Related papers: Interfacing Automatic Proof Agents in Atelier B: I…
Intelligent Process Automation (IPA) is an emerging technology with a primary goal to assist the knowledge worker by taking care of repetitive, routine and low-cognitive tasks. Conversational agents that can interact with users in a natural…
Interactive proof assistants make it possible for ordinary mathematicians to write definitions and theorems in a formal proof language, like a programming language, so that a computer can parse them and check them against the rules of a…
Formal reasoning and automated theorem proving constitute a challenging subfield of machine learning, in which machines are tasked with proving mathematical theorems using formal languages like Lean. A formal verification system can check…
Following an early work of Dwork and Stockmeyer on interactive proof systems whose verifiers are two-way probabilistic finite automata, the authors initiated in 2004 a study on the computational power of quantum interactive proof systems…
The Agora system is a prototypical Wiki for formal mathematics: a web-based system for collaborating on formal mathematics, intended to support informal documentation of formal developments. This system requires a reusable proof editor…
We introduce a resource adaptive agent mechanism which supports the user in interactive theorem proving. The mechanism uses a two layered architecture of agent societies to suggest appropriate commands together with possible command…
We present a novel approach to automated proof generation for the TLA+ Proof System (TLAPS) using Large Language Models (LLMs). Our method combines two key components: a sub-proof obligation generation phase that breaks down complex proof…
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…
We consider the problem of automated reasoning about dynamically manipulated data structures. The state-of-the-art methods are limited to the unfold-and-match (U+M) paradigm, where predicates are transformed via (un)folding operations…
We present a prototype of an integrated reasoning environment for educational purposes. The presented tool is a fragment of a proof assistant and automated theorem prover. We describe the existing and planned functionality of the theorem…
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…
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…
We propose a minimal agentic baseline that enables systematic comparison across different AI-based theorem prover architectures. This design implements the core features shared among state-of-the-art systems: iterative proof refinement,…
Accurate auto-formalization of theorem statements is essential for advancing automated discovery and verification of research-level mathematics, yet remains a major bottleneck for LLMs due to hallucinations, semantic mismatches, and their…
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…
The problem-solving in automated theorem proving (ATP) can be interpreted as a search problem where the prover constructs a proof tree step by step. In this paper, we propose a deep reinforcement learning algorithm for proof search in…
There are two kinds of systems that programming language researchers use for their work. Semantics engineering tools let them interactively explore their definitions, while proof assistants can be used to check the proofs of their…
Proof assistants are computer softwares that allow us to write mathematical proofs so as to assess their correctness. In November 2021, I started the project of checking the simplicity of the alternating groups within the Lean theorem…
Formal verification using interactive theorem provers ensures high-quality software. However, writing proof scripts for interactive theorem provers is labor-intensive and requires deep expertise. Recent studies have leveraged deep learning…
Largely adopted by proof assistants, the conventional induction methods based on explicit induction schemas are non-reductive and local, at schema level. On the other hand, the implicit induction methods used by automated theorem provers…