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^
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^ is an esolang by User:None1. It is the smallest esolang that is impossible to solve the halting problem.
Commands
The only command
^
performs an infinite loop if this program halts otherwise it does nothing.
Uncomputability proof
If this esolang in computable, consider this program:
^
If it halts, it will not halt, otherwise it will halt. So this esolang is uncomputable.
To sum up, this esolang is not computable for it can solve the halting problem.
Interpreter
It is of course impossible to make an interpreter of ^ in a computable esolang because it is uncomputable.