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Isabelle is a generic theorem prover, designed for interactive reasoning in a variety of formal theories. At present it provides useful proof procedures for Constructive Type Theory, various first-order logics, Zermelo-Fraenkel set theory,…

Automated theorem provers are now commonly used within interactive theorem provers to discharge an increasingly large number of proof obligations. To maintain the trustworthiness of a proof, the automatically found proof must be verified…

In the era of large language models, Text-to-SQL, as a natural language interface for databases, is playing an increasingly important role. The sota Text-to-SQL models have achieved impressive accuracy, but their performance critically…

Dependent type theory gives an expressive type system facilitating succinct formalizations of mathematical concepts. In practice, it is mainly used for interactive theorem proving with intensional type theories, with PVS being a notable…

In this article we present an ongoing effort to formalise quantum algorithms and results in quantum information theory using the proof assistant Isabelle/HOL. Formal methods being critical for the safety and security of algorithms and…

Discrete Fourier Transform (DFT) libraries are one of the most critical software components for scientific computing. Inspired by FFTW, a widely used library for DFT HPC calculations, we apply compiler technologies for the development of…

Large Language Models (LLMs) have shown potential for solving mathematical tasks. We show that LLMs can be utilized to generate proofs by induction for hardware verification and thereby replace some of the manual work done by Formal…

Transformer has demonstrated its great power to learn contextual word representations for multiple languages in a single model. To process multilingual sentences in the model, a learnable vector is usually assigned to each language, which…

The Isabelle/HOL proof assistant has a powerful library for continuous analysis, which provides the foundation for verification of hybrid systems. However, Isabelle lacks automated proof support for continuous artifacts, which means that…

Significant progress has been made in the field of handwritten mathematical expression recognition, while existing encoder-decoder methods are usually difficult to model global information in $LaTeX$. Therefore, this paper introduces a…

Existing Machine Learning approaches for local citation recommendation directly map or translate a query, which is typically a claim or an entity mention, to citation-worthy research papers. Within such a formulation, it is challenging to…

Recent curriculum reinforcement learning for large language models (LLMs) typically rely on difficulty-based annotations for data filtering and ordering. However, such methods suffer from local optimization, where continual training on…

We present a mechanized embedding of higher-order logic (HOL) and algebraic data types (ADT) into first-order logic with ZFC axioms. We implement this in the Lisa proof assistant for schematic first-order logic and its library based on…

In many real-world applications, users rely on natural language instructions to guide large language models (LLMs) across a wide range of tasks. These instructions are often complex, diverse, and subject to frequent change. However, LLMs do…

In-context learning (ICL) allows transformer-based language models that are pre-trained on general text to quickly learn a specific task with a few "task demonstrations" without updating their parameters, significantly boosting their…

The Isabelle proof assistant comes equipped with a very powerful tactic for term simplification. While tremendously useful, the results of simplifying a term do not always match the user's expectation: sometimes, the resulting term is not…

Identifying linguistic differences between dialects of a language often requires expert knowledge and meticulous human analysis. This is largely due to the complexity and nuance involved in studying various dialects. We present a novel…

We provide simple equational principles for deriving rely-guarantee-style inference rules and refinement laws based on idempotent semirings. We link the algebraic layer with concrete models of programs based on languages and execution…

It is our intention here only to discuss the nature, complexity and tools concerning the design of Smart Help, an expert help facility for aiding users of Computer Algebra Systems. Although the expert help system presented here has been…

Pretrained language models (LLMs) are often constrained by their fixed tokenization schemes, leading to inefficiencies and performance limitations, particularly for multilingual or specialized applications. This tokenizer lock-in presents…