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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…
We present a trustworthy connection between the Leon verification system and the Isabelle proof assistant. Leon is a system for verifying functional Scala programs. It uses a variety of automated theorem provers (ATPs) to check verification…
Proof assistants, such as Isabelle/HOL, offer tools to facilitate inductive theorem proving. Isabelle experts know how to use these tools effectively; however, they did not have a systematic way to encode their expertise. To address this…
Foundational verification considers the functional correctness of programming languages with formalized semantics and uses proof assistants (e.g., Coq, Isabelle) to certify proofs. The need for verifying complex programs compels it to…
We present megas, a new software tool that improves the simulation of the Micromegas gas detectors. Our tool offers the possibility to configure multiple arrangements with one or more layers of MM detectors. A series of simple commands can…
We present Prover Agent, a novel AI agent for automated theorem proving that integrates large language models (LLMs) with a formal proof assistant, Lean. Prover Agent coordinates an informal reasoning LLM, a formal prover model, and…
A logic for specification and verification is derived from the axioms of Zermelo-Fraenkel set theory. The proofs are performed using the proof assistant Isabelle. Isabelle is generic, supporting several different logics. Isabelle has the…
Steganalysis as a method to detect whether image contains se-cret message, is a crucial study avoiding the imperils from abus-ing steganography. The point of steganalysis is to detect the weak embedding signals which is hardly learned by…
The Mid-infrared ELT Imager and Spectrograph (METIS) is a first-generation instrument for the Extremely Large Telescope (ELT), Europe's next-generation 39 m ground-based telescope for optical and infrared wavelengths. METIS will offer…
Since the first termination competition in 2004 it is of great interest, whether a proof that has been automatically generated by a termination tool, is indeed correct. The increasing number of termination proving techniques as well as the…
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…
The material presented in this paper contributes to establishing a basis deemed essential for substantial progress in Automated Deduction. It identifies and studies global features in selected problems and their proofs which offer the…
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,…
Large formal mathematical libraries consist of millions of atomic inference steps that give rise to a corresponding number of proved statements (lemmas). Analogously to the informal mathematical practice, only a tiny fraction of such…
This paper explores verification of constituent systems within the context of the Symphony tool platform for Systems of Systems (SoS). Our SoS modelling language, CML, supports various contractual specification elements, such as state…
Fully automated verification of large-scale software and hardware systems is arguably the holy grail of formal methods. Large language models (LLMs) have recently demonstrated their potential for enhancing the degree of automation in formal…
In logical reasoning, it is often the case that only some of a collection of assumptions are needed to reach a conclusion. A strengthening lemma is an assertion that a given conclusion is independent in this sense of a particular…
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 a semantic framework for the deductive verification of hybrid systems with Isabelle/HOL. It supports reasoning about the temporal evolutions of hybrid programs in the style of differential dynamic logic modelled by flows or…
This paper presents meta-logical investigations based on category theory using the proof assistant Isabelle/HOL. We demonstrate the potential of a free logic based shallow semantic embedding of category theory by providing a formalization…