&brainfuck

&brainfuck (pronounced "reference brainfuck") is a brainfuck variant discovered by User:Orby in May of 2020.

Model

&brainfuck uses a right-unbounded tape of unbounded non-negative cells. Decrementing a data pointer that is zero, decrementing a cell that is zero, and decrementing an indirection level that is zero all produce undefined behavior.

Commands

Command	Action
>	Increment the data pointer
<	Decrement the data pointer
*	Increment the level of indirection
&	Decrement the level of indirection
[	If the cell pointed to by the data pointer is zero, jump after matching ]
]	If the cell pointed to by the data pointer is non-zero, jump after matching [

The level of indirection begins at zero. At this point all commands behave normally. When the level of indirection is one, > becomes "Increment the cell pointed to by the data pointer". When the level of indirection is two, > becomes "Increment the cell pointed to by the cell pointed to by the data pointer", and so on. Therefore, + can be represented as *>& and - can be represented as *<&. Notice that [ and ] inherently contain one level of indirection, but their level of indirection is also increased with * and decreased with &.

Reversible variant

A reversible variant of &brainfuck can be achieved by altering the loop construct.

Command	Action
[	If the cell pointed to by the data pointer is zero, jump after matching ]
]	If the cell pointed to by the data pointer is zero, jump after matching [

To compute the inverse of a program, simply reverse the program string and replace characters according to the following table

Command	Inverse
>	<
<	>
*	&
&	*
[	]
]	[

Converting from brainfuck

Brainfuck programs can trivially be converted to &brainfuck programs, but the converse is not true.

bf	&bf
>	>
<	<
+	*>&
-	*<&
[	[
]	]

See also

• *brainfuck
• brainfuck
• Befinde
• Symbolic Brainfuck
• Git for reference implementation in C.
• Git branch for Rust implementation with absolute addressing