Related papers: Proof Pattern Search in Coq/SSReflect

We present ML4PG - a machine learning extension for Proof General. It allows users to gather proof statistics related to shapes of goals, sequences of applied tactics, and proof tree structures from the libraries of interactive higher-order…

ML4PG is a machine-learning extension that provides statistical proof hints during the process of Coq/SSReflect proof development. In this paper, we use ML4PG to find proof patterns in the CoqEAL library -- a library that was devised to…

Development of Interactive Theorem Provers has led to the creation of big libraries and varied infrastructures for formal proofs. However, despite (or perhaps due to) their sophistication, the re-use of libraries by non-experts or across…

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…

We present an in-context learning agent for formal theorem-proving in environments like Lean and Coq. Current state-of-the-art models for the problem are finetuned on environment-specific proof data. By contrast, our approach, called COPRA,…

The Coq Platform is a continuously developed distribution of the Coq proof assistant together with commonly used libraries, plugins, and external tools useful in Coq-based formal verification projects. The Coq Platform enables reproducing…

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…

We describe a method for building composable and extensible verification procedures within the Coq proof assistant. Unlike traditional methods that rely on run-time generation and checking of proofs, we use verified-correct procedures with…

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…

This paper develops an algorithmic-based approach for proving inductive properties of propositional sequent systems such as admissibility, invertibility, cut-elimination, and identity expansion. Although undecidable in general, these…

The advancement of Large Language Models (LLMs) has brought substantial attention to the Chain of Thought (CoT) approach, primarily due to its ability to enhance the capability of LLMs on complex reasoning tasks. Moreover, the significance…

In the realm of formal theorem proving, the Coq proof assistant stands out for its rigorous approach to verifying mathematical assertions and software correctness. Despite the advances in artificial intelligence and machine learning, the…

Matching logic is a formalism for specifying, and reasoning about, mathematical structures, using patterns and pattern matching. Growing in popularity, it has been used to define many logical systems such as separation logic with recursive…

Proofs in proof assistants like Rocq can be brittle, breaking easily in response to changes. To address this, recent work introduced an algorithm and tool in Rocq to automatically repair broken proofs in response to changes that correspond…

We present the design and implementation of the Small Scale Reflection proof methodology and tactic language (a.k.a. SSR) for the Lean 4 proof assistant. Like its Coq predecessor SSReflect, our Lean 4 implementation, dubbed LeanSSR,…

We present a system that utilizes machine learning for tactic proof search in the Coq Proof Assistant. In a similar vein as the TacticToe project for HOL4, our system predicts appropriate tactics and finds proofs in the form of tactic…

Sequential recommendation aims to predict a user's next action in large-scale recommender systems. While traditional methods often suffer from insufficient information interaction, recent generative recommendation models partially address…

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…

This paper describes a formal proof library, developed using the Coq proof assistant, designed to assist users in writing correct diagrammatic proofs, for 1-categories. This library proposes a deep-embedded, domain-specific formal language,…

We present CoqPilot, a VS Code extension designed to help automate writing of Coq proofs. The plugin collects the parts of proofs marked with the admit tactic in a Coq file, i.e., proof holes, and combines LLMs along with…