Octave and Math Languages

[giandomenico . sica]

Dear All,

I'm writing to this list since am looking for a cooperation.
I'm working about the development of a mathematical theory of languages.
It defines a language as a set of elements which can be combined or associated
(see the PS for an example).
I'd like to cooperate with a computer scientist in order to define a Octave
package useful to create and to analyse a catalog of mathematical languages.
This package should be placed in the public domain, freely accessible to anyone
who might be interested.
In the continuation of the message I send a sample function to include in the
package, useful to understand the difficulty and the commitment.
Please accept my sincere apologies for the trouble.
This is not a spam message or an activity with commercial or profit purposes.
I hope someone can be interested.
Please feel free to contact me for any question.
Really many thanks.

All the best,
Nico Sica
http://www.polimetrica.com/polimetrica/view/people/Sica,_Giandomenico.html

PS
An example: consider the so-called computer language. To generate the multiple
programming languages, people started from combinations of 01010101, then have
associated some of these combinations to commands in natural language (e.g.
PRINT, GO TO etc.), then they have combined these new commands each other; then
they have created new commands and associated these new commands to the old ones
and so on...repeating the game.
This is a basic example of the simple theoretical mechanism.

FUNCTION 1
create_catalog_languages(n)

Description.
This function should create a txt file including a catalog of languages with up
to n elements.

Possible methodology.
I explain it through an example which aims to define a catalog of all the
languages with up to 3 elements.
At the beginning, we have an empty catalog.
So we take an element "a" and an element "b".
We've a couple "a", "b" and three possible options:
1) "a" is combined to "b"
2) "a" is associated to "b"
3) "a" is combined to "b" and "a" is associated to "b"
>From these 3 options we can construct in our txt file 3 languages:
L1
Elements: a,b
Combinations: (a,b)
Associations: nothing
L2
Elements: a,b
Combinations: nothing
Associations: (a,b)
L3
Elements: a,b
Combinations: (a,b)
Associations: (a,b)
Now we've a catalog of languages with up to 2 elements.
To develop our catalog, we take the first language (L1) and an element "c".
We've two possible new couples: "a","c" and "b","c".
For each couple we've the previous three options:
"a","c":
1) "a" is combined to "c"
2) "a" is associated to "c"
3) "a" is combined to "c" and "a" is associated to "c"
"b","c":
1) "b" is combined to "c"
2) "b" is associated to "c"
3) "b" is combined to "c" and "b" is associated to "c"
>From these 3+3 options we can construct 15 languages:
3 languages from the first 3 options.
3 languages from the second 3 options.
9 languages from the combination of the two different set of options (taking one
option from each set):
1,1; 1,2; 1,3; 2,1; 2,2; 2,3; 3,1; 3,2; 3,3.
I don't write here the list of 15 languages since it should be quite intuitive.
Now we've to proceed in the same way also for L2 and L3 and then we've completed
our catalog of all the languages with up to 3 elements.
If we want to create a catalog of all the languages with up to n elements, we've
to iterate the same procedure.