The present volume contains a considered choice of the existing literature on Automath. Many of the papers included in the book have been published in journals or conference proceedings, but a number have only circulated as research reports or have remained unpublished. The aim of the editors is to present a representative selection of existing articles and reports and of material contained in dissertations, giving a compact and more or less complete overview of the work that has been done in the Automath research field, from the beginning to the present day. Six different areas have been distinguished, which correspond to Parts A to F of the book. These areas range from general ideas and motivation, to detailed syntactical investigations.
Author(s): R.P. Nederpelt, J.H. Geuvers, R.C. de Vrijer (editors)
Series: Studies in Logic and the Foundations of Mathematics 133
Publisher: North-Holland
Year: 1994
Language: English
Pages: 1045
Cover......Page 1
Contents......Page 12
Series......Page 3
Title......Page 4
Copyright......Page 5
Dedication......Page 6
Photo of N.G. de Bruijn......Page 7
Preface......Page 8
Acknowledgements......Page 9
Editorial Notes......Page 16
The References......Page 17
Functional application......Page 18
Reduction and conversion......Page 19
Typing......Page 20
Introduction......Page 22
Twenty-Five Years of Automath Research, R.P. Nederpelt and J.H. Geuvers......Page 24
Part A: Motivation and Exposition......Page 76
Verification of Mathematics Proofs by a Computer – A preparatory study for a project Automath, N.G. de Bruijn......Page 78
The Mathematical Language Automath, its Usage, and Some of its Extensions, N.G. de Bruijn......Page 94
A Description of Automath and Some Aspects of its Language Theory, D.T. van Daalen......Page 122
Forrnalization of Classical Mathematics in Automath, J. Zucker......Page 148
A Survey of the Project Automath, N.G. de Bruijn......Page 162
The Language Theory of Automath – Chapter I, Sections 1-5 (Introduction), D.T. van Daalen......Page 184
Reflections on Automath, N.G. de Bruijn......Page 222
Type Systems – Basic Ideas and Applications, R.P. Nederpelt......Page 250
Part B: Language Definition and Special Subjects......Page 270
Description of AUT-68, L.S. van Benthem Jutting......Page 272
AUT-SL, a Single Line Version of Automath, N.G. de Bruijn......Page 296
Some Extensions of Automath: The AUT-4 Family, N.G. de Bruijn......Page 304
AUT-QE without Type Inclusion, N.G. de Bruijn......Page 310
Checking Landau’s “Grundlagen” in the Automath System – Appendix 9 (AUT-SYNT), L.S. van Benthem Jutting......Page 320
The Language Theory of Automath – Chapter VIII, 1 and 2 (AUT-II), D.T. van Daalen......Page 324
Generalizing Automath by Means of a Lambda-Typed Lambda Calculus, N.G. de Bruijn......Page 334
Lambda calculus extended with segments – Chapter 1, Sections 1.1 and 1.2 (Introduction), H. Balsters......Page 360
Part C: Theory......Page 390
A Normal Form Theorem in a λ-Calculus with Types, L.S. van Benthem Jutting......Page 392
Lambda Calculus Notation with Nameless Dummies, a Tool for Automatic Formula Manipulation, with Application to the Church-Rosser Theorem, N.G. de Bruijn......Page 396
Strong Normalization in a Typed Lambda Calculus with Lambda Structured Types, R.P. Nederpelt......Page 410
Big Trees in a λ-Calculuswith λ-Expressions as Types, R.C. de Vrijer......Page 490
The Language Theory of Automath – Parts of Chapters II, IV, V-VIII, D.T. van Daalen......Page 514
The Language Theory of Λ∞, a Typed λ-Calculus where Terms are Types, L.S. van Benthem Jutting......Page 676
Part D: Text Examples......Page 706
Example of a Text written in Automath, N.G. de Bruijn......Page 708
Checking Landau’s “Grundlagen” in the Automath System – Parts of Chapters 0, 1 and 2 (Introduction, Preparation, Translation), L.S. van Benthem Jutting......Page 722
Checking Landau’s “Grundlagen” in the Automath System – Chapter 4 (Conclusions), L.S. van Benthem Jutting......Page 742
A Text Fragment from Zucker’s “Real Analysis”, L.S. van Benthem Jutting and R.C. de Vrijer......Page 754
Checking Landau’s “Grundlagen” in the Automath System – Appendices 3 and 4 (The PN-lines; Excerpt for “Satz 27”), L.S. van Benthem Jutting......Page 784
Part E: Verification......Page 802
A Verifying Program for Automath, I. Zandleven......Page 804
Checking Landau’s “Grundlagen” in the Automath System – Parts of Chapter 3 (Verification), L.S. van Benthem Jutting......Page 826
An Implementation of Substitution in a X-Calculus with Dependent Types, L.S. van Benthem Jutting......Page 830
Part F: Related Topics......Page 860
Set Theory with Type Restrictions, N.G. de Bruijn......Page 862
Formalization of Constructivity in Automath, N.G. de Bruijn......Page 870
The Mathernatical Vernacular, A Language for Mathematics with Typed Sets, N.G. de Bruijn......Page 886
Relational Semantics in an Integrated System, R.M.A. Wieringa......Page 958
Computer Program Semantics in Space and Time, N.G. de Bruijn......Page 968
Bibliography......Page 994
References......Page 996
Indexes......Page 1016
Index of Names......Page 1018
Index of Notations......Page 1024
Index of Subjects......Page 1026
