Related papers: VDM recursive functions in Isabelle/HOL
Mask Diffusion-based Vision Language Models (MDVLMs) have achieved remarkable progress in multimodal understanding tasks. However, these models are unable to correct errors in generated tokens, meaning they lack self-correction capability.…
Learning functional programming requires learning a substitution-based computational model. While substitution should be a familiar concept from high-school algebra, students often have difficulty applying it to new settings, such as…
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CSV is a widely used format for data representing systems control, information exchange and processing, logging, etc. Nevertheless, the format is riddled with tricky corner cases and inconsistencies, which can make input data unreliable,…
A theory of recursive and corecursive definitions has been developed in higher-order logic (HOL) and mechanized using Isabelle. Least fixedpoints express inductive data types such as strict lists; greatest fixedpoints express coinductive…
Recently, a growing number of researchers have applied machine learning to assist users of interactive theorem provers. However, the expressive nature of underlying logics and esoteric structures of proof documents impede machine learning…
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We present a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the predicate calculus as well as a formal induction principle. We introduce recursive systems generating…
Multimodal large language models (MLLMs) have demonstrated remarkable capabilities in vision-language answering tasks. Despite their strengths, these models often encounter challenges in achieving complex reasoning tasks such as…
An approach for encoding abstract dialectical frameworks and their semantics into classical higher-order logic is presented. Important properties and semantic relationships are formally encoded and proven using the proof assistant…
Diffusion Language Models (DLMs) have recently achieved strong results in text generation. However, their multi-step sampling leads to slow inference, limiting practical use. To address this, we extend Inverse Distillation, a technique…
Reinforcement learning (RL) has recently shown strong potential in improving the reasoning capabilities of large language models and is now being actively extended to vision-language models (VLMs). However, existing RL applications in VLMs…
In call-by-value languages, some mutually-recursive value definitions can be safely evaluated to build recursive functions or cyclic data structures, but some definitions (let rec x = x + 1) contain vicious circles and their evaluation…
Linear programming describes the problem of optimising a linear objective function over a set of constraints on its variables. In this paper we present a solver for linear programs implemented in the proof assistant Isabelle/HOL. This…
Large language models (LLMs) often struggle to use tools reliably in domain-specific settings, where APIs may be idiosyncratic, under-documented, or tailored to private workflows. This highlights the need for effective adaptation to…
Automatically assessing handwritten mathematical solutions is an important problem in educational technology with practical applications, but it remains a significant challenge due to the diverse formats, unstructured layouts, and symbolic…
Formally specifying, let alone verifying, properties of systems involving multiple programming languages is inherently challenging. We introduce Heterogeneous Dynamic Logic (HDL), a framework for combining reasoning principles from distinct…
Modern machine learning pipelines are built on numerical algorithms. Reliable numerical methods are thus a prerequisite for trustworthy machine learning and cyber-physical systems. Therefore, we contribute a framework for verified numerical…
Modern functional-logic programming languages like Toy or Curry feature non-strict non-deterministic functions that behave under call-time choice semantics. A standard formulation for this semantics is the CRWL logic, that specifies a proof…