Phone Number Question

-- Question of the Day
-- Given a phone number, write a function that outputs every
-- possible letter combination for that number.

-- First, we can make an auxiliary function
-- that will take a number and convert it
-- to its corresponding telephone numpad.
-- This function is done via recursion and concatenation with the cons operator.
phoneToString :: Integer -> [String]
phoneToString 0 = []
phoneToString n = (numPick (n `mod` 10)):(phoneToString $ fromIntegral $ floor ((fromIntegral n)/10) )
    where numPick d = case d of 1 -> " "
                                2 -> "abc"
                                3 -> "def"
                                4 -> "ghi"
                                5 -> "jkl"
                                6 -> "mno"
                                7 -> "pqrs"
                                8 -> "tuv"
                                9 -> "wxyz"
                                0 -> " "


-- Then we do a quick n'dirty list comprehension.
-- Just a note that the earlier function actually
-- has the list in reverse because the least sig. num
-- has the most precedence, so we use reverse to get it
-- to the correct order.
phoneNumberMapper :: Integer -> [String]
phoneNumberMapper num
    | ( (num < 10^6) || (num > 10^7) ) = ["INVALID"] -- Assuming that a phone number is only 7-digits.
    | otherwise = [ [d0]++[d1]++[d2]++[d3]++[d4]++[d5]++[d6] |
                    d0 <- (numList !! 0),
                    d1 <- (numList !! 1),
                    d2 <- (numList !! 2),
                    d3 <- (numList !! 3),
                    d4 <- (numList !! 4),
                    d5 <- (numList !! 5),
                    d6 <- (numList !! 6)
                    ]
        where numList = reverse $ phoneToString num