Versioned Arrays

I just learned of a method of creating functional data structures from mutable types called versioning. Basically, if you have mutable data like an array, you can implement functional changes of the data structure by storing the differences between multiple references. This is a might bit better than copying the data structure, particularly in the case of a large array. For an array of size $N$, versioned arrays can hold two arrays with $m$ changes between them using only $O(N+m)$ space. Further, while the access time for an element when the array is $m$ away from it's version is $O(m)$, many use cases require only accessing arrays a fixed number of changes away, making access time $O(1)$.

A Simple Implementation using Lists

This can be implemented simply enough using cons cells and lists. Implementing in Common Lisp, accessing an element is as follows:

1. A versioned array is list whose last element is an array
   
2. The values before the last element are a list of changes that need to occur
   to mutate the array into the one we are interested in.
   
3. Access to the array involves applying all changes to the array and inverting
   the changes as we a moving the array to the other side of them (I'll try to
   clarify later)
   
4. Leaving you with a list of length one, containing an array with the desired
   values in it, at which point you can access the data.
   

By moving the array to the version we are currently accessing from, we are betting that more accesses will happen from this, or a similar, version. This will mean the rest of the accesses will be faster than the first.

(defpackage :versioned-arrays
    (:use :cl :bt :iter :modf)
  (:export #:make-versioned-array
           #:varef ))

(in-package :versioned-arrays)

(defun make-versioned-array (dimensions
                             &rest args
                             &key (element-type t)
                             initial-element initial-contents
                             adjustable fill-pointer
                             displaced-to displaced-index-offset )
  "Make a versioned array."
  (when (or adjustable fill-pointer displaced-to displaced-index-offset)
    (error "The capabilities: adjustable, fill-pointer, displaced-to,
    displaced-index-offset are not implemented yet") )
  (list (apply #'make-array dimensions args)) )

(defun varef (v-arr &rest idx)
  (multiple-value-bind (array changes) (get-array v-arr)
    (invert-changes (cdr v-arr) changes v-arr)
    (setf (car v-arr) array
          (cdr v-arr) nil )
    (apply #'aref (car v-arr) idx) ))

(defun get-array (v-arr)
  (if (arrayp (car v-arr))
      (values (car v-arr) nil)
      (multiple-value-bind (array changes)
          (get-array (cdr v-arr))
        (destructuring-bind (new-val &rest idx) (car v-arr)
          (let ((old-val (apply #'aref array idx)))
            (setf (apply #'aref array idx) new-val)
            (values array
                    (cons (cons old-val idx) changes) ))))))

(defun invert-changes (old-v-arr changes last)
  (cond ((null changes) nil)
        (t (setf (cdr old-v-arr) last
                 (car old-v-arr) (car changes) )
         (invert-changes (cdr old-v-arr) (cdr changes) old-v-arr) )))

First, let's consider a simple linear version history. This would happen if you had an array and only modified the original or the latest versions of the array. Using the standard cons cell diagrams where red is the car and blue is the cdr, our linear versioned array would look something like this:

Accessing an element in a linear versioned array. This is the way the structure would change if the last access was via Ref 2 and the next was via Ref 1. Any cons cell is a valid version of this array before and after the "rebase"

Modification goes very similarly:

1. Given that we want to modify the value at indices idx to new-val
   
2. We first store the current value at idx. This has the side effect of
   moving our array to the current version.
   
3. We cons a new cell to store the array in, place the delta where the array
   currently is, and modify the cdr of that cell to point to the new one.
   

This can be simply coded using my Modf library:

(define-modf-function varef 1 (new-val v-arr &rest idx)
  (let ((old-value
         ;; This moves the array to our version
         (apply #'varef v-arr idx) ))
    (let ((arr (car v-arr)))
      (setf (apply #'aref (car v-arr) idx) new-val)
      (setf (cdr v-arr) (list arr)
            (car v-arr) (cons old-value idx) )))
  (cdr v-arr) )

When looking at what is above, it is important to note that this is a mutation filled computation. This does not involve building lists the normal way with cons. Instead we are modifying lists in place. This is necessary as we need any changes we make to be seen by any reference to the versioned array. This is what I meant by inverting the changes. Inverting means reversing the order of the deltas as well as swapping the values in the deltas with the values in the array. The issue here is that we may have any given number of references to this data structure floating about. We need to modify the values that might be referenced so that if we use those reference later, they will still work.

So things might be coming into focus, although a versioned array is a list of deltas with it's last element an array, many other versioned arrays (or versions of the array) might be sharing some structure with this array. If they truly are versions of the same array, they at the very least share the last element in the list, which contains the array they are versioning. In the following figures we see the structure of a more complicated array as elements are accessed and modified (edited).

Accessing an element in a versioned array. This array has several versions. As demonstrated here, the version history is in general a tree. Upon access, the array is moved to the access point and all deltas are adjusted to maintain the array.

Accessing an element on a different branch of the version tree. Notice that no version is invalidated by this operation, not even the versions on the branch that isn't considered at all.

Editing an element in the array is much like an access except that at the end it creates another delta with the specified edit.

Multithreading

The very fact that we are messing around with mutation should clue you in that we are probably going to have thread safety issues. In fact, even reading is a mutating operation for this structure, so it isn't even safe to read from multiple threads at the same time. Due to this, everything inside the internals of this data structure needs to be wrapped in a lock unique to the structure. I chose to switch from a list to a structure so I could hold the lock in a straight-forward manner (and so I can have a type to specialize print-object on).

There is a single lock on the array. This means that, unlike tree based implementations of functional arrays, working with one version will halt any work with another version.

Performance

Let's see how this performs on the well known N-Queens problem. This involves backtracking, which is one of those use cases where we are only interested in array versions a constant number of deltas away from the current. If we ignore how simple the queens problem is and explicitly build a chess board to check the other attacking squares, we would get something like what follows. Here I have a version based on versioned arrays, and one sketched out for standard arrays. I also implemented this for a functional array based on FSet, which uses some kind of trees.

(defun place-queen (board i j)
  "This complicated bit is to test if a queen can attack another."
  (if (and (iter (for k from 0 below (va-dimension board 0))
                 (never (and (/= i k) (varef board k j))) )
           (iter (for k from 0 below (va-dimension board 1))
                 (never (and (/= j k) (varef board i k))) )
           (iter (for k1 from i downto 0)
                 (for k2 from j downto 0)
                 (never (and (/= k1 i) (/= k2 j) (varef board k1 k2))) )
           (iter (for k1 from i below (va-dimension board 0))
                 (for k2 from j below (va-dimension board 1))
                 (never (and (/= k1 i) (/= k2 j) (varef board k1 k2))) )
           (iter (for k1 from i downto 0)
                 (for k2 from j below (va-dimension board 1))
                 (never (and (/= k1 i) (/= k2 j) (varef board k1 k2))) )
           (iter (for k1 from i below (va-dimension board 0))
                 (for k2 from j downto 0)
                 (never (and (/= k1 i) (/= k2 j) (varef board k1 k2))) ))
      (modf (varef board i j) t)
      nil ))

(defun n-queens (board n row)
  "Simple enough backtracking algorithm."
  (if (= row n)
      board
      (iter (for i below n)
            (let ((result (place-queen board i row)))
              (when result
                (thereis (n-queens result n (+ row 1))) )))))

(defun place-queen* (board i j)
  "This complicated bit is to test if a queen can attack another."
  (if (and ...similar-tests...)
      t
      nil ))

(defun n-queens* (board n row)
  "A bit more convoluted backtracking algorithm."
  (if (= row n)
      board
      (let (winning-board)
        (iter (for i below n)
              (let ((result (place-queen* board i row)))
                (when result
                  (setf (aref board i row) t)
                  (let ((try (n-queens* board n (+ row 1))))
                    (when try
                      (setf winning-board try)
                      (finish) )
                  (setf (aref board i row) nil) ))
              (finally (return winning-board)) )))))

Comparing the two, we naturally see that the functional form is more elegant and understandable. The speed is another matter though…

$N$	Array	Versioned Array	FSet Array	VA/Array	FSet/Array
11	1	4	4	4	4
12	2	24	41	12	20.5
13	1	12	12	12	12
14	17	255	277	15	16.294118
15	14	207	231	14.785714	16.5
16	116	1726	1937	14.879310	16.698276
17	68	1006	1167	14.794118	17.161765
18	595	8775	10073	14.747899	16.929412
19	40	584	694	14.6	17.35

The functional version is easier to understand, of course, though using something like screamer would hide most if not all of the side effect annoyances. Speed wise, though, the functional approaches seem to be around a factor of 15 slower. The FSet method is consistently slower, but not by enough to say definitively that versioned arrays are going to be faster for this problem. We do see a slow growth in the FSet implementation. We are probably seeing the $O(\log N)$ access time. There might be a completely different story to tell with proper optimization of the versioned arrays. Particularly if someone tried to get it closer to the metal, so to speak.

Conclusions

A little side note: since starting the post, I have found out that Haskell uses something similar to this in its Diff Array library with the notable exception that the version history is forced to be linear. This is done by forcing a copy if a version other than the most recent is changed. This seems like it could lead to mysterious poor performance for small changes in your algorithm and certainly doesn't seem appropriate for backtracking. Fortunately, the person who let me know about data structure in the first place is currently implementing a library for this for Haskell.

One thing to note is when this doesn't work well. It doesn't work well when you have references to versions of an array with very different deltas. For instance, if you saved some initial state of an array, made many changes, and used both arrays by, say, comparing them element by element, things could get pretty slow. To curb this, several people have developed schemes to split the versioning tree if too many deltas are in between two particular arrays. Typically this is done probabilistically, randomly splitting the delta tree with probability $\frac 1 N$. With this modification, we have an expected amortized edit time of $O(1)$ (worst case $O(N)$ which is a steep price) and an expected worst case access time to be $O(N)$. The true worst case access time is $O(m)$ for arbitrarily bad luck on the RNG, but the expected $O(N)$ is a much needed improvement over knowing it is $O(m)$ where $m$ can be arbitrarily large. Since all of the work is done in walking the deltas and rebasing the array, edits and accesses have the same time complexity.

This all sounds like gloom and doom, but really, there are a large class of problems that don't require access from very different arrays. Further, much of this trouble can be resolved by breaking the abstraction and allowing the user to explicitly force a copy.

I was thinking about it, and there is nothing here limiting you to arrays. I could, in principle, implement this kind of versioning for any mutable structure. Instead of storing indices, the arguments of the setter function, store the function and the arguments and the setter can be inverted the same way it is in Modf. It doesn't sound like too bad of an idea to have a generic functionality to stick any object into and get back an immutable object with reasonable asymptotic performance. Maybe this should be a future extension for Modf.

Syncing Emacs with Google Documents

Before anything, sorry for the long post. If I had more time, I would have made it shorter. I made a promise to myself that I would spend the time to write up things I do, mainly so I get practice doing so, and to have a record of things I've done.

Recently I had an interview with Google. At Google they try to weed out applicants with a quick technical phone interview before they fly you out for an actual interview. As part of this interview, a shared Google Document is set up as a kind of virtual white-board so you can show your programming ability. Never mind that I would rather be sharing a Screen session, VNC connection, or even a live screen cast of my desktop, this is the way they decided to do it. The problem is, Google Documents are not meant to be code editor, they are meant to be a tool for writing documents. As such, I would be left without the aid of auto-completion, argument lists, and (most importantly) the Emacs key bindings, that, by now, are etched into my spinal column. So, a few minutes after receiving an email stating a Google Document would be used, I started coding up a program that would allow me to program in Emacs, but have my work displayed in Google Documents. See the video for an idea of what I'm talking about.

I quickly found the hooks: before-change-functions and after-change-functions. Actually, they are not hooks, I believe, as Emacs has a strictly specified meaning and argument passing protocol for hooks, they are just a list of functions that are called before and after each change, respectively. These would allow me to find what changes are being made locally so I can send them to Google Docs.

Now came one hurdle: how do I interface with Google Docs? There is a Greasemonkey and Python script that allows you to download Google Documents from the command line. Unfortunately, I could not find a script made for uploading documents, which is really the main part of this. Further, while the script worked for downloading, it was far too slow for interactive editing. The time from hitting return to retrieved document was on order 5-10 seconds. I needed something that could be run extremely fast, like on the order of the time it takes to type a key.

I eventually decided that I should try to mirror the edits between the two document by sending keystrokes to the browser window. Next hurdle: in X, as far as I know, keystrokes are only sent to the focused window. And since I would be using Emacs, I couldn't rightly send keystrokes to Firefox at the same time. Or can I? I quickly decided to run a separate X server which would run an instance of Firefox which could be focused at the same time as Emacs on my normal X server. Now there are several ways to do this (e.g. actually run a new server on a different virtual terminal, or playing around with Xnest which runs an X server inside a window in your host X server) but in the end I decided to use the awesome programs xpra and Xvfb. Xpra is a program designed to be an alternative to X forwarding.

Xpra and Xvfb

As an aside, X forwarding allows you to run graphical applications on remote machines while having the graphics display locally. This is different from VNC and RDP in that you don't have access to the entire X session, just windows associated with applications you are running. X forwarding has become less used in the Unix world, mostly due to a lack of knowledge of its existence, I believe. This is not to say that there aren't good reasons for it not be used. It actually has a pretty severe problem on high latency network (a.k.a high ping time) connections.

Xpra was also designed to get around X forwarding poor performance as well as to add abilities like detaching GUI programs and re-attaching from a different point on the network, just like with screen. It truly is very neat. All of it's neatness aside, I just wanted to use it to handle Xvfb, which is a virtual X server, like Xnest, but one that doesn't have to be displayed at all. You can start programs under an Xvfb server and they will happily do their business thinking they are displaying windows, but no window is drawn to any screen. Xvfb sounds just like what I needed. First I started the Xvfb server on display ":1" by using the Xpra:

xpra :1

I started Firefox under the Xvfb server via:

DISPLAY=:1 firefox -no-remote -P some-other-profile

This is more complicated than normal because I leave Firefox running. The options -no-remote tells Firefox to not check for other, currently running instances of Firefox before starting it. If Firefox sees a running instance of itself, it will choose to just open a new window rather than start a new instance. The option -P tells Firefox to use a different profile (which you must create prior to this) for the session. This is necessary as a different running instance of Firefox will have a lock held on your normal profile. If you are willing to just close Firefox, you can omit both of those options.

At this point, nothing should be displayed. If you want to attach the Firefox window to the current X server via Xpra, just use xpra attach and it should appear. You can navigate this to your Google Document.

Sending input to the window

Up until now, we have not even discussed how you are going to send input to the window. Luckily, this can be accomplished by many tools. In fact, I ran into three without even looking really (Xnee which includes gnee and cnee, xte, and xdotool). I have even heard people describing directly inserting characters into the input devices in /dev. I ended up using xdotool because (1) it seemed more powerful than xte and (2) cnee crashed my (main ":0") X server. With xdotool you can send keys (with modifiers), strings, mouse motion and clicks, and manipulate windows, like bringing them into focus.

# Send an 'a', a 'B', and a 'C'
DISPLAY=:1 xdotool key a B shift+c

# This types "hello how are you"
DISPLAY=:1 xdotool type "hello how are you"

# This moves the mouse to 100,100 relative to the top-left corner of the window,
# then right click (presses and releases the 3rd button)
DISPLAY=:1 xdotool mousemove --window 41466948 100 100 click 3

# This brings window with id 41466948 into focus
DISPLAY=:1 xdotool focusWindow 41466948

This is fine and dandy, but what if we want to input large sections of text. Even if we use the type command, xdotool is still just typing every letter, albeit ~100 characters/second. Further, due to a bug/shortcoming/whatever in xdotool, I couldn't figure out how to make it send text that includes a newline character (or an ampersand or question mark for that matter). It seems worth our while to come up with other ways of interfacing with the Google Documents window. The other way I came up with is the clipboard.

X has a clipboard (actually it has three), and that clipboard can be accessed via the command line. Again, there are multiple tools that can do this including xclip and xsel. While the functionality of the two programs are near identical, I chose to use xsel as it seemed a little more robust. Using xsel, we can send large sections of text to the clipboard on display ":1" (remember, each X server has it's own clipboard), then send a "ctrl+v" using xdotool. More interestingly, however, is that copying in the ":1" server allows us to gain some information on what is in the other file and more importantly, as it turns out, the location of the point in the Google Document.

Putting it together

Most of this involves coding in Emacs Lisp. The point of everything here is to keep track of where the point in the Google Document while making alterations. If we ever lose track of where the point is in the document, we will corrupt the document with every edit. In the following, I use the word "document" to refer to the Google document and "document point" to refer to the cursor location in that document. The word "buffer" refers to things in Emacs, and "buffer point" refers to the point in the Emacs buffer, i.e. the cursor position. I use the word function here because that's what Emacs calls them. In reality these are all procedures called for their side effects.

We will need some basics:

1. A function that will send a key to the window
   
2. A function that will send a string to the window
   
3. A function to properly escape strings sent through the shell
   
4. Functions that move left and right
   
5. A function that moves the point by some relative amount
   

   (defvar gd-point 0 "A variable holding the document point")
   
   (defun gdmir-gdocify-string (str)
     "Escape every character.  This means that the shell shouldn't
   mess with any of this."
     (replace-regexp-in-string "\\(.\\)" "\\\\\\1" str))
   
   ;; The parameter INSTANT is used in the buffered input optimiztion, but not
   ;; here.
   (defun gdmir-send-key (keys &optional instant)
     (shell-command (concat "DISPLAY=:1 xdotool windowFocus 4194333 key "
                            keys )))
   
   (defun gdmir-send-string (string)
     (shell-command (concat "DISPLAY=:1 xdotool windowFocus 4194333 type "
                            string )))
   
   (defun gdmir-move-left (n)
     "Move the buffer N characters left, reducing GD-POINT by N.
   The buffer point doesn't change."
     (loop repeat n
           do (gdmir-send-key "Left")
              (decf gd-point)) )
   
   (defun gdmir-move-right (n)
     "Move the buffer N characters right, increasing GD-POINT by N.
   The buffer point doesn't change."
     (loop repeat n
           do (gdmir-send-key "Right")
              (incf gd-point) ))
   
   (defun gdmir-move-to-relative-point (point-difference)
     "Move the buffer point to \(+ GD-POINT POINT-DIFFERENCE).  The
   buffer point doesn't change."
     (if (< point-difference 0)
         (gdmir-move-left (abs point-difference))
         (gdmir-move-right (abs point-difference)) ))
   

Now for the meat and potatoes: the hook functions. We will define a function that sets the after and before change functions. The before function, gdmir-before-edit, which receives the start and end point of the forthcoming edit, moves the document point to the end of the edit range, then saves the original string, and finally deletes the original text¹. The after function, gdmir-after-edit, sends commands required to type the new text.

(defun split-for-xdotool (string)
  "This function runs through the input and replaces instances of
`?', `&', and newlines with symbols corresponding to these
characters.  We return a list containing strings and the special
symbols in the order they should be output.  We have to use the
special symbols due to the fact that xdotool, or bash, or
something cannot handle these symbols, even if they are quoted."
  (rest
   (let ((count 0))
     (loop for segment in (split-string string "[\n?&]")
           appending
        (list (when (> count 0)
                (cond ((eql (aref string (- count 1)) (aref "?" 0))
                       'question )
                      ((eql (aref string (- count 1)) (aref "&" 0)) 'amp)
                      ((eql (aref string (- count 1)) (aref "\n" 0))
                       'ret )))
              segment )
           do (incf count (1+ (length segment))) ))))

(defvar *prechange-text* nil "This holds the contents of the
edited region prior to the edit.  We don't use this, but I can
think of a few reasons we might want to save it." )

(defun gdmir-before-edit (start end)
  (gdmir-move-to-relative-point (- end gd-point))
  (setf *prechange-text* (list start end (buffer-substring start end)))
  ;; Delete the string in GD before in Emacs
  (loop for i below (- end start)
        do (decf gd-point)
           (gdmir-send-key "BackSpace") ))

(defun gdmir-after-edit (start end old-length)
  (when (< 0 (- end start))
    (loop for line in (split-for-xdotool (buffer-substring start end))
          do (cond ((eql line 'question)
                    (gdmir-send-key "shift+slash") )
                   ((eql line 'amp)
                    (gdmir-send-key "shift+7") )
                   ((eql line 'ret)
                    (gdmir-send-key "Return")
                    (gdmir-send-string "\\|") )
                   ((< 0 (length line))
                    (gdmir-send-string (gdmir-gdocify-string line)) )))
    (incf gd-point (length (buffer-substring start end))) ))

(defun insert-change-hook ()
  (setf *change-hook-in-effect* t)
  (push
   'gdmir-before-edit
   before-change-functions )
  (push
   'gdmir-after-edit
   after-change-functions ))

We also can use a few helper functions which we will implement as key-bindings.

1. A function that syncs the points in the buffers (C-x SPC when mirroring is on)
   
2. A function that turns the mirroring on and off (C-x SPC when off will turn
   it on, if it's on and the point is already synced, it will be turned off)
   
3. A set of functions that moves the point in the browser window (M-<direction
   keys>). These are really handy for a quick reposition of the document
   point.
   

   (defun sync-points ()
     "Set GD-POINT to the buffer point."
     (setf gd-point (point)) )
   
   (defvar *change-hook-in-effect* nil "Used to determine if our
   change hooks are already doing their thing.")
   
   (defun setup-mirror ()
     "Set up the mirroring environment.  This should really be a
   minor mode, but since this is basically a throw away hack, I'm
   not going to bother."
     (setf old-after-change-functions after-change-functions
           old-before-change-functions before-change-functions )
     (local-set-key (kbd "M-<left>")
                    (lambda () (interactive) (gdmir-send-key "Left" t)) )
     (local-set-key (kbd "M-<right>")
                    (lambda () (interactive) (gdmir-send-key "Right" t)) )
     (local-set-key (kbd "M-<up>")
                    (lambda () (interactive) (gdmir-send-key "Up" t)) )
     (local-set-key (kbd "M-<down>")
                    (lambda () (interactive) (gdmir-send-key "Down" t)) )
     (local-set-key (kbd "C-x SPC")
                    (lambda ()
                      (interactive)
                      (cond ((and after-change-functions
                                  *change-hook-in-effect*
                                  (= (point) gd-point) )
                             (message "Mirroring disabled")
                             (setf *change-hook-in-effect* nil
                                   after-change-functions old-after-change-functions
                                   before-change-functions old-before-change-functions ))
                            ((and after-change-functions
                                  *change-hook-in-effect* )
                             (message "Syncing points")
                             (sync-points) )
                            (t
                             (message "Mirroring enabled")
                             (setf *change-hook-in-effect* t)
                             (insert-change-hook)
                             (sync-points) )))))
   

Optimizations

While all of this works, it works quite slowly. Just moving from one point to another in the document can take a considerable time as it involves moving side to side perhaps thousands of times. Here we consider two areas where there can be considerable improvements.

Incorporating other moves than side to side

The first optimization I made was to allow for motion using the up and down keys. This is difficult as we don't know how the lines are wrapped on the Google Doc, so we don't know how far that moves in the file. This can be attacked by noting that if we hold down shift as we move, the region will be selected. We can copy that to the clipboard² and read it in Emacs, allowing us to find length of the string selected, and therefore the motion in the document. This almost works. However, it turns out that whitespace at the beginning and end of selections are often times elided when copied to the clipboard (not sure why). Another issue, if you make a selection of only whitespace, it may not be copied to the clipboard at all, leaving what was on there before.

This means that we may lose track of our document point if we start or end on white space in a vertical move. The way I chose to deal with this is to place a vertical bar, "|", at the beginning of each line. To move vertically, I move the point to the beginning of the line (before the vertical bar) and then move up or down selecting the difference. This method ensures that the selection includes no end whitespace (other than the newline at the end. The newline at the end of the selection is deleted but it is compensated for by the vertical bar. As long as we only move one line at a time, we can tell how far we've gone in the vertical direction.

To add this change, we must modify the gdmir-move-left and gdmir-move-right functions to take two steps when we pass a newline in order to skip over the vertical bar in the left hand column. We must also have our change hooks check to see if we are deleting a newline (we must delete an extra character) and if we are inserting a newline (we must add a new vertical bar).

(defun gdmir-move-left (n)
  (save-excursion
    (goto-char gd-point)
    (loop repeat n
          do (when (= 0 (current-column))
               (gdmir-send-key "Left") )
             (gdmir-send-key "Left")
             (decf gd-point)
             (backward-char) )))

(defun gdmir-move-right (n)
  (save-excursion
    (goto-char gd-point)
    (loop repeat n
          do (gdmir-send-key "Right")
             (incf gd-point)
             (forward-char)
             (when (= 0 (current-column))
               (gdmir-send-key "Right") ))))

(defun gdmir-before-edit (start end)
  (gdmir-move-to-relative-point (- end gd-point))
  (setf *prechange-text* (list start end (buffer-substring start end)))
  ;; Delete the string in GD before in Emacs
  (save-excursion
    (goto-char gd-point)
    (loop for i below (- end start)
          do (progn
               (when (= 0 (current-column))
                 ;; Clear out code marker
                 (gdmir-send-key "BackSpace") )
               (decf gd-point)
               (gdmir-send-key "BackSpace")
               (backward-char) ))))

(defun gdmir-after-edit (start end old-length)
  (when (< 0 (- end start))
    (loop for line in (split-for-xdotool (buffer-substring start end))
          do (cond ((eql line 'question)
                    (gdmir-send-key "shift+slash") )
                   ((eql line 'amp)
                    (gdmir-send-key "shift+7") )
                   ((eql line 'ret)
                    (gdmir-send-key "Return")
                    (gdmir-send-string "\\|") )
                   ((< 0 (length line))
                    (gdmir-send-string (gdmir-gdocify-string line)) )))
    (incf gd-point (length (buffer-substring start end))) ))

(defun insert-change-hook ()
  (setf *change-hook-in-effect* t)
  (push
   'gdmir-before-edit
   before-change-functions )
  (push
   'gdmir-after-edit
   after-change-functions ))

Then we can introduce gdmir-move-up, gdmir-move-down, and extend gdmir-move-to-relative-point so it makes use of this new ability.

;; *EMS-PER-LINE* will be used to guess at when a line might be wrapped.  if we
;; *over-estimate, vertical moves will be broken
(defvar *ems-per-line* 50
  "A conservative estimate for how many `m's are in a line in the google document." )

(defun gdmir-move-to-zero-column ()
  (flush-commands)
  (save-excursion
   (goto-char gd-point)
   (gdmir-move-left (max (- (current-column) (- *ems-per-line* 1)) 0))
   (goto-char (- gd-point (max (- (current-column) (- *ems-per-line* 1)) 0)))
   (cond ((< (current-column) *ems-per-line*)
          (gdmir-send-key "Home Right" t)
          (setf gd-point (line-beginning-position)) )
         (t (gdmir-move-left
             (current-column) )))))

(defun gdmir-grab-selection ()
  "To read from the clipboard"
  (gdmir-send-key "ctrl+c" t)
  (shell-command-to-string "xsel --display :1 -o -b") )

(defun gdmir-move-up ()
  (flush-commands)
  (save-excursion
    (goto-char gd-point)
    ;; More to the left most position on the screen
    (gdmir-move-to-zero-column)
    (goto-char gd-point)
    ;; Move to the left of the code delimiter
    (shell-command "DISPLAY=:1 xdotool windowFocus 4194333 key Left")
    ;; move up selecting the differnce
    (let ((orig-line (line-number-at-pos)))
      (loop until (/= (line-number-at-pos) orig-line)
            do (shell-command "DISPLAY=:1 xdotool windowFocus 4194333 key shift+Up")
               (let ((selection (gdmir-grab-selection)))
                 (backward-char (length selection)) )
               ;; This doesn't move the point, it just moves to the left of the
               ;; selection and unselects the text.
            (shell-command "DISPLAY=:1 xdotool windowFocus 4194333 key Left") ))
    (setf gd-point (point))
    ;; Move to the right of the code delimiter
    (shell-command "DISPLAY=:1 xdotool windowFocus 4194333 key Right") ))

(defun gdmir-move-down ()
  (flush-commands)
  (save-excursion
    (goto-char gd-point)
    ;; More to the left most position on the screen
    (gdmir-move-to-zero-column)
    (goto-char gd-point)
    ;; Move to the left of the code delimiter
    (shell-command "DISPLAY=:1 xdotool windowFocus 4194333 key Left")
    ;; move down selecting the differnce
    (let ((orig-line (line-number-at-pos)))
      (loop until (/= (line-number-at-pos) orig-line)
            do (shell-command "DISPLAY=:1 xdotool windowFocus 4194333 key shift+Down")
               (let ((selection (gdmir-grab-selection)))
                 (forward-char (length selection)) )
               ;; This doesn't move the point, it just moves to the left of the
               ;; selection and unselects the text.
            (shell-command "DISPLAY=:1 xdotool windowFocus 4194333 key Right") ))
    (setf gd-point (point))
    ;; Move to the right of the code delimiter
    (shell-command "DISPLAY=:1 xdotool windowFocus 4194333 key Right") ))

(defun gdmir-move-to-relative-point (point-difference)
  (let ((target (+ gd-point point-difference)))
    ;; 80 is a guess at how far we have to be going before moving vertically
    ;; might be of benefit
    (cond ((< point-difference -80)
           ;; Go until you have passed the point.
           (while (> gd-point target)
             (gdmir-move-up) ))
          ((> point-difference 80)
           ;; Go until you have passed the point.
           (while (< gd-point target)
             (gdmir-move-down) )))
    ;; Then we will finish off with side to side movement
    (let ((point-difference (- target gd-point)))
      (if (< point-difference 0)
          (gdmir-move-left (abs point-difference))
          (gdmir-move-right (abs point-difference)) ))))

The motion to the beginning of the line is still annoying but as you can see we sped that up slightly by using the "home" key. This moves the point to the beginning of the line. You don't even have to select in this move as we can calculate the point at the beginning of the line in Emacs. There is one problem with this, however, since lines can wrap, and pressing "home" in Google Docs brings you to the beginning of the visible line, this cannot be used if you are on a wrapped line. I have the program move horizontally until it is within a conservative estimate of the maximum line width, then us the "home" key. You might think it a good idea to use the "shift+home" key combo repeatedly interspersed with "left" key presses counting how far we've gone, but the same issue remains, if we happen to start on some whitespace, we may miss some characters at the end of the line.

Buffering Commands

Buffering the input commands speeds things up in general because it removes some overhead to the input sending process. The way we have it set up right now is to have each keystroke start a bash shell and run the xdotool command to send input to the document. Just starting bash contributes a pretty big overhead. By buffering the commands, we can collect several commands and send them all at once, defeating the overhead. All in all this seems to speed up input by a factor of two, or so. This is a pretty significant improvement³. In fact, this beats the above method of motion for all but very long yet unwrapped lines.

In order to incorporate this kind of buffering from within Emacs, we can just hold of list of pending commands that need to be sent to the document. We will modify the gdmir-send-key function to push onto that list rather than actually send it to via xdotool. If the buffer gets to a certain size, we flush the commands to the document. In addition, since sending a string via xdotool is the last thing one can do in an invocation to xdotool, we also must force a flush of all stored commands before we send the string.

(defvar *pending-keys* nil)

(defun flush-commands (&optional string)
  (let* ((cmd (if *pending-keys*
                  (apply #'concat "key " (mapcar (lambda (x) (concat " " x)) (reverse *pending-keys*)))
                  " " ))
         (cmd (if string
                  (concat cmd " type " string)
                  cmd )))
    (when (or *pending-keys* string)
      (shell-command (concat "DISPLAY=:1 xdotool windowFocus 4194333 " cmd)) )
    (setf *pending-keys* nil)
    (setf *last-flush* (float-time)) ))

(defun gdmir-send-key (keys &optional instant)
  (push keys *pending-keys*)
  (when (or instant (< 20 (length *pending-keys*)))
    (flush-commands) ))

(defun gdmir-send-string (string)
  (flush-commands string) )

In addition to all of this, we will also need to alter several other functions to force flushing as some of them require synchronous execution, like anything that involves the clipboard.

(defun gdmir-move-to-zero-column ()
  (flush-commands)
  (save-excursion
   (goto-char gd-point)
   (gdmir-move-left (max (- (current-column) (- *ems-per-line* 1)) 0))
   (goto-char (- gd-point (max (- (current-column) (- *ems-per-line* 1)) 0)))
   (cond ((< (current-column) *ems-per-line*)
          (gdmir-send-key "Home Right" t)
          (setf gd-point (line-beginning-position)) )
         (t (gdmir-move-left
             (current-column) )))))

(defun gdmir-move-up ()
  (flush-commands)
  (save-excursion
    (goto-char gd-point)
    ;; More to the left most position on the screen
    (gdmir-move-to-zero-column)
    (goto-char gd-point)
    ;; Move to the left of the code delimiter
    (shell-command "DISPLAY=:1 xdotool windowFocus 4194333 key Left")
    ;; move up selecting the differnce
    (let ((orig-line (line-number-at-pos)))
      (loop until (/= (line-number-at-pos) orig-line)
            do (shell-command "DISPLAY=:1 xdotool windowFocus 4194333 key shift+Up")
               (let ((selection (gdmir-grab-selection)))
                 (backward-char (length selection)) )
               ;; This doesn't move the point, it just moves to the left of the
               ;; selection and unselects the text.
            (shell-command "DISPLAY=:1 xdotool windowFocus 4194333 key Left") ))
    (setf gd-point (point))
    ;; Move to the right of the code delimiter
    (shell-command "DISPLAY=:1 xdotool windowFocus 4194333 key Right") ))

(defun gdmir-move-down ()
  (flush-commands)
  (save-excursion
    (goto-char gd-point)
    ;; More to the left most position on the screen
    (gdmir-move-to-zero-column)
    (goto-char gd-point)
    ;; Move to the left of the code delimiter
    (shell-command "DISPLAY=:1 xdotool windowFocus 4194333 key Left")
    ;; move down selecting the differnce
    (let ((orig-line (line-number-at-pos)))
      (loop until (/= (line-number-at-pos) orig-line)
            do (shell-command "DISPLAY=:1 xdotool windowFocus 4194333 key shift+Down")
               (let ((selection (gdmir-grab-selection)))
                 (forward-char (length selection)) )
               ;; This doesn't move the point, it just moves to the left of the
               ;; selection and unselects the text.
               (shell-command "DISPLAY=:1 xdotool windowFocus 4194333 key Right") ))
    (setf gd-point (point))
    ;; Move to the right of the code delimiter
    (shell-command "DISPLAY=:1 xdotool windowFocus 4194333 key Right") ))

(defun gdmir-before-edit (start end)
  (gdmir-move-to-relative-point (- end gd-point))
  (setf *prechange-text* (list start end (buffer-substring start end)))
  ;; Delete the string in GD before in Emacs
  (save-excursion
    (goto-char gd-point)
    (loop for i below (- end start)
          do (progn
               (when (= 0 (current-column))
                 ;; Clear out code marker
                 (gdmir-send-key "BackSpace") )
               (decf gd-point)
               (gdmir-send-key "BackSpace")
               (backward-char) ))))

(defun gdmir-after-edit (start end old-length)
  (when (< 0 (- end start))
    (loop for line in (split-for-xdotool (buffer-substring start end))
          do (cond ((eql line 'question)
                    (gdmir-send-key "shift+slash") )
                   ((eql line 'amp)
                    (gdmir-send-key "shift+7") )
                   ((eql line 'ret)
                    (gdmir-send-key "Return")
                    (gdmir-send-string "\\|") )
                   ((< 0 (length line))
                    (gdmir-send-string (gdmir-gdocify-string line)) )))
    (incf gd-point (length (buffer-substring start end))) )
  (flush-commands) )

(defun insert-change-hook ()
  (setf *change-hook-in-effect* t)
  (push
   'gdmir-before-edit
   before-change-functions )
  (push
   'gdmir-after-edit
   after-change-functions ))

And lastly we probably want to set an idle timer to run flush-commands when nothing is happening. This will make it so no changes will sit indefinitely in the key buffer. After waiting around a few seconds (four here) and pending keys are sent to the document.

(setf *idle-flusher*
  (run-with-idle-timer 4 t (lambda () (flush-commands))) )

Two other thoughts of speeding things up come to mind, though I did not attempt this for free time reasons.

1. Asynchonous Input: Buffering commands is also a good idea for a completely
   different reason if we can buffer them outside of Emacs. Emacs, as lovely
   as it is, doesn't allow for multiple threads. This means that we have to
   wait as the commands are processed. If we are able to buffer commands to a
   different process, we could have a concurrent execution. We only need to
   have to synchronize the input with Emacs when we want to get contents of the
   Google Doc, i.e. when we are examining the clipboard.
   
2. Command optimization: The commands can also be optimized. For instance,
   when you yank to an Emacs buffer (a.k.a. paste), Emacs apparently writes it,
   then deletes it, then writes it again. I'm not sure why this happens, nor
   did I ever notice until the mechanism of writing and deleting was slowed
   down by a factor of 1000 or so. In principle, before the buffer is flushed
   to output, it could pass the contents through an optimizer, that would
   reduce this particular delete-redraw cycle to no action.
   

Conclusions

Let me take a moment to relay a few observations I made while developing this interface with a "cloud" program. First, this was very hard and convoluted. I don't think that Google has any interest in stopping me from doing this, but at times I actually thought there was an antagonistic entity on the other end thwarting my attempts. If you copy and paste from a Google Doc, whitespace might get eaten (I think this is happening due to X), or indentation might get messed up (this is almost certainly happening on the Google side). I had weird cases where more than four spaces in a row were converted to tabs, and bizarre rules on what and how much whitespace was eaten at the beginning and end of the selection. You saw how we dealt with this in the code (adding an vertical bar before each line), but it is just the nature of the beast that this is a fragile set up. It would really be nice if Google made a true virtual white-board, or used an existing one (they must exist). They could put a public API on it and anyone trying to do this would be giddy.

Second, because it's a cloud application, Google can upgrade and make incompatible changes at any time. The compatibility doesn't matter much to humans as they are adaptable, but to a program, it really throws a wrench in the works. For instance, I swear that when I first started developing, copying a block of text and pasting it in a Google Doc preserved the indentation. A few days later I tried it and this was no longer the case. It seemed like a bug that would bother people, so I wouldn't be surprised if it is fixed by now. Many people are excited by how fast an application can move when the developer decides the upgrade schedule. I guess I often times prefer the stability of getting to decide that myself.

In the end this worked well enough to use, which is the most important thing. It is pretty basic functionality, but good enough to really help when programming in Google Docs⁴. I wouldn't be surprised at all, though, if I tried this in a few weeks and found that it didn't work anymore. In the very end, however, it was ultimately unused as the phone interview consisted only of pen and paper questions. Not to despair, however, the problem was a fun one to tackle. It included interesting things like pushing the X windowing system further than most users ever do, really exploiting the extensibility of Emacs, and playing with the flexibility of the GNU/Linux operative system in general. A few years ago I would have thought this too hard to actually do and over a decade ago in Windows I would have thought this impossible (this might be possible in OS X, I imagine fiddling with the clipboard and sending keys might be the hard bits). All in all, this was a fun little project during some of the development.

Footnotes:

¹ There is actually a bug here. Emacs sometimes specifies that the
change area before isn't the change area specified in after. For instance,
check the command M-x capitalize-word, which will delete the word, but only
write the first letter of the word. I'm not sure if this is my misunderstanding
of the arguments Emacs sends, or if it is a bug in Emacs itself. Luckily it
seems to be very rare.

² Yeah, I know, if it's selected it is already on the selection clipboard.
I use the ctrl+c/ctrl+v one as it gives a bit more control.

³ To go further, one could attempt to reduce the xdotool delay
between key presses (which defaults to 13 ms). I didn't attempt this as I
assumed that it might reduce the robustness of the method (i.e. keystrokes might
be missed).

⁴ I originally had visions of actually mirroring the buffers.
I.e. you tell Emacs which buffers you want displayed in the document and it will
grab them, insert the code marker, perhaps a simple frame marking the buffer you
are in, and send it to the clipboard to be pasted on the document. I actually
had Emacs sending entire buffers at one point. After I started hitting more and
more issues with clipboards and how Google Docs messes with indentation, or
whitespace, or other things, I decided that this was not worth the effort.

Quicklisp

I just started using Quicklisp.  I was very slow to adopt largely due to the fact that my current library situation is so fragile and difficult to maintain that I figured switching to a new one would be take more time than I had at the time.  I was wrong, it seems.  After encountering some issues building CL-Graph, and not wanting to get into trying to track down where the problem is, I gave Quicklisp a try.  I have been using Quicklisp for about the last hour and have found that it will work just fine for day to day work, and should reduce my "staying current" headaches.

Excluding my personal packages, Quicklisp already holds most (if not all) of the libraries that I use on a daily basis.  This means that my method of maintaining packages, manual downloads, updates, and versioning, is basically obsolete (I had long ago ditched ASDF-Install because it was doing things I didn't want it to).  To really sweeten the pot, Quicklisp builds several large and/or complicated to build systems that are hard to keep working.

Quicklisp easily integrates with your own packages.  It acts as a last ditch solution to loading a system.  This means that if you have a package in your ASDF path, it will use that first.  Only if ASDF cannot find the requested system, does it check the Quicklisp systems (either on disk or on-line).

But perhaps the thing that I find most satisfying about Quicklisp is that it forces libraries into a more standard format, and that it has generated momentum to get a large number of Lisp libraries canned and dead simple to install on any operating system.

Several people have noted that Quicklisp isn't the first search result for Lisp libraries, so I definitely putting a link here and strongly recommend people use it (for to manage their libraries and perhaps to publish their libraries).

Bitcoin is for drug lords and terrorists?

I was at a diner party this evening and, due to my social ineptitude, I ended up steering the conversation to Android phones.  Eventually we touched on the new Google Wallet.  I expressed my disappointment in the concept which seemed little more than a glorified attempt to shoe-horn a credit card like payment system into a phone.  There seemed to be nothing new to me.  Now if only Google had chosen to make payment available with other, albeit less popular, forms of payment, like the amazing bitcoin currency.

For those who don't know, bitcoin is something new and old at the same time.  It is digital cash, or as the creators might put it, digital gold.  Instead of talking about the mathematics and technology behind it, which is very interesting, let's just discuss the properties.  Like cash, bitcoins can be traded between individuals as payment for goods.  Unlike cash, bitcoins can be traded over the Internet.  Like cash, no third party needs to know who gave what currency to whom; it's anonymous.  Unlike cash, no third party controls the circulation, printing, and distribution of currency at all (actually the entire community is the third party).  Like cash, bitcoins cannot be easily counterfeit.  Unlike cash, which can and has been copied, counterfeit bitcoins are largely accepted to be a practical impossibility (although shy of a mathematical proof, it is based on the same math as strong encryption).  Comparing to credit cards and PayPal, the main forms of payment over the Internet, bitcoins have much to offer.

After describing what a bitcoin is, the first response I hear is (as verbatim as I can remember it),

Hostess: "Wow, it seems like that would be good for drug lords."

Me: (Shocked) "Yeah, I guess... but I would say it's useful anytime you want to send money to people without any third party involved.  Like if you wanted to make contributions to someone your government didn't particularly like..."

Hostess: "Right, people could use it to send funds to al-Qaeda or the Taliban..."

Me: (Bewildered) "I was thinking more like sending donations to groups rebelling in authoritarian regimes, or... do you remember that whole Wikileaks thing?"

Hostess: "Yeah...?"

Me: "Well there was a movement to try to get it declared as a terrorist organization back when all that hit the fan, which would of made it illegal to donate funds to them.  Bitcoins would have made it possible to do so more safely, if you believed in what they were doing and wanted to give them money..."

Hostess: "oh... something, something, PayPal."

Me: "But that's part of my point.  Because a third party is involved, you open yourself to all kind of possible bad things.  Worst of all PayPal has a pretty notorious past when it comes to messing with their clients' transactions, like freezing or closing accounts at their discretion just because they don't like what you are doing."

Conversation continues about PayPal and eBay

No kidding.  I don't know what, if anything, I did to put bitcoins in the light of, useful for drug lords, criminals, and terrorists.  I guess it is just a case of if you aren't doing anything wrong, you should care if you have privacy or not.  Saying bitcoins would be good for drug lords is like saying cars would be good for drug lords because you could use them to smuggle drugs.  It's true, but kind of missing the point.

Modf ready for the public

I believe that modf is now ready for public testing and usage, so go ahead and give it a try.  Its dependencies are just Alexandria and Closer-MOP and FSet if you want to use that library.  It is broken into a main Modf library and an FSet add on library.  FUNDS support is going to pushed to the back burner because after looking at it, again, it seemed kind of under documented and annoying to deal with.  Plus, my experiences with FUNDS vs FSet has told me in the past that FSet runs quite a bit faster than FUNDS, so is probably preferred by the community anyway.

Edit: I went ahead with the FUNDS support, but it isn't really much.  Unlike FSet, FUNDS doesn't intend to be a replacement to the fundamental Lisp types.  Most FUNDS data structures do not include the ability to edit arbitrary elements.  FUNDS has trees, and Modf functions are defined for those, but the queue, stack, and heap data structures don't really make sense with Modf.  You access them in a different place than you add elements.

This library is small, but kind of reaching completion.  Any suggestions or patches are welcome.

Introducting Modf: Setf for functional programming

Setf is such a wonderful macro. Sometimes we forget. It is one of the first things I find missing when I have to resort to an imperative language, which is exactly the place where you want to use it the most. But there seems to be a shortcoming in Common Lisp when it comes to functional programming. What I mean is, it is incredibly easy to mutate state with setf, but when we want to use data in a functional way, it becomes much more cumbersome to do what is needed. For example…

;; Let's try something in a non-fuctional way
(let ((list '(1 2 3 4 5 6 7)))
  ...
  ;; Change the 5th element in the list to t
  (setf (fifth list) t)
  ... )

;; Let's try it functionally
(let ((list '(1 2 3 4 5 6 7)))
  ...
  ;; Change the 5th element in the list to t
  (labels
      ((replace-nth (nth list new-val)
         (if (> nth 0)
             (cons (car list) (replace-nth (- nth 1) (cdr list) new-val))
             (cons new-val (cdr list)) )))
    (setf list (replace-nth 4 list t)) )
  ... )

The cleanest way I could think to do this (barring what will follow) is to define a function that would do this for me. There is nothing wrong with that, and many will state that this general function should be placed in a toolbox so it can be used in the future saving me such effort from now on.

I find, however, that such functions are defined and often never used again, not because I don't need them but because I forget the work I've done in the past. (Not to mention that the function above isn't nearly general enough. What happens if you want to replace the cdr of the n^th element, or the cadar?).

If you've read Graham's On Lisp, there are probably a couple of functions (ttrav, trec) floating around in your head that might serve our purposes here. I believe that Graham would state that making functions like the one above easier to write alleviates the problem. I find that using such "one off" methods still uses a bit too much mental overhead when coding.

Now, look at what setf does for us. It hides functions like rplaca and rplacd which no sane individual should spend grey matter on. Setf knows how to invert (car x) and (cdr x) into the proper mutating "function". Wouldn't it be nice if we had a functionality like setf that keeps track of and inserts the proper functional manipulation code. To this end I have created modf.

Modf is a macro that behaves like setf, except it returns a new object with the requested properties rather than makes the changes in place. It changes functional example from above into…

;; Let's try it functionally
(let ((list '(1 2 3 4 5 6 7)))
  ...
  ;; Change the 5th element in the list to t
  (modf (nth 4 list) t)
  ... )

Right, that's all well and good, but that isn't nearly the most use you can get out of this. Let's say we were using the FSet seq data structure to hold a Sudoku board. We might use a seq of seq structures to represent our board. If we want to set a number on the board, we would do this…

(let ((board (make-board)))
  ;; Set element (4,3) to a 2
  (modf (fset:@ (fset:@ board 4) 3) 2) )

…instead of like this…

(let ((board (make-board)))
  ;; Set element (4,3) to a 2
  (fset:with board 4 (fset:with (fset:@ board 4) 3 2)) )

…which is considerably more convoluted. But to really nail this home, consider we have a mess like crazy-datastructure which is a mixture of classes, arrays, lists, and strings…

(defclass test-class ()
  ((slot1 :initform 1 :initarg :slot1)
   (slot2 :initform 2 :initarg :slot2)
   (array :initform #() :initarg :array) ))

(defparameter crazy-datastructure
  (list 1 (make-instance 'test-class
                         :array (vector 'a 'b "hello") )
        3 4 ))

(defmethod print-object ((obj test-class) str)
  (with-slots (slot1 slot2 array) obj
    (format str "#<TEST-CLASS: SLOT1: ~S, SLOT2: ~S, ARRAY: ~S>"
            slot1 slot2 array )))

CL-USER> (subseq (aref (slot-value (second crazy-datastructure) 'array) 2) 1 3)
"el"

Let's say we want to modify that substring to "EL" instead.

CL-USER> 
(modf (subseq (aref (slot-value (second crazy-datastructure) 'array) 2) 1 3) "EL")
(1 #<TEST-CLASS: SLOT1: 1, SLOT2: 2, ARRAY: #(A B "hELlo")> 3 4)

CL-USER> 
;; And the original CRAZY-DATASTRUCTURE remains unchanged
crazy-datastructure
(1 #<TEST-CLASS: SLOT1: 1, SLOT2: 2, ARRAY: #(A B "hello")> 3 4)

CL-USER> 
;; If we compare to the SETF form
(setf (subseq (aref (slot-value (second crazy-datastructure) 'array) 2) 1 3) "EL")
"EL"

CL-USER> crazy-datastructure
(1 #<TEST-CLASS: SLOT1: 1, SLOT2: 2, ARRAY: #(A B "hELlo")> 3 4)

If we consider how we might perform this functional modification without modf…

CL-USER> 
(cons (car crazy-datastructure)
      (cons 
       (make-instance 'test-class
                      :slot1 (slot-value (second crazy-datastructure) 'slot1)
                      :slot2 (slot-value (second crazy-datastructure) 'slot2)
                      :array (vector
                              (aref (slot-value (second crazy-datastructure)
                                                'array) 0)
                              (aref (slot-value (second crazy-datastructure)
                                                'array) 1)
                              (concatenate 'string
                                           (subseq 
                                            (aref (slot-value
                                                   (second crazy-datastructure)
                                                   'array) 2)
                                            0 1)
                                           "EL"
                                           (subseq 
                                            (aref (slot-value
                                                   (second crazy-datastructure)
                                                   'array) 2)
                                            3))))
       (cddr crazy-datastructure) ))

Here we made it simple to functionally modify parts of a data structure that includes a string nested in an array nested in a class nested in a list. Modf acts as a shorthand for complicated functional manipulations. If you examine the macro expansion of the modf form, you will see something very similar to the hand written code to change the deeply nested substring.

How it works

Really, when it comes down to it, modf is a simpler functionality than setf because any modifier can be represented as a function. This isn't true with setf. Consider…

(let ((x 5))
  (setf x 5) )

…there is no function you can call with arguments x and 5 which has the effect of setting the lexical variable x to 5 in this scope. This isn't true of functional changes as we are returning the modified value. That is not to say that this didn't turn out to be a tricky macro to write. This is due to the fact that the construction mechanism has to be in the reverse order of the access forms encountered during the expansion.

You can define macro like "rewrites" with define-modf-rewrite that translate access code into other access code that modf knows how to deal with (e.g. (cadr x) -> (car (cdr x))).

You define expansion functions similar (defun (setf func) ...) and (defmethod (setf func) ...) with define-modf-function and define-modf-method, respectively.

You define expansions based on the lexical structure of the code via define-modf-expander (this is analogous in some sense to define-setf-expander). This allows you to invert forms like (car x) to the builder code (cons new-value (cdr x)). These functions return new code that will replace the old code that was passed as an argument to the function.

There is a big difference between these functions and the setf equivalents. You need to specify which argument in the form contains the object that is being modified. This is taken as an extra argument right after the name of the expander.

In principle there is no need to have define-modf-expander, since any modifier can be expressed as a function. It might be beneficial to "open code" certain modf expansions as it will give the compiler a crack at optimizing the resultant code.

There is one special form in the "modf syntax," modf-eval. Modf-eval marks sections of code that modf shouldn't try to invert, and should just leave for the Lisp system to evaluate or compile as it will (the same way modf treats any atom it encounters). This is important if so you can have code like this…

(modf (second (modf-eval '(1 2 3 4 5))) 5)

Without modf-eval, modf would try to invert the form (quote (1 2 3 4 5)), rather than modify the list (1 2 3 4 5). You can even go so far as…

(modf (second (modf-eval
               (modf (third (modf-eval '(1 2 3 4 5))) 10) )) 5)

Which allows you to chain modf statements. This can get a little clunky, so to ease the reuse of previously calculated results, you can use extra modf arguments to reuse previous results.

(modf (third (modf-eval '(1 2 3 4 5))) 10
      last-result
      (second last-result) 5 )
== (let ((last-result (modf (third (modf-eval '(1 2 3 4 5))))))
      (modf (second last-result) 5) )

You can even use previous results in non-trivial ways…

(let ((lst '(1 2 3 4 5)))
  (modf (third lst) 10
        result-a
        (second lst) 5
        result-b
        (fourth lst) (list result-a result-b) ))
==> (1 2 3 ((1 2 10 4 5) (1 5 3 4 5)) 5)

An Example

As an example of how to use this, here is how you might set up modf to work with an affine matrix data structure based on FSet seqs.

;;; First we define how our data structure like we always would.
(defclass fset-matrix ()
  ((dims :initarg :dims :accessor mat-dimensions :accessor dims-of)
   (seq :initarg :seq :accessor seq :accessor seq-of)
   (a :initarg :a :initform #(1 0 0 1) :type (array integer (4)) :accessor a-of)
   (b :initarg :b :initform #(0 0) :type (array integer (2)) :accessor b-of) ))

(defun make-fset-matrix (dims &key (initial-element 0))
  (let ((arr (make-instance 'fset-matrix
                            :seq (fset:with (fset:empty-seq initial-element)
                                            (apply #'* dims) initial-element )
                            :dims dims )))
    arr ))

(defun fref (mat &rest idx)
  (destructuring-bind (i j) idx
    (aif2 (fset:@ (seq-of mat)
                  (+ (* (car (dims-of mat))
                        (+ (* (aref (a-of mat) 0) i)
                           (* (aref (a-of mat) 1) j)
                           (aref (b-of mat) 0) ))
                     (+ (* (aref (a-of mat) 2) i)
                        (* (aref (a-of mat) 3) j)
                        (aref (b-of mat) 1) )))
          it
          (error "Indicies ~A out of bounds ~A." idx (dims-of mat)) )))

(defun (setf fref) (val mat &rest idx)
  (setf (seq-of mat)
        (destructuring-bind (i j) idx
          (fset:with (seq-of mat)
                     (+ (* (car (dims-of mat))
                           (+ (* (aref (a-of mat) 0) i)
                              (* (aref (a-of mat) 1) j)
                              (aref (b-of mat) 0) ))
                        (+ (* (aref (a-of mat) 2) i)
                           (* (aref (a-of mat) 3) j)
                           (aref (b-of mat) 1) ))
                     val )))
  val )

;; Then we define a modf function that will inform modf how to invert
;; access function.

(define-modf-function fref (val mat &rest idx)
  (destructuring-bind (i j) idx
    (modf (fset:@ (slot-value mat 'seq)
                  (+ (* (car (dims-of mat))
                        (+ (* (aref (a-of mat) 0) i)
                           (* (aref (a-of mat) 1) j)
                           (aref (b-of mat) 0) ))
                     (+ (* (aref (a-of mat) 2) i)
                        (* (aref (a-of mat) 3) j)
                        (aref (b-of mat) 1) )))
          val )))

The Code

I am putting up a clone of my repository on Github. I am not sure that the code is ready for public consumption, yet. I will try, in the somewhat near future, to strip out some of the dependencies and make sure it builds on Lisp images other than mine. I would like to see the removal of the dependency on my toolbox library and implementing facilities for FUNDS.

Backtracking with the Common Lisp Condition System

The Common Lisp condition system is a pretty nice facility. I use it extensively in my work. One of its strongest benefits from my point of view is the smooth transition between programmatic error handling and interactive error handling.

The Common Lisp condition system is capable of much more than handling errors, though. However, I have yet to find time to really learn its "ins and outs". I decided try out a project using the condition system in a way that most wouldn't. Here I will show you how to use the CL condition system to implement a backtracking framework.

Update (June 2015): You can read some Reddit discussion on this. Nikodemus Siivola provided a superior roll-your-own backtracking method, pointing out that using the condition system is wasteful for this purpose. He is right, of course.

The Basic Idea

A failure of an assertion is a condition. For example, if we co-opt the error condition for our purposes…

(let ((options '(2 4 6 7 2)))  ; These are our options
  (labels
      ((fail (&rest args)    ; If we fail, for what ever reason
         (error "Failed: ~A" args) )
       (success (&rest args) ; If we find a successful condition, call this
         args )
       ;; This is our re-entry point
       (retry-with (x)
         (handler-case
             ;; This is the actual body of our function
             (if (oddp x)
                 (success x)
                 (fail x) )
           ;; If we find an error...
           (error (cond)
             (warn "Failed: ~A" cond)
             (if options
                 ;; ...we recall the function
                 (retry-with (pop options))
                 (error "No solution found") )))))
    (retry-with (pop options)) ))

All we need is to write a macro that translates the following into that.

(let ((x '(2 4 6 7 2)))
  (if (oddp x)
      (success x)
      (fail x) ))

Of course, using the error condition is a bit of a faux pas. Instead, let's define our own condition type, failure. Finding a solution to the problem could also be a condition, if we choose, and we will this time. While we're at it, we'll define two functions, fail and success, that are pretty self explanatory.

;; Define a parent type for flexibility...
(define-condition success (backtracking-condition) ())
;; NOTE can hold some data about how it failed
(define-condition failure (backtracking-condition) ((note :initarg :note)))
;; VALUE holds the solution
(define-condition success (backtracking-condition) ((value :initarg :value)))

(defun fail (&rest args)
  "For whatever reason, this has failed.  Backtrack."
  (signal 'failure :note args) )
(defun success (&rest args)
  "We found a solution.  Either return it, or add it onto the list of solutions
depending on the value of *MODE* \(as set by WITH-BACKTRACKING)."
  (cond ((eql *mode* 'find-one)
         (signal 'success :value args) )
        ((eql *mode* 'find-all)
         (push args *solutions*)
         (signal 'failure :value args) )))

These really don't do anything by themselves. We need to define a special way to bind nondeterministic variables, or variables that will change their values during the search. I've done this with the bt-let* macro, which is the real meat and potatoes of this. It behaves like let* except that it recognizes two special forms, one-of and one-in (one for objects, one for a list of objects), that perform these nondeterministic bindings. It's not perfect, these forms have to be in simple locations, but it works. We have to have a macro that sets up an environment to do things like handle success conditions, control the way the search is performed, and set up variables that save solutions that are found. This environment is set up with with-backtracking.

(defmacro bt-let* (bindings &body body)
  "Like LET*, but if you find a special nondeterministic choice form like ONE-OF
or ONE-IN, treat it specially by setting up the framework for nondeterministic
search."
  (let (bt-var
        (option-list (gensym))
        rest-bindings )
    `(let* ,(iter (for (binding . rest) on bindings)
                  (until bt-var)
                  (cond ((and (consp binding)
                              (consp (second binding))
                              (eql 'one-of (first (second binding))) )
                         (setf bt-var (first binding)
                               rest-bindings rest )
                         (collect (list option-list
                                        (cons 'list (rest (second binding))) )))
                        ((and (consp binding)
                              (consp (second binding))
                              (eql 'one-in (first (second binding))) )
                         (setf bt-var (first binding)
                               rest-bindings rest )
                         (collect (list option-list
                                        (second (second binding)) )))
                        (t (collect binding)) ))
       ,(if bt-var
            `(labels
                 ((try-with (,bt-var)
                    (handler-case (bt-let* ,rest-bindings ,@body)
                      (failure ()
                        (if ,option-list
                            (try-with (pop ,option-list))
                            (fail) )))))
               (try-with (pop ,option-list)) )
            `(progn ,@body) ))))

(defmacro with-backtracking ((mode) &body body)
  "Set up the environment where backtracking can be performed.  MODE can be set
as one of FIND-ONE or FIND-ALL in order to specify where just the first or all
possible solutions should be returned."
  `(let ((*mode* ',mode)
         *solutions* )
     (handler-case
         (progn ,@body)
       (failure ()
         (cond ((eql 'find-one *mode*)
                (error "No solutions found.") )
               ((eql 'find-all *mode*)
                *solutions* )))
       (success (cond)
         (slot-value cond 'value) ))))

Pythagorean Triples

Pythagorean Triples are three integers, $a$, $b$, and $c$, that satisfy the equation, $a^{2} + b^{2} = c^{2}$. In other words, $a$, $b$, and $c$ are the lengths of the sides of a right triangle.

(defun pyth-triples (n)
  (with-backtracking
    (bt-let* ((a (one-in (iter (for i from 1 below n) (collect i))))
              (b (one-in (iter (for i from 1 below n) (collect i))))
              (c (one-in (iter (for i from 1 below n) (collect i)))) )
      (if (= (+ (* a a) (* b b)) (* c c))
          (success (list a b c))
          (fail) ))))

Performance

Common Lisp already has a pretty good backtracking library, Screamer. We can compare the performance of our library with Screamer. Here's our version…

CL-USER> (time (pyth-triples 100))
Evaluation took:
  0.892 seconds of real time
  0.880000 seconds of total run time (0.840000 user, 0.040000 system)
  [ Run times consist of 0.030 seconds GC time, and 0.850 seconds non-GC time. ]
  98.65% CPU
  2,135,319,408 processor cycles
  345,196,992 bytes consed

…and the Screamer version?

CL-USER> (time (screams::pythagorean-triples 100))
Evaluation took:
  0.060 seconds of real time
  0.060000 seconds of total run time (0.060000 user, 0.000000 system)
  100.00% CPU
  143,821,854 processor cycles
  490,032 bytes consed

So, looks like around a factor of ten. Not so good, but maybe it's not so bad that people can't use it. Now, it might seem like exhaustive search is the time, if there ever is one, where we should be the most concerned about performance. That has some truth, but we should also remember that if we ever really rely on the exhaustive search to do the work, we probably have already lost the battle. Being ten times faster will allow you to handle an input size one larger than the slow version. I like to use nondeterminism to write an algorithm that's guaranteed correct, then improve from there. So, perhaps the slow version isn't unusable after all.

Conclusions

Well, this method is a pretty simple method of implementing backtracking in Common Lisp. It is less performant and versatile than Screamer, but Screamer is a pretty gigantic library.