2 \markboth{Preface}{Preface}
4 This volume is a self-contained introduction to interactive proof
5 in higher-order logic (HOL), using the proof assistant Isabelle 2002.
6 Compared with existing Isabelle documentation,
7 it provides a direct route into higher-order logic, which most people
8 prefer these days. It bypasses first-order logic and minimizes
9 discussion of meta-theory. It is written for potential users rather
10 than for our colleagues in the research world.
12 Another departure from previous documentation is that we describe Markus
13 Wenzel's proof script notation instead of ML tactic scripts. The latter
14 make it easier to introduce new tactics on the fly, but hardly anybody
15 does that. Wenzel's dedicated syntax is elegant, replacing for example
16 eight simplification tactics with a single method, namely \isa{simp},
17 with associated options.
19 The book has three parts.
22 The first part, \textbf{Elementary Techniques},
23 shows how to model functional programs in higher-order logic. Early
24 examples involve lists and the natural numbers. Most proofs
25 are two steps long, consisting of induction on a chosen variable
26 followed by the \isa{auto} tactic. But even this elementary part
27 covers such advanced topics as nested and mutual recursion.
29 The second part, \textbf{Logic and Sets}, presents a collection of
30 lower-level tactics that you can use to apply rules selectively. It
31 also describes Isabelle/HOL's treatment of sets, functions and
32 relations and explains how to define sets inductively. One of the
33 examples concerns the theory of model checking, and another is drawn
34 from a classic textbook on formal languages.
36 The third part, \textbf{Advanced Material}, describes a variety of
37 other topics. Among these are the real numbers, records and
38 overloading. Esoteric techniques are described involving induction and
39 recursion. A whole chapter is devoted to an extended example: the
40 verification of a security protocol.
43 The typesetting relies on Wenzel's theory presentation tools. An
44 annotated source file is run, typesetting the theory
45 % and any requested Isabelle responses
46 in the form of a \LaTeX\ source file. This book is derived almost entirely
47 from output generated in this way. The final chapter of Part~I explains how
48 users may produce their own formal documents in a similar fashion.
50 Isabelle's \hfootref{http://isabelle.in.tum.de/}{web site} contains links to
51 the download area and to documentation and other information. Most Isabelle
52 sessions are now run from within David Aspinall's\index{Aspinall, David}
53 wonderful user interface, \hfootref{http://www.proofgeneral.org/}{Proof
54 General}, even together with the
55 \hfootref{http://x-symbol.sourceforge.net}{X-Symbol} package for XEmacs. This
56 book says very little about Proof General, which has its own documentation.
57 In order to run Isabelle, you will need a Standard ML compiler. We recommend
58 \hfootref{http://www.polyml.org/}{Poly/ML}, which is free and gives the best
59 performance. The other fully supported compiler is
60 \hfootref{http://cm.bell-labs.com/cm/cs/what/smlnj/index.html}{Standard ML of
63 This tutorial owes a lot to the constant discussions with and the valuable
64 feedback from the Isabelle group at Munich: Stefan Berghofer, Olaf
65 M{\"u}ller, Wolfgang Naraschewski, David von Oheimb, Leonor Prensa Nieto,
66 Cornelia Pusch, Norbert Schirmer and Martin Strecker. Stephan
67 Merz was also kind enough to read and comment on a draft version. We
68 received comments from Stefano Bistarelli, Gergely Buday and Tanja
71 The research has been funded by many sources, including the {\sc dfg} grants
72 Ni~491/2, Ni~491/3, Ni~491/4 and the {\sc epsrc} grants GR\slash K57381,
73 GR\slash K77051, GR\slash M75440, GR\slash R01156\slash 01 and by the
74 \textsc{esprit} working groups 21900 and IST-1999-29001 (the \emph{Types}