How do I format a tree so that it works with Clojure's zipper?

Question

I am creating trees of s-expressions for a genetic programming problem, and need to alter parts of the trees during the evolution process. I came across the Clojure zipper function that seems like it should be perfect, but for the life of me I can't figure out how to use it.

For example, say I create a zipper with

(def zipped (zip/seq-zip `(+ (- 1 2) 3)))

I understand this to represent a tree with + at the root, one that looks like this:

   +
 -   3
1 2

My zipper, though, doesn't agree with this: If I ask for the first node with (-> zipped zip/down zip/node) it gives me + (which is correct) but it (-> zipped zip/down zip/down) doesn't take me to -, instead it returns nil. Indeed, (-> zipped zip/down zip/rights) gives the rest of the tree as siblings to the right of the root, which suggests to me that I don't have a tree at all:

user> (-> zipped zip/down zip/rights)
((clojure.core/- 1 2) 3)

I'm pretty sure I'm representing my trees correctly because when I execute them I get the right answer. Does zipper expect a different layout?

Answer 1

The tree isn't how you've diagrammed it. The root node has 3 children: +, (- 1 2), and 3. When you do down from the root node, it defaults to the left-most child, hence why you see +.

To get to the - you'd need to call:

user=> (-> zipped zip/down zip/right zip/down zip/node)
clojure.core/-

Answer 2

The problem is that there are two different ideas of tree going on here. Your tree is a graph of how the values percolate through the evaluation, but LISP is thinking about lists of lists, and using prefix notation:

'(+ (- 1 2) 3) is also (list + (list - 1 2) 3), which is actually this tree:

+  .     3
   - 1 2

(-> zipped down node) gives you the first element, +, an atom. (-> zipped down down) thus gives you nil because the first element, +, is an atom. (-> zipped down right down node) gives you the minus sign you want because that's the first element of the second element of the expression.