Abstract
Methods for computerised mathematics have found little appeal among mathematicians because they call for additional skills which are not available to the typical mathematician. We herein propose to reconcile computerised mathematics to mathematicians by restoring natural language as the primary medium for mathematical authoring. Our method associates portions of text with grammatical argumentation roles and computerises the informal mathematical style of the mathematician. Typical abbreviations like the aggregation of equations a = b > c, are not usually accepted as input to computerised languages. We propose specific annotations to explicate the morphology of such natural language style, to accept input in this style, and to expand this input in the computer to obtain the intended representation (i.e., a = b and b > c). We have named this method syntax souring in contrast to the usual syntax sugaring. All results have been implemented in a prototype editor developed on top of \({\rm\kern-.15em T\kern-.1667em\lower.7ex\hbox{E}\kern-.125emX}\) \(_{{\rm {\sc MACS}}}\) as a GUI for the core grammatical aspect of MathLang, a framework developed by the ULTRA group to computerise and formalise mathematics.
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References
Nipkow, T., Paulson, L.C., Wenzel, M.: Isabelle/HOL. LNCS, vol. 2283. Springer, Heidelberg (2002)
LogiCal Project, INRIA Rocquencourt, France: The Coq Proof Assistant Reference Manual – Version 8.0 (2004), ftp://ftp.inria.fr/INRIA/coq/V8.0/doc/
Audebaud, P., Rideau, L.: TeXmacs as authoring tool for publication and dissemination of formal developments. ENTCS, Rome, vol. 103, pp. 27–48 (2003)
Autexier, S., Benzmüller, C., Fiedler, A., Lesourd, H.: Integrating proof assistants as reasoning and verification tools into a scientific WYSIWIG (ed.) In: User Interfaces for Theorem Provers (UITP 2005) [Workshop], Edinburgh (2005)
Mamane, L.E., Geuvers, H.: A document-oriented Coq plugin for TeXmacs. In: Mathematical User-Interfaces Workshop 2006 [Workshop], Workingham (2006)
Rudnicki, P.: An overview of the Mizar project. In: Proceedings of the 1992 Workshop on Types for Proofs and Programs (1992)
Wenzel, M.: 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)
Autexier, S., Sacerdoti Coen, C.: A formal correspondence between OMDoc with alternative proofs and the \(\bar\lambda\mu\tilde\mu\)-calculus. [24],pp. 67–81
Brown, C.E.: Verifying and invalidating textbook proofs using Scunak. [24], pp. 110–123
Kohlhase, M.: OMDoc – An Open Markup Format for Mathematical Documents [version 1.2]. LNCS (LNAI), vol. 4180. Springer, Heidelberg (2006)
Asperti, A., Padovani, L., Sacerdoti Coen, C., Schena, I.: HELM and the semantic math-web. In: Boulton, R.J., Jackson, P.B. (eds.) TPHOLs 2001. LNCS, vol. 2152, pp. 59–74. Springer, Heidelberg (2001)
Kamareddine, F., Maarek, M., Wells, J.B.: Flexible encoding of mathematics on the computer. In: Asperti, A., Bancerek, G., Trybulec, A. (eds.) MKM 2004. LNCS, vol. 3119, pp. 160–174. Springer, Heidelberg (2004)
Padovani, L., Zacchiroli, S.: From notation to semantics: There and back again. [24], pp. 194–207
Kerber, M., Pollet, M.: A tough nut for mathematical knowledge management. In: Kohlhase, M. (ed.) MKM 2005. LNCS (LNAI), vol. 3863, pp. 81–95. Springer, Heidelberg (2006)
Pollet, M., Sorge, V., Kerber, M.: Intuitive and formal representations: The case of matrices. In: Asperti, A., Bancerek, G., Trybulec, A. (eds.) MKM 2004. LNCS, vol. 3119, pp. 19–21. Springer, Heidelberg (2004)
Gallian, J.A.: Contemporary Abstract Algebra. 5th edn. Houghton Mifflin Company (2002)
Kamareddine, F., Wells, J.: MathLang: A new language for mathematics, logic, and proof checking. A research proposal to UK funding body (2001)
Kamareddine, F., Maarek, M., Wells, J.B.: Toward an object-oriented structure for mathematical text. In: Kohlhase, M. (ed.) MKM 2005. LNCS (LNAI), vol. 3863, pp. 217–233. Springer, Heidelberg (2006)
de Bruijn, N.G.: Checking mathematics with computer assistance. Notices of the American Mathematical Society 38, 8–15 (1991)
Kanahori, T., Sexton, A., Sorge, V., Suzuki, M.: Capturing abstract matrices from paper. [24], pp. 124–138
Raja, A., Rayner, M., Sexton, A., Sorge, V.: Towards a parser for mathematical formula recognition. [24], pp. 139–151
Knuth, D.E.: Literate programming. The. Computer Journal 27, 97–111 (1984)
Farrell, P.: Grammatical Relations. Oxford Surveys in Syntax and Morphology. Oxford Linguistics (2005)
Borwein, J.M., Farmer, W.M. (eds.): MKM 2006. LNCS (LNAI), vol. 4108. Springer, Heidelberg (2006)
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Kamareddine, F., Lamar, R., Maarek, M., Wells, J.B. (2007). Restoring Natural Language as a Computerised Mathematics Input Method. In: Kauers, M., Kerber, M., Miner, R., Windsteiger, W. (eds) Towards Mechanized Mathematical Assistants. MKM Calculemus 2007 2007. Lecture Notes in Computer Science(), vol 4573. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73086-6_23
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