Related papers: Toward SMT-Based Refinement Types in Agda
Prompt programming treats large language model prompts as software components with typed interfaces. Based on a literature survey of 15 recent works from 2023 to 2025, we observe a consistent trend: type systems are central to emerging…
We study SMT problems over the reals containing ordinary differential equations. They are important for formal verification of realistic hybrid systems and embedded software. We develop delta-complete algorithms for SMT formulas that are…
Recent work has proposed a promising approach to improving scalability of program synthesis by allowing the user to supply a syntactic template that constrains the space of potential programs. Unfortunately, creating templates often…
We present the type system $\mathtt{d}$, an extended type system with lambda-typed lambda-expressions. It is related to type systems originating from the Automath project. $\mathtt{d}$ extends existing lambda-typed systems by an existential…
We study the complexity of reasoning tasks for logics in team semantics. Our main focus is on the data complexity of model checking but we also derive new results for logically defined counting and enumeration problems. Our approach is…
Machine translation systems require semantic knowledge and grammatical understanding. Neural machine translation (NMT) systems often assume this information is captured by an attention mechanism and a decoder that ensures fluency. Recent…
We present a notion of bounded quantification for refinement types and show how it expands the expressiveness of refinement typing by using it to develop typed combinators for: (1) relational algebra and safe database access, (2)…
To assist humans in efficiently validating RAG-generated content, developing a fine-grained attribution mechanism that provides supporting evidence from retrieved documents for every answer span is essential. Existing fine-grained…
This study provides some results about two-level type-theoretic notions in a way that the proofs are fully formalizable in a proof assistant implementing two-level type theory such as Agda. The difference from prior works is that these…
Static resource analysis determines the resource consumption (e.g., time complexity) of a program without executing it. Among the numerous existing approaches for resource analysis, affine type systems have been one dominant approach.…
A coverage type generalizes refinement types found in many functional languages with support for must-style underapproximate reasoning. Property-based testing frameworks are one particularly useful domain where such capabilities are useful…
We present an approach to develop folds for nested data types using dependent types. We call such folds $\textit{dependently typed folds}$, they have the following properties. (1) Dependently typed folds are defined by well-founded…
Proof-oriented programs mix computational content with proofs of program correctness. However, the human effort involved in programming and proving is still substantial, despite the use of Satisfiability Modulo Theories (SMT) solvers to…
In this paper we present our current development on a new formalization of nominal sets in Agda. Our first motivation in having another formalization was to understand better nominal sets and to have a playground for testing type systems…
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 investigate the class of models of a general dependent theory. We continue math.LO/0702292 in particular investigating so called "decomposition of types"; thesis is that what holds for stable theory and for Th(Q,<) hold for dependent…
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…
The increasing complexity of modern configurable systems makes it critical to improve the level of automation in the process of system configuration. Such automation can also improve the agility of the development cycle, allowing for rapid…
Modal automata are a classic formal model for component-based systems that comes equipped with a rich specification theory supporting abstraction, refinement and compositional reasoning. In recent years, quantitative variants of modal…
The convergence of deep learning and formal mathematics has spurred research in formal verification. Statement autoformalization, a crucial first step in this process, aims to translate informal descriptions into machine-verifiable…