Related papers: Integrating Testing and Interactive Theorem Provin…
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…
Large Language Models (LLMs) have been successful in mathematical reasoning tasks such as formal theorem proving when integrated with interactive proof assistants like Lean. Existing approaches involve training or fine-tuning an LLM on a…
Theorem proving is a fundamental aspect of mathematics, spanning from informal reasoning in natural language to rigorous derivations in formal systems. In recent years, the advancement of deep learning, especially the emergence of large…
In recent years we have explored using Haskell alongside a traditional mathematical formalism in our large-enrolment university course on topics including logic and formal languages, aiming to offer our students a programming perspective on…
This work discusses an approach to teach to mathematicians the importance and effectiveness of the application of Interactive Theorem Proving tools in their specific fields of interest. The approach aims to motivate the use of such tools…
The LCF tradition of interactive theorem proving, which was started by Milner in the 1970-ies, appears to be tied to the classic READ-EVAL-PRINT-LOOP of sequential and synchronous evaluation of prover commands. We break up this loop and…
We present a novel technique for combining statistical machine learning for proof-pattern recognition with symbolic methods for lemma discovery. The resulting tool, ACL2(ml), gathers proof statistics and uses statistical pattern-recognition…
Recent advances in large language models (LLMs) have shown promise in formal theorem proving, yet evaluating semantic correctness remains challenging. Existing evaluations rely on indirect proxies such as lexical overlap with…
Test or prove? These two approaches to software verification have long been presented as opposites. One is dynamic, the other static: a test executes the program, a proof only analyzes the program text. A different perspective is emerging,…
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…
We aim to solve the problem of temporal-constraint learning from demonstrations to reproduce demonstration-like logic-constrained behaviors. Learning logic constraints is challenging due to the combinatorially large space of possible…
As language models continue to rapidly improve, we can expect their actions and reasoning to become difficult or impossible for weaker agents and humans to follow, undermining interpretability and oversight. With an eye on long-term…
We introduce LADDER (Learning through Autonomous Difficulty-Driven Example Recursion), a framework which enables Large Language Models to autonomously improve their problem-solving capabilities through self-guided learning by recursively…
Interactive theorem provers such as Coq are powerful tools to formally guarantee the correctness of software. However, using these tools requires significant manual effort and expertise. While Large Language Models (LLMs) have shown promise…
We present IntelliProof, an interactive system for analyzing argumentative essays through LLMs. IntelliProof structures an essay as an argumentation graph, where claims are represented as nodes, supporting evidence is attached as node…
LLM-based formal proof assistants (e.g., in Lean) hold great promise for automating mathematical discovery. But beyond syntactic correctness, do these systems truly understand mathematical structure as humans do? We investigate this…
ACL2(ml) is an extension for the Emacs interface of ACL2. This tool uses machine-learning to help the ACL2 user during the proof-development. Namely, ACL2(ml) gives hints to the user in the form of families of similar theorems, and…
Machine-assisted theorem proving refers to the process of conducting structured reasoning to automatically generate proofs for mathematical theorems. Recently, there has been a surge of interest in using machine learning models in…
Software testing plays a critical role in ensuring that systems behave as intended. However, existing automated testing approaches struggle to match the capabilities of human engineers due to key limitations such as test locality, lack of…
The heterogeneous nature of the logical foundations used in different interactive proof assistant libraries has rendered discovery of similar mathematical concepts among them difficult. In this paper, we compare a previously proposed…