Zhegalkin polynomial by truth table

import Data.List (intercalate)

xor a b = (a || b) && not (a && b)

triangle [] = []
triangle l@(x:xs) = [l] ++ (triangle $ zipWith xor l xs)

num2string _ _ 0 = "1"
num2string result var n
    | mod n 2 == 0 = num2string result (pred var) $ div n 2
    | n == 1 = (var:result)
    | otherwise = num2string (var:result) (pred var) $ div n 2

letter x n
    | n <= 1 = x
    | otherwise = letter (succ x) (pred n)

zhegalkin [] = []
zhegalkin l
    | l == [] = "1"
    | (length l) /= 2 ^ varCount = error "Incorrect list length"
    | otherwise = intercalate "+" $ filter (/= "") $ map stringFactor $ zip (map head (triangle l)) [0..]
    where   stringFactor x
            | fst x = num2string "" (letter 'A' varCount) $ snd x
            | otherwise = []
        varCount = truncate $ logBase 2 $ fromIntegral $ length l