Control operators and dependent types have been used to solve major challenges in natural language semantics. However, in programming language semantics, combining control operators and dependent types is an open problem. In this talk, we present a model of a dependently typed language with shift and reset, and a prototype implementation of the model in Cur, a dependently typed language with support for safe and sophisticated user-defined extensions. The model is useful for representing certain classes of natural language sentences and provides insights into the problem adding control operators to dependently typed languages.