Implementing mathematics with the Nuprl proof development system
Implementing mathematics with the Nuprl proof development system
A generic approach to building user interfaces for theorem provers
Journal of Symbolic Computation - Special issue graphical user interfaces and protocols
Verbalization of high-level formal proofs
AAAI '99/IAAI '99 Proceedings of the sixteenth national conference on Artificial intelligence and the eleventh Innovative applications of artificial intelligence conference innovative applications of artificial intelligence
A Natural Language Explanation for Formal Proofs
LACL '96 Selected papers from the First International Conference on Logical Aspects of Computational Linguistics
Mathematical Vernacular and Conceptual Well-Formedness in Mathematical Language
LACL '97 Selected papers from the Second International Conference on Logical Aspects of Computational Linguistics
TLCA '95 Proceedings of the Second International Conference on Typed Lambda Calculi and Applications
Connecting Proof Checkers and Computer Algebra Using OpenMath
TPHOLs '99 Proceedings of the 12th International Conference on Theorem Proving in Higher Order Logics
Specification and Integration of Theorem Provers and Computer Algebra Systems
AISC '98 Proceedings of the International Conference on Artificial Intelligence and Symbolic Computation
Information and Computation
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There is a wealth of interactive mathematics available on the web. Examples range from animated geometry to computing the nth digit in the expansion of π. However, proofs seem to remain static and at most they provide interaction in the form of links to definitions and other proofs. In this paper, we want to show how interactivity can be included in proofs themselves by making them executable, human-readable, and yet formal. The basic ingredients are formal proof-objects, OpenMath-related languages, and the latest eXtensible Markup Language (XML) technology. We exhibit, by an example taken from a formal development in number theory, the final product of which we believe to be a truly interactive mathematical document.