2 \markboth{Preface}{Preface} %or Preface ?
3 \addcontentsline{toc}{chapter}{Preface}
5 \index{Isabelle!object-logics supported}
7 Most theorem provers support a fixed logic, such as first-order or
8 equational logic. They bring sophisticated proof procedures to bear upon
9 the conjectured formula. An impressive example is the resolution prover
10 Otter, which Quaife~\cite{quaife-book} has used to formalize a body of
13 ALF~\cite{alf}, Coq~\cite{coq} and Nuprl~\cite{constable86} each support a
14 fixed logic too, but one far removed from first-order logic. They are
15 explicitly concerned with computation. A diverse collection of logics ---
16 type theories, process calculi, $\lambda$-calculi --- may be found in the
17 Computer Science literature. Such logics require proof support. Few proof
18 procedures exist, but the theorem prover can at least check that each
21 A {\bf generic} theorem prover is one that can support many different
22 logics. Most of these \cite{dawson90,mural,sawamura92} work by
23 implementing a syntactic framework that can express the features of typical
24 inference rules. Isabelle's distinctive feature is its representation of
25 logics using a meta-logic. This meta-logic is just a fragment of
26 higher-order logic; known proof theory may be used to demonstrate that the
27 representation is correct~\cite{paulson89}. The representation has much in
28 common with the Edinburgh Logical Framework~\cite{harper-jacm} and with
29 Felty's~\cite{felty93} use of $\lambda$Prolog to implement logics.
31 An inference rule in Isabelle is a generalized Horn clause. Rules are
32 joined to make proofs by resolving such clauses. Logical variables in
33 goals can be instantiated incrementally. But Isabelle is not a resolution
34 theorem prover like Otter. Isabelle's clauses are drawn from a richer,
35 higher-order language and a fully automatic search would be impractical.
36 Isabelle does not join clauses automatically, but under strict user
37 control. You can conduct single-step proofs, use Isabelle's built-in proof
38 procedures, or develop new proof procedures using tactics and tacticals.
40 Isabelle's meta-logic is higher-order, based on the typed
41 $\lambda$-calculus. So resolution cannot use ordinary unification, but
42 higher-order unification~\cite{huet75}. This complicated procedure gives
43 Isabelle strong support for many logical formalisms involving variable
46 The diagram below illustrates some of the logics distributed with Isabelle.
47 These include first-order logic (intuitionistic and classical), the sequent
48 calculus, higher-order logic, Zermelo-Fraenkel set theory~\cite{suppes72},
49 a version of Constructive Type Theory~\cite{nordstrom90}, several modal
50 logics, and a Logic for Computable Functions. Several experimental
51 logics are also available, such a term assignment calculus for linear
54 \centerline{\epsfbox{Isa-logics.eps}}
57 \section*{How to read this book}
58 Isabelle is a large system, but beginners can get by with a few commands
59 and a basic knowledge of how Isabelle works. Some knowledge of
60 Standard~\ML{} is essential because \ML{} is Isabelle's user interface.
61 Advanced Isabelle theorem proving can involve writing \ML{} code, possibly
62 with Isabelle's sources at hand. My book on~\ML{}~\cite{paulson91} covers
63 much material connected with Isabelle, including a simple theorem prover.
65 The Isabelle documentation is divided into three parts, which serve
68 \item {\em Introduction to Isabelle\/} describes the basic features of
69 Isabelle. This part is intended to be read through. If you are
70 impatient to get started, you might skip the first chapter, which
71 describes Isabelle's meta-logic in some detail. The other chapters
72 present on-line sessions of increasing difficulty. It also explains how
73 to derive rules define theories, and concludes with an extended example:
76 \item {\em The Isabelle Reference Manual\/} contains information about most
77 of the facilities of Isabelle, apart from particular object-logics. This
78 part would make boring reading, though browsing might be useful. Mostly
79 you should use it to locate facts quickly.
81 \item {\em Isabelle's Object-Logics\/} describes the various logics
82 distributed with Isabelle. Its final chapter explains how to define new
83 logics. The other chapters are intended for reference only.
85 This book should not be read from start to finish. Instead you might read
86 a couple of chapters from {\em Introduction to Isabelle}, then try some
87 examples referring to the other parts, return to the {\em Introduction},
88 and so forth. Starred sections discuss obscure matters and may be skipped
93 \section*{Releases of Isabelle}\index{Isabelle!release history}
94 Isabelle was first distributed in 1986. The 1987 version introduced a
95 higher-order meta-logic with an improved treatment of quantifiers. The
96 1988 version added limited polymorphism and support for natural deduction.
97 The 1989 version included a parser and pretty printer generator. The 1992
98 version introduced type classes, to support many-sorted and higher-order
99 logics. The 1993 version provides greater support for theories and is
102 Isabelle is still under development. Projects under consideration include
103 better support for inductive definitions, some means of recording proofs, a
104 graphical user interface, and developments in the standard object-logics.
105 I hope but cannot promise to maintain upwards compatibility.
107 Isabelle is available by anonymous ftp:
109 \item University of Cambridge\\
110 host {\tt ftp.cl.cam.ac.uk}\\
113 \item Technical University of Munich\\
114 host {\tt ftp.informatik.tu-muenchen.de}\\
115 directory {\tt local/lehrstuhl/nipkow}
117 My electronic mail address is {\tt lcp\at cl.cam.ac.uk}. Please report any
118 errors you find in this book and your problems or successes with Isabelle.
121 \subsection*{Acknowledgements}
122 Tobias Nipkow has made immense contributions to Isabelle, including the
123 parser generator, type classes, the simplifier, and several object-logics.
124 He also arranged for several of his students to help. Carsten Clasohm
125 implemented the theory database; Markus Wenzel implemented macros; Sonia
126 Mahjoub and Karin Nimmermann also contributed.
128 Nipkow and his students wrote much of the documentation underlying this
129 book. Nipkow wrote the first versions of \S\ref{sec:defining-theories},
130 Chap.\ts\ref{simp-chap}, Chap.\ts\ref{Defining-Logics} and part of
131 Chap.\ts\ref{theories}, and App.\ts\ref{app:TheorySyntax}. Carsten Clasohm
132 contributed to Chap.\ts\ref{theories}. Markus Wenzel contributed to
133 Chap.\ts\ref{Defining-Logics}.
135 David Aspinall, Sara Kalvala, Ina Kraan, Zhenyu Qian, Norbert Voelker and
136 Markus Wenzel suggested changes and corrections to the documentation.
138 Martin Coen, Rajeev Gor\'e, Philippe de Groote and Philippe No\"el helped
139 to develop Isabelle's standard object-logics. David Aspinall performed
140 some useful research into theories and implemented an Isabelle Emacs mode.
141 Isabelle was developed using Dave Matthews's Standard~{\sc ml} compiler,
144 The research has been funded by numerous SERC grants dating from the Alvey
145 programme (grants GR/E0355.7, GR/G53279, GR/H40570) and by ESPRIT (projects
146 3245: Logical Frameworks and 6453: Types).