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\title{Introduction to Isabelle}   
\author{{\em Lawrence C. Paulson}\\
        Computer Laboratory \\ University of Cambridge \\[2ex]
        {\small{\em Electronic mail\/}: {\tt [e-mail]}}
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{\small Copyright \copyright{} \number\year{} by Lawrence C. Paulson}
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\part*{Preface}
\index{Isabelle!overview}
\index{Isabelle!object-logics supported}
Isabelle~\cite{paulson86,paulson89,paulson700} is a generic theorem prover.
It has been instantiated to support reasoning in several object-logics:
\begin{itemize}
\item first-order logic, constructive and classical versions
\item higher-order logic, similar to that of Gordon's {\sc
hol}~\cite{gordon88a}
\item Zermelo-Fraenkel set theory~\cite{suppes72}
\item an extensional version of Martin-L\"of's Type Theory~\cite{nordstrom90}
\item the classical first-order sequent calculus, {\sc lk}
\item the modal logics $T$, $S4$, and $S43$
\item the Logic for Computable Functions~\cite{paulson87}
\end{itemize}
A logic's syntax and inference rules are specified declaratively; this
allows single-step proof construction.  Isabelle provides control
structures for expressing search procedures.  Isabelle also provides
several generic tools, such as simplifiers and classical theorem provers,
which can be applied to object-logics.

\index{ML}
Isabelle is a large system, but beginners can get by with a small
repertoire of 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.  Users must be familiar with logic as
used in computer science; there are many good
texts~\cite{galton90,reeves90}.

\index{LCF}
{\sc lcf}, developed by Robin Milner and colleagues~\cite{gordon79}, is an
ancestor of {\sc hol}, Nuprl, and several other systems.  Isabelle borrows
ideas from {\sc lcf}: formulae are~\ML{} values; theorems belong to an
abstract type; tactics and tacticals support backward proof.  But {\sc lcf}
represents object-level rules by functions, while Isabelle represents them
by terms.  You may find my other writings~\cite{paulson87,paulson-handbook}
helpful in understanding the relationship between {\sc lcf} and Isabelle.

Isabelle does not keep a record of inference steps.  Each step is checked
at run time to ensure that theorems can only be constructed by applying
inference rules.  An Isabelle proof typically involves hundreds of
primitive inferences, and would be unintelligible if displayed.
Discarding proofs saves vast amounts of storage.  But can Isabelle be
trusted?  If desired, object-logics can be formalized such that each
theorem carries a proof term, which could be checked by another program.
Proofs can also be traced.

\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 current version provides
greater support for theories and is much faster.  Isabelle is still under
development and will continue to change.

\subsubsection*{Overview} 
This manual consists of three parts.  
Part~I discusses the Isabelle's foundations.
Part~II, presents simple on-line sessions, starting with forward proof.
It also covers basic tactics and tacticals, and some commands for invoking
Part~III contains further examples for users with a bit of experience.
It explains how to derive rules define theories, and concludes with an
extended example: a Prolog interpreter.

Isabelle's Reference Manual and Object-Logics manual contain more details.
They assume familiarity with the concepts presented here.


\subsubsection*{Acknowledgements} 
Tobias Nipkow contributed most of the section on ``Defining Theories''.
Sara Kalvala and Markus Wenzel suggested improvements.

Tobias Nipkow has made immense contributions to Isabelle, including the
parser generator, type classes, and the simplifier.  Carsten Clasohm, Sonia
Mahjoub, Karin Nimmermann and Markus Wenzel also made improvements.
Isabelle was developed using Dave Matthews's Standard~{\sc ml} compiler,
Poly/{\sc ml}.  Many people have contributed to Isabelle's standard
object-logics, including Martin Coen, Philippe de Groote, Philippe No\"el.
The research has been funded by the SERC (grants GR/G53279, GR/H40570) and
by ESPRIT (projects 3245: Logical Frameworks, and 6453: Types).

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\begin{quote}
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{\sanssi
You can only find truth with logic\\
if you have already found truth without it.}\\
\bigskip

G.K. Chesterton, {\em The Man who was Orthodox}
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