Streams and Trees

I've been trying to build an index for Skinny recently. This is important to me, I need people to be able to subscribe to my blog and for that I need a feed and for that I need a sensible index. Currently I'm hand making the index and it's not easy to turn into something else. I really don't want to get into XSLT management of this stuff again.

So if the index needs to be easier to maintain the best thing would be Emacs org-mode. I came up with an outline fairly quickly:

* index
** Provisioning Emacs apps
*** [[/blog/2012_10/provision-and-deploy-emacs-apps.creole]]
** EmacsLisp and BigNums for MongoDB
*** [[/blog/2012_08/bignums-with-emacslisp.creole]]

There is other stuff I'd like to be able to keep in there... but that's the basics.

Org-mode has some hacking tools. But they're not extensive. Most interesting is org-map-entries which let's you map over the entries in an org file.

That let's us spit out a stream fairly quickly using this code:

  (lambda ()
    (let* ((level1 (get-text-property (point) 'org-level-1))
           (item (buffer-substring-no-properties
           (props (org-entry-properties (line-end-position)))
           (data (progn
                    ;; If we have tags it's a different regex
                    (if (aget props "TAGS")
                        "\\*+ \\(.*[^ ]\\) +:\\(.*\\):"
                        "\\*+ \\(.*[^ ]\\) *")
                   (match-string 1 item))))
      (list data
            :level level
            :props props))) nil 'file)

It produces a stream like this:

("index" :level 1)
("Provisioning Emacs apps" :level 2)
("[[/blog/2012_10/provision-and-deploy-emacs-apps.creole]]" :level 3)
("EmacsLisp and BigNums for MongoDB" :level 2)
("[[/blog/2012_08/bignums-with-emacslisp.creole]]" :level 3)
("" :level 3)

But this is not much use. I really need something with the original org-mode structure but in Lisp. This is what I'm aiming for:

 :level 1 
 (("Provisioning Emacs apps" 
    :level 2 
      :level 3)))
  ("EmacsLisp and BigNums for MongoDB"
    :level 2 
      :level 3)
      :level 3)))))

Streams and lists and lists and trees

A stream is a flat list, only one element deep with some indication of what the tree structure it represents is encoded within each element. A tree is a deep, nested list with the structure modelled by the list. Notice that the original structure of the org-mode text is a tree, represented by the text.

The stream produced by the org-map-entries code above is a specifying stream, the structure of the resulting tree is encoded in specified data in the stream. Namely the :level properties.

I need to turn that into the my desired tree structure. Turns out this isn't easy to do. It's also not common. I immediately thought of other stream parsers:

But in both those cases the structure of the tree is defined by stream events marking the beginning and end of the structure, so this XML:

    <c>test 1</c>

is represented by this stream:

TEXT "test 1"
END "c"
END "b"
END "a"

Parsing event streams

The way you deal with this is to have a parser that pushes creates and closes the structure with those events, they're like instructions on a tape:

(let (stack result)
  (loop for (operator operand) in stream
    do (case operator
          (let ((element (list operand)))
            (if stack
                  (setcdr (elt stack 0) (list element))
                  (push element stack))
                (setq stack (list element))
                (setq result stack))))
          (setcdr (elt stack 0) (list operand)))
          (pop stack)))) result)

Note: (elt stack 0) is (peek stack)

So we keep a stack to make accessing the deep structure easy, because we use the stack rather than traversing the structure, we also need to keep a pointer to the result, which is what we return.

The START case:

STACK BEFORE   | ("b") | ("a" ("b")) | ...
INSERT         ("c")
STACK AFTER    | ("c") | ("b" ("c")) | ("a" ("b" ("c"))) | ...

The TEXT case:

STACK BEFORE   | ("c") | ("b" ("c")) | ...
INSERT         "test 1"
STACK AFTER    | ("c test1") | ("b" ("c test1")) | ...

It works and you can read it, mostly, even though it's not very functional.

Parsing specifier streams

In our org-mode example though, the structure of the list is defined by the level values specified in the stream so the stack operation is not so simple.

When we find a level we must check that the stack has the appropriate level of element in it or it's the top of the stack.

Here's a solution to the org-mode problem:

(defun stream->tree (stream level-fn content-fn)
  (when (and (listp stream) (car stream))
    (let ((stack (list)) (result (list)))
      (dolist (item stream)
        (let* ((il (funcall level-fn item))
               ;; the parent of the current item, by level
                (let ((peeked (elt stack 0)))
                  (while (and peeked (<= il (funcall level-fn peeked)))
                    (pop stack)
                    (setq peeked (elt stack 0)))
          (let ((content (funcall content-fn stack-parent)))
            (if content
                (nconc content (list item))
                ;; Else
                (if stack-parent
                     (elt stack 0)
                     (funcall content-fn stack-parent (list item)))
                    ;; Else
                    (push (list item) stack)))
            ;; Update the stack
            (if (> il (length stack))
                (push item stack)
                ;; else
                (setf (elt stack 0) item))
            ;; Update the result
            (when (equal il 1) (push item result)))))

I've abstracted the level detection and the content detection so they could be anything. In my case the items are plists with an annoying header element, so the following functions suffice for level and content:

(content-fn (object &optional to-set)
  (if to-set
        (car object)
        (plist-put (cdr object) :content to-set))
      (plist-get (cdr object) :content)))

(level-fn (object)
  (plist-get (cdr object) :level))

I really don't like this approach. It is very imperative and the abstractions were necessary just to make it readable.

Parsing specifier streams by conversion to events

As I wrote this post it became clear that a better alternative was to write a stream converter from the level specifying stream to the event stream. This could even be lazy and non-blocking (although I haven't tried that yet). But here's something that would do that:

(let ((stream
       '(("index" :level 1)
         ("Provisioning Emacs" :level 2)
         ("[[/blog/2012_10/provision-and-deploy-emacs-apps.creole]]" :level 3)
         ("Doing something else" :level 1)))
      (last-level 0))
  (loop for (head . item) in stream
     if (> (plist-get item :level) last-level)
     collect (list 'START head) into result
     if (< (plist-get item :level) last-level)
     append (append
             (loop repeat (+ 1 (- last-level (plist-get item :level)))
                collect (list 'END))
             (list (list 'START head))) into result
     finally return
       (append result
               (loop repeat (+ 1 (- last-level (plist-get item :level)))
                collect (list 'END)))
     do (setq last-level (plist-get item :level))))

So this produces a stream like this:

((START "index") 
 (START "Provisioning Emacs") 
 (START "[[/blog/2012_10/provision-and-deploy-emacs-apps.creole]]")
 (START "Doing something else")

Which could then be consumed by a less complex event/stack parser.

In order to introduce lazyness I think that the loop needs replacing by something that produces stream events and passes them to some callback.


It seems like the event stream is fundamentally easier to reason about. I expect it would be possible to find a functional solution to the event stream, but even the iterative one I have above is not that bad.

My solution to converting other types of streams to event streams is also imperative but again, not so imperative that it's problematic. It's easy enough to see the reasoning in there.

So that's what I'll do I think.