Related papers: Recycling Proof Patterns in Coq: Case Studies
Large Language Models (LLMs) have demonstrated significant promise in formal theorem proving. In this study, we investigate the ability of LLMs to discover novel theorems and produce verified proofs. We propose a pipeline called…
A step-by-step presentation of the code for a small theorem prover introduces theorem-proving techniques. The programming language used is Standard ML. The prover operates on a sequent calculus formulation of first-order logic, which is…
As deep learning based models are increasingly being used for information retrieval (IR), a major challenge is to ensure the availability of test collections for measuring their quality. Test collections are generated based on pooling…
Automated theorem proving has long been a key task of artificial intelligence. Proofs form the bedrock of rigorous scientific inquiry. Many tools for both partially and fully automating their derivations have been developed over the last…
In order to help students learn how to write mathematical proofs, we adapt the Coq proof assistant into an educational tool we call Waterproof. Like with other interactive theorem provers, students write out their proofs inside the software…
We introduce a proof recommender system for the HOL4 theorem prover. Our tool is built upon a transformer-based model [2] designed specifically to provide proof assistance in HOL4. The model is trained to discern theorem proving patterns…
Large language models (LLMs) have been used to generate formal proofs of mathematical theorems in proofs assistants such as Lean. However, we often want to optimize a formal proof with respect to various criteria, depending on its…
Computer-supported learning is an increasingly important form of study since it allows for independent learning and individualized instruction. In this paper, we discuss a novel approach to developing an intelligent tutoring system for…
This paper contains a discussion of a library of formalized mathematics for the proof assistant Coq which the author worked on in 2011-13.
Automated theorem proving is essential for the formal verification of safety-critical systems. As the corpus of formal proofs grows, a natural paradigm is to learn from existing proofs. However, current learning-based approaches…
Large Language Models (LLMs) have demonstrated significant potential in generating mathematical proofs. However, a persistent challenge is that LLMs occasionally make mistakes, while even a minor mistake can invalidate an entire proof.…
We present a reinforcement learning toolkit for experiments with guiding automated theorem proving in the connection calculus. The core of the toolkit is a compact and easy to extend Prolog-based automated theorem prover called plCoP. plCoP…
Large language models (LLMs) can potentially help with verification using proof assistants by automating proofs. However, it is unclear how effective LLMs are in this task. In this paper, we perform a case study based on two mature Rocq…
Proof assistants like Coq are increasingly popular to help mathematicians carry out proofs of the results they conjecture. However, formal proofs remain highly technical and are especially difficult to reuse. In this paper, we present a…
We introduce Repro, an open-source library which aims at improving the reproducibility and usability of research code. The library provides a lightweight Python API for running software released by researchers within Docker containers which…
The use of machine learning techniques has expanded in education research, driven by the rich data from digital learning environments and institutional data warehouses. However, replication of machine learned models in the domain of the…
Many automatic theorem-provers rely on rewriting. Using theorems as rewrite rules helps to simplify the subgoals that arise during a proof. LCF is an interactive theorem-prover intended for reasoning about computation. Its implementation of…
Aiming to offer a framework for blended learning to the teaching of proof theory, the present paper describes an interactive tutorial, called \textsc{TryLogic}, teaching how to solve logical conjectures either by proofs or refutations. The…
During 2024 and 2025 the discussion about the theorem-proving capabilities of large language models started reporting interesting success stories, mostly to do with difficult exercises (such as problems from the International Mathematical…
Information retrieval (IR) systems play a critical role in navigating information overload across various applications. Existing IR benchmarks primarily focus on simple queries that are semantically analogous to single- and multi-hop…