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\chapter*{Preface}

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

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%%\addcontentsline{toc}{chapter}{Preface}

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Most theorem provers support a fixed logic, such as firstorder or

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equational logic. They bring sophisticated proof procedures to bear upon

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the conjectured formula. The resolution prover Otter~\cite{wosbledsoe} is

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an impressive example.

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{\sc alf}~\cite{alf}, Coq~\cite{coq} and Nuprl~\cite{constable86} each

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support a fixed logic too. These are higherorder type theories,

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explicitly concerned with computation and capable of expressing

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developments in constructive mathematics. They are far removed from

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classical firstorder logic.

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A diverse collection of logics  type theories, process calculi,

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$\lambda$calculi  may be found in the Computer Science literature.

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Such logics require proof support. Few proof procedures are known for

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them, but the theorem prover can at least automate routine steps.

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A {\bf generic} theorem prover is one that supports a variety of logics.

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Some generic provers are noteworthy for their user interfaces

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\cite{dawson90,mural,sawamura92}. Most of them work by implementing a

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syntactic framework that can express typical inference rules. Isabelle's

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distinctive feature is its representation of logics within a fragment of

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higherorder logic, called the metalogic. The proof theory of

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higherorder logic may be used to demonstrate that the representation is

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correct~\cite{paulson89}. The approach has much in common with the

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Edinburgh Logical Framework~\cite{harperjacm} and with

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

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

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

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

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

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language and a fully automatic search would be impractical. Isabelle does

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not resolve clauses automatically, but under user direction. You can

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conduct singlestep proofs, use Isabelle's builtin proof procedures, or

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develop new proof procedures using tactics and tacticals.

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Isabelle's metalogic is higherorder, based on the simply typed

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

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higherorder unification~\cite{huet75}. This complicated procedure gives

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Isabelle strong support for many logical formalisms involving variable

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binding.

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

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These include firstorder logic (intuitionistic and classical), the sequent

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calculus, higherorder logic, ZermeloFraenkel set theory~\cite{suppes72},

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

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logics, and a Logic for Computable Functions~\cite{paulson87}. Several

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experimental logics are being developed, such as linear logic.

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\centerline{\epsfbox{gfx/Isalogics.eps}}

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\section*{How to read this book}

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

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

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

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

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

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

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The Isabelle documentation is divided into three parts, which serve

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distinct purposes:

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\begin{itemize}

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

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

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

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describes Isabelle's metalogic in some detail. The other chapters

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present online sessions of increasing difficulty. It also explains how

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

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a Prolog interpreter.

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\item {\em The Isabelle Reference Manual\/} provides detailed information

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about Isabelle's facilities, excluding the objectlogics. This part

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

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should use it to locate facts quickly.

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\item {\em Isabelle's ObjectLogics\/} describes the various logics

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distributed with Isabelle. The chapters are intended for reference only;

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they overlap somewhat so that each chapter can be read in isolation.

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\end{itemize}

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

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

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

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

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on a first reading.

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\section*{Releases of Isabelle}

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

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higherorder metalogic with an improved treatment of quantifiers. The

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1988 version added limited polymorphism and support for natural deduction.

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

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version introduced type classes, to support manysorted and higherorder

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

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much faster.

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Isabelle is still under development. Projects under consideration include

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

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graphical user interface, and developments in the standard objectlogics.

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I hope but cannot promise to maintain upwards compatibility.

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Isabelle can be downloaded from .

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\begin{quote}

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{\tt http://www.cl.cam.ac.uk/Research/HVG/Isabelle/dist/}

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\end{quote}

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The electronic distribution list {\tt isabelleusers\at cl.cam.ac.uk}

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provides a forum for discussing problems and applications involving

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Isabelle. To join, send me a message via {\tt lcp\at cl.cam.ac.uk}.

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Please notify me of any errors you find in this book.

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\section*{Acknowledgements}

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Tobias Nipkow has made immense contributions to Isabelle, including the

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parser generator, type classes, the simplifier, and several objectlogics.

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

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implemented the theory database; Markus Wenzel implemented macros; Sonia

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Mahjoub and Karin Nimmermann also contributed.

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Nipkow and his students wrote much of the documentation underlying this

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

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\S\ref{sec:refdefiningtheories}, Chap.\ts\ref{DefiningLogics},

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Chap.\ts\ref{simpchap} and App.\ts\ref{app:TheorySyntax}\@. Carsten

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

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to Chap.\ts\ref{chap:syntax}. Nipkow also provided the quotation at

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the front.

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David Aspinall, Sara Kalvala, Ina Kraan, Chris Owens, Zhenyu Qian, Norbert

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V{\"o}lker and Markus Wenzel suggested changes and corrections to the

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documentation.

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

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to develop Isabelle's standard objectlogics. David Aspinall performed

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

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

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Poly/{\sc ml}.

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

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

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3245: Logical Frameworks and 6453: Types).
