In this paper, we formalize a type system based on set-theoretic types for dynamic languages that support both functional and imperative programming paradigms. We adapt prior work in the typing of overloaded and generic functions to support an impure lambda-calculus, focusing on imperative features commonly found in dynamic languages such as JavaScript, Python, and Julia. We introduce a general notion of parametric opaque data types using set-theoretic types, enabling precise modeling of mutable data structures while promoting modularity, clarity, and readability. Finally, we compare our approach to existing work and evaluate our prototype implementation on a range of examples.