Haskell help, pattern match list of variants

Example.hs

data Alphabet = A Int | B Float | C String

cool :: [Alphabet] -> Bool
cool [] = error "Should not call `cool` with empty list"
cool alphabetList = case alphabetList of
                       [A] -> coolInt alphabetList
                       [B] -> coolFloat alphabetList
                       [C] -> coolString alphabetList
                       _ -> error "Shouldn't call `cool` with list of different variants"
                       
-- suppose there are coolInt, coolFloat and coolString functions