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Indexed inductive types are essential in dependently-typed programming languages, enabling precise and expressive specifications of data structures and properties. Recognizing that programming and proving with dependent types could benefit from the ...

Since the arrival of gradual typing, which allows partially typed code in a single program, efficient implementations of gradual typing have been an active research topic. In this paper, we study the space-efficiency problem of gradual typing in the ...

Bringing the benefits of gradual typing to a language with parametric polymorphism like System F, while preserving relational parametricity, has proven extremely challenging: first attempts were formulated a decade ago, and several designs have been ...

Gradualizing the Calculus of Inductive Constructions (CIC) involves dealing with subtle tensions between normalization, graduality, and conservativity with respect to CIC. Recently, GCIC has been proposed as a parametrized gradual type theory that admits ...

Graduality and parametricity have proven to be extremely challenging notions to bring together. Intuitively, enforcing parametricity gradually requires possibly sealing values in order to detect violations of uniform behavior. Toro et al. (2019) argue ...

We investigate gradual variations on the Calculus of Inductive Construction (CIC) for swifter prototyping with imprecise types and terms. We observe, with a no-go theorem, a crucial trade-off between graduality and the key properties of normalization and ...

In this paper, we describe our experience incorporating gradual types in a statically typed functional language with Hindley-Milner style type inference. Where most gradually typed systems aim to improve static checking in a dynamically typed ...

• We present Pallene, a typed and ahead-of-time-compiled subset of Lua.
• Pallene ...

The simplicity and flexibility of dynamic languages make them popular for prototyping and scripting, but the lack of compile-time type information makes it challenging to generate efficient executable code.

Inspired by ideas ...

Consistent subtyping is employed in some gradual type systems to validate type conversions. The original definition by Siek and Taha serves as a guideline for designing gradual type systems with subtyping. Polymorphic types à la System F also induce a ...

Gradual typing enables programmers to combine static and dynamic typing in the same language. However, ensuring sound interaction between the static and dynamic parts can incur runtime cost. In this paper, we analyze the performance of the transient ...

Both static and dynamic typing provide different benefits to the programmer. Statically typed languages support earlier type error detection and more opportunities for compiler optimizations. Dynamically typed languages facilitate the ...

Bringing the benefits of gradual typing to a language with parametric polymorphism like System F, while preserving relational parametricity, has proven extremely challenging: first attempts were formulated a decade ago, and several designs were recently ...

Mixing static and dynamic type checking in the same language is catching on, with the TypeScript and Flow variants of JavaScript, the MyPy and Reticulated variants of Python, the Strongtalk and Gradualtalk variants of Smalltalk, as well as Typed Racket,...

Programmers in dynamic languages wishing to constrain and understand the behavior of their programs may turn to gradually-typed languages, which allow types to be specified optionally and check values at the boundary between dynamic and static code. ...

We propose a type system for functional languages with gradual types and set-theoretic type connectives and prove its soundness. In particular, we show how to lift the definition of the domain and result type of an application from non-gradual types to ...

We introduce several blame strategies for gradual effect systems. Blame strategies are the part of a language semantics that aims to identify the cause of a runtime check failure. Gradual effect systems are a framework that combines static and dynamic ...

Programmers have come to embrace dynamically-typed languages for prototyping and delivering large and complex systems. When it comes to maintaining and evolving these systems, the lack of explicit static typing becomes a bottleneck. In response, ...

Being able to combine static and dynamic typing within the same language has clear benefits in order to support the evolution of prototypes or scripts into mature robust programs. While being an emblematic dynamic object-oriented language, Smalltalk is ...

Gradual type systems offer a smooth continuum between static and dynamic typing by permitting the free mixture of typed and untyped code. The runtime systems for these languages, and other languages with hybrid type checking, typically enforce function ...