a3 = apply o3
        result = rx `a1` ry `a2` rz `a3` rw
    in  if denominator result == 1 
        then Just $ (truncate.fromRational) result
        else Nothing

main = do
    args <- liftM (map (\x -> read x :: Int)) getArgs
    if length args /= 4 then error "Input length must be 4" else return ()
    mapM_ print $ nub.filter (\x -> calc x == Just 10) $ make10 args