Haskell - Zippers

Zippers in Haskell are basically pointers that point to some specific location of a data structure such as a tree.

Let us consider a tree having 5 elements [45,7,55,120,56] which can be represented as a perfect binary tree. If I want to update the last element of this pst, then I need to traverse through all the elements to reach at the last element before updating it. Right?

But, what if we could construct our tree in such a manner that a tree of having N elements is a collection of [(N-1),N]. Then, we need not traverse through all the unwanted (N-1) elements. We can directly update the Nth element. This is exactly the concept of Zipper. It focuses or points to a specific location of a tree where we can update that value without traversing the entire tree.

In the following example, we have implemented the concept of Zipper in a List. In the same way, one can implement Zipper in a tree or a file data structure.

data List a = Empty | Cons a (List a) deriving (Show, Read, Eq, Ord)
type Zipper_List a = ([a],[a])    

go_Forward :: Zipper_List a -> Zipper_List a   
go_Forward (x:xs, bs) = (xs, x:bs)   
   
go_Back :: Zipper_List a -> Zipper_List a   
go_Back (xs, b:bs) = (b:xs, bs)    

main = do 
   let pst_Ex = [1,2,3,4] 
   print(go_Forward (pst_Ex,[]))       
   print(go_Back([4],[3,2,1])) 

([2,3,4],[1]) 
([3,4],[2,1])