相关论文: Denotational Semantics of Gradual Typing using Syn…
Just like any other branch of mathematics, denotational semantics of programming languages should be formalised in type theory, but adapting traditional domain theoretic semantics, as originally formulated in classical set theory to type…
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…
Clocked Cubical Type Theory is a new type theory combining the power of guarded recursion with univalence and higher inductive types (HITs). This type theory can be used as a metalanguage for synthetic guarded domain theory in which one can…
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…
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].…
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…
Session types have emerged as a powerful paradigm for structuring communication-based programs. They guarantee type soundness and session fidelity for concurrent programs with sophisticated communication protocols. As type soundness proofs…
Gradually typed languages allow statically typed and dynamically typed code to interact while maintaining benefits of both styles. The key to reasoning about these mixed programs is Siek-Vitousek-Cimini-Boyland's (dynamic) gradual…
Reasoning about the sensitivity of functions with respect to their inputs has interesting applications in various areas, such as differential privacy. In order to check and enforce sensitivity, several approaches have been developed,…
Notions of guardedness serve to delineate admissible recursive definitions in various settings in a compositional manner. In recent work, we have introduced an axiomatic notion of guardedness in symmetric monoidal categories, which serves…
Constructive type theory combines logic and programming in one language. This is useful both for reasoning about programs written in type theory, as well as for reasoning about other programming languages inside type theory. It is…
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…
The gradual guarantee is an important litmus test for gradually typed languages, that is, languages that enable a mixture of static and dynamic typing. The gradual guarantee states that changing the precision of a type annotation does not…
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…
Programs written in dynamic languages make heavy use of features --- run-time type tests, value-indexed dictionaries, polymorphism, and higher-order functions --- that are beyond the reach of type systems that employ either purely syntactic…
We present the guarded lambda-calculus, an extension of the simply typed lambda-calculus with guarded recursive and coinductive types. The use of guarded recursive types ensures the productivity of well-typed programs. Guarded recursive…
We give a domain-theoretic semantics to a statistical programming language, using the plain old category of dcpos, in contrast to some more sophisticated recent proposals. Remarkably, our monad of minimal valuations is commutative, which…
Probabilistic programming languages have recently gained a lot of attention, in particular due to their applications in domains such as machine learning and differential privacy. To establish invariants of interest, many such languages…
We present the guarded lambda-calculus, an extension of the simply typed lambda-calculus with guarded recursive and coinductive types. The use of guarded recursive types ensures the productivity of well-typed programs. Guarded recursive…
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…