Turing tarpit full of math, fun and alien technologies. Designed especially to be computable with your fingers!
(NOTE: language authors aren't responsible for results of computations on incompatible fingers!)
version 0.1
As all of you know, good language should be based on a lot of very specialized mathematics, such as category theory and of course should have some monoids (like Haskell :) ). It also should be based on some unknown alien technology (like Lisp :) ). And, of course, it should be very simple (like HQ9+ ;) for example).
BraidF-ck is good language. It is based on deep mathematics of braid groups and braided categories. It is simple because you can execute programs with your palm and fingers. It is surely based on unknown alien technology (if you have enough fingers and fingertips to execute non-trivial BraidF-ck program, you surely have some alien technology)
Technically, every BraidF-ck program is just some braid on n points
w = \sigma_{i_1}^{k_1} \sigma_{i_2}^{k_2} \ldots \sigma_{i_m}^{k_m}
where k_j equal to -1 or 1 and i_j lies between 1 and n-1
It is executed as follows.
First of all it is simplified (braid ends are tighted and we get normalized form)
Then on word consisting of n elements x_i of group S_4 braid w acts as follows:
\sigma_i <x_1, \ldots, x_{i-1}, x_i, x_{i+1}, x_{i+2}, \ldots, x_n> =
= <x_1, \ldots, x_{i-1}, x_{i+1}, x_i^{-1} x_{i+1} x_i, x_{i+2}, \ldots, x_n>
That is, \sigma_i exchanges x_i and x_{i+1} elements and x_i is twisted
by the inner authomorphism corresponding to x_{i+1}.
Technically, input is one of small English letter, except y and z
Each letter encodes corresponding permutation in S_4 in lexicographical order:
a = (0 1 2 3) g = (1 0 2 3) m = (2 0 1 3) s = (3 0 1 2)
b = (0 1 3 2) h = (1 0 3 2) n = (2 0 3 1) t = (3 0 2 1)
c = (0 2 1 3) i = (1 2 0 3) o = (2 1 0 3) u = (3 1 0 2)
d = (0 2 3 1) j = (1 2 3 0) p = (2 1 3 0) v = (3 1 2 0)
e = (0 3 1 2) k = (1 3 0 2) q = (2 3 0 1) w = (3 2 0 1)
f = (0 3 2 1) l = (1 3 2 0) r = (2 3 1 0) x = (3 2 1 0)
Input of length m is feeded to upper m strands; following k strands are work space and
the remaining n strands are output. Output is encoded as input
Every BraidF-ck program is written as some palm position after header of program:
# comment
# more comment
Braid 0.1
# even more comments
Palm 2 2 1
_______________
| }
>---------------
| }
>---------------
| }
>---------------
| }
>---------------
|_______________}
Header can have of one or several lines of comments that begins with # symbol.
First non-comment line must contain word Braid with next word being version of language.
First non-comment line must not contain more than one Braid word (in such capitalization).
Second non-comment line must contain syntax name (Palm for casual syntax, Lines for syntax sugar
and L33t for mathematical over-simplified l33t syntax) with length of input, work space and output.
Length of output must be greater than zero, length of input and workspace must be greater or equal to zero.
Previous image shows identity program -- program that returns nothing.
Braid 0.1
Palm 2 2 1
______ _______
| \/ }
>-----\ \/------
| \ }
>------/\-------
| }
>---------------
| }
>---------------
|_______________}
This image demonstrates base concept of braids: crossing.
Finger-count could be not equal to five (we will accept alien civilizations too)
Braid 0.1
Lines 1 0 1
--\ /----------------
-/ \-----------------
Note that first strand goes over second
Lines:
Braid 0.1
L33t 1 1 1
1 2 -1 2
is equivalent to
Braid 0.1
Lines 1 1 1
--\ /------\ /-------
-/ \---\ /--/ \--\ /-
------/ \-------/ \--
- Internal representation
- Parser of math syntax
- Interpreter
- Converter to lines and palm syntax
- Parser of lines syntax
- Parser of palm syntax
- Compiler
count on the fingers of one hand cross fingers fingers were made before forks