A type system is complete when every error-free program is well-typed. This is, afaik, seldom the case.
I was using the term more informally. In fact it is the operational semantics of your hypothetical language that is not complete in the sense that you will have a hard time putting it into a form that allows you to do anything meaningful (e.g. proof absence of certain errors) with it.
Interestingly, you can define such a language with side effects (think ML), by actually pulling the state monad into your meta-level (for instance by turning your reduction relation into an instance of a state monad).
I was using the term more informally. In fact it is the operational semantics of your hypothetical language that is not complete in the sense that you will have a hard time putting it into a form that allows you to do anything meaningful (e.g. proof absence of certain errors) with it.
Interestingly, you can define such a language with side effects (think ML), by actually pulling the state monad into your meta-level (for instance by turning your reduction relation into an instance of a state monad).