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July 23, 2006, 8:52 am
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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 Php
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
I hope someone can be interested.
Please feel free to contact me for any question.
Really many thanks.
All the best,
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
This is a basic example of the simple theoretical mechanism.
This function should create a txt file including a catalog of languages
with up to n elements.
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:
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:
1) "a" is combined to "c"
2) "a" is associated to "c"
3) "a" is combined to "c" and "a" is associated to "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
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.