Related papers: Comparison of Two Theorem Provers: Isabelle/HOL an…
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,…
Mechanized theorem proving is becoming the basis of reliable systems programming and rigorous mathematics. Despite decades of progress in proof automation, writing mechanized proofs still requires engineers' expertise and remains labor…
Inductive theorem proving is an important long-standing challenge in computer science. In this extended abstract, we first summarize the recent developments of proof by induction for Isabelle/HOL. Then, we propose united reasoning, a novel…
Proof assistants are important tools for teaching logic. We support this claim by discussing three formalizations in Isabelle/HOL used in a recent course on automated reasoning. The first is a formalization of System W (a system of…
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…
G\"odel's ontological proof has been analysed for the first-time with an unprecedent degree of detail and formality with the help of higher-order theorem provers. The following has been done (and in this order): A detailed natural deduction…
The Isabelle/PIDE platform addresses the question whether proof assistants of the LCF family are suitable as technological basis for educational tools. The traditionally strong logical foundations of systems like HOL, Coq, or Isabelle have…
We propose a synthesis of the two proof styles of interactive theorem proving: the procedural style (where proofs are scripts of commands, like in Coq) and the declarative style (where proofs are texts in a controlled natural language, like…
We present an approach for testing student learning outcomes in a course on automated reasoning using the Isabelle proof assistant. The approach allows us to test both general understanding of formal proofs in various logical proof systems…
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…
Mechanical reasoning is a key area of research that lies at the crossroads of mathematical logic and artificial intelligence. The main aim to develop mechanical reasoning systems (also known as theorem provers) was to enable mathematicians…
How difficult are interactive theorem provers to use? We respond by reviewing the formalization of Hilbert's tenth problem in Isabelle/HOL carried out by an undergraduate research group at Jacobs University Bremen. We argue that, as…
Theorem provers are important tools for people working in formal verification. There are a myriad of interactive systems available today, with varying features and approaches motivating their development. These design choices impact their…
This report describes three particular technological advances in formal proofs. The HOL Light proof assistant will be used to illustrate the design of a highly reliable system. Today, proof assistants can verify large bodies of advanced…
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…
Mathematical theorems are human knowledge able to be accumulated in the form of symbolic representation, and proving theorems has been considered intelligent behavior. Based on the BHK interpretation and the Curry-Howard isomorphism, proof…
The growing complexity and diversity of models used in the engineering of dependable systems implies that a variety of formal methods, across differing abstractions, paradigms, and presentations, must be integrated. Such an integration…
This paper describes a formal theory of smooth vector fields, Lie groups and the Lie algebra of a Lie group in the theorem prover Isabelle. Lie groups are abstract structures that are composable, invertible and differentiable. They are…
Recently, a growing number of researchers have applied machine learning to assist users of interactive theorem provers. However, the expressive nature of underlying logics and esoteric structures of proof documents impede machine learning…
An Isabelle/HOL formalisation of G\"odel's two incompleteness theorems is presented. The work follows \'Swierczkowski's detailed proof of the theorems using hereditarily finite (HF) set theory. Avoiding the usual arithmetical encodings of…