Related papers: Interactive Proof Presentations with Cobra
This book can be seen either as a text on theorem proving that uses techniques from general algebra, or else as a text on general algebra illustrated and made concrete by practical exercises in theorem proving. The book considers several…
In this paper we propose a new perspective on the evolution and history of the idea of mathematical proof. Proofs will be studied at three levels: syntactical, semantical and pragmatical. Computer-assisted proofs will be give a special…
Inquiry-based modeling is essential to scientific practice. However, modeling is difficult for novice scientists in part due to limited domain-specific knowledge and quantitative skills. VERA is an interactive tool that helps users…
Large Language Models (LLMs) have shown significant promise in automated theorem proving, yet progress is often constrained by the scarcity of diverse and high-quality formal language data. To address this issue, we introduce…
A proof is one of the most important concepts of mathematics. However, there is a striking difference between how a proof is defined in theory and how it is used in practice. This puts the unique status of mathematics as exact science into…
Cadabra is a new computer algebra system designed specifically for the solution of problems encountered in field theory. It has extensive functionality for tensor polynomial simplification taking care of Bianchi and Schouten identities, for…
To be usable in practice, interactive theorem provers need to provide convenient and efficient means of writing expressions, definitions, and proofs. This involves inferring information that is often left implicit in an ordinary…
We present Ax-Prover, a multi-agent system for automated theorem proving in Lean that can solve problems across diverse scientific domains and operate either autonomously or collaboratively with human experts. To achieve this, Ax-Prover…
We propose a novel approach to interactive theorem-proving (ITP) using deep reinforcement learning. The proposed framework is able to learn proof search strategies as well as tactic and arguments prediction in an end-to-end manner. We…
Context: Developing compilers and static analysis tools ("language tools") is a difficult and time-consuming task. We have previously presented *property probes*, a technique to help the language tool developer build understanding of their…
In this paper, we introduce CIBER (Claim Investigation Based on Evidence Retrieval), an extension of the Retrieval-Augmented Generation (RAG) framework designed to identify corroborating and refuting documents as evidence for scientific…
In theorem proving, the task of selecting useful premises from a large library to unlock the proof of a given conjecture is crucially important. This presents a challenge for all theorem provers, especially the ones based on language…
Isabelle is an interactive theorem prover that supports a variety of logics. It represents rules as propositions (not as functions) and builds proofs by combining rules. These operations constitute a meta-logic (or `logical framework') in…
The demand for synthetic data in mathematical reasoning has increased due to its potential to enhance the mathematical capabilities of large language models (LLMs). However, ensuring the validity of intermediate reasoning steps remains a…
Today's lectures are often talks following a straight line of slides. In many lectures the process of content teaching is not as efficient as it could be. Technologies, such as smart-phones and wireless communication, enable a new level of…
An efficient intuitionistic first-order prover integrated into Coq is useful to replay proofs found by external automated theorem provers. We propose a two-phase approach: An intuitionistic prover generates a certificate based on the matrix…
Labeled data for imitation learning of theorem proving in large libraries of formalized mathematics is scarce as such libraries require years of concentrated effort by human specialists to be built. This is particularly challenging when…
The Abella interactive theorem prover has proven to be an effective vehicle for reasoning about relational specifications. However, the system has a limitation that arises from the fact that it is based on a simply typed logic:…
The recent increase in the volume of online meetings necessitates automated tools for managing and organizing the material, especially when an attendee has missed the discussion and needs assistance in quickly exploring it. In this work, we…
Multimedia verification requires not only accurate conclusions but also transparent and contestable reasoning. We propose a contestable multi-agent framework that integrates multimodal large language models, external verification tools, and…