Supervised P with Printing
Supervised P with Printing is a program which uses artificial intelligence. Specifically, it uses a supervised learning algorithm to correlate certain kinds of input to certain kinds of output.
Specification
The code needs to be split into two parts: the training code and expected effect, and the testing code.
In the former, valid Brainfuck code is correlated with the final state of the tape and the expected output, if any. The way the tape and expected output are displayed isn't fundamentally important.
The testing code basically ensures whether the interpreter in question is a "valid" interpreter. There are two levels of validity:
Easy Level: The interpreter is valid if it can tell whether or not the code outputs anything and whether or not it changes the tape. Hard Level: The interpreter is capable of correctly predicting the output of the test suite and the final state of the board over 50% of the time (no, really think about it, that's actually very hard).
The training code and expected output train the algorithm while the resultant code is the one you actually want to run.
Computational Class
The language is not Turing-complete because it is total. It literally cannot indicate that an infinite loop would happen. It can pretend that an infinite loop would happen, but it will always halt on any input.