I think most of my colleagues that care about such distinctions would say that in the most reductive form one does not need an operator or a goal for the comput

I think most of my colleagues that care about such distinctions would say that in the most reductive form one does not need an operator or a goal for the computation. This is the typical assumption I would have when discussing this formalization of the laws of physics. By the way, if you are fan of SciFi, Greg Egan has very fun stories that play with these ideas (nothing rigorous or seriously scientific, but certainly fun).