A Comparison of Mizar and Isar
Journal of Automated Reasoning
CADE-18 Proceedings of the 18th International Conference on Automated Deduction
Journal of Functional Programming
A Refinement of de Bruijn's Formal Language of Mathematics
Journal of Logic, Language and Information
TYPES'02 Proceedings of the 2002 international conference on Types for proofs and programs
PlatΩ: A Mediator between Text-Editors and Proof Assistance Systems
Electronic Notes in Theoretical Computer Science (ENTCS)
Formal Representation of Mathematics in a Dependently Typed Set Theory
Calculemus '07 / MKM '07 Proceedings of the 14th symposium on Towards Mechanized Mathematical Assistants: 6th International Conference
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
Recent developments in mega's proof search programming language
ACM Communications in Computer Algebra
Verifying and invalidating textbook proofs using scunak
MKM'06 Proceedings of the 5th international conference on Mathematical Knowledge Management
A tactic language for declarative proofs
ITP'10 Proceedings of the First international conference on Interactive Theorem Proving
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Unlike computer algebra systems, automated theorem provers have not yet achieved considerable recognition and relevance in mathematical practice. A significant shortcoming of mathematical proof assistance systems is that they require the fully formal representation of mathematical content, whereas in mathematical practice an informal, natural-language-like representation where obvious parts are omitted is common. We aim to support mathematical paper writing by integrating a scientific text editor and mathematical assistance systems such that mathematical derivations authored by human beings in a mathematical document can be automatically checked. To this end, we first define a calculus-independent representation language for formal mathematics that allows for underspecified parts. Then we provide two systems of rules that check if a proof is correct and at an acceptable level of granularity. These checks are done by decomposing the proof into basic steps that are then passed on to proof assistance systems for formal verification. We illustrate our approach using an example textbook proof.