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\title{\includegraphics[scale=0.5]{isabelle} \\[4ex] Old Introduction to Isabelle}   

\author{{\em Lawrence C. Paulson}\\

        Computer Laboratory \\ University of Cambridge \\

        \texttt{lcp@cl.cam.ac.uk}\\[3ex] 

        With Contributions by Tobias Nipkow and Markus Wenzel

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\emph{Note}: this document is part of the earlier Isabelle documentation, 

which is largely superseded by the Isabelle/HOL

\emph{Tutorial}~\cite{isa-tutorial}. It describes the old-style theory 

syntax and shows how to conduct proofs using the 

ML top level. This style of interaction is largely obsolete:

most Isabelle proofs are now written using the Isar 

language and the Proof General interface. However, this paper contains valuable 

information that is not available elsewhere. Its examples are based 

on first-order logic rather than higher-order logic.

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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{paulson-natural,paulson-found,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{mgordon-hol}

\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.

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

repertoire of commands and a basic knowledge of how Isabelle works.  

The Isabelle/HOL \emph{Tutorial}~\cite{isa-tutorial} describes how to get started. Advanced Isabelle users will benefit from some

knowledge of Standard~\ML{}, because Isabelle is written in \ML{};

\index{ML}

if you are prepared to writing \ML{}

code, you can get Isabelle to do almost anything.  My book

on~\ML{}~\cite{paulson-ml2} 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{mgordon79}, 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.

\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 1994 version introduced

greater support for theories.  The most important recent change is the

introduction of the Isar proof language, thanks to Markus Wenzel.  

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 them.  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.

Stefan Berghofer, Sara Kalvala and Viktor Kuncak suggested improvements.

Tobias Nipkow has made immense contributions to Isabelle, including the parser

generator, type classes, and the simplifier.  Carsten Clasohm and Markus

Wenzel made major contributions; Sonia Mahjoub and Karin Nimmermann also

helped.  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 EPSRC (grants GR/G53279, GR/H40570,

GR/K57381, GR/K77051, GR/M75440) and by ESPRIT (projects 3245: Logical

Frameworks, and 6453: Types), and by the DFG Schwerpunktprogramm

\emph{Deduktion}.

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\begin{quote}

\raggedleft

{\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}

\end{quote}

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