Skip to main content
SpringerLink
Log in

N.G. de Bruijn (1918–2012) and his Road to Automath, the Earliest Proof Checker

  • Article
  • Published:
The Mathematical Intelligencer Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Agda. http://wiki.portal.chalmers.se/agda/.

  2. The Automath Archive. Hosted at Eindhoven University of Technology: http://www.win.tue.nl/automath/.

  3. H. P. Barendregt. Lambda Calculi with Types. Chapter 2 (pp. 117–309) of S. Ambramsky et al. (eds.): Handbook of Logic in Computer Science, Vol. 2, Oxford University Press, 1992.

  4. H. Barendregt and H. Geuvers. Proof-Assistants using Dependent Type Systems. Chapter 18 (pp. 1149–1238) of J. A. Robinson and A. Voronkov (eds.): Handbook of Automated Reasoning, Vol. 2, Elsevier and The MIT Press, 2001.

  5. L. S. van Benthem Jutting. Checking Landau’s “Grundlagen” in the Automath System. Ph.D. thesis, Technische Hogeschool Eindhoven, 1977.

  6. Aart Blokhuis and Jack van Lint. In memoriam: Johan Jacob Seidel. Nieuw Archief voor Wiskunde, 5/2(3):207–209, September 2001.

  7. N. G. de Bruijn. Over modulaire vormen van meer veranderlijken. Ph.D. thesis, Vrije Universiteit Amsterdam, 1943.

  8. N. G. de Bruijn. Eenige beschouwingen over de waarde der wiskunde (“Some observations on the value of mathematics”). Inaugural speech as professor of pure and applied mathematics and theoretical mechanics at Delft University of Technology, 1946.

  9. N. G. de Bruijn. Programmeren van de Pentomino Puzzel (“Programming the Pentomino Puzzle”). Euclides, 47:90–104, 1971/1972.

    Google Scholar 

  10. N. G. de Bruijn. Wiskundige modellen voor het levende brein (“Mathematical models for the living brain”). Report of the common meeting of the physics section of the KNAW, 83, No. 10, 1974.

  11. N. G. de Bruijn. Lambda calculus with namefree formulas involving symbols that represent reference transforming mappings. Indagationes Math. 40:348–356, 1978.

    Google Scholar 

  12. N. G. de Bruijn. Remembering Kloosterman. Nieuw Archief voor Wiskunde, 5/1(2):130–134, June 2000.

  13. N. G. de Bruijn. Jaap Seidel, a friend. Nieuw Archief voor Wiskunde, 5/2(3):204–206, September 2001.

  14. R. L. Constable et al. Implementing Mathematics with the Nuprl Development System, Prentice-Hall, NJ, 1986.

  15. The Coq Development Team. The Coq Proof Assistant, Reference Manual, Version 8.3. http://coq.inria.fr/refman/.

  16. Th. Coquand and G. Huet. The calculus of constructions. Information and Computation, 76:95–120, 1988.

  17. M. J. C. Gordon, T. F. Melham. Introduction to HOL: A theorem proving environment for higher order logic. Cambridge University Press, 1993.

  18. R. Harper, F. Honsell, and G. Plotkin. A framework for defining logics. In Proceedings Second Symposium of Logic in Computer Science, Ithaca, N.Y., pp. 194–204, IEEE, Washington, DC, 1987.

  19. W. A. Howard. The formulas-as-types notion of construction. In: J. P. Seldin, J. R. Hindley (eds.): To H. B. Curry: Essays on Combinatory logic, Lambda calculus and Formalism. Academic Press, pp. 479–490, 1980.

  20. Isabelle. http://isabelle.in.tum.de/.

  21. F. Kamareddine. Thirty-five years of automating mathematics. Workshop. Kluwer Academic Publishers, Dordrecht, Boston, 2003. ISBN 1402016565.

  22. E. Kamke. Theory of Sets. Dover Publications, 1950. Re-edition.

  23. D. Knuth. Dancing Links. Paper P159 at http://www-cs-faculty.stanford.edu/~uno/preprints.html.

  24. E. Landau. Grundlagen der Analysis. First ed.: Leipzig, 1930. Third ed.: Chelsea Publ. Comp. New York, 1960.

  25. Mathematics, Logic and Computation. A satellite workshop of ICALP03, in honour of N. G. de Bruijn’s 85th anniversary. 4–5 July 2003. http://www.cedar-forest.org/forest/events/Bruijn03/.

  26. R. P. Nederpelt, J. H. Geuvers, and R. C. de Vrijer (eds.): Selected Papers on Automath, volume 133 of Studies in Logic and the Foundations of Computer Science. Elsevier, 1994.

  27. B. Nordström, K. Petersson, and J. M. Smith. Programming in Martin-Löf’s Type Theory. Oxford University Press, 1990.

  28. G. Plotkin. LCF considered as a programming language. Theor. Comp. Sci. 5:223–255, 1977.

    Google Scholar 

  29. PVS. http://pvs-wiki.csl.sri.com/index.php/Main_Page.

  30. F. Schuh. Leerboek der Elementaire Theoretische Rekenkunde (“Textbook on Elementary Theoretical Arithmetic”). Noordhoff. Part 1: De gehele getallen (“The Integers”), 1919. Part 2: De meetbare Getallen (“The Measurable Numbers”), 1921.

  31. The Twelf Project. http://twelf.plparty.org/wiki/Main_Page.

  32. N. G. de Bruijn. Asymptotic Methods in Analysis. North Holland Publishing Company and P. Noordhoff, 1958; Dover Publications, Inc., New York, 1981.

  33. N. G. de Bruijn. Ein Satz über schlichte Funktionen (“A theorem on schlicht functions”). Nederl. Akad. Wetensch. Proceedings, 44:47–49, 1941. (=Indagationes Math., 3:8–10, 1941).

    Google Scholar 

  34. N. G. de Bruijn. On Mahler’s partition problem. Nederl. Akad. Wetensch. Proceedings, 51: 659–669, 1948. (=Indagationes Math., 10:210–220, 1948).

    Google Scholar 

  35. N. G. de Bruijn. The roots of trigonometric integrals. Duke Math. J., 17:197–226, 1950.

    Google Scholar 

  36. N. G. de Bruijn. On bases for the set of integers. Publ. Math. Debrecen, 1:232–242, 1950.

    Google Scholar 

  37. N. G. de Bruijn. On the number of positive integers ≤ x and free of prime factors > y. Nederl. Akad. Wetensch. Proceedings, 53:813–821, 1950. (=Indagationes Math., 12:257–265, 1950).

    Google Scholar 

  38. N. G. de Bruijn. Functions whose differences belong to a given class. Nieuw Archief Wiskunde (2) 23:194–218, 1951.

    Google Scholar 

  39. N. G. de Bruijn. Function theory in Banach algebras. Ann. Acad. Sci. Fennicae Ser. A. I. Math. 250/5, 1958. 12 pp.

    Google Scholar 

  40. N. G. de Bruijn. Generalization of Pólya’s fundamental theorem in enumerative combinatorial analysis. Nederl. Akad. Wetensch. Proceedings Ser. A 62: 59–69, 1959. (=Indagationes Math. 21).

    Google Scholar 

  41. N. G. de Bruijn. The mathematical language Automath, its usage, and some of its extensions. Symposium on Automatic Demonstration (Versailles, December 1968). Lecture Notes in Mathematics, vol. 125. Springer-Verlag, 1970, pp. 29–61. Reprinted in [26], pp. 73–100.

  42. N. G. de Bruijn. A theory of generalized functions, with applications to Wigner distribution and Weyl correspondence. Nieuw Archief Wiskunde (3) 21:205–280, 1973.

    Google Scholar 

  43. N. G. de Bruijn. Defining reals without the use of rationals. Nederl. Akad. Wetensch. Proceedings Ser. A 79:100–108, 1976. (=Indagationes Math. 36).

  44. N. G. de Bruijn. Algebraic theory of Penrose’s non-periodic tilings of the plane. Nederl. Akad. Wetensch. Proceedings Ser. A 84:38–66, 1981. (=Indagationes Math. 43). Reprinted in: The Physics of Quasicrystals, P. J. Steinhardt and S. Ostlund (eds.), World Scientific Publ. Comp., Singapore, 1987, pp. 673–700.

  45. N. G. de Bruijn. Can people think? Journal of Consciousness Studies, Vol. 3, 1996, pp. 425–447.

Download references

Acknowledgments

We are grateful to the recently deceased N. G. de Bruijn for his willingness to discuss the contents of this article. We also thank H. Geuvers, M. Senechal, F. W. Steutel, and the anonymous referee for their helpful comments.

Author information

Authors and Affiliations

  1. Delft University of Technology, Delft, The Netherlands

    Francien Dechesne

  2. Eindhoven University of Technology, Eindhoven, The Netherlands

    Rob Nederpelt

Authors
  1. Francien Dechesne
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Rob Nederpelt
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Rob Nederpelt.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dechesne, F., Nederpelt, R. N.G. de Bruijn (1918–2012) and his Road to Automath, the Earliest Proof Checker. Math Intelligencer 34, 4–11 (2012). https://doi.org/10.1007/s00283-012-9324-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00283-012-9324-x

Keywords

Search

Navigation