Data.Generics.Traversable.Zipper

Based on «Scrap Your Zippers: A Generic Zipper for Heterogeneous Types. Michael D. Adams. WGP '10: Proceedings of the 2010 ACM SIGPLAN workshop on Generic programming, 2010» (http://michaeldadams.org/papers/scrap_your_zippers/).

Compared to the original syz package, this implementation (based on GTraversable) gives more flexibility as to where a zipper may point to and what is considered as siblings.

Specifically, a zipper may point to any element which gtraverse applies its function to.

Example

syz

Consider the classical example: lists. With syz, a list is interpreted as a right-balanced tree.

>>> let z = fromJust . down' $ toZipper ['a'..'d']
>>> getHole z :: Maybe Char
Just 'a'

The zipper z points to the first element of the list. Now let's move to the right:

>>> let z' = fromJust . right $ z
>>> getHole z' :: Maybe Char
Nothing
>>> getHole z' :: Maybe [Char]
Just "bcd"

Instead of pointing to the second element of the list, as one might expect, the zipper z' points to the tail of the list. In order to actually move to the second element, we need another down':

>>> let z'' = fromJust . down' $ z'
>>> getHole z'' :: Maybe Char
Just 'b'

traverse-with-class

GTraversable-based zippers behave more intuitively in this regard, thanks to the uniform instance for lists.

>>> let z = fromJust . down' $ toZipper ['a'..'d'] :: Zipper Typeable [Char]
>>> getHole z :: Maybe Char
Just 'a'

So far it's more or less the same as with syz. We needed to add a type annotation for the zipper itself to clarify the context which should be available at each hole (Typeable in this case). Now let's see what's to the right of us:

>>> let z' = fromJust . right $ z
>>> getHole z' :: Maybe Char
Just 'b'

That is, we jumped right to the second element of the list. Likewise,

>>> let z'' = rightmost z
>>> getHole z'' :: Maybe Char
Just 'd'

So, unlike in syz, all of the list elements are siblings.

Core types

data Zipper (c :: * -> Constraint) root

A generic zipper with a root object of type root.

Core interface

Injection and projection

toZipper :: Rec c a => a -> Zipper c a

Create a zipper. The focus starts at the root of the object.

fromZipper :: Zipper c a -> a

Move up a zipper to the root and return the root object.

Basic movement

left :: Zipper c a -> Maybe (Zipper c a)

Move left. Returns Nothing iff already at leftmost sibling.

right :: Zipper c a -> Maybe (Zipper c a)

Move right. Returns Nothing iff already at rightmost sibling.

down :: forall a c. Zipper c a -> Maybe (Zipper c a)

Move down. Moves to rightmost immediate child. Returns Nothing iff at a leaf and thus no children exist.

down' :: Zipper c a -> Maybe (Zipper c a)

Move down. Move to the leftmost immediate child. Returns Nothing iff at a leaf and thus no children exist.

up :: Zipper c a -> Maybe (Zipper c a)

Move up. Returns Nothing iff already at root and thus no parent exists.

leftmost :: Zipper c a -> Zipper c a

Move to the leftmost sibling.

rightmost :: Zipper c a -> Zipper c a

Move to the rightmost sibling.

Basic hole manipulation

query :: (forall d. Rec c d => d -> b) -> Zipper c a -> b

Apply a generic query to the hole.

trans :: (forall d. Rec c d => d -> d) -> Zipper c a -> Zipper c a

Apply a generic transformation to the hole.

transM :: Monad m => (forall d. Rec c d => d -> m d) -> Zipper c a -> m (Zipper c a)

Apply a generic monadic transformation to the hole

Convenience hole manipulation interface

It does not appear easy to make these functions polymorphic over the constraint c.

If you want these functions for your own constraint (which entails Typeable), you need to copy their definitions and change Typeable to your constraint in the Zipper 's argument.

getHole :: Typeable b => Zipper Typeable a -> Maybe b

Get the value in the hole. Returns Nothing iff a is not the type of the value in the hole.

setHole :: Typeable a => a -> Zipper Typeable b -> Zipper Typeable b

Set the value in the hole. Does nothing iff a is not the type of the value in the hole.

setHole' :: Typeable a => a -> Zipper Typeable b -> Maybe (Zipper Typeable b)

Set the value in the hole. Returns Nothing iff a is not the type of the value in the hole.