Related papers: Towards Smart Proof Search for Isabelle

The Isabelle proof assistant comes equipped with a very powerful tactic for term simplification. While tremendously useful, the results of simplifying a term do not always match the user's expectation: sometimes, the resulting term is not…

We introduce Aristotle, an AI system that combines formal verification with informal reasoning, achieving gold-medal-equivalent performance on the 2025 International Mathematical Olympiad problems. Aristotle integrates three main…

We introduce a new theorem prover for classical higher-order logic named auto2. The prover is designed to make use of human-specified heuristics when searching for proofs. The core algorithm is a best-first search through the space of…

Auto2 is a recently introduced prover for the proof assistant Isabelle. It is designed to be both highly customizable from within Isabelle, and also have a powerful proof search mechanism. In this paper, we apply auto2 to the verification…

Artificial intelligence assisted mathematical proof has become a highly focused area nowadays. One key problem in this field is to generate formal mathematical proofs from natural language proofs. Due to historical reasons, the formal proof…

We present Isabellm, an LLM-powered theorem prover for Isabelle/HOL that performs fully automatic proof synthesis. Isabellm works with any local LLM on Ollama and APIs such as Gemini CLI, and it is designed to run on consumer grade…

The need for formal definition of the very basis of mathematics arose in the last century. The scale and complexity of mathematics, along with discovered paradoxes, revealed the danger of accumulating errors across theories. Although,…

We present an automated verification of the well-known modal logic cube in Isabelle/HOL, in which we prove the inclusion relations between the cube's logics using automated reasoning tools. Prior work addresses this problem but without…

Consensus protocols are crucial for a blockchain system as they are what allow agreement between the system's nodes in a potentially adversarial environment. For this reason, it is paramount to ensure their correct design and implementation…

Network administration is an inherently complex task, in particular with regard to security. Using the Isabelle interactive proof assistant, we develop two automated, formally verified tools which help uncovering and preventing bugs in…

We introduce a language, PSL, designed to capture high level proof strategies in Isabelle/HOL. Given a strategy and a proof obligation, PSL's runtime system generates and combines various tactics to explore a large search space with low…

Verifying software correctness has always been an important and complicated task. Recently, formal proofs of critical properties of algorithms and even implementations are becoming practical. Currently, the most powerful automated proof…

Proof by induction plays a central role in formal verification. However, its automation remains as a formidable challenge in Computer Science. To solve inductive problems, human engineers often have to provide auxiliary lemmas manually. We…

Interactive theorem provers (ITPs) are powerful tools for the formal verification of mathematical proofs down to the axiom level. However, their lack of a natural language interface remains a significant limitation. Recent advancements in…

Automated theorem provers and formal proof assistants are general reasoning systems that are in theory capable of proving arbitrarily hard theorems, thus solving arbitrary problems reducible to mathematics and logical reasoning. In…

Formal verification via interactive theorem proving is increasingly used to ensure the correctness of critical systems, yet constructing large proof scripts remains highly manual and limits scalability. Advances in large language models…

Interactive theorem provers are complex systems that require sophisticated platform efforts - and hence systems programming environments - to manage effectively. The Isabelle platform exemplifies this with its Isabelle/Scala systems…

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…

A number of flexible tactic-based logical frameworks are nowadays available that can implement a wide range of mathematical theories using a common higher-order metalanguage. Used as proof assistants, one of the advantages of such powerful…

Automated proof generation for formal software verification remains largely unresolved despite advances in large language models (LLMs). While LLMs perform well in NLP, vision, and code generation, formal verification still requires…