[nihils]

If you want immutable data structures that simulate the behavior of mutable data structures look into Zippers. In this case, a list zipper.

[nihils]

For example, this problem of modifying the diagonal of a matrix can be solved quite easily:

  type Zipper a = ([a],[a])
  
  cursorOnDiagonal :: [[Int]] -> [Zipper Int]
  cursorOnDiagonal matrix = map (\(n,x) -> splitAt n x) (zip [0..(length matrix)-1] matrix) 

  flipToOneAtCursor :: [Zipper Int] -> [Zipper Int]
  flipToOneAtCursor = map (\(ys,x:xs) -> (ys,1:xs))   

  backToList :: [Zipper Int] -> [[Int]] 
  backToList = map (\(ys,xs) -> ys ++ xs)

If matrix == [[0,0,0,0],[0,0,0,0],[0,0,0,0],[0,0,0,0]], then:

  backToList . flipToOneAtCursor . cursorOnDiagonal $ matrix == [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]