# Isabelle/HOL

## A Proof Assistant for Higher-Order Logic

• Tobias Nipkow
• Markus Wenzel
• Lawrence C. Paulson
Textbook

Part of the Lecture Notes in Computer Science book series (LNCS, volume 2283)

1. Front Matter
Pages I-XIII
2. ### Elementary Techniques

1. Pages 3-8
2. Pages 9-26
3. Pages 27-51
4. Pages 53-64
3. ### Logic and Sets

1. Pages 67-104
2. Pages 105-126
3. Pages 127-145

1. Pages 149-174
2. Pages 175-193
3. Pages 195-205
5. Back Matter
Pages 207-218

### Introduction

This volume is a self-contained introduction to interactive proof in high- order logic (HOL), using the proof assistant Isabelle 2002. Compared with existing Isabelle documentation, it provides a direct route into higher-order logic, which most people prefer these days. It bypasses ?rst-order logic and minimizes discussion of meta-theory. It is written for potential users rather than for our colleagues in the research world. Another departure from previous documentation is that we describe Markus Wenzel’s proof script notation instead of ML tactic scripts. The l- ter make it easier to introduce new tactics on the ?y, but hardly anybody does that. Wenzel’s dedicated syntax is elegant, replacing for example eight simpli?cation tactics with a single method, namely simp, with associated - tions. The book has three parts. – The ?rst part, Elementary Techniques, shows how to model functional programs in higher-order logic. Early examples involve lists and the natural numbers. Most proofs are two steps long, consisting of induction on a chosen variable followed by the auto tactic. But even this elementary part covers such advanced topics as nested and mutual recursion. – The second part, Logic and Sets, presents a collection of lower-level tactics that you can use to apply rules selectively. It also describes I- belle/HOL’s treatment of sets, functions, and relations and explains how to de?ne sets inductively. One of the examples concerns the theory of model checking, and another is drawn from a classic textbook on formal languages.

### Keywords

Formal Methods Formal Reasoning Formal Specification Formal Verification Functional Programming Higher-Order Logic Interactive Proof Systems Isabelle Proof Assistants Proof Theory Theorem Proving Type Theory logic predicate logic verification

### Editors and affiliations

• Tobias Nipkow
• 1
• Markus Wenzel
• 1
• Lawrence C. Paulson
• 2
1. 1.Institut für InformatikTechnische Universität MünchenMünchenGermany
2. 2.Computer LaboratoryUniversity of CambridgeCambridgeUK

### Bibliographic information

• DOI https://doi.org/10.1007/3-540-45949-9
• Copyright Information Springer-Verlag Berlin Heidelberg 2002
• Publisher Name Springer, Berlin, Heidelberg
• eBook Packages
• Print ISBN 978-3-540-43376-7
• Online ISBN 978-3-540-45949-1
• Series Print ISSN 0302-9743
• Buy this book on publisher's site