UID:
almahu_9947367963602882
Umfang:
1 online resource (1045 p.)
ISBN:
1-281-77901-6
,
9786611779016
,
0-08-088718-X
Serie:
Studies in logic and the foundations of mathematics, v. 133
Inhalt:
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published in journals or conference proceedings, but a number have only circulated as research reports or have remained unpublished.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 dist
Anmerkung:
Description based upon print version of record.
,
Front Cover; Selected Papers on Authomath; Copyright Page; Preface; Contents; Hints for the reader; Notation; Introduction; Twenty-five years of Automath research; Part A: Motivation and exposition; Chapter A.1. Verification of mathematical proofs by a computer; Chapter A.2. The mathematical language Automath, its usage, and some of its extensions; Chapter A.3. A description of Automath and some aspects of its language theory; Chapter A.4. Formalization of classical mathematics in Automath; Chapter A.5. A survey of the project Automath; Chapter A.6. The language theory of Automath
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Chapter A.7. Reflections on AutomathChapter A.8. Type systems - basic ideas and applications; Part B: Language deflnition and special subjects; Chapter B.1. Description of AUT-68; Chapter B.2. AUT-SL, a single line version of Automath; Chapter B.3. Some extensions of Automath: the AUT-4 family; Chapter B.4. AUT-QE without type inclusion; Chapter B.5. Checking Landau's ''Grundlagen" in the Automath system; Chapter B.6. The language theory of Automath; Chapter B.7. Generalizing Automath by means of a lambda- typed lambda calculus; Chapter B.8. Lambda calculus extended with segments
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Part C: TheoryChapter C.1. A normal form theorem in a λ-calculus with types; Chapter C.2. Lambda calculus notation with nameless dummies, a tool for automatic formula manipulation, with application t o the Church-Rosser theorem; Chapter C.3. Strong normalization in a typed lambda calculus with lambda structured types; Chapter C.4. Big trees in λ-calculus with λ-expressions as types; Chapter C.5. The language theory of Automath; Chapter C.6. The language theory of A infinty, a typed λ-calculus where terms are types; PART D: Text examples; Chapter D.1. Example of a text written in Automath
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Chapter D.2. Checking Landau's "Grundlagen" in the Automath systemChapter D.3. Checking Landau's "Grundlagen" in the Automath system; Chapter D.4. A text fragment from Zucker's "Real Analysis"; Chapter D.5. Checking Landau's "Grundlagen" in the Automath system; PART E: Verification; Chapter E.1. A verifying program for Automath; Chapter E.2. Checking Landau's "Grundlagen'' in the Automath system.; Chapter E.3. An implementation of substitution in λ-calculus with dependent types; PART F: Related topics; Chapter F.1. Set theory with type restrictions
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Chapter F.2. Formalisation of constructivity in AuthomathChapter F.3. The Mathematical Vernacular, a language for mathematics with typed sets; Chapter F.4. Relational semantics in an integrated system; Chapter F.5. Computer program semantics in space and time; Bibliography; References; Indexes; Index of Names; Index of Notations; Index of Subjects
,
English
Weitere Ausg.:
ISBN 0-444-89822-0
Sprache:
Englisch
