Thirty Five Years of Automating Mathematics by F.D. KamareddineThirty Five Years of Automating Mathematics by F.D. Kamareddine

Thirty Five Years of Automating Mathematics

EditorF.D. Kamareddine

Paperback | October 22, 2010

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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. In the 1960s he became fascinated by the new computer technology and decided to start the Automath project where he could check, with the help of the computer, the correctness of books on mathematics. Through his work on Automath de Bruijn started a revolution in using the computer for verification, and since, we have seen more and more proof-checking and theorem-proving systems. Automath was written in Algol 60 and implemented on the primitive computers of the sixties. Thirty years on, both technology and theory have evolved a lot leading to impressive new directions in using the computer for manipulating and checking mathematics. This volume is a collection of papers with a personal flavour. It consists of 11 articles which propose interesting variations to or examples of mechanising mathematics and illustrate differ developments in symbolic computation in the past 35 years. The first paper is by de Bruijn himself where he uses his experience of automating mathematics to reason about the human mind. After that a number of intriguing articles have been contributed by amongst others Henk Barendregt, who proposes a mathematical proof language between informal and formalised mathematics which helps make proof assistants more user friendly, and Robert Constable, explaining how Automath's telescopes, books and definitions compare to recent developments in computational type theory made by his Nuprl group. The volume further includes a strong argumentation by Arnon Avron that for automated reasoning, there is an interesting logic, somewhere strictly between first and second order logic, determined essentially by an analysis of transitive closure, yielding induction; and Murdoch Gabbay presenting an interesting generalisation of Fraenkel-Mostowski (FM) set theory within higher-order logic, and applying it to model Milner's p-calculus.

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Title:Thirty Five Years of Automating MathematicsFormat:PaperbackDimensions:329 pages, 9.25 × 6.1 × 0 inPublished:October 22, 2010Publisher:Springer NetherlandsLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:9048164400

ISBN - 13:9789048164400

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Table of Contents

Contributors. Editorial Preface; F.D. Kamareddine. A Mathematical Model for Biological Memory and Consciousness; N.G. de Bruijn. Towards an Interactive Mathematical Proof Mode; H. Barendregt. Recent Results in Type Theory and their Relationship to Automath; R.L. Constable. Linear Contexts, Sharing Functors: Techniques for Symbolic Computation; G. Huet. De Bruijn's Automath and Pure Type Systems; F.D. Kamareddine, A. Laan, R. Nederpelt. Hoare Logic with Explicit Contexts; M. Franssen. Transitive Closure and the Mechanization of Mathematics; A. Avron. Polymorphic Type-checking for the Ramified Theory of Types of Principia Mathematica; M.R. Holmes. Termination in ACL2 using Multiset Relations; J.L. Ruiz-Reina, J.A. Alonso, M.J. Hidalgo, F.J. Martin-Mateos. The pi-Calculus in FM; M.J. Gabbay. Proof Development with Omegamega: The Irrationality of SQRT2; J. Siekmann, C. Benzmüller, A. Fiedler, A. Meier, I. Normann, M. Pollet. Index.