Safely adding computational effects to a multi-stage language has been an open problem. In previous work, a closed type constructor was used to provide a safe mechanism for executing dynamically generated code. This paper proposes a general notion of closed type as a simple approach to safely introducing computational effects into multi-stage languages. We demonstrate this approach formally in a core language called Mini-ML_ref ^BN. This core language combines safely multi-stage constructs and ML-style references. In addition to incorporating state, Mini-ML _ref ^BN also embodies a number of technical improvements over previously proposed core languages for multi-stage programming.