Palamedes, knucklebones and virtual dice rollers

[krusader74]

Uploaded build 30 of palamedes with the following changes:

• Added a recur operator to generate recurrences. E.g., recur (_1+_2),[0,1] generates the Fibonacci sequence to ∞ which is set to 100 by default. The format is recur expr, initial where expr is an expression in parens. This expression may contain variables of the form _k which get set to result[n-k] where n is the number of results accumulated so far. And initial is the initial value of the result array. The expr has to be an actual expression -- it can't be a variable holding an expression, but this constraint may disappear in a future release. See the NEWS file for more examples.
• Added the sqrt function. This is different from root which is a dyadic operator rather than a function, e.g., 3 root 10 produces the cube root of 10. In general, functions need parens, operators don't. But the sqrt function is threadable over vectors/matrices/tensors, and parens are optional around things enclosed in square brackets, e.g., sqrt [0..4] is OK. TMTOWTDI: sqrt(2) produces the same result as 2 root 2 and √2 and 2^.5
• Added the trig reciprocal functions: cot, coth, csc, csch, sec, sech
• Added sign function to return the sign of a number: 1, 0 or -1.
• Added fix(x,n) function to display decimal numbers x with a fixed number n of decimal places. The number n defaults to 2. This function is threadable, so parens are optional around vectors and matrices as long as the default number of decimal places is used.
• Added size function to return the size of its input: 0 means its a scalar; a positive number n means its a vector of length n; and an array [m,n] means its a matrix with m rows and n columns. Additionally, -1 indicates its a JSON object; -2 indicates its a JavaScript function; and -3 indicates its type is unknown.
• Added trace function: tr. Input is a square matrix. Output is sum of diagonal elements. This is a non-threadable function--at most one input which must be in parens.
• Added the norm function to return the p-norm of a vector or matrix. By default, p is 2. But see the NEWS for more details.
• Fixed a minor bug that caused the output of while(a){b;c;d} to display as while(a){b,c,d} with commas instead of semicolons.

See the NEWS for more details and examples. Or download the SOURCE code.

[krusader74]

Just in time for Hanukkah, I've implemented a detailed Dreidel example in Palamedes.

The first part of the example simulates the spinning top in way that lets you choose the language on the 4 sides from English, Yiddish or Hebrew.



And the second part of the example presents code capable of simulating a gambling game of Dreidel with any number of players. The rules are recapitulated in the above link.

Aside from the Dreidel simulation, I've also implemented Bayesian belief nets. And there's an essay that explains how the 5th century BC philosopher Gorgias introduced an informal forerunner of the Bayes net in his speech, The Defense of Palamedes, which was another inspiration for the name of this software.

The software is nearing the end of the alpha stage. Hopefully, around the new year, it will be feature-complete and the beta stage will start. The beta will focus on testing and documentation.

[kesher]

That is beyond awesome...

[krusader74]

There is a 2min 47sec screencast showing off some of the new features in Palamedes alpha build 61 (2016-09-17). The demo is done in Mozilla Firefox 48.0.1. It's running on an Ubuntu 15.10 desktop. The screencast was recorded using GTK-recordMyDesktop, a free app written in Python. It's hosted on screencast.com. There's no audio (I don't have a mic), so I kept it short. Instead of a soundtrack, here's a written outline of what you're seeing:

1. The home page palamedes.altervista.org/
   a. The home page uses a command-line interface in the right panel
   b. The left panel has a list of short examples you can click on. I click on a few:
   - rolling 3 6-siders
   - table of probabilitties for 3d6
   - barchart for 3d6
2. Towards the bottom of the main page is a link to edit and run lengthy scripts. I click it (00:24). This takes me to palamedes.altervista.org/editor.html
3. The editor page has a left panel for scripts and a right panel for results.
4. At the bottom of the right panel is a drop-down list of scripts hosted on the website. The first one is the OD&D Treasure Generator. I click the Load button (00:30). Click the Run button (00:35). In the right-panel, you'll see a drop-down list for treasure types and a generate button appear. On the left-panel I click the Hide Code button, so the app expands to fit the entire browser window (00:40). I generate 3 Type A/Land and 3 Type F.
5. I click the Show Code button to go back to the script (1:10), scroll through it, and then click the New button to reset the page (1:22).
6. In the left panel I select the Common Dice Rolls app from the drop down list and click Load (1:29), Run (1:33), and Hide Code (1:38).
7. The top line are buttons for polyhedral dice -- I click these. The second line are dice throws for generating characters (1:51). The third line allows you to input an arbitrary dice expression.
   a. The default text is min(2#d6). There are buttons to Roll, see a table of Probabilities, Statistics, and a Barchart. I click these (1:57).
   b. I input the dice expression 4d6k3 and click (2:16) the buttons to Roll, see a table of Probabilities, Statistics, and a Barchart.
8. I click the Show Code button to re-expand the left panel. Then I end the screencast (2:40).

You can see the two scripts I use:

• palamedes.altervista.org/Treasure.pal
• palamedes.altervista.org/Dice.pal

The language is fairly readable/easy to understand. For example, the Treasure Table script is mostly just lookup tables like this:

   Ring_Lu <- lookup [ z%, ...
       01--09  => "Invisibility",          81--85  => "Protection, 5'' r.", ...
       10--15  => "Mammal Control",        86--90  => "Regeneration", ...
       16--21  => "Human Control",         91--92  => "Djinn Summoning", ...
       22--30  => "Weakness",              93--94  => "Telekinesis", ...
       31--39  => "Protection",            95--96  => "X-Ray Vision", ...
       40--49  => "Three Wishes",          97--98  => "Spell Turning", ...
       50--60  => "Delusion",                99    => "Spell Storing", ...
       61--70  => "Water Walking",           00    => "Many Wishes (" + 4d6 + ")", ...
       71--80  => "Fire Resistance" ]

Note that the Treasure Generator script is incomplete: I haven't done:

• The code to generate swords
• The spell tables needed for scrolls and rings of storing

Note also that Palamedes is still in early development (alpha stage). I am still adding features. There are bugs. It doesn't tolerate synatax errors gracefully. The help system and documentation are still primitive.

I want to thank waysoftheearth for writing the first cut of the Treasure Generator script and for providing valuable feedback on Palamedes as I continue to develop it!