Concrete Semantics: With Isabelle/HOL

✍ Scribed by Tobias Nipkow, Gerwin Klein (auth.)

• Publisher: Springer International Publishing
• Year: 2014
• Tongue: English
• Leaves: 304
• Edition: 1
• Category: Library

✦ Synopsis

Part I of this book is a practical introduction to working with the Isabelle proof assistant. It teaches you how to write functional programs and inductive definitions and how to prove properties about them in Isabelle’s structured proof language. Part II is an introduction to the semantics of imperative languages with an emphasis on applications like compilers and program analysers. The distinguishing feature is that all the mathematics has been formalised in Isabelle and much of it is executable. Part I focusses on the details of proofs in Isabelle; Part II can be read even without familiarity with Isabelle’s proof language, all proofs are described in detail but informally.

The book teaches the reader the art of precise logical reasoning and the practical use of a proof assistant as a surgical tool for formal proofs about computer science artefacts. In this sense it represents a formal approach to computer science, not just semantics. The Isabelle formalisation, including the proofs and accompanying slides, are freely available online, and the book is suitable for graduate students, advanced undergraduate students, and researchers in theoretical computer science and logic.

✦ Table of Contents

Front Matter....Pages I-XIII
Front Matter....Pages 1-2
Introduction....Pages 3-4
Programming and Proving....Pages 5-25
Case Study: IMP Expressions....Pages 27-36
Logic and Proof Beyond Equality....Pages 37-52
Isar: a Language for Structured Proofs....Pages 53-69
Front Matter....Pages 71-72
Programming and Proving....Pages 73-74
IMP: A Simple Imperative Language....Pages 75-94
Compiler....Pages 95-114
Types....Pages 115-142
Program Analysis....Pages 143-178
Denotational Semantics....Pages 179-190
Hoare Logic....Pages 191-217
Abstract Interpretation....Pages 219-280
Back Matter....Pages 281-298

✦ Subjects

Logics and Meanings of Programs; Programming Languages, Compilers, Interpreters; Mathematical Logic and Formal Languages