Thirty Five Years of Automating Mathematics

1. Front Matter

   Pages i-8

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2. A Mathematical Model for Biological Memory and Consciousness

   • N. G. De Bruijn

   Pages 9-23

3. Towards an Interactive Mathematical Proof Mode

   • Henk Barendregt

   Pages 25-36

4. Recent Results in Type Theory and Their Relationship to Automath

   • Robert L. Constable

   Pages 37-48

5. Linear Contexts, Sharing Functors: Techniques for Symbolic Computation

   • Gérard Huet

   Pages 49-69

6. De Bruijn’s Automath and Pure Type Systems

   • Fairouz Kamareddine, Twan Laan, Rob Nederpelt

   Pages 71-123

7. Hoare Logic with Explicit Contexts

   • Michael Franssen

   Pages 125-148

8. Transitive Closure and the Mechanization of Mathematics

   • Arnon Avron

   Pages 149-171

9. Polymorphic Type-Checking for the Ramified Theory of Types of Principia Mathematica

   • M. Randall Holmes

   Pages 173-215

10. Termination in ACL2 Using Multiset Relations

    • J. L. Ruiz-Reina, J. A. Alonso, M. J. Hidalgo, F. J. Martín-Mateos

    Pages 217-245

11. The π-Calculus in FM

    • Murdoch J. Gabbay

    Pages 247-269

12. Proof Development with Ωmega: The Irrationality of \(\sqrt 2\)

    • Jörg Siekmann, Christoph Benzmüller, Armin Fiedler, Andreas Meier, Immanuel Normann, Martin Pollet

    Pages 271-314

13. Back Matter

    Pages 315-320

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THIRTY FIVE YEARS OF AUTOMATING MATHEMATICS: DEDICATED TO 35 YEARS OF DE BRUIJN'S AUTOMATH N. G. de Bruijn was a well established mathematician before deciding in 1967 at the age of 49 to work on a new direction related to Automating Mathematics. By then, his contributions in mathematics were numerous and extremely influential. His book on advanced asymptotic methods, North­ Holland 1958, was a classic and was subsequently turned into a book in the well known Dover book series. His work on combinatorics yielded influential notions and theorems of which we mention the de Bruijn-sequences of 1946 and the de Bruijn-Erdos theorem of 1948. De Bruijn's contributions to mathematics also included his work on generalized function theory, analytic number theory, optimal control, quasicrystals, the mathematical analysis of games and much more. In the 1960s de Bruijn became fascinated by the new computer technology and as a result, decided to start the new AUTOMATH project where he could check, with the help of the computer, the correctness of books of mathematics. In each area that de Bruijn approached, he shed a new light and was known for his originality and for making deep intellectual contributions. And when it came to automating mathematics, he again did it his way and introduced the highly influential AUTOMATH. In the past decade he has also been working on theories of the human brain.

• Mathematica
• Principia Mathematica
• calculus
• computer
• linear optimization
• logic
• proof
• set theory
• type theory
• verification

• School of Mathematical and Computer Sciences, Heriot-Watt University, Riccarton, Edinburgh, Scotland, UK

  Fairouz D. Kamareddine

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