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Combining static and dynamic typing within the same language offers clear benefits to programmers. It provides dynamic typing in situations that require rapid prototyping, heterogeneous data structures, and reflection, while supporting static typing when safety, modularity, and efficiency are primary concerns. Siek and Taha (2006) introduced an approach to combining static and dynamic typing in a fine-grained manner through the notion of type consistency in the static semantics and run-time casts in the dynamic semantics. However, many open questions remain regarding the semantics of gradually typed languages.In this paper we present Reticulated Python, a system for experimenting with gradual-typed dialects of Python. The dialects are syntactically identical to Python 3 but give static and dynamic semantics to the type annotations already present in Python 3. Reticulated Python consists of a typechecker and a source-to-source translator from Reticulated Python to Python 3. Using Reticulated Python, we evaluate a gradual type system and three approaches to the dynamic semantics of mutable objects: the traditional semantics based on Siek and Taha (2007) and Herman et al. (2007) and two new designs. We evaluate these designs in the context of several third-party Python programs.

Combining static and dynamic typing within the same language offers clear benefits to programmers. It provides dynamic typing in situations that require rapid prototyping, heterogeneous data structures, and reflection, while supporting static typing when safety, modularity, and efficiency are primary concerns. Siek and Taha (2006) introduced an approach to combining static and dynamic typing in a fine-grained manner through the notion of type consistency in the static semantics and run-time casts in the dynamic semantics. However, many open questions remain regarding the semantics of gradually typed languages.In this paper we present Reticulated Python, a system for experimenting with gradual-typed dialects of Python. The dialects are syntactically identical to Python 3 but give static and dynamic semantics to the type annotations already present in Python 3. Reticulated Python consists of a typechecker and a source-to-source translator from Reticulated Python to Python 3. Using Reticulated Python, we evaluate a gradual type system and three approaches to the dynamic semantics of mutable objects: the traditional semantics based on Siek and Taha (2007) and Herman et al. (2007) and two new designs. We evaluate these designs in the context of several third-party Python programs.

Gradual typing combines static and dynamic typing in the same language, offering programmers the error detection and strong guarantees of static types and the rapid prototyping and flexible programming idioms of dynamic types. Many gradually typed languages are implemented by translation into an untyped target language (e.g., Typed Clojure, TypeScript, Gradualtalk, and Reticulated Python). For such languages, it is desirable to support arbitrary interaction between translated code and legacy code in the untyped language while maintaining the type soundness of the translated code. In this paper we formalize this goal in the form of the open-world soundness criterion. We discuss why it is challenging to achieve open-world soundness using the traditional proxy-based approach for higher-order casts. We then show how an alternative, the transient design, satisfies open-world soundness by presenting a formal semantics for the transient design and proving that the semantics satisfies open-world soundness. In this paper we also solve a challenging problem for the transient design: how to provide blame tracking without proxies. We define a semantics for blame and prove the Blame Theorem. We also prove that the Gradual Guarantee holds for this system, ensuring that programs can be evolved freely between static and dynamic typing. Finally, we demonstrate that the runtime overhead of the transient approach is low in the context of Reticulated Python, an implementation of gradual typing for Python.