Brainhype

From Esolang

Brainhype is an esoteric programming language based on Brainfuck.

The instructions:

+	Increments the cell under the pointer.
-	Decrements the cell under the pointer.
<	Moves the pointer to the left.
>	Moves the pointer to the right.
,	Inputs a character to the current cell.
.	Outputs a character from the current cell.
[	While the current cell is nonzero...
]	End while.
{...}	Zeroes the current cell if the Brainhype program between the braces (no
I/O allowed), run on the current tape with the current pointer position, will
end at some point.

This language is "super-Turing-complete" because it solves the halting problem for Turing machines.

A Brainhype interpreter cannot be written in Brainhype: given some description of a Brainhype program on its tape, the interpreter can determine whether it halts or not. Therefore it is possible to build a program that, given some description of a Brainhype program on its tape, will determine whether that program, given its own description, will halt. This program will infinite loop if the given program will halt, and halt otherwise. Therefore, feeding this program its own description will result in it determining whether it itself will halt, and halting if and only if it does not halt. This is a contradiction, so a Brainhype interpreter written in Brainhype cannot exist. However, you can write a Brainhype interpreter in Scheme-omega.

See also: onoz