Related papers: FindFacts: A Scalable Theorem Search
The Archive of Formal Proofs (AFP) is an online repository of formal proofs for the Isabelle proof assistant. It serves as a central location for publishing, discovering, and viewing libraries of proofs. We conducted an online survey in…
This is an overview of the Isabelle technology behind the Archive of Formal Proofs (AFP). Interactive development and quasi-interactive build jobs impose significant demands of scalability on the logic (usually Isabelle/HOL), on Isabelle/ML…
The Isabelle Archive of Formal Proofs has grown to a significant size in the past years. It makes up for an impressive body of research, which enables a number of statistical approaches to various aspects in theorem proving, and has not yet…
Isabelle/PIDE has emerged over more than 10 years as the standard Prover IDE for interactive theorem proving in Isabelle. The well-established Archive of Formal Proofs (AFP) testifies the success of such applications of formalized…
In interactive theorem proving, formalization quality is a key factor for maintainability and re-usability of developments and can also impact proof-checking performance. Commonly, anti-patterns that cause quality issues are known to…
The libraries of proof assistants like Isabelle, Coq, HOL are notoriously difficult to interpret by external tools: de facto, only the prover itself can parse and process them adequately. In the case of Isabelle, an export of the library…
How is a factual claim made credible? We propose the novel task of Epistemic Appeal Identification, which identifies whether and how factual statements have been anchored by external sources or evidence. To advance research on this task, we…
Isabelle is a generic theorem prover, designed for interactive reasoning in a variety of formal theories. At present it provides useful proof procedures for Constructive Type Theory, various first-order logics, Zermelo-Fraenkel set theory,…
Interactive theorem provers have developed dramatically over the past four decades, from primitive beginnings to today's powerful systems. Here, we focus on Isabelle/HOL and its distinctive strengths. They include automatic proof search,…
Despite the recent progress in automatic theorem provers, proof engineers are still suffering from the lack of powerful proof automation. In this position paper we first report our proof strategy language based on a meta-tool approach.…
Formal verification (FV) has witnessed growing significance with current emerging program synthesis by the evolving large language models (LLMs). However, current formal verification mainly resorts to symbolic verifiers or hand-craft rules,…
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…
Large language models (LLM), such as Google's Minerva and OpenAI's GPT families, are becoming increasingly capable of solving mathematical quantitative reasoning problems. However, they still make unjustified logical and computational…
Assurance cases are often required to certify critical systems. The use of formal methods in assurance can improve automation, increase confidence, and overcome errant reasoning. However, assurance cases can never be fully formalised, as…
In a recent paper, new theorems linking apparently unrelated mathematical objects (event structures from concurrency theory and full graphs arising in computational biology) were discovered by cross-site data mining on huge databases, and…
Isabelle is an interactive theorem prover that supports a variety of logics. It represents rules as propositions (not as functions) and builds proofs by combining rules. These operations constitute a meta-logic (or `logical framework') in…
Searching for mathematical results remains difficult: most existing tools retrieve entire papers, while mathematicians and theorem-proving agents often seek a specific theorem, lemma, or proposition that answers a query. While semantic…
Unstructured model editing aims to update models with real-world text, yet existing methods often memorize text holistically without reliable fine-grained fact access. To address this, we propose FABLE, a hierarchical framework that…
An interactive theorem prover, Isabelle, is under development. In LCF, each inference rule is represented by one function for forwards proof and another (a tactic) for backwards proof. In Isabelle, each inference rule is represented by a…
Isabelle is a generic theorem prover with a fragment of higher-order logic as a metalogic for defining object logics. Isabelle also provides proof terms. We formalize this metalogic and the language of proof terms in Isabelle/HOL, define an…