Logical Frameworks

doi:10.1017/CBO9780511569807

This 1991 volume contains the proceedings of the first international workshop on Logical Frameworks. The contributions are concerned with the application of logical reasoning and proof theory in computer science and its relevance to automatic theorem proving, and consequently topics such as artificial intelligence. It is the only source for much of this material and will be a necessary purchase for mathematicians and computer scientists undertaking research at the interface of logic and software engineering.

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Contents

Frontmatter
pp i-iv
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Contents
pp v-vi
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Preface
pp vii-viii
- By G. Huet, INRIA, Rocquencourt, G. Plotkin, Edinburgh University
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Introduction
pp ix-xii
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Frameworks
pp 1-2
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Two frameworks of theories and their implementation in Isabelle
pp 3-39
- By Peter Aczel, Computer Science Department Manchester University Manchester, M13 9PL, David P. Carlisle, Computer Science Department Manchester University Manchester, M13 9PL, Nax Mendler, Computer Science Department Manchester University Manchester, M13 9PL
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A plea for weaker frameworks
pp 40-68
- By N.G. de Bruijn, Eindhoven University of Technology
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Nederpelt's calculus extended with a notion of context as a logical framework
pp 69-86
- By Philippe de Groote, Université Catholique de Louvain, Unité d'informatique, B-1348 Louvain-la-Neuve, Belgique
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Implementations
pp 87-88
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The Boyer-Moore prover and Nuprl: an experimental comparison
pp 89-119
- By David Basin, Department of Artificial Intelligence, University of Edinburgh, Edinburgh Scotland, Matt Kaufmann, Computational Logic, Inc. Austin, Texas 78703 USA
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Goal directed proof construction in type theory
pp 120-148
- By Leen Helmink, Philips Research Laboratories, P.O. Box 80.000, 5600 JA Eindhoven, the Netherlands, René Ahn, Philips Research Laboratories, P.O. Box 80.000, 5600 JA Eindhoven, the Netherlands
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Logic programming in the LF logical framework
pp 149-182
- By Frank Pfenning, Carnegie Mellon University
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Representing Formal Systems
pp 183-184
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Operational semantics in a natural deduction setting
pp 185-214
- By Rod Burstall, University of Edinburgh, Furio Honsell, University of Udine
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Encoding dependent types in an intuitionistic logic
pp 215-252
- By Amy Felty, INRIA Rocquencourt Domaine de Voluceau 78153 Le Chesnay Cedex, France
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Type Theory
pp 253-254
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An algorithm for testing conversion in type theory
pp 255-279
- By Thierry Coquand, INRIA and University of Göteborg/Chalmers
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Inductive sets and families in Martin-Löf's type theory and their set-theoretic semantics
pp 280-306
- By Peter Dybjer, Department of Computer Sciences Chalmers University of Technology and University of Göteborg S-412 96 Göteborg, Sweden
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Proofs and Computation
pp 307-308
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Proof-search in the λΠ-calculus
pp 309-340
- By David Pym, University of Edinburgh Scotland, U.K., Lincoln Wallen, University of Oxford England, U.K.
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Finding computational content in classical proofs
pp 341-362
- By Robert Constable, Cornell University, Chet Murthy, Cornell University
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Logical Issues
pp 363-364
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Models of partial inductive definitions
pp 365-384
- By Lars Hallnäs, Department of Computer Sciences, Chalmers University of Technology and University of Göteborg, 412 96 Göteborg, Sweden
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Structural frameworks, substructural logics, and the role of elimination inferences
pp 385-403
- By Peter Schroeder-Heister, Universität Tübingen/SNS Biesingerstr. 10, 7400 Tübingen, Germany
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Logical Frameworks

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Contents

Frontmatter
pp i-iv

Contents
pp v-vi

Preface
pp vii-viii

Introduction
pp ix-xii

Frameworks
pp 1-2

Two frameworks of theories and their implementation in Isabelle
pp 3-39

A plea for weaker frameworks
pp 40-68

Nederpelt's calculus extended with a notion of context as a logical framework
pp 69-86

Implementations
pp 87-88

The Boyer-Moore prover and Nuprl: an experimental comparison
pp 89-119

Goal directed proof construction in type theory
pp 120-148

Logic programming in the LF logical framework
pp 149-182

Representing Formal Systems
pp 183-184

Operational semantics in a natural deduction setting
pp 185-214

Encoding dependent types in an intuitionistic logic
pp 215-252

Type Theory
pp 253-254

An algorithm for testing conversion in type theory
pp 255-279

Inductive sets and families in Martin-Löf's type theory and their set-theoretic semantics
pp 280-306

Proofs and Computation
pp 307-308

Proof-search in the λΠ-calculus
pp 309-340

Finding computational content in classical proofs
pp 341-362

Logical Issues
pp 363-364

Models of partial inductive definitions
pp 365-384

Structural frameworks, substructural logics, and the role of elimination inferences
pp 385-403

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