\chapter*{Preface}

\markboth{Preface}{Preface}   %or Preface ?

\addcontentsline{toc}{chapter}{Preface} 

\index{Isabelle!object-logics supported}

Most theorem provers support a fixed logic, such as first-order or

equational logic.  They bring sophisticated proof procedures to bear upon

the conjectured formula.  An impressive example is the resolution prover

Otter, which Quaife~\cite{quaife-book} has used to formalize a body of

mathematics.

ALF~\cite{alf}, Coq~\cite{coq} and Nuprl~\cite{constable86} each support a

fixed logic too, but one far removed from first-order logic.  They are

explicitly concerned with computation.  A diverse collection of logics ---

type theories, process calculi, $\lambda$-calculi --- may be found in the

Computer Science literature.  Such logics require proof support.  Few proof

procedures exist, but the theorem prover can at least check that each

inference is valid.

A {\bf generic} theorem prover is one that can support many different

logics.  Most of these \cite{dawson90,mural,sawamura92} work by

implementing a syntactic framework that can express the features of typical

inference rules.  Isabelle's distinctive feature is its representation of

logics using a meta-logic.  This meta-logic is just a fragment of

higher-order logic; known proof theory may be used to demonstrate that the

representation is correct~\cite{paulson89}.  The representation has much in

common with the Edinburgh Logical Framework~\cite{harper-jacm} and with 

Felty's~\cite{felty93} use of $\lambda$Prolog to implement logics.

An inference rule in Isabelle is a generalized Horn clause.  Rules are

joined to make proofs by resolving such clauses.  Logical variables in

goals can be instantiated incrementally.  But Isabelle is not a resolution

theorem prover like Otter.  Isabelle's clauses are drawn from a richer,

higher-order language and a fully automatic search would be impractical.

Isabelle does not join clauses automatically, but under strict user

control.  You can conduct single-step proofs, use Isabelle's built-in proof

procedures, or develop new proof procedures using tactics and tacticals.

Isabelle's meta-logic is higher-order, based on the typed

$\lambda$-calculus.  So resolution cannot use ordinary unification, but

higher-order unification~\cite{huet75}.  This complicated procedure gives

Isabelle strong support for many logical formalisms involving variable

binding.

The diagram below illustrates some of the logics distributed with Isabelle.

These include first-order logic (intuitionistic and classical), the sequent

calculus, higher-order logic, Zermelo-Fraenkel set theory~\cite{suppes72},

a version of Constructive Type Theory~\cite{nordstrom90}, several modal

logics, and a Logic for Computable Functions.  Several experimental

logics are also available, such a term assignment calculus for linear

logic.  

\centerline{\epsfbox{Isa-logics.eps}}

\section*{How to read this book}

Isabelle is a large system, but beginners can get by with a few commands

and a basic knowledge of how Isabelle works.  Some knowledge of

Standard~\ML{} is essential because \ML{} is Isabelle's user interface.

Advanced Isabelle theorem proving can involve writing \ML{} code, possibly

with Isabelle's sources at hand.  My book on~\ML{}~\cite{paulson91} covers

much material connected with Isabelle, including a simple theorem prover.

The Isabelle documentation is divided into three parts, which serve

distinct purposes:

\begin{itemize}

\item {\em Introduction to Isabelle\/} describes the basic features of

  Isabelle.  This part is intended to be read through.  If you are

  impatient to get started, you might skip the first chapter, which

  describes Isabelle's meta-logic in some detail.  The other chapters

  present on-line sessions of increasing difficulty.  It also explains how

  to derive rules define theories, and concludes with an extended example:

  a Prolog interpreter.

\item {\em The Isabelle Reference Manual\/} contains information about most

  of the facilities of Isabelle, apart from particular object-logics.  This

  part would make boring reading, though browsing might be useful.  Mostly

  you should use it to locate facts quickly.

\item {\em Isabelle's Object-Logics\/} describes the various logics

  distributed with Isabelle.  Its final chapter explains how to define new

  logics.  The other chapters are intended for reference only.

\end{itemize}

This book should not be read from start to finish.  Instead you might read

a couple of chapters from {\em Introduction to Isabelle}, then try some

examples referring to the other parts, return to the {\em Introduction},

and so forth.  Starred sections discuss obscure matters and may be skipped

on a first reading.

\section*{Releases of Isabelle}\index{Isabelle!release history}

Isabelle was first distributed in 1986.  The 1987 version introduced a

higher-order meta-logic with an improved treatment of quantifiers.  The

1988 version added limited polymorphism and support for natural deduction.

The 1989 version included a parser and pretty printer generator.  The 1992

version introduced type classes, to support many-sorted and higher-order

logics.  The 1993 version provides greater support for theories and is

much faster.  

Isabelle is still under development.  Projects under consideration include

better support for inductive definitions, some means of recording proofs, a

graphical user interface, and developments in the standard object-logics.

I hope but cannot promise to maintain upwards compatibility.

Isabelle is available by anonymous ftp:

\begin{itemize}

\item University of Cambridge\\

        host {\tt ftp.cl.cam.ac.uk}\\

        directory {\tt ml}

\item Technical University of Munich\\

        host {\tt ftp.informatik.tu-muenchen.de}\\

        directory {\tt local/lehrstuhl/nipkow}

\end{itemize}

My electronic mail address is {\tt lcp\at cl.cam.ac.uk}.  Please report any

errors you find in this book and your problems or successes with Isabelle.

\subsection*{Acknowledgements} 

Tobias Nipkow has made immense contributions to Isabelle, including the

parser generator, type classes, the simplifier, and several object-logics.

He also arranged for several of his students to help.  Carsten Clasohm

implemented the theory database; Markus Wenzel implemented macros; Sonia

Mahjoub and Karin Nimmermann also contributed.  

Nipkow and his students wrote much of the documentation underlying this

book.  Nipkow wrote the first versions of \S\ref{sec:defining-theories},

Chap.\ts\ref{simp-chap}, Chap.\ts\ref{Defining-Logics} and part of

Chap.\ts\ref{theories}, and App.\ts\ref{app:TheorySyntax}.  Carsten Clasohm

contributed to Chap.\ts\ref{theories}.  Markus Wenzel contributed to

Chap.\ts\ref{Defining-Logics}.

David Aspinall, Sara Kalvala, Ina Kraan, Zhenyu Qian, Norbert Voelker and

Markus Wenzel suggested changes and corrections to the documentation.

Martin Coen, Rajeev Gor\'e, Philippe de Groote and Philippe No\"el helped

to develop Isabelle's standard object-logics.  David Aspinall performed

some useful research into theories and implemented an Isabelle Emacs mode.

Isabelle was developed using Dave Matthews's Standard~{\sc ml} compiler,

Poly/{\sc ml}.  

The research has been funded by numerous SERC grants dating from the Alvey

programme (grants GR/E0355.7, GR/G53279, GR/H40570) and by ESPRIT (projects

3245: Logical Frameworks and 6453: Types).

\index{ML}