So I've been reading a bit about the Zipper pattern in Haskell (and other functional languages, I suppose) to traverse and modify a data structure, and I thought that this would be a good chance for me to hone my skills at creating type classes in Haskell, since the class could present a common traversal interface for me to write code to, independent of the data structure traversed.
I thought I'd probably need two classes - one for the root data structure, and one for the special data structure created to traverse the first:
module Zipper where
class Zipper z where
go'up :: z -> Maybe z
go'down :: z -> Maybe z
go'left :: z -> Maybe z
go'right :: z -> Maybe z
class Zippable t where
zipper :: (Zipper z) => t -> z
get :: (Zipper z) => z -> t
put :: (Zipper z) => z -> t -> z
But when I tried these with some simple datastructures like a list:
-- store a path through a list, with preceding elements stored in reverse
data ListZipper a = ListZipper { preceding :: [a], following :: [a] }
instance Zipper (ListZipper a) where
go'up ListZipper { preceding = [] } = Nothing
go'up ListZipper { preceding = a:ps, following = fs } =
Just $ ListZipper { preceding = ps, following = a:fs }
go'down ListZipper { following = [] } = Nothing
go'down ListZipper { preceding = ps, following = a:fs } =
Just $ ListZipper { preceding = a:ps, following = fs }
go'left _ = Nothing
go'right _ = Nothing
instance Zippable ([a]) where
zipper as = ListZipper { preceding = [], following = as }
get = following
put z as = z { following = as }
Or a binary tree:
-- binary tree that only stores values at the leaves
data Tree a = Node { left'child :: Tree a, right'child :: Tree a } | Leaf a
-- store a path down a Tree, with branches not taken stored in reverse
data TreeZipper a = TreeZipper { branches :: [Either (Tree a) (Tree a)], subtree :: Tree a }
instance Zipper (TreeZipper a) where
go'up TreeZipper { branches = [] } = Nothing
go'up TreeZipper { branches = (Left l):bs, subtree = r } =
Just $ TreeZipper { branches = bs, subtree = Node { left'child = l, right'child = r } }
go'up TreeZipper { branches = (Right r):bs, subtree = l } =
Just $ TreeZipper { branches = bs, subtree = Node { left'child = l, right'child = r } }
go'down TreeZipper { subtree = Leaf a } = Nothing
go'down TreeZipper { branches = bs, subtree = Node { left'child = l, right'child = r } } =
Just $ TreeZipper { branches = (Right r):bs, subtree = l }
go'left TreeZipper { branches = [] } = Nothing
go'left TreeZipper { branches = (Right r):bs } = Nothing
go'left TreeZipper { branches = (Left l):bs, subtree = r } =
Just $ TreeZipper { branches = (Right r):bs, subtree = l }
go'right TreeZipper { branches = [] } = Nothing
go'right TreeZipper { branches = (Left l):bs } = Nothing
go'right TreeZipper { branches = (Right r):bs, subtree = l } =
Just $ TreeZipper { branches = (Left l):bs, subtree = r }
instance Zippable (Tree a) where
zipper t = TreeZipper { branches = [], subtree = t }
get TreeZipper { subtree = s } = s
put z s = z { subtree = s }
I couldn't get it to compile, I'd just get a lot of errors like this for each of my Zippable
instance definitions:
Zipper.hs:28:14: Couldn't match expected type `z' against inferred type `ListZipper a' `z' is a rigid type variable bound by the type signature for `zipper' at Zipper.hs:10:20 In the expression: ListZipper {preceding = [], following = as} In the definition of `zipper': zipper as = ListZipper {preceding = [], following = as} In the definition for method `zipper'
So I'm not sure where to go from here. I suspect that my issue is that I'm trying to bind these two instances
together, when the (Zipper z) =>
declaration just wants z
to be any Zipper
.