XML-izing Mizar: Making Semantic Processing and Presentation of MML Easy
Since version 7.2 the Mizar system produces quite detailed XML-based semantic description of Mizar articles during their verification. This format is now used natively for most of the processing done by Mizar, e.g., also for the whole Mizar internal database. The main motivation for switching to this XML-based representation is to make semantic communication with Mizar and presentation of the MML more accessible to a variety of external tools and systems. This article briefly describes this format and its current implementation, and shows examples of its usage. These examples include presentation of linked Mizar articles in modern XML-capable browsers like Mozilla, authoring assistance in the Mizar mode for Emacs, and experiments with XML-based querying languages like XQuery over the Mizar Mathematical Library loaded into a native XML databases like eXist. This work makes the currently largest repository of formal mathematics available to many kinds of presentational, data-mining, and automated reasoning applications and experiments, and the goal of this article is also to encourage, facilitate and provide recipes for the development of such applications.
KeywordsAutomate Reasoning External Tool Proof Check Mizar Mathematical Library Mizar Processing
Unable to display preview. Download preview PDF.
- [CCRR99]Carlson, A.J., Cumby, C.M., Rosen, J.L., Roth, D.: Snow user’s guide. Technical Report UIUC-DCS-R-99-210, UIUC (1999)Google Scholar
- [Jas34]Jaskowski, S.: On the rules of suppositions. Studia Logica 1 (1934)Google Scholar
- [McC94]McCune, W.W.: Otter 3.0 reference manual and guide. Technical Report ANL-94/6, Argonne National Laboratory, Argonne, Illinois (1994)Google Scholar
- [MR04]Matuszewski, R., Rudnicki, P.: Mizar: the first 30 years. In: Bancerek, G. (ed.) MKM Workshop on 30 Years of Mizar (2004)Google Scholar
- [RSV01]Ramakrishnan, I.V., Sekar, R., Voronkov, A.: Handbook of Automated Reasoning, chapter Term Indexing, pp. 1853–1964. Elsevier/MIT Press (2001)Google Scholar
- [Rud92]Rudnicki, P.: An overview of the Mizar project. In: 1992 Workshop on Types for Proofs and Programs, Chalmers University of Technology, Bastad, pp. 311–332 (1992)Google Scholar
- [Urb05a]Urban, J.: MizarMode - an integrated proof assistance tool for the Mizar way of formalizing mathematics. Journal of Applied Logic (2005), forthcoming, available online at http://ktiml.mff.cuni.cz/~urban/mizmode.ps
- [Urb05b]Urban, J.: MoMM - fast interreduction and retrieval in large libraries of formalized mathematics. International Journal on Artificial Intelligence Tools (2005), forthcoming, available online at http://ktiml.mff.cuni.cz/~urban/MoMM/momm.ps