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 recently proposed, with varying syntax, behavior, and properties. Starting from a detailed review of the challenges and tensions that affect the design of gradual parametric languages, this work presents an extensive account of the semantics and metatheory of GSF, a gradual counterpart of System F. In doing so, we also report on the extent to which the Abstracting Gradual Typing methodology can help us derive such a language. Among gradual parametric languages that follow the syntax of System F, GSF achieves a unique combination of properties. We clearly establish the benefits and limitations of the language, and discuss several extensions of GSF towards a practical programming language.
Gradual typing combines static and dynamic typing in the same program. One would hope that the performance in a gradually typed language would range between that of a dynamically typed language and a statically typed language. Existing implementations of gradually typed languages have not achieved this goal due to overheads associated with runtime casts. Takikawa et al. (2016) report up to 100$\times$ slowdowns for partially typed programs. In this paper we present a compiler, named Grift, for evaluating implementation techniques for gradual typing. We take a straightforward but surprisingly u…
Gradual typing enables programmers to combine static and dynamic typing in the same language. However, ensuring a sound interaction between the static and dynamic parts can incur significant runtime cost. In this paper, we perform a detailed performance analysis of the transient gradual typing approach implemented in Reticulated Python, a gradually typed variant of Python. The transient approach inserts lightweight checks throughout a program rather than installing proxies on higher order values. We show that, when running Reticulated Python and the transient approach on CPython, performance d…
Gradual typing combines static and dynamic typing in the same language, offering the benefits of both to programmers. Static typing provides error detection and strong guarantees while dynamic typing enables rapid prototyping and flexible programming idioms. For programmers to fully take advantage of a gradual type system, however, they must be able to trust their type annotations, and so runtime checks must be performed at the boundaries of static and dynamic code to ensure that static types are respected. Higher order and mutable values cannot be completely checked at these boundaries, and s…
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 language, we approach it from the opposite perspective and promote dynamic checking in a statically typed language. Our approach provides a glimpse into how languages like SML and OCaml might handle gradual typing. We discuss our implementation and challenges faced -- specifically how gradual typing rules apply to our representation of composite and recur…
Gradually-typed programming languages permit the incremental addition of static types to untyped programs. To remain sound, languages insert run-time checks at the boundaries between typed and untyped code. Unfortunately, performance studies have shown that the overhead of these checks can be disastrously high, calling into question the viability of sound gradual typing. In this paper, we show that by building on existing work on soft contract verification, we can reduce or eliminate this overhead. Our key insight is that while untyped code cannot be trusted by a gradual type system, there is …
Abstracting Gradual Typing (AGT) is a systematic approach to designing gradually-typed languages. Languages developed using AGT automatically satisfy the formal semantic criteria for gradual languages identified by Siek et al. [2015]. Nonetheless, vanilla AGT semantics can still have important shortcomings. First, a gradual language's runtime checks should preserve the space-efficiency guarantees inherent to the underlying static and dynamic languages. To the contrary, the default operational semantics of AGT break proper tail calls. Second, a gradual language's runtime checks should enforce b…
This work studies gradual typing for row types and row polymorphism. Key ingredients in this work are the dynamic row type, which represents a statically unknown part of a row, and consistency for row types, which allows injecting static row types into the dynamic row type and, conversely, projecting the dynamic row type to any static row type. While consistency captures the behavior of the dynamic row type statically, it makes the semantics of a gradually typed language incoherent when combined with row equivalence which identifies row types up to field reordering. To solve this problem, we d…
Information flow type systems enforce the security property of noninterference by detecting unauthorized data flows at compile-time. However, they require precise type annotations, making them difficult to use in practice as much of the legacy infrastructure is written in untyped or dynamically-typed languages. Gradual typing seamlessly integrates static and dynamic typing, providing the best of both approaches, and has been applied to information flow control, where information flow monitors are derived from gradual security types. Prior work on gradual information flow typing uncovered tensi…
A long-standing shortcoming of statically typed functional languages is that type checking does not rule out pattern-matching failures (run-time match exceptions). Refinement types distinguish different values of datatypes; if a program annotated with refinements passes type checking, pattern-matching failures become impossible. Unfortunately, refinement is a monolithic property of a type, exacerbating the difficulty of adding refinement types to nontrivial programs. Gradual typing has explored how to incrementally move between static typing and dynamic typing. We develop a type system of grad…
Expressive static typing disciplines are a powerful way to achieve high-quality software. However, the adoption cost of such techniques should not be under-estimated. Just like gradual typing allows for a smooth transition from dynamically-typed to statically-typed programs, it seems desirable to support a gradual path to certified programming. We explore gradual certified programming in Coq, providing the possibility to postpone the proofs of selected properties, and to check "at runtime" whether the properties actually hold. Casts can be integrated with the implicit coercion mechanism of Coq…
Session types are a rich type discipline, based on linear types, that lifts the sort of safety claims that come with type systems to communications. However, web-based applications and microservices are often written in a mix of languages, with type disciplines in a spectrum between static and dynamic typing. Gradual session types address this mixed setting by providing a framework which grants seamless transition between statically typed handling of sessions and any required degree of dynamic typing. We propose Gradual GV as a gradually typed extension of the functional session type system GV…
Abstracting Gradual Typing (AGT) is an approach to systematically deriving gradual counterparts to static type disciplines. The approach consists of defining the semantics of gradual types by interpreting them as sets of static types, and then defining an optimal abstraction back to gradual types. These operations are used to lift the static discipline to the gradual setting. The runtime semantics of the gradual language then arises as reductions on gradual typing derivations. To demonstrate the flexibility of AGT, we gradualize $λ_\text{SEC}$, the prototypical security-typed language, with re…
We revisit occurrence typing, a technique to refine the type of variables occurring in type-cases and, thus, capturesome programming patterns used in untyped languages. Although occurrence typing was tied from its inceptionto set-theoretic types-union types, in particular-it never fully exploited the capabilities of these types. Here weshow how, by using set-theoretic types, it is possible to develop a general typing framework that encompasses andgeneralizes several aspects of current occurrence typing proposals and that can be applied to tackle other problemssuch as the reconstruction of inte…
Herman et al. pointed out that the insertion of run-time checks into a gradually typed program could hamper tail-call optimization and, as a result, worsen the space complexity of the program. To address the problem, they proposed a space-efficient coercion calculus, which was subsequently improved by Siek et al. The semantics of these calculi involves eager composition of run-time checks expressed by coercions to prevent the size of a term from growing. However, it relies also on a nonstandard reduction rule, which does not seem easy to implement. In fact, no compiler implementation of gradua…
Harnessing the power of dependently typed languages can be difficult. Programmers must manually construct proofs to produce well-typed programs, which is not an easy task. In particular, migrating code to these languages is challenging. Gradual typing can make dependently-typed languages easier to use by mixing static and dynamic checking in a principled way. With gradual types, programmers can incrementally migrate code to a dependently typed language. However, adding gradual types to dependent types creates a new challenge: mixing decidable type-checking and incremental migration in a full-f…
Dependent types help programmers write highly reliable code. However, this reliability comes at a cost: it can be challenging to write new prototypes in (or migrate old code to) dependently-typed programming languages. Gradual typing makes static type disciplines more flexible, so an appropriate notion of gradual dependent types could fruitfully lower this cost. However, dependent types raise unique challenges for gradual typing. Dependent typechecking involves the execution of program code, but gradually-typed code can signal runtime type errors or diverge. These runtime errors threaten the s…
Garcia and Cimini study a type inference problem for the ITGL, an implicitly and gradually typed language with let-polymorphism, and develop a sound and complete inference algorithm for it. Soundness and completeness mean that, if the algorithm succeeds, the input term can be translated to a well-typed term of an explicitly typed blame calculus by cast insertion and vice versa. However, in general, there are many possible translations depending on how type variables that were left undecided by static type inference are instantiated with concrete static types. Worse, the translated terms may be…
Elixir is a functional programming language with dynamic typing. We propose a gradual type system that makes it possible to perform type-checking on a significant fragment of the language. An important feature of the type system is that it does not require any syntactic change to Elixir. Type information is provided by means of function signatures which are declared in terms of Elixir typespec directives. The proposed type system is based on subtyping and is backward compatible, as it allows the presence of untyped code fragments. We have implemented a prototype of the type-checker in Elixir i…
Transient gradual typing imposes run-time type tests that typically cause a linear slowdown in programs' performance. This performance impact discourages the use of type annotations because adding types to a program makes the program slower. A virtual machine can employ standard just-in-time optimizations to reduce the overhead of transient checks to near zero. These optimizations can give gradually-typed languages performance comparable to state-of-the-art dynamic languages, so programmers can add types to their code without affecting their programs' performance.
Gradually typed languages are designed to support both dynamically typed and statically typed programming styles while preserving the benefits of each. While existing gradual type soundness theorems for these languages aim to show that type-based reasoning is preserved when moving from the fully static setting to a gradual one, these theorems do not imply that correctness of type-based refactorings and optimizations is preserved. Establishing correctness of program transformations is technically difficult, and is often neglected in the metatheory of gradual languages. In this paper, we propose…
Context: Gradually-typed languages allow typed and untyped code to interoperate, but typically come with significant drawbacks. In some languages, the types are unreliable; in others, communication across type boundaries can be extremely expensive; and still others allow only limited forms of interoperability. The research community is actively seeking a sound, fast, and expressive approach to gradual typing. Inquiry: This paper describes Static Python, a language developed by engineers at Instagram that has proven itself sound, fast, and reasonably expressive in production. Static Python's ap…
