Coquelicot: A User-Friendly Library of Real Analysis for Coq (original) (raw)

References

  1. Baccalauréat général, Série S, Mathématiques, Session 2013, June 2013 (2013). http://eduscol.education.fr/prep-exam/sujets/13MASCOMLR1.pdf
  2. Bertot, Y.: Proving the convergence of a sequence based on algebraic-geometric means to π (2013). http://www-sop.inria.fr/members/Yves.Bertot/proofs.html
  3. Bertot, Y., Castéran, P.: Interactive Theorem Proving and Program Development. Coq’Art: The Calculus of Inductive Constructions. Texts in Theoretical Computer Science. Springer, Berlin (2004)
  4. Besson, F.: Fast reflexive arithmetic tactics: the linear case and beyond. In: Proceedings of the International Workshop on Types for Proofs and Programs (TYPES’06), Nottingham, UK. Lecture Notes in Computer Science, vol. 4502, pp. 48–62 (2006)
  5. Boldo S., Clément F., Filliâtre J.-C., Mayero M., Melquiond G., Weis P.: Wave equation numerical resolution: a comprehensive mechanized proof of a C program. J. Autom. Reason. 50(4), 423–456 (2013)
    Article MATH Google Scholar
  6. Boldo, S., Lelay, C., Melquiond, G.: Improving real analysis in Coq: a user-friendly approach to integrals and derivatives. In: Hawblitzel, C., Miller, D. (eds.) Proceedings of the 2nd International Conference on Certified Programs and Proofs (CPP), Kyoto, Japan. Lecture Notes in Computer Science, vol. 7679, pp. 289–304 (2012)
  7. Boldo, S., Lelay, C., Melquiond, G.: Formalization of real analysis: a survey of proof assistants and libraries. Math. Struct. Comput. Sci. (2014, to be published). http://hal.inria.fr/hal-00806920
  8. Cohen, C.: Reasoning about big enough numbers in Coq. In: Proceedings of the 4th Coq Workshop, Princeton, NJ, USA (2012)
  9. Cruz-Filipe, L., Geuvers, H., Wiedijk, F.: C-CoRN: the constructive Coq repository at Nijmegen. In: Asperti, A., Bancerek, G., Trybulec, A. (eds.) Proceedings of the 3rd International Conference of Mathematical Knowledge Management (MKM). Lecture Notes in Computer Science, vol. 3119, pp. 88–103 (2004)
  10. Cruz-Filipe, L.: A constructive formalization of the fundamental theorem of calculus. In: Geuvers, H., Wiedijk, F. (eds.) Proceedings of the International Workshop on Types for Proofs and Programs (TYPES’02). Lecture Notes in Computer Science, vol. 2646, pp. 108–126. Springer, Berlin (2003)
  11. Daumas M., Lester D., Muñoz C.: Verified real number calculations: a library for interval arithmetic. IEEE Trans. Comput. 58(2), 226–237 (2009)
    Article MathSciNet Google Scholar
  12. Dutertre, B.: Elements of mathematical analysis in PVS. In: von Wright, J., Grundy, J., Harrison, J. (eds.) Proceedings of the 9th International Conference Theorem Proving in Higher Order Logics (TPHOLs). Lecture Notes in Computer Science, vol. 1125, pp. 141–156 (1996)
  13. Fleuriot, J.: On the mechanization of real analysis in Isabelle/HOL. In: Aagaard, M., Harrison, J. (eds.) Proceeding of the 13th International Conference of Theorem Proving in Higher Order Logics (TPHOLs). Lecture Notes in Computer Science, vol. 1869, pp. 145–161 (2000)
  14. Gamboa R., Kaufmann M.: Nonstandard analysis in ACL2. J. Autom. Reason. 27(4), 323–351 (2001)
    Article MATH MathSciNet Google Scholar
  15. Geuvers, H., Niqui, M.: Constructive reals in Coq: axioms and categoricity. In: Callaghan, P., Luo, Z., McKinna, J., Pollack, R. (eds.) Proceedings of the International Workshop on Types for Proofs and Programs (TYPES’00). Lecture Notes in Computer Science, vol. 2277, pp. 79–95 (2002)
  16. Harrison J.: Constructing the real numbers in HOL. Form. Methods Syst. Des. 5(1–2), 35–59 (1994)
    Article MATH Google Scholar
  17. Harrison, J.: HOL light: an overview. In: Berghofer, S., Nipkow, T., Urban, C., Wenzel, M. (eds.) Proceedings of the 22nd International Conference on Theorem Proving in Higher Order Logics (TPHOLs), Munich, Germany. Lecture Notes in Computer Science, vol. 5674, pp. 60–66 (2009)
  18. Harrison J.: The HOL light theory of Euclidean space. J. Autom. Reason. 50, 173–190 (2013)
    Article MATH Google Scholar
  19. Hölzl, J., Immler, F., Huffman, B.: Type classes and filters for mathematical analysis in Isabelle/HOL. In: Blazy, S., Paulin-Mohring, C., Pichardie, D. (eds) Proceedings of the 4th International Conference on Interactive Theorem Proving (ITP), Rennes, France. Lecture Notes in Computer Science, vol. 7998, pp. 279–294 (2013)
  20. Kaliszyk C., O’Connor R.: Computing with classical real numbers. J. Formaliz. Reason. 2(1), 27–39 (2009)
    MathSciNet Google Scholar
  21. Krebbers, R., Spitters, B.: Type classes for efficient exact real arithmetic in Coq. Log. Methods Comput. Sci. 9(1:1), 1–27 (2013)
  22. Lelay, C.: A new formalization of power series in Coq. In: 5th Coq Workshop, Rennes, France, July 2013, pp. 1–2 (2013). http://coq.inria.fr/coq-workshop/2013#Lelay
  23. Lelay, C., Melquiond, G.: Différentiabilité et intégrabilité en Coq. Application à la formule de d’Alembert. In: 23èmes Journées Francophones des Langages Applicatifs, Carnac, France, pp. 119–133 (2012)
  24. Mayero, M.: Formalisation et automatisation de preuves en analyses réelle et numérique. PhD thesis, Université Paris VI (2001)
  25. McLaughlin, S., Harrison, J.: A proof-producing decision procedure for real arithmetic. In: Nieuwenhuis, R. (ed.) Proceedings of the 20th International Conference on Automated Deduction (CADE-20), Tallinn, Estonia. Lecture Notes in Computer Science, vol. 3632, pp. 295–314 (2005)
  26. Melquiond, G.: Proving bounds on real-valued functions with computations. In: Armando, A., Baumgartner, P., Dowek, G. (eds.) Proceedings of the 4th International Joint Conference on Automated Reasoning (IJCAR), Sydney, Australia. Lecture Notes in Artificial Intelligence, vol. 5195, pp. 2–17 (2008)
  27. Muñoz C., Narkawicz A.: Formalization of a Bernstein polynomials and applications to global optimization. J. Autom. Reason. 51(2), 151–196 (2013)
    Article Google Scholar
  28. Naumowicz, A., Korniłowicz, A.: A brief overview of Mizar. In: Berghofer, S., Nipkow, T., Urban, C., Wenzel, M. (eds.) Proceedings of the 22th International Conference on Theorem Proving in Higher Order Logics (TPHOLs). Lecture Notes in Computer Science, vol. 5674, pp. 67–72 (2009)
  29. O’Connor R.: A monadic, functional implementation of real numbers. Math. Struct. Comput. Sci. 17(1), 129–159 (2007)
    Article MATH MathSciNet Google Scholar
  30. O’Connor R., Spitters B.: A computer-verified monadic functional implementation of the integral. Theor. Comput. Sci. 411(37), 3386–3402 (2010)
    Article MATH MathSciNet Google Scholar
  31. Owre, S., Rushby, J., Shankar, N.: PVS: a prototype verification system. In: Kapur, D. (ed.) Proceedings of the 11th International Conference on Automated Deduction (CADE), Saratoga, NY, June 1992. Lecture Notes in Artificial Intelligence, vol. 607, pp. 748–752 (1992)
  32. Pottier, L.: Connecting Gröbner bases programs with Coq to do proofs in algebra, geometry and arithmetics. In: Sutcliffe, G., Rudnicki, P., Schmidt, R.A., Konev, B., Schulz, S. (eds.) Knowledge Exchange: Automated Provers and Proof Assistants. CEUR Workshop Proceedings, Doha, Qatar, pp. 67–76 (2008)
  33. Rushby J., Owre S., Shankar N.: Subtypes for specifications: predicate subtyping in PVS. IEEE Trans. Softw. Eng. 24(9), 709–720 (1998)
    Article Google Scholar
  34. Trybulec, A.: Some features of the Mizar language. In: Proceedings of the ESPRIT Workshop, Torino, Italy (1993)
  35. Trybulec, A.: Non negative real numbers. Part I. J. Formal. Math. (1998). Addenda

Download references