Related papers: Integrating Testing and Interactive Theorem Provin…
Theorem proving serves as a major testbed for evaluating complex reasoning abilities in large language models (LLMs). However, traditional automated theorem proving (ATP) approaches rely heavily on formal proof systems that poorly align…
Generating code from natural-language requirements has become a primary route for LLM-assisted software development. Although LLMs can successfully complete small programming tasks, generating an entire complex project remains unreliable…
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…
Mechanical reasoning is a key area of research that lies at the crossroads of mathematical logic and artificial intelligence. The main aim to develop mechanical reasoning systems (also known as theorem provers) was to enable mathematicians…
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…
Hybrid games model cyber-physical systems (CPS), like cars, trains, and airplanes, where discrete control decisions interact with continuous physical dynamics. We use Large Language Models (LLMs) to scale formal verification and synthesis…
The ACL2 Workshop series is the major technical forum for users of the ACL2 theorem proving system to present research related to the ACL2 theorem prover and its applications. ACL2 is an industrial-strength automated reasoning system, the…
GL is a verified tool for proving ACL2 theorems using Boolean methods such as BDD reasoning and satisfiability checking. In its typical operation, GL recursively traverses a term, computing a symbolic object representing the value of each…
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…
The rapid integration of Large Language Models (LLMs) into software engineering practice is reshaping how software testing activities are performed. LLMs are increasingly used to support software testing. Consequently, software testing…
Humans prove theorems by relying on substantial high-level reasoning and problem-specific insights. Proof assistants offer a formalism that resembles human mathematical reasoning, representing theorems in higher-order logic and proofs as…
Despite the success of large language models (LLMs), the task of theorem proving still remains one of the hardest reasoning tasks that is far from being fully solved. Prior methods using language models have demonstrated promising results,…
We present Cobra, a modern proof presentation framework, leveraging cutting-edge presentation technology together with a state of the art interactive theorem prover to present formalized mathematics as active documents. Cobra provides both…
The ACL2 theorem prover is a complex system. Its libraries are vast. Industrial verification efforts may extend this base with hundreds of thousands of lines of additional modeling tools, specifications, and proof scripts. High quality…
This paper considers the development of an AI-based provably-correct mathematical proof tutor. While Large Language Models (LLMs) allow seamless communication in natural language, they are error prone. Theorem provers such as Lean allow for…
This paper considers the development of an AI-based provably-correct mathematical proof tutor. While Large Language Models (LLMs) allow seamless communication in natural language, they are error prone. Theorem provers such as Lean allow for…
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…
In this paper, we introduce a system called GamePad that can be used to explore the application of machine learning methods to theorem proving in the Coq proof assistant. Interactive theorem provers such as Coq enable users to construct…
Large language models (LLMs) often struggle with complex logical reasoning due to logical inconsistencies and the inherent difficulty of such reasoning. We use Lean, a theorem proving framework, to address these challenges. By formalizing…
In-context learning (ICL) has proven highly effective across diverse large language model (LLM) tasks. However, its potential for enhancing tasks that demand step-by-step logical deduction, such as mathematical reasoning, remains…