Related papers: Certified HLints with Isabelle/HOLCF-Prelude
Refinement types -- types qualified with logical predicates -- have proven effective for lightweight verification in languages like Liquid Haskell, F*, and Dafny. However, in these systems refinements are either written in a separate…
We introduce generalized Hernandez-Leclerc modules over $U_q(\widehat{\mathfrak{sl}_{n+1}})$ as a generalization of Hernandez-Leclerc modules of type A, and prove that they are real and prime via monoidal categorifications of cluster…
We show that a partial-correctness assertion about an iterative program is provable in Hoare Logic iffit is provable in standard second-order logic with comprehension restricted to first-order predicates. This equivalence was claimed twice…
We present an approach to constrained Horn clause (CHC) verification combining three techniques: abstract interpretation over a domain of convex polyhedra, specialisation of the constraints in CHCs using abstract interpretation of…
Neural sequence models can generate highly fluent sentences, but recent studies have also shown that they are also prone to hallucinate additional content not supported by the input. These variety of fluent but wrong outputs are…
Identifiers (IDs) are pervasive throughout our modern life. We suggest that these IDs would be easier to manage and remember if they were easily readable, spellable, and pronounceable. As a solution to this problem we propose using…
Prompting with natural language instructions has recently emerged as a popular method of harnessing the capabilities of large language models. Given the inherent ambiguity present in natural language, it is intuitive to consider the…
Fractional calculus is a generalization of classical theories of integration and differentiation to arbitrary order (i.e., real or complex numbers). In the last two decades, this new mathematical modeling approach has been widely used to…
The success of large-scale contrastive vision-language pretraining (CLIP) has benefited both visual recognition and multimodal content understanding. The concise design brings CLIP the advantage in inference efficiency against other…
This paper explores a hierarchical prompting mechanism for the hierarchical image classification (HIC) task. Different from prior HIC methods, our hierarchical prompting is the first to explicitly inject ancestor-class information as a…
Traditional language models face a challenge from hallucinations. Their very presence casts a large, dangerous shadow over the promising realm of natural language processing. It becomes crucial to understand the various kinds of…
Consensus protocols are crucial for a blockchain system as they are what allow agreement between the system's nodes in a potentially adversarial environment. For this reason, it is paramount to ensure their correct design and implementation…
Formal verification of complex algorithms is challenging. Verifying their implementations goes beyond the state of the art of current automatic verification tools and usually involves intricate mathematical theorems. Certifying algorithms…
This article presents iALC, an intuitionistic version of the classical description logic ALC, based on the framework for constructive modal logics presented by Simpson \cite{simpson95} and related to description languages, via hybrid…
We present the first formalization and metatheory of language soundness for a user-schedulable language, the widely used array processing language Halide. User-schedulable languages strike a balance between abstraction and control in…
This paper presents the design of HELIX, an end-to-end verified code generation system with a focus on the intersection of high-performance and high-assurance numerical computing. The code generation can be fine-tuned to generate efficient…
A common approach to hallucination detection casts it as a natural language inference (NLI) task, often using LLMs to classify whether the generated text is entailed by corresponding reference texts. Since entailment classification is a…
The growing complexity and diversity of models used in the engineering of dependable systems implies that a variety of formal methods, across differing abstractions, paradigms, and presentations, must be integrated. Such an integration…
Large language models (LLMs) increasingly rely on chain-of-thought (CoT) prompting to solve mathematical and logical reasoning tasks. Yet, a central question remains: to what extent are these generated rationales \emph{faithful} to the…
We present a novel formalisation of tensor semantics for linear temporal logic on finite traces (LTLf), with formal proofs of correctness carried out in the theorem prover Isabelle/HOL. We demonstrate that this formalisation can be…