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Literate Proving: Presenting and Documenting Formal Proofs

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Mathematical Knowledge Management (MKM 2005)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3863))

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Abstract

Literate proving is the analogue for literate programming in the mathematical realm. That is, the goal of literate proving is for humans to produce clear expositions of formal mathematics that could even be enjoyable for people to read whilst remaining faithful representations of the actual proofs. This paper describes maze, a generic literate proving system. Authors markup formal proof files, such as Mizar files, with arbitary XML and use maze to obtain the selected extracts and transform them for presentation, e.g. as LATEX. To aid its use, maze has built in transformations that include pretty printing and proof sketching for inclusion in LATEX documents. These transformations challenge the concept of faithfulness in literate proving but it is argued that this should be a distinguishing feature of literate proving from literate programming.

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References

  1. Asperti, A., Buchberger, B., Davenport, J.H. (eds.): MKM 2003. LNCS, vol. 2594. Springer, Heidelberg (2003)

    Google Scholar 

  2. Asperti, A., et al.: Mathematical Knowledge Management in HELM. Annals of Mathematics and Artificial Intelligence 38(1), 27–46 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  3. Bertot, Y., Castéran, P.: Coq’Art: The Calculus of Inductive Constructions. Springer, Heidelberg (2004), See also http://coq.inria.fr/

  4. Cairns, P., Gow, J.: A theoretical analysis of hierarchical proofs. In: [1], pp. 175–187 (2003)

    Google Scholar 

  5. Cairns, P., Gow, J.: Using and parsing Mizar. Electronic Notes in Theoretical Computer Sci. 93, 60–69 (2004)

    Article  Google Scholar 

  6. Cairns, P., Gow, J., Collins, P.: On dynamically presenting a topology course. Annals of Mathematics and Artificial Intelligence 38, 91–104 (2003)

    Article  MATH  Google Scholar 

  7. Cruz-Filipe, L., Geuvers, H., Wiedijk, F.: C-CoRN, the constructive Coq repository at Nijmegen. In: Asperti, A., Bancerek, G., Trybulec, A. (eds.) MKM 2004. LNCS, vol. 3119, pp. 88–103. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  8. Knuth, D.E.: Literate programming. The Computer Journal 27, 97–111 (1984)

    Article  MATH  Google Scholar 

  9. McConnell, S.: Code Complete: A practical handbook of software construction. Microsoft Press, Redmond (1993)

    Google Scholar 

  10. The Mizar Mathematical Library, http://mizar.org

  11. Paulson, L.: Isabelle: a generic theorem prover. Springer, Heidelberg (1994)

    MATH  Google Scholar 

  12. Raffalli, C., David, R.: Computer Assisted Teaching in Mathematics. In: Proc. Workshop on 35 Years of Automath, Edinburgh (2002)

    Google Scholar 

  13. Thimbleby, H.: Experiences of ‘literate programming’ using cweb (a variant of Knuth’s WEB). The Computer Journal 29(3), 201–211 (1986)

    Article  MATH  Google Scholar 

  14. Thimbleby, H.: Explaining code for publication. Software — Practice and Experience 33, 975–1001 (2003)

    Article  Google Scholar 

  15. Wiedijk, F.: Irrationality of e. Journal of Formalized Mathematics 11(42) (1999)

    Google Scholar 

  16. Wiedijk, F. (2000), The De Bruijn Factor, Poster at TPHOL (2000)

    Google Scholar 

  17. Wiedijk, F.: Formal Proof Sketches. In: Berardi, S., Coppo, M., Damiani, F. (eds.) TYPES 2003. LNCS, vol. 3085, pp. 378–393. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  18. Wysocki, M., Darmochwał, A.: Subsets of topological spaces. Journal of Formalized Mathematics 1(28) (1989)

    Google Scholar 

  19. Zinn, C.: Understanding Informal Mathematical Discourse. PhD Thesis, Arbeitsberichter des Instituts für Informatik, Friedrich-Alexander-Universität, 37(4) (2004)

    Google Scholar 

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© 2006 Springer-Verlag Berlin Heidelberg

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Cairns, P., Gow, J. (2006). Literate Proving: Presenting and Documenting Formal Proofs. In: Kohlhase, M. (eds) Mathematical Knowledge Management. MKM 2005. Lecture Notes in Computer Science(), vol 3863. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11618027_11

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  • DOI: https://doi.org/10.1007/11618027_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-31430-1

  • Online ISBN: 978-3-540-31431-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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