Monotonic Doublefuck

Monotonic Doublefuck is an esolang User:ChuckEsoteric08 which is a derivative of brainfuck made to explore monotonic computation.

Specification

Monotonic Doublefuck works on a binary tape infinite to the right, with cells initizaled as zeros

Command list

Command	Description
>	Move tape pointer to the right
<	Move tape pointer to the left
[	If current cell is zero jump past matching ]
]	Jump to matching [
xy	Both x and y are bits. It adds bit x to the left of current cell and adds bits y to the right of current bit.

Computational class

Monotonic Doublefuck is Turing-complete as Bitwise Cyclic Tag can be translated into it. It uses following layout:

00000 1101x 1101x ... 1101x 10x 10x ... 10x 000

Here 10x reprsents existing data bit and 1101x represents deleted bit

Program starts with:

>>>>>

All data bits except the last are translated like that:

• 0 is 10>>
• 1 is 11>>

Last bit is translated like that:

• 0 is 10<
• 1 is 11<

Then it is followed by:

[<<<]>>>[

And then instructions are translated:

• 0 is >[>>>>>]11<[<<<<<]>>>>
• 10 is >[>>>>>]>[>[>>>]10>]<<[<<<]<[<<<<<]>>>>
• 11 is >[>>>>>]>[>[>>>]11>>>>]<<<<<[<<<]<[<<<<<]>>>>

Translated code ends with ].