Experimental Arithmetic-Bitwise-Cyclic-Tag-over-HTTP server.
This is an arithmetic implementation of the low-level Turing complete esoteric programming language Bitwise Cyclic Tag
It works as a webserver which redirects (303) between /<program>/<datastring>/ states. When/if the data string is empty, it returns a 200.
Additionally, it provides UTF-8 output in response JSON and collects all output in cookies when the datastring ever contains STX ETX delimited bytes with correct start/stop bits.
./abct-web 8080
Browsers tend to complain about too many redirects when used with most programs.
The following is a curl command demonstrating how to disable redirect limits, and view cookie output for the "Hello, World!" example:
curl -sLc- --max-redirs -1 localhost:8080/5814709794364855124394590463104036274829130886495847474077938692059840777884347510099960415045708498000107405098735286987994946170377558/2
There is also a /b/ path that will redirect raw binary BCT data to the corresponding program Gödel number,
localhost:8080/b/011/0
will redirect to
localhost:8080/13/0
The numbering convention used in this arithmetic implementation of Bitwise Cyclic Tag is simply interpreting a bitstring as a little-endian bijective base-2 numeral.
This can be accomplished as a two step process:
- Convert the bitstring to its arithmetic (place value index) order (i.e. reverse the string)
- Convert the symbols to bijective base-2 (
1→2,0→1)
A BCT program bitstring is processed left-ro-right, as strings are generally read. For ease of arithmetic processing it is helpful to use this processing order index as the place value of each bit.
The left-most bit is treated as the least significant bit of the resulting numeral. This results in reversing the original bitstring from its LTR little-endian order to the conventional numeric positional notation (BE).
01000 → 00010
Now interpret this as a bijective base-2 numeral. This allows both symbols to be meaningful in the MSB position, unlike in binary where leftmost zeros do not affect the value.
00010 → 11121
11121 as a bijective base-2 numeral represents 33.
This can be checked by passing the bitstring as a program with a null data string to the abct endpoint https://abctag.herokuapp.com/b/01000/0 which will redirect to the arithmetic version: https://abctag.herokuapp.com/33/0/
{
"program": "01000",
"data": ""
}
| bitstring (LE) | bijective base-2 | value |
|---|---|---|
| 0 | ||
0 |
1 | 1 |
1 |
2 | 2 |
00 |
11 | 3 |
10 |
12 | 4 |
01 |
21 | 5 |
11 |
22 | 6 |
000 |
111 | 7 |
100 |
112 | 8 |
010 |
121 | 9 |
110 |
122 | 10 |
Note, the above is just one of many possible conventions for converting bitstrings into numeric values for arithmetic interpretation of Bitwise Cyclic Tag. Other conventions will require different arithmetic equations, but the underlying cyclic tag concept and computation will be the same. This implementation uses a slightly different Gödel numbering from the one described at esolangs.org. The program string numbering is identical (reverse the bitstring), but the esolangs' article uses a different system for the data string where the bitstring is not reversed. I didn't want to implent two bitstring conversions, so here program and data bitstrings are converted the same way. For our data strings: data is appended as the MSB, and deletions occur at the LSB (i.e. bitshift right, or divde-by-2).
There is also a command line utility for testing:
./abct-cli $(<examples/hello-world.abct) 2
2 is the initial data value representing a binary bitstring 1
1 represents binary bitstring 0
0 represents the empty datastring, or null, and is the halt condtion.
Arithmetic BCT programs require an initial starting input of at least 2 to perform any active computation.
For the 'zero' case (BCT 10 = bijective base-2 12 = input value 4):
./abct-cli $(<examples/truth-machine.abct) 4 | grep OUTPUT
which gives a single output line:
39217909666694773142903776444132544299164543308230190564477239295 3026142152962 11000000100100110000010000101001000000110 OUTPUT>>> 0
For the 'one' case (BCT 11 = bijective base-2 22 = input value 6):
./abct-cli $(<examples/truth-machine.abct) 6 | grep OUTPUT
which repeats indefinitely:
39217909666697766298257028305177290289800352374943150376712755052 12104570709002 1101000000100100110001010000101001000000110 OUTPUT>>> 1
The CLI output columns represent:
- PROGRAM VALUE.
- DATA VALUE.
- DATA as binary.
- The string
OUTPUT>>>if any output was completed on this step. - Decoded OUTPUT, if any.