Related papers: Developments in Formal Proofs
Interactive proof assistants are computer programs carefully constructed to check a human-designed proof of a mathematical claim with high confidence in the implementation. However, this only validates truth of a formal claim, which may…
Comparing provers on a formalization of the same problem is always a valuable exercise. In this paper, we present the formal proof of correctness of a non-trivial algorithm from graph theory that was carried out in three proof assistants:…
Proof assistants enable users to develop machine-checked proofs regarding software-related properties. Unfortunately, the interactive nature of these proof assistants imposes most of the proof burden on the user, making formal verification…
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…
Formally verifying software properties is a highly desirable but labor-intensive task. Recent work has developed methods to automate formal verification using proof assistants, such as Coq and Isabelle/HOL, e.g., by training a model to…
Most of the engineering and physical systems are generally characterized by differential and difference equations based on their continuous-time and discrete-time dynamics, respectively. Moreover, these dynamical models are analyzed using…
Chain-of-Thought (CoT) prompting has become the de facto method to elicit reasoning capabilities from large language models (LLMs). However, to mitigate hallucinations in CoT that are notoriously difficult to detect, current methods such as…
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…
The ever-growing complexity of mathematical proofs makes their manual verification by mathematicians very cognitively demanding. Autoformalization seeks to address this by translating proofs written in natural language into a formal…
Large formal mathematical libraries consist of millions of atomic inference steps that give rise to a corresponding number of proved statements (lemmas). Analogously to the informal mathematical practice, only a tiny fraction of such…
The interoperability of proof assistants and the integration of their libraries is a highly valued but elusive goal in the field of theorem proving. As a preparatory step, in previous work, we translated the libraries of multiple proof…
Large computer-understandable proofs consist of millions of intermediate logical steps. The vast majority of such steps originate from manually selected and manually guided heuristics applied to intermediate goals. So far, machine learning…
The research in AI-based formal mathematical reasoning has shown an unstoppable growth trend. These studies have excelled in mathematical competitions like IMO and have made significant progress. This paper focuses on formal verification,…
In the recent years, we have linked a large corpus of formal mathematics with automated theorem proving (ATP) tools, and started to develop combined AI/ATP systems working in this setting. In this paper we first relate this project to the…
The formalisation of mathematics is starting to become routine, but the value of this technology to the work of mathematicians remains to be shown. There are few examples of using proof assistants to verify brand-new work. This paper…
This article introduces Globular, an online proof assistant for the formalization and verification of proofs in higher-dimensional category theory. The tool produces graphical visualizations of higher-dimensional proofs, assists in their…
This notes explains how standard algorithms that construct sorting networks have been formalised and proved correct in the Coq proof assistant using the SSReflect extension.
In mathematics, it is common practice to have several constructions for the same objects. Mathematicians will identify them modulo isomorphism and will not worry later on which construction they use, as theorems proved for one construction…
Current approaches for formal verification of algorithms face important limitations. For specification, they cannot express algorithms naturally and concisely, especially for algorithms with states and flexible control flow. For…
Despite the recent progress in automatic theorem provers, proof engineers are still suffering from the lack of powerful proof automation. In this position paper we first report our proof strategy language based on a meta-tool approach.…