N.G. de Bruijn. Re ections on Automath. Eindhoven University of Technology, 1990. Also in [34], pages 201-228. Home/Search Document Not in Database Summary Related Articles Check |
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Automath and Pure Type Systems - Kamareddine, Laan, Nederpelt (2003) (Correct)
....of modern proof checkers like Coq [13] and Nuprl [10] The project started in 1967 by N.G. de Bruijn: it was not just meant as a technical system for veri cation of mathematical texts, it was rather a life style with its attitudes towards understanding, developing and teaching mathematics. [8]; see [24] p. 201) Email: fairouz macs.hw.ac.uk Email: twan.laan wxs.nl Email: r.p.nederpelt tue.nl c 2003 Published by Elsevier Science B. V. Thus, the roots of Automath are not to be found in logic or type theory, but in mathematics and the mathematical vernacular [7] For some years, ....
....things like mathematical axioms that have to be explained to the reader. 3. The way mathematical material is to be presented to the system should correspond to the usual way we write mathematics. The only things to be added should be details that are usually omitted in standard mathematics. [8]; see [24] pp. 209 210) Goal 1 was achieved: Van Benthem Jutting [2] translated and veri ed Landau s Grundlagen der Analysis [23] in Automath and Zucker [29] formalised classical real analysis in Automath. As for goal 2, de Bruijn used types and a propositions as types (pat) principle that ....
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N.G. de Bruijn. Re ections on Automath. Eindhoven University of Technology, 1990. Also in [24], pages 201-228.
Mechanizing and Automating Mathematics: In honor of N.G. de.. - Automath Started In Self-citation (De bruijn) (Correct)
.... isomorphism (also referred to as the Curry Howard de Bruijn isomorphism) Independently of Curry and Feys [7] and Howard [9] we nd a variant of the propositions as types principle in the rst Automath system of de Bruijn (Aut 68 [12, 4] Though de Bruijn was probably in uenced by Heyting (see [5] in [12] p. 211) his ideas arose independently from Curry, Feys and Howard. This can be clearly seen in Section 2.4 of [3] where propositions as types (or better: proofs as terms) is implemented in a way which di ers from the method of Curry and Howard (see [10] The Landau book [11] on the ....
N.G. de Bruijn. Re ections on Automath. Eindhoven University of Technology, 1990. Also in [12], pages 201-228.
Revisiting the Notion of Function - Kamareddine, Laan, Nederpelt (Correct)
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N.G. de Bruijn. Re ections on Automath. Eindhoven University of Technology, 1990. Also in [34], pages 201-228.
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