Older blog entries for tampe (starting at number 110)

25 Jul 2011 (updated 25 Jul 2011 at 21:44 UTC) »

Ordering the functional Ilands

note I use the word continuation below for a closures. This is not exactly what is meant by a continuation in scheme but the used closure function as a sort of delayed computation. Then
this computation object is passed as an argument to various functions until it under the right circumstances is evaluated. So call CPS semantics. Continuations can be implemented to a large degree with the help of this technique though.

Using the guile-2.0 virtual machine and adding a few opcodes targeting the evaluation of prolog programs yields quite good performance (from a few tests maybe less then 2x of gprologs VM). This is accomplished although continuations allocated from the heap are used. The conclusion is that this overhead is not too visible compared to the VM overhead. Actually the version I use combine setjmp like sematics for backtracking with continuation that represents a delayed computation and hence lead to slightly less need of heap compared to using continuations for the backtracking as well.

How are these features used? let's consider the quest of a tree search to solve for example the n-queens puzzle. What features do we have? Well for one thing we need variables that we can set to values that should be visible down the tree as we go out on a limb. If then a failure in the search is signaled we would like to go back and the movie for the values of a variable should be played backwards in order to restore a state at a branch point further up so the search can continue. Another thing is the need to sequence facts, first A should be true, then B and so on. lets write this as


(%and% A B ...)


Another basic building block is to model a branch point e.g. try A, if fail then try B etc. e.g.


(%or% A B ...)


finally we need a way to express that we fail if the fact is true e.g.


(%not% A)


In code %and% could be translated as


(compute (%and% A B) CC Fail)
=
(compute A (/.(Fail2) (compute B CC Fail2)) Fail)


where CC represents what should be computed after (%and% A B) have been computed (/.(arguments ...) code ...) can be looked at like a definition of a function with associated variables inside A B etc. captured e.g. the variable addresses is stored in them. This happens indirectly as in scheme or If you look at /. the creation as a creation of a object from a compute (used variables would then have to be passed explicitly on in the constructor arguments). Fail is the backtracker and is a continuation or can be a setjmp like backtracking. Let's assume that it is the continuation computation that represents whats need to be done if the computation fails. Now over to %or%


(compute (%or% A B) CC Fail)
=
(compute A CC (/.() (unwind) (compute B CC Fail)))


Note here that we need to unwind the variables int the failur computation ((/. ()) e.g. run the movie backwards before we restart computing the next branch. Also the failure computation does not have any arguments.
And finally %not%,

(compute (%not% A) CC Fail)
=
(compute A (/.(Fail2) (Fail)) (/.() (unwind) (CC Fail)))


Note here as well if we success e.g. A fails, we will undo any changes to the variables.

This is a closer look at some of the elements needed to construct prolog like semantics. There are something left like unifications and matching But this is a description to better understand the thoughts flowing out on my posts.


Now I have made a little macro package that outputs from a scheme like language pure c-code. I added closures without a correct set! semantics, allocating the closures from the heap. Also a tail call trampoline framework was added. The generated code is three times slower then compiled gprolog and also it's quite obvious that a lot time is lost due to a hefty use of gc and the heap. So this system did not have a significant improvement compared to the VM approach with a setjmp semantics replacing the failure continuation computation. My next quest will therefore be to modify the macro package to allow allocating the closures from a stack instead. Here the key fact to note are that the Failure continuation should be able to reset to the same position on the stack at a branch. In all there should be hope that memory consumption can be bounded enough to make it practical.

Have fun

A parallel brain is more expressive then an unparallel one

Assume that we have deduced a state S and there are two possible choices S1 and S2 to go from there how to zip them together?

One idea is to assume S1 outputs z1 and S2 outputs z2 and just combine these outputs e.g.


(zip-1 (z1 z2)
     (subshell S1 z1)
     (subshell S2 z2))
Here we create z1 and z2 on an outer stack, then run S1, it produces a value into z1 that are deduced on an inner stack. Then it will keep z1 and revert back to the initial state but store a continuation that are reinstated at back-tracking. This will be able to mimic generator behavior through back tracking. It is safe code because the interface is clear and has a potential performance bottleneck in that we need to reinstall the state of S1 and S2 at back tracking.

The other idea is to consider the stack as a DAG and use two branches of the stack describing the deduction S1 and then deduction S2. First S1 is done, then S2. and the state will be done on-top of each other but the action will be stored in branches e.g. a storage of a variable pointer and a value. But at backtracking, then we will just first backtrack S2 and by doing this not touch the other stack branch. Then we will backtrack S1 and not do the undos on the S2 stack branch. If there are a variable touched in both S1 and S2, with backtracking touching it only in S1 or only in S1 unpredictable things can happen. So this method is faster but can produce strange bugs.

Again parallel generation of sequences can be simulated using this trick.

In all, zip patterns call's for a more delicate stack engine then the common stack implementation one need to manage a forest of DAG's that should support continuation style of separation and storage. linked structures are attractive here due to it's simplicity in these situations, on the other hand the speed of allocations from a stack represented by an array is also attractive. Maybe a combination.

Life on a t-shirt

Oh and now over to that jolly song from all of yo together on that crucifix hill in easter time, one two three ...

One of my favorite t-shirt ideas is to have all the religious celebrities together on crucifixes, (mohammed pained as a cloud with perheps lips showing that he sings along) and all of them singing and smiling :-) And the song should of cause be the one from the life of brian - Always look on the bright side ...)

This picture tell the simple minded theo/philo-egoists in the world to fuck off to some deep cave and keep us hard working people to continue with what we are good at, or, Hey teacher, We don't need your silly religious war, leave them kids alone, or simply C.U. cooperate stupid.

Over to some cool mathematical play. Did you know that the fundamental law's of force physics is non-linear? This have a kind of cool direction, let's call it the twilight direction. The thing is that a common theme to express solution to non-linearity, especially when the nonlinear part is weak, is to first just solve for the linear solution X, then solve for the twighlight solution T, which we get by solving the linear equations again but with a source that represent the nonlinear part applied to X and construct the solution as X + T. Similarly this technique can under a fix-point theorem result in an infinite expansion that lead to a solution to the nonlinear equation.

So, basically T is small ripples that lives on top of the real fat and dirty reality called X. And if the connection is really weak we would never detect T. We should have seen it already if that was the case right! Now over to crystallography. What's cool with this technology is that if you can build a crystal of say hemoglobin, (e.g. the same molecule is reproduced over and over again in a periodic lattice), then you can sort of overlay picture signals of all entities in the crystal and by statistical laws the details get many times more clear then by just looking at one single entity with some kind of microscope. So consider some kind of periodic twighlight ripple T. and consider sensors in billions of places throught a volume, wouldn't that magnify the probability of detection considerable, I wonder if humans have build any similar device to try detect the twilight zone, I know the homo crackpottus have tried it in another universe somewhere.

Oh, I put a little "easter egg" somewhere in _this_ universe so that you can perhaps understand my math (yes a little prose attached to the math) ;-) ... happy reading

functionasm

Alex Shinn, has written a library for scheme that does formatting tasks in a functional style, the fmt library. In this library there is a package for outputting c code. Let's play with that.

A next step might be to be able schemify c code. e.g. introduce <define>, <let*>, <begin>, <if> and <recur> + the operators. The innovation needed to do this is to make sure that everything return values and are able to be composed together with some kind of "sewing" mechanism.

The idea of attacking this is to try keep everything functional as far as possible and then at the final step add syntactic sugars in the form of macros. When trying to do this one realizes that we need two phases of evaluation. The reason are this, consider a function application:


int f(int),
----------------
f((<let*> ((a (+ b c))) (<if> q a b)) + b)?
Now the idea of modelling is to let the statments evaluate to a lambda that takes as an argument #f or a symbol. The lambda applied to a symbol will mean that the result of that expression will generate c-code where the tail expressions will set the symbol to the return result. so we do stuff like,

(define (f-if p x y)
    (lambda (ret)
       (let ((pred (gensym "pred"))
         (c-block
           (c-var 'int pred)   ; define pred integer
           (p pred)            ; execute p expression
                               ; pred is the result
           (c-if pred (x ret) (y ret))))))
This will illustrate the technique (we are using autoquoting features in the macro package). Over to the function application. Here we conclude that in order to be general we need to use

   (int arg)
   ((((<let*> ((a (+ b c))) (<if> q a b)) + b)
    arg)
   (c= ret `(f ,arg))
E.g. we introduce an arg symbol to be able to set it. Doing this we need to know about the function signature. Designing the <define> as a function means that we are not able to register the function signature before the body is evaluated and the function signature needed in case of recursion. So one need one extra lambda dereference. I thught that was too complicated though and used macros in stead to accomplish correct registration order.

The function example lack some wow factor. But for the loop construct in clambda, the <recur> statement, it's a must. Here is how the idea of this works


(<recur> loop ((int n 100) (int s 0)
    (<if> (< n 0)
          s
          (<next> loop (+ s 314))))
====================================
Aproximate translation
====================================
 int n = 100;
 int s = 0
loop:
 if (n < 0)
    ret = s;
 else
 {
    s = s + 314;
    goto loop;
  }

This is kind of handy loop construct and again one need to register the loop symbols this time in order to be able to expand the <next> statement later on.

This is about 300 lines of code. For 600 I guess you would be able to introduce a good enough c to produce workable code with syntax line numbers introduced as well to be able to debug after gcc has found your bugs.

Now this is not that complicated and everything is just a quite simple idea of syntactic sugars. But this will enable scheme macro facilities to your c-code (for one thing you will be able to track source code line numbers to be able to debug your macros correctly. Also going between clambda and pure scheme is a smaller step then between c and scheme this means that you can keep a large part of say guile c-code both in c and scheme at the same time.

Have fun

o.o

Can strange things happen, that matters. I don't know, but strange indeed are the day's I live in. To keep sane is a big struggle and without ears plugged with music. I would not know where I would be.

Anyhow here is a spooky story.

I met an old woman a couple a weeks back and she talked about many things, fools and queens, high and low. But what I previously did not remember was how she spoke about a book, her exact words I don't know, but she talked about an o and a dot.

Then I forget about her, and a week later I sat down and thought a poem on a piece of math would be so perfect. Thinking about my old ford and the day's back when I was young I got into the right mood of writing the poem. And the dance went on. At the end I saw that it was not perfect. I wanted to move the text to the right and wrote "o." at the beginning without knowing why, I just did it cause writing a poem is to express feelings and then I just relax and let the hand walk across the keyboard. So, focus! It struck me, just struck me, don't ask me why,..., why don't write "o.o" instead of "o." and so I did. And so I did.

And so I did, I need to keep that python syntax correct, don't I.

And time passes, life went boring and I took a walk to the library. I stood there just feeling empty and pointed the finger at a shelf of books, letting the finger wander from book to book, reading the titles without thinking, and then I picked, as it felt, randomly, the Illusionist by Fowler.

This is a kind of cool book and in the beginning the character of importance move to a lonely place, becomes depressed and decide to shoot himself with a shotgun. And at the moment the trigger is supposed to go off, Fowler writes the characters o and dot. Probably, to make an illusion of end of life.

The effect of this happening to me is tremendous. I had a brother you know, and his life did not end with an illusion. I took a long walk and did not calm down until I met a family of deers that just stood there about 10m in front of me, relaxing, and reminded me about how life goes on.

o.o

8 Apr 2011 (updated 8 Apr 2011 at 15:24 UTC) »
When thoughts flow too fast

Fasten your seat-belts, earplugs in and here we go. The city flows silently and the leaves dance together with plastic bags in an urban eddy. Music in the blood and so much feelings pressing when you take in everything. Silent shadows with faces that pass by and I think, oh well I need to freeze this moment and carve it into a stone cake, the ones you find in the book: uncle tungsten.

I'm planning to be much more moveable in the future and are preparing a smaller laptop with linux for guile-unify development. I had a stress breakthrough and need to take a brake from work. And of cause the most relaxing thing for me to do is to code like an artist and not like a monkey. Probably the resulting code will be too poetic, but I don't care. I hunt for pieces of ideas. Not running them through the fingers like the end is near. In the end I will return to normal productivity but that's for later. Most important thing for universe minus me in the near future is to shelve out a release of this stuff. Then people who would like to play a tune of two of that weird poetry can do that with some guidance. Or at least not need to read the mind of a sole on the other side of the Atlantic see.

Oh, I'm also trying to push out a physics paper, but that have to take the time it takes. What's cool here is that I will try to make it as a combination of poetry and science - if they dare.

So, for me life can be stated with the one liner:

Play it again Sam!

Dream on folks!

6 Jan 2011 (updated 20 Jan 2011 at 05:53 UTC) »
A flow of thoughts

So, I start as usually with my bad prefix.

I haven't had so much fun for ages. The Yang Mill theory is a really great work of illusion. My bet is that people who analyze the equations will not realize the true nature and continue with their hopeless task. You really have to think out of the box in order to solve this.

The world may look straight. But in reality looks queer. (freely translated from Copernicus with help of Einstein)

A huge hug to you all

4 Jan 2011 (updated 15 Jan 2011 at 17:00 UTC) »
New year's mini search.

So, it's Christmas, and the New year went by. as usually at this time of the year. The family have been relaxing and the my mind have been floating around fishing ideas on the pond of imagination.

So, as usual I spend some time trying to solve a very interesting puzzle. What the are nature made up by. One thing I just can't understand is why we make such a fuzz out of the number dimension of space. It's the numbers of freedoms in the model. But for god sake a pencil have 6 freedoms. Three rotational degrees of freedom and three translational degrees of freedom. My point is that it is likely that there are a local structure that we cannot see that have a gazillion of freedoms (well this is a free source blog aren't it :-).

It looks to me that it is pretty premature to twist peoples mind about talking about high dimensional space in the way we do. On the other hand the number of freedoms are important mathematically no doubt about that.

The next things that just forces me to try to think by my own is how we argue about the fundamental parameters in space. In some science shows I seen on the tube they only explain this by saying that we would not be here to analyze it and simply that's why. And this is why they are feasible and not a small distance away from it leading to an unfeasible solution.

Here is where the engineer in me just go into rocket mode. What!!!, this is not the only argument. It is just as likely that the reason is that the laws are simpler and demand less parameters. To visualize, We have a higher dimension model that works really well. A simpler model with fewer parameters will then be embedded very much like a surface in space e.g. move a little in the wrong direction and you are out of the surface. And the setup will be unphysical.

Have fun!

9 Sep 2010 (updated 15 Jan 2011 at 18:38 UTC) »
Gardening

After a couple of weeks hacking fixing bugs etc in the guile-unify module the example in my previous post runs effectively according to the discussion in my last post - not the hackish slow method I used previously. So it seams to work - cool. The next step is to understand another problem one have when trying breath first like algorithms. It can have to much of computational complexity.

I've been wondering what example to use. And I think that it would be interesting to go after automatic proof generation. I decided to play with the leanCop prolog solver for this application in order to understand needs. A first approach will be to make proof searches that postpone against stack usage. E.g. try to search for a simple proof before a more complex one. </b>

Now, there is this piece left that is needed in order to dive into this problem. That is one probably need a way to cut out branches and trim the reasoning trees. How can this algorithm be constructed? Well, assume a certain level L. One will hit at some point a memory barrier K. Then one need to decide about Cutting out a fraction F from the tree because of the high complexity of typical algorithms. This can be done randomly or e.g. according to an importance index. So the tactic here is to bring out all the importance numbers, sort them and search for the level separating the whole tree in correct fractions. Notice that it can be smart to add a small random variable to the index in case there are many similar importance numbers - and one get a random sample. After finding the threshold the c-code can make sure to trim the tree according to the threshold in a adaptive and globally sound way.

And of cause there are some holes remaining like making sure scheme variables sit in the redo tree get garbage collected. but this is boring though important technical stuff.

There is another idea I later would like to follow. The redo tree can be seen as a storage of a set of permutations of a few symbols or numbers. Therefore, later on, some kind of compression of the redo tree will be used. So typically you have a sequence of (type pointer val type pointer val ...) where the pointer points to a scheme variable or immediate. That will be reset to the new value. now currently we waste space by storing (type pointer val) as three 64 bit elements on a 64 bit platform. Type can be just one byte and we could device a control byte describing the the size of pointer and val around stored base points. e.g. choose between 1,2,4 or 8 byte representations around 4 stored values. many application will then just need 4-5 bytes to be able to restore a state for a variable which is maybe a 6 fold saving of memory (this is the benefits of C). Of cause one can let a control bit decide if there need to be a resetting of a stored base value and use some kind of adaptive learning to compress but I leave that out for now. actually any technique found in gzip can of cause be used if one likes. We will do it in the order of one extra scan of the tree not doing an actual redo and therefore loss of addresses due to variable sized atoms may not have such a great impact. On the other hand it is possible to store pointers to speed up plain tree searches in the redo tree.

I hoped I'm not bored you here. But one of the reasons I do write this is to help me think about what to do next. Ergo it help OSS ;-)

Have fun

27 Aug 2010 (updated 27 Aug 2010 at 10:29 UTC) »

Compress that for me, please

So, if you are in a habit of analyze lists and tree structures like code, and like pattern matching, you may end up writing ton's of code like.


(def sum-of-leaves
   ((X . L)      (+ (sum-of-leaves X) (sum-of-leaves L)))
   (()           0)
   ( X           X))

e.g. if you have a list sum the first and the sum of rest the empty list yields 0 and all non list elements -the leaves, assumed numbers - end up being just counted as the value they represent.

So how should we code this destruction into a primitive lang? One idea I used is to work with the guile VM directly and use a few extra primitives there.

So consider destructuring


(define (f A)  (match A ((X 'a (X . L) . U) (list X L U) ...)

we could do this with a stack machine like,


(push A)         ;; Stack -> (A)
(explode-cons)   ;; Stack -> ((car A) (cdr A))
(set X)          ;; Stack -> ((cdr A))
(explode-cons)   ;; Stack -> ((cadr A) (cddr A))
(match-eq? 'a)   ;; Stack -> ((cddr A))   
(explode-cons)   ;; Stack -> ((caddr A)  (cdddr  A))
(explode-cons)   ;; Stack -> ((caaddr A) (cdaddr A)
(cdddr A)))
(match-eq? X)    ;; Stack -> ((cdaddr A) (cdddr A))
(set L)          ;; Stack -> ((cddr A))
(set U)          ;; Stack -> ()
(list X L U)
;;; note if an explode-cons or eq? fails it will 
;;; reset and the next pattern will be tried.

And what you note is that this is a more compact reduction of pattern matching then doing it with the standard VM of guile. So the end results is that code executed on this VM is both faster and more compact then using the standard setup. But of cause if we would like to compile this to the native platform then the standard compilation to pure scheme probably has an edge.

Interestingly though (I'm implementing a prolog on top of guile), this pattern can be generalized to the case where A - the input is a unifying variable. The destruction will look almost the same, but we need to tell the VM that we are in a mode of destructing a unifying variable. Meaning that if X is not bound we will set that variable to a cons and push two new unbound variables (car A) and (cdr A) onto the stack.

Cheers!

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