Boolfuck

Boolfuck is a variation of Brainfuck where cells store booleans instead of integers. Boolfuck is Turing complete.

Language Overview

Boolfuck operates on an array of memory cells, each initially set to False.

Like in a Turing machine, there is a pointer, initially pointing to the first memory cell.

Programs are composed of commands, represented with symbols:

Command	Operation
>	Move pointer right
<	Move pointer left
*	Flip current cell
[	Jump forward past matching ] if current cell is False
]	Jump back to matching [ if current cell is True

Boolfuck Busy Beaver

Σ_boolf(n) returns the maximum True cells count a program with n instructions can have when halting.

n	Σboolf(n)	Example Champion
1	= 1	*
2	= 1	*>
3	= 2	*>*
4	= 2	*>*>
5	= 3	*>*>*
6	= 3	*>*>*>
7	= 4	*>*>*>*
8	= 4	*>*>*>*>
9	= 5	*>*>*>*>*
10	= 5	*>*>*>*>*>
11	= 6	*>*>*>*>*>*
12	= 7	*[>*>>>*<<<]
13	≥ 8	*[>*>>>*<<<]*
14	≥ 11	*[>>*[<<<*<]>]
15	≥ 12	*[>>*[<<<*<]>]*
16	≥ 15	*[>>*[[<<<]*<]>]
17	≥ 31	*[>*[>>*[<<]*>]>]

S_boolf(n) returns the maximum runtime of a halting program with n instructions.

n	Sboolf(n)	Example Champion
1	= 1	*
2	= 2	*>
3	≥ 3	*>*
4	≥ 4	*>*>
5	≥ 5	*>*>*
6	≥ 8	*>*[<]
7	≥ 10	*>*[*<]

[page under construction]