and $ map can be shortened to all in many places. I'd use pointless style more: row = (!!) The function valid has a lot of repetition, maybe the repeating par

and $ map can be shortened to all in many places. I'd use pointless style more: row = (!!) The function valid has a lot of repetition, maybe the repeating part can be abstracted of? Instead of length possible > 0, you can use not $ null possible. This is faster, since it doesn't go through the whole list. Instead of pattern matching on Maybe (tile), you can use Prelude's maybe.