How to flatten a list of lists of lists in haskell
All I want to do is what I ask. The type signature of the function should be this:
flatten::[[[Int]]] -> [[Int]]
I tried to search some flatten code but they define new types and that confuses me. Any help? Thanks in advance.
Answer
There are (at least) two ways to write
flatten::[[[Int]]] -> [[Int]]
One is
flatten1 = concat
-- Example: flatten [[[1], [2]], [[3]]] = [[1], [2], [3]] :: [[Int]]
Another one is
flatten2 = map concat
-- Example: flatten [[[1], [2]], [[3]]] = [[1,2], [3]] :: [[Int]]
Basically, flatten1 flattens the "middle" level of brackets, while flatten2 flattens the "innermost" level of brackets.
As an exercise, you might want to convince yourself that
concat . flatten1 = concat . flatten2 :: [[[Int]]] -> [Int]
Indeed, both would produce [1,2,3] on the example above.
A more advanced remark
The law above is actually a very famous one, since it is a special case of the monad law
join . fmap join = join . join :: Monad m => m (m (m a)) -> m a
where m = [] (i.e., in the list monad), and a=Int