Pragmatic Gradual Polymorphism with References

Abstract Gradualizing System F has been widely discussed. A big challenge is to preserve relational parametricity and/or the gradual guarantee. Most past work focused on preservation of parametricity, but often without few recent works satisfy both properties by giving up syntax, or with some restrictions and introduction sophisticated mechanisms in dynamic semantics. While important for polymorphic languages, most mainstream languages typically do not it, a variety different reasons. In this paper, we explore design space that guarantee, parametricity. When goal, can be considerably simplified. Moreover, it becomes easy add features are practical importance, such as mutable references. We present new gradually typed calculus, called $$\lambda ^{G}_{gpr}$$ λ gpr G , references an proof addition, compared other polymorphism work, defined using Type-Directed Operational Semantics (TDOS), which allows semantics directly instead elaborating target cast language. all proofs paper formalized Coq.