Abstract
Converting mathematical documents from a human-friendly natural language to a form that can be readily processed by computers is often a tedious, manual task. Translating between varied computerised forms is also a difficult problem. MathLang, a system of methods and representations for computerising mathematics, tries to make these tasks more tractable by breaking the translation down into manageable portions. This paper presents a method for creating rules to translate documents from MathLang’s internal representation of mathematics to documents in the language of the Isabelle proof assistant. It includes a set of example rules applicable for a particular document. The resulting documents are not completely verifiable by Isabelle, but they represent a point to which a mathematician may take a document without the involvement of an Isabelle expert.
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Kamareddine, F., Lamar, R., Maarek, M., Wells, J.B.: Restoring natural language as a computerised mathematics input method. In: MKM 2007 [20], pp. 280–295 (2007)
Kamareddine, F., Maarek, M., Wells, J.B.: Toward an object-oriented structure for mathematical text. In: Kohlhase, M. (ed.) MKM 2005. LNCS, vol. 3863, pp. 217–233. Springer, Heidelberg (2006)
Kamareddine, F., Maarek, M., Retel, K., Wells, J.B.: Narrative structure of mathematical texts. In: MKM 2007 [20], pp. 296–311 (2007)
Rudnicki, P.: An overview of the Mizar project. In: Proceedings of the 1992 Workshop on Types for Proofs and Programs (1992)
Buchberger, B., Crǎciun, A., Jebelean, T., Kovács, L., Kutsia, T., Nakagawa, K., Piroi, F., Popov, N., Robu, J., Rosenkranz, M., Windsteiger, W.: Theorema: Towards Computer-Aided Mathematical Theory Exploration. Journal of Applied Logic, 470–504 (2006)
Nipkow, T., Paulson, L.C., Wenzel, M.T.: Isabelle/HOL. LNCS, vol. 2283. Springer, Heidelberg (2002)
Wenzel, M.T.: Isar – a generic interpretative approach to readable formal proof documents. In: Bertot, Y., Dowek, G., Hirschowitz, A., Paulin, C., Théry, L. (eds.) TPHOLs 1999. LNCS, vol. 1690, pp. 167–184. Springer, Heidelberg (1999)
Humayoun, M.: Software specifications and mathematical proofs in natural languages. Poster in Journées scientifiques du cluster, ISLE Rhône-Alpes, Domaine universitaire, Grenoble, France (2008)
Ranta, A.: Grammatical framework: A type-theoretical grammar formalism. Journal of Functional Programming 14(2), 145–189 (2004)
Heath, T.L.: The 13 Books of Euclid’s Elements. Dover, New York (1956); in 3 volumes. Sir Thomas Heath originally published this in 1908
Landau, E.: Grundlagen der Analysis. Chelsea (1930)
LogiCal Project, INRIA, Rocquencourt, France. The Coq Proof Assistant Reference Manual – Version 8.0 (June 2004), ftp://ftp.inria.fr/INRIA/coq/V8.0/doc/
Grue, K.: The layers of Logiweb. In: Towards Mechanized Mathematical Assistants (Calculemus 2007 and MKM 2007 Joint Proceedings), pp. 250–264 (2007)
Knuth, D.E., Levy, S.: The CWEB System of Structured Documentation: Version 3.0. Addison-Wesley/ Longman Publishing Co., Inc., Boston (1994)
Gallian, J.A.: Contemporary Abstract Algebra, 5th edn. Houghton Mifflin Company (2002)
Kamareddine, F., Wells, J.B.: Computerizing mathematical text with MathLang. In: Ayala-Rincon, M., Heusler (eds.) Proc. Second Workshop on Logical and Semantic Frameworks, with Applications, Ouro Preto, Minas Gerais, Brazil, pp. 5–30. Elsevier, Amsterdam (2008); The LSFA 2007 (post-event) proceedings is published as vol. 205 (2008-04-06) Elec. Notes in Theoret. Comp. Sci.
Maarek, M.: Mathematical Documents Faithfully Computerised: the Grammatical and Text & Symbol Aspects of the MathLang Framework. PhD thesis, Heriot-Watt University, Edinburgh, Scotland (June 2007)
Clark, J., DeRose, S.: XML Path Language (XPath) Version 1.0. W3C (World Wide Web Consortium) (1999), http://www.w3.org/TR/xpath
Chaieb, A.: Semiring normalization and Groebner bases. File Groebner_Basis.thy, in Isabelle2007 distribution (October 2007)
Kauers, M., Kerber, M., Miner, R., Windsteiger, W. (eds.): MKM/Calculemus 2007. LNCS (LNAI), vol. 4573. Springer, Heidelberg (2007)
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Lamar, R., Kamareddine, F., Wells, J.B. (2009). MathLang Translation to Isabelle Syntax. In: Carette, J., Dixon, L., Coen, C.S., Watt, S.M. (eds) Intelligent Computer Mathematics. CICM 2009. Lecture Notes in Computer Science(), vol 5625. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02614-0_30
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DOI: https://doi.org/10.1007/978-3-642-02614-0_30
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