Information and Randomness: An Algorithmic Perspective
Information and Randomness: An Algorithmic Perspective
Analogy in Inductive Theorem Proving
Journal of Automated Reasoning
Proof Development with Omega-MEGA: sqrt(2) Is Irrational
LPAR '02 Proceedings of the 9th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
Proof General: A Generic Tool for Proof Development
TACAS '00 Proceedings of the 6th International Conference on Tools and Algorithms for Construction and Analysis of Systems: Held as Part of the European Joint Conferences on the Theory and Practice of Software, ETAPS 2000
Isar - A Generic Interpretative Approach to Readable Formal Proof Documents
TPHOLs '99 Proceedings of the 12th International Conference on Theorem Proving in Higher Order Logics
Interactive Theorem Proving and Program Development
Interactive Theorem Proving and Program Development
Random Testing in Isabelle/HOL
SEFM '04 Proceedings of the Software Engineering and Formal Methods, Second International Conference
OMDoc -- An Open Markup Format for Mathematical Documents [version 1.2]: Foreword by Alan Bundy (Lecture Notes in Computer Science)
Calculemus '07 / MKM '07 Proceedings of the 14th symposium on Towards Mechanized Mathematical Assistants: 6th International Conference
Bounded Model Generation for Isabelle/HOL
Electronic Notes in Theoretical Computer Science (ENTCS)
as Authoring Tool for Formal Developments
Electronic Notes in Theoretical Computer Science (ENTCS)
SWiM - a semantic wiki for mathematical knowledge management
ESWC'08 Proceedings of the 5th European semantic web conference on The semantic web: research and applications
A generic modular data structure for proof attempts alternating on ideas and granularity
MKM'05 Proceedings of the 4th international conference on Mathematical Knowledge Management
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Hilbert's concept of formal proof is an ideal of rigour for mathematics which has important applications in mathematical logic, but seems irrelevant for the practice of mathematics. The advent, in the last twenty years, of proof assistants was followed by an impressive record of deep mathematical theorems formally proved. Formal proof is practically achievable. With formal proof, correctness reaches a standard that no pen-and-paper proof can match, but an essential component of mathematics -- the insight and understanding -- seems to be in short supply. So, what makes a proof understandable? To answer this question we first suggest a list of symptoms of understanding. We then propose a vision of an environment in which users can write and check formal proofs as well as query them with reference to the symptoms of understanding. In this way, the environment reconciles the main features of proof: correctness and understanding.