Preface: Mechanizing and Automating Mathematics: In honour of N.G. de Bruijn

Abstract

– De Bruijn indices [6] still play an important role in the implementation of programming languages and theorem provers. – De Bruijn’s new type systems were influential in the discovery of new powerful type systems [7]. – De Bruijn re-invented the Curry–Howard isomorphism (also referred to as the Curry–Howard–de Bruijn isomorphism). Independently of Curry and Feys [8] and Howard [9], we find a variant of the propositions as types principle in the first Automath system of de Bruijn (AUT-68 [12, 4]). Though de Bruijn was probably influenced by Heyting (see [5] in [12], p. 211), his ideas arose independently from Curry, Feys, and Howard, as can be clearly seen in Section 2.4 of [3], where propositions as types (or better: proofs as terms) are implemented in a way that differs from the method of Curry and Howard (see [10]). – The Landau book [11] on the foundations of analysis remains the only fully encoded and checked mathematical book in any theorem prover. The Landau book was encoded in Automath in the seventies by Bert van Benthem-Jutting (who was a Ph.D. student of de Bruijn at that time) [1, 2].

DOI: 10.1023/A:1021977414812

Cite this paper

@article{Kamareddine2002PrefaceMA, title={Preface: Mechanizing and Automating Mathematics: In honour of N.G. de Bruijn}, author={Fairouz Kamareddine}, journal={Journal of Automated Reasoning}, year={2002}, volume={29}, pages={183-188} }