Abstract
We present C-CoRN, the Constructive Coq Repository at Nijmegen. It consists of a mathematical library of constructive algebra and analysis formalized in the theorem prover Coq. We explain the structure and the contents of the library and we discuss the motivation and some (possible) applications of such a library.
The development of C-CoRN is part of a larger goal to design a computer system where ‘a mathematician can do mathematics’, which covers the activities of defining, computing and proving. An important proviso for such a system to be useful and attractive is the availability of a large structured library of mathematical results that people can consult and build on. C-CoRN wants to provide such a library, but it can also be seen as a case study in developing such a library of formalized mathematics and deriving its requirements. As the actual development of a library is very much a technical activity, the work on C-CoRN is tightly bound to the proof assistant Coq.
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References
Asperti, A., Buchberger, B., Davenport, J.H. (eds.): MKM 2003. LNCS, vol. 2594. Springer, Heidelberg (2003)
Asperti, A., Wegner, B.: MOWGLI – A New Approach for the Content Description in Digital Documents. In: Proc. of the 9th Intl. Conference on Electronic Resources and the Social Role of Libraries in the Future, vol. 1, Autonomous Republic of Crimea, Ukraine (2002)
Bailey, A.: The machine-checked literate formalisation of algebra in type theory, PhD thesis. University of Manchester (1998)
Bishop, E.: Foundations of Constructive Analysis. McGraw-Hill, New York (1967)
Buchberger, B., et al.: An Overview on the Theorema project. In: Kuechlin, W. (ed.) Proceedings of ISSAC 1997, Maui, Hawaii. ACM Press, New York (1997)
Constructive Coq Repository at Nijmegen, http://c-corn.cs.kun.nl/
Cairns, P., Gow, J.: A theoretical analysis of hierarchical proofs, In: Asperti, et al., [1], pp. 175–187
The CALCULEMUS Initiative, http://www.calculemus.net/
Callaghan, P., Luo, Z., McKinna, J., Pollack, R. (eds.): TYPES 2000. LNCS, vol. 2277. Springer, Heidelberg (2002)
Caprotti, O., Carlisle, D.P., Cohen, A.M.: The OpenMath Standard, version 1.1 (2002), http://www.openmath.org/cocoon/openmath/standard/
Cohen, A., Cuypers, H., Sterk, H.: Algebra Interactive! Springer, Heidelberg (1999)
Constable, R.L., et al.: Implementing Mathematics with the Nuprl Development System. Prentice-Hall, NJ (1986)
The Coq Development Team, The Coq Proof Assistant Reference Manual, Version 7.2 (January 2002), http://pauillac.inria.fr/coq/doc/main.html
Cruz-Filipe, L.: Formalizing real calculus in Coq, Technical report, NASA, Hampton, VA (2002)
Cruz-Filipe, L.: A constructive formalization of the Fundamental Theorem of Calculus. In: Geuvers, Wiedijk [20], pp. 108–126
Cruz-Filipe, L., Spitters, B.: Program extraction from large proof developments. In: Basin, D., Wolff, B. (eds.) TPHOLs 2003. LNCS, vol. 2758, pp. 205–220. Springer, Heidelberg (2003)
Filliâtre, J.-C.: CoqDoc: a Documentation Tool for Coq, Version 1.05, The Coq Development Team (September 2003), http://www.lri.fr/~filliatr/coqdoc/
Geuvers, H., Niqui, M.: Constructive reals in Coq: Axioms and categoricity. In: [9], pp. 79–95
Geuvers, H., Pollack, R., Wiedijk, F., Zwanenburg, J.: The algebraic hierarchy of the FTA Project. Journal of Symbolic Computation, pp. 271–286 (2002)
Geuvers, H., Wiedijk, F. (eds.): Types for Proofs and Programs. LNCS, vol. 2464. Springer, Heidelberg (2003)
Geuvers, H., Wiedijk, F., Zwanenburg, J.: Equational reasoning via partial reflection. In: Aagaard, M.D., Harrison, J. (eds.) TPHOLs 2000. LNCS, vol. 1869, pp. 162–178. Springer, Heidelberg (2000)
Geuvers, H., Wiedijk, F., Zwanenburg, J.: A constructive proof of the Fundamental Theorem of Algebra without using the rationals. In: [9], pp. 96–111
Guidi, F., Schena, I.: A query language for a metadata framework about mathematical resources. In: Asperti, et al., [1], pp. 105–118
Harrison, J.: The HOL Light manual (1.1) (2000), http://www.cl.cam.ac.uk/users/jrh/hol-light/manual-1.1.ps.gz
Kohlhase, M.: OMDoc: Towards an Internet Standard for the Administration, Distribution and Teaching of Mathematical Knowledge. In: Proceedings of Artificial Intelligence and Symbolic Computation. LNCS (LNAI). Springer, Heidelberg (2000)
Letouzey, P.: A new extraction for Coq. In: Geuvers, Wiedijk [20], pp. 200–219
Mayero, M.: Formalisation et automatisation de preuves en analyses réelle et numérique, PhD thesis, Université Paris VI (December 2001)
Muzalewski, M.: An Outline of PC Mizar, Fond. Philippe le Hodey, Brussels (1993), http://www.cs.kun.nl/~freek/mizar/mizarmanual.ps.gz
Naumov, P., Stehr, M.-O., Meseguer, J.: The HOL/NuPRL Proof Translator: A Practical Approach to Formal Interoperability. In: Boulton, R.J., Jackson, P.B. (eds.) TPHOLs 2001. LNCS, vol. 2152, pp. 329–345. Springer, Heidelberg (2001)
Nipkow, T., Paulson, L.C., Wenzel, M.T.: Isabelle/HOL. LNCS, vol. 2283. Springer, Heidelberg (2002)
Shankar, N., Owre, S., Rushby, J.M., Stringer-Calvert, D.W.J.: The PVS System Guide, SRI International (December 2001), http://pvs.csl.sri.com/
Siekmann, J.: Proof Development with Omega. In: Voronkov, A. (ed.) CADE 2002. LNCS (LNAI), vol. 2392, p. 144. Springer, Heidelberg (2002)
Slind, K.: HOL98 Draft User’s Manual, Cambridge UCL (January 1999), http://hol.sourceforge.net/
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Cruz-Filipe, L., Geuvers, H., Wiedijk, F. (2004). C-CoRN, the Constructive Coq Repository at Nijmegen. In: Asperti, A., Bancerek, G., Trybulec, A. (eds) Mathematical Knowledge Management. MKM 2004. Lecture Notes in Computer Science, vol 3119. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27818-4_7
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DOI: https://doi.org/10.1007/978-3-540-27818-4_7
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