Related papers: DeLaM: A Dependent Layered Modal Type Theory for M…
Modern quantum programming languages integrate quantum resources and classical control. They must, on the one hand, be linearly typed to reflect the no-cloning property of quantum resources. On the other hand, high-level and practical…
This paper introduces and explores a new programming paradigm, Model-based Programming, designed to address the challenges inherent in applying deep learning models to real-world applications. Despite recent significant successes of deep…
The lambda-Pi-calculus modulo theory is a logical framework in which many type systems can be expressed as theories. We present such a theory, the theory U, where proofs of several logical systems can be expressed. Moreover, we identify a…
This work presents an analytical framework for the design and analysis of LLM-based algorithms, i.e., algorithms that contain one or multiple calls of large language models (LLMs) as sub-routines and critically rely on the capabilities of…
Models of dependent type theories are contextual categories with some additional structure. We prove that if a theory $T$ has enough structure, then the category $T\text{-}\mathbf{Mod}$ of its models carries the structure of a model…
We present a type theory dealing with non-linear, "ordinary" dependent types (which we will call cartesian) and linear types, where both constructs may depend on terms of the former. In the interplay between these, we find new type formers…
The aim of staged compilation is to enable metaprogramming in a way such that we have guarantees about the well-formedness of code output, and we can also mix together object-level and meta-level code in a concise and convenient manner. In…
Large language models (LLMs) have shown astonishing capability of generating software code, leading to its use to support developers in programming. Proposed tools have relied either on assistants for improved auto-complete or multi-agents,…
We define a general class of dependent type theories, encompassing Martin-L\"of's intuitionistic type theories and variants and extensions. The primary aim is pragmatic: to unify and organise their study, allowing results and constructions…
We present TLLC which extends the Two-Level Linear dependent type theory (TLL) with session-based concurrency. Equipped with Martin-L\"{o}f style dependency, the session types of TLLC allow protocols to specify properties of communicated…
In this paper we describe how to leverage higher-order unification to type check a dependently typed language with meta-variables. The literature usually presents the unification algorithm as a standalone component, however the need to…
Dependent pattern matching is a key feature in dependently typed programming. However, there is a theory-practice disconnect: while many proof assistants implement pattern matching as primitive, theoretical presentations give semantics to…
Nakano's later modality can be used to specify and define recursive functions which are causal or synchronous; in concert with a notion of clock variable, it is possible to also capture the broader class of productive (co)programs. Until…
A type theory is presented that combines (intuitionistic) linear types with type dependency, thus properly generalising both intuitionistic dependent type theory and full linear logic. A syntax and complete categorical semantics are…
A type system is introduced for a generic Object Oriented programming language in order to infer resource upper bounds. A sound andcomplete characterization of the set of polynomial time computable functions is obtained. As a consequence,…
We present gradual type theory, a logic and type theory for call-by-name gradual typing. We define the central constructions of gradual typing (the dynamic type, type casts and type error) in a novel way, by universal properties relative to…
MetaML-style metaprogramming languages allow programmers to construct, manipulate and run code. In the presence of higher-order references for code, ensuring type safety is challenging, as free variables can escape their binders. In this…
Language Models have demonstrated remarkable capabilities on some tasks while failing dramatically on others. The situation has generated considerable interest in understanding and comparing the capabilities of various Language Models (LMs)…
While vision and multimodal foundation models underpin critical tasks from perception to complex reasoning, they remain highly vulnerable to adversarial attacks. However, traditional adversarial attacks are typically limited to single,…
Formal theorem proving with TLA+ provides rigorous guarantees for system specifications, but constructing proofs requires substantial expertise and effort. While large language models have shown promise in automating proofs for tactic-based…