Well actually unbounded recursion and infinite memory is what is required for turing equivalence. Conditioning can be present in a non turing complete language. I added the practically because all computers on which language models are built on are finite. It is easier to get turing completeness than to ensure you haven't accidently allowed it to sneak in - as evinced in C++ templates.
http://en.wikipedia.org/wiki/Primitive_recursive_function#Co...