相关论文: A Framework for Dependent Types and Effects
We introduce two extensions of the $\lambda$-calculus with a probabilistic choice operator, $\Lambda_\oplus^{cbv}$ and $\Lambda_\oplus^{cbn}$, modeling respectively call-by-value and call-by-name probabilistic computation. We prove that…
Over twenty years ago, Abadi et al. established the Dependency Core Calculus (DCC) as a general purpose framework for analyzing dependency in typed programming languages. Since then, dependency analysis has shown many practical benefits to…
We introduce a probabilistic extension of Levy's Call-By-Push-Value. This extension consists simply in adding a " flipping coin " boolean closed atomic expression. This language can be understood as a major generalization of Scott's PCF…
This paper presents preliminary work on a general system for integrating dependent types into substructural type systems such as linear logic and linear type theory. Prior work on this front has generally managed to deliver type systems…
For those of us who generally live in the world of syntax, semantic proof techniques such as reducibility, realizability or logical relations seem somewhat magical despite -- or perhaps due to -- their seemingly unreasonable effectiveness.…
Real world programming languages crucially depend on the availability of computational effects to achieve programming convenience and expressive power as well as program efficiency. Logical frameworks rely on predicates, or dependent types,…
We present a type theory combining both linearity and dependency by stratifying typing rules into a level for logics and a level for programs. The distinction between logics and programs decouples their semantics, allowing the type system…
We study a dependently typed extension of a multi-stage programming language \`a la MetaOCaml, which supports quasi-quotation and cross-stage persistence for manipulation of code fragments as first-class values and an evaluation construct…
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…
A system of linear dependent types for the lambda calculus with full higher-order recursion, called dlPCF, is introduced and proved sound and relatively complete. Completeness holds in a strong sense: dlPCF is not only able to precisely…
The purpose of this text is to prove all technical aspects of our model for dependent type theory with parametric quantifiers [Nuyts, Vezzosi and Devriese, 2017]. It is well-known that any presheaf category constitutes a model of dependent…
We present a novel dependent linear type theory in which the multiplicity of some variable-i.e., the number of times the variable can be used in a program-can depend on other variables. This allows us to give precise resource annotations to…
In the Calculus of Dependent Lambda Eliminations (CDLE), a pure Curry-style type theory, it is possible to generically {\lambda}-encode inductive datatypes which support course-of-values (CoV) induction. We present a datatype subsystem for…
In this report we define an encoding of Levys call-by-push-value lambda-calculus (CBPV) in the pi-calculus, and prove that our encoding is both sound and complete. We present informal (by-hand) proofs of soundness, completeness, and all…
The ability to cast values between related types is a leitmotiv of many flavors of dependent type theory, such as observational type theories, subtyping, or cast calculi for gradual typing. These casts all exhibit a common structural…
The good properties of Plotkin's call-by-value lambda-calculus crucially rely on the restriction to weak evaluation and closed terms. Open call-by-value is the more general setting where evaluation is weak but terms may be open. Such an…
Large language model (LLM) agents are increasingly capable of orchestrating complex tasks in low-code environments. However, these agents often exhibit hallucinations and logical inconsistencies because their inherent reasoning mechanisms…
In dependent type theory, being able to refer to a type universe as a term itself increases its expressive power, but requires mechanisms in place to prevent Girard's paradox from introducing logical inconsistency in the presence of…
We adapt Fiore, Plotkin, and Turi's treatment of abstract syntax with binding, substitution, and holes to account for languages with second-class sorts. These situations include programming calculi such as the Call-by-Value lambda-calculus…
In their usual form, representation independence metatheorems provide an external guarantee that two implementations of an abstract interface are interchangeable when they are related by an operation-preserving correspondence. If our…