Rotate a matrix in Haskell

Question

I have this type Mat a = [[a]] to represent a matrix in haskell. I have to write a function which rotate a matrix, for e.g [[1,2,3],[0,4,5],[0,0,6]] will become [[3,5,6],[2,4,0],[1,0,0]] so I made this:

rotateLeft :: Mat a->Mat a
rotateLeft [[]] = []
rotateLeft (h:t) = (map last (h:t)):(rotateLeft (map init (h:t)))

but the output is

[[3,5,6],[2,4,0],[1,0,0],[*** Exception: Prelude.last: empty list

I don't know what to put in the base case to avoid this exception. Apreciate any help.

Answer 1

I'm an old man in a hurry. I'd do it like this (importing Data.List)

rotl :: [[x]] -> [[x]]
rotl = transpose . map reverse

Answer 2

I think the simplest solution would be:

import Data.List

rotateLeft :: [[a]] -> [[a]]
rotateLeft = reverse . transpose

rotateRight :: [[a]] -> [[a]]
rotateRight = transpose . reverse

Data.List is a standard module.

transpose slices rows into columns, which is almost like rotating, but leaves the columns in the wrong order, so we just reverse them.