If we're being pedantic, it's pretty trivial in any Turing complete language (which I imagine Brainfuck is in, since I think it's supposed to be essentially jus

If we're being pedantic, it's pretty trivial in any Turing complete language (which I imagine Brainfuck is in, since I think it's supposed to be essentially just syntax over the idea of a Turing machine); there are definitely languages that aren't able to express non-halting programs by design (like Coq, which I think is primitive recursive).