-- | all decompositions of a string into multi-part (nonempty) pieces
-- >>> parts "abc"
-- [["abc"],["a","bc"], ["ab","c"], ["a","b","c"]]
-- must not use drop, take, splitAt. must make use of list monad (listcomp/do notation)

parts :: [a] -> [[[a]]]
parts [] = []
parts [x] = [[[x]]]
parts l@(x:y:[]) = [[l], [[x], [y]]]
parts l@(x:xs) = addElem (parts xs) x

addElem :: [[[a]]] -> a -> [[[a]]]
addElem [] e = [[[e]]]
addElem l@(x:xs) e = [[e] : listOfStrings| listOfStrings <- l]