Arithmetic.hs

import Data.List

data Op = P | M | X | D deriving (Enum, Eq, Ord)
data Ex = Nobe Op Ex Ex | Leaf Rational deriving Ord

instance Show Ex where
    show (Leaf x) = show $ floor x 
    show (Nobe o e1 e2) = "(" ++ show e1 ++ ["+-x/" !! fromEnum o] ++ show e2 ++ ")" 

instance Eq Ex where
    Leaf x == Leaf y = x == y
    Nobe o x y == Nobe p z w | o == p = (x,y) == (z,w) || elem o [P,X] && (x,y) == (w,z)
    e1 == e2 = False

eval (Leaf x) = Just x
eval (Nobe D e1 e2) | eval e2 == Just 0 = Nothing
eval (Nobe o e1 e2) = [(+),(-),(*),(/)] !! fromEnum o <$> eval e1 <*> eval e2

allexprs [x] = [Leaf x]
allexprs xs = [Nobe o l r | (ls, rs) <- nub $ splitAt <$> [1..length xs-1] <*> permutations xs,
                            l <- allexprs ls, o <- [P,M,X,D], r <- allexprs rs]
                            
main = do print $ nub $ filter ((== Just 17) . eval) $ allexprs [6,6,5,2]
          print $ nub $ filter ((== Just 24) . eval) $ allexprs [8,8,3,3]
          print $ nub $ filter ((== Just 41) . eval) $ allexprs [2,3,5,7]