Knowledge-based proof planning
Artificial Intelligence
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
CADE-18 Proceedings of the 18th International Conference on Automated Deduction
Reconstruction Proofs at the Assertion Level
CADE-12 Proceedings of the 12th International Conference on Automated Deduction
CADE-13 Proceedings of the 13th International Conference on Automated Deduction: Automated Deduction
System Description: TPS: A Theorem Proving System for Type Theory
CADE-17 Proceedings of the 17th International Conference on Automated Deduction
Interactive Theorem Proving and Program Development
Interactive Theorem Proving and Program Development
Dialog-driven adaptation of explanations of proofs
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 2
Interactive Theorem Proving with Tasks
Electronic Notes in Theoretical Computer Science (ENTCS)
PlatΩ: A Mediator between Text-Editors and Proof Assistance Systems
Electronic Notes in Theoretical Computer Science (ENTCS)
Authoring Verified Documents by Interactive Proof Construction and Verification in Text-Editors
Proceedings of the 9th AISC international conference, the 15th Calculemas symposium, and the 7th international MKM conference on Intelligent Computer Mathematics
Verification of Proof Steps for Tutoring Mathematical Proofs
Proceedings of the 2007 conference on Artificial Intelligence in Education: Building Technology Rich Learning Contexts That Work
Formal Proof: Reconciling Correctness and Understanding
Calculemus '09/MKM '09 Proceedings of the 16th Symposium, 8th International Conference. Held as Part of CICM '09 on Intelligent Computer Mathematics
Granularity-Adaptive Proof Presentation
Proceedings of the 2009 conference on Artificial Intelligence in Education: Building Learning Systems that Care: From Knowledge Representation to Affective Modelling
Presenting proofs with adapted granularity
KI'09 Proceedings of the 32nd annual German conference on Advances in artificial intelligence
A formal correspondence between OMDoc with alternative proofs and the λµµ-calculus
MKM'06 Proceedings of the 5th international conference on Mathematical Knowledge Management
Synthesizing proof planning methods and Ω-ants agents from mathematical knowledge
MKM'06 Proceedings of the 5th international conference on Mathematical Knowledge Management
lim+, δ+, and Non-Permutability of β-Steps
Journal of Symbolic Computation
| Hi-index | 0.00 |
A practically useful mathematical assistant system requires the sophisticated combination of interaction and automation. Central in such a system is the proof data structure, which has to maintain the current proof state and which has to allow the flexible interplay of various components including the human user. We describe a parameterized proof data structure for the management of proofs, which includes our experience with the development of two proof assistants. It supports and bridges the gap between abstract level proof explanation and low-level proof verification. The proof data structure enables, in particular, the flexible handling of lemmas, the maintenance of different proof alternatives, and the representation of different granularities of proof attempts.