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\title{Introduction to Isabelle}


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


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Computer Laboratory \\ University of Cambridge \\[2ex]


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{\small{\em Electronic mail\/}: {\tt lcp@cl.cam.ac.uk}}


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\begin{document}


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{\small Copyright \copyright{} \number\year{} by Lawrence C. Paulson}


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\part*{Preface}

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\index{Isabelle!overview} \index{Isabelle!objectlogics supported}


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Isabelle~\cite{paulsonnatural,paulsonfound,paulson700} is a generic theorem


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prover. It has been instantiated to support reasoning in several


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objectlogics:

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\begin{itemize}


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\item firstorder logic, constructive and classical versions


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\item higherorder logic, similar to that of Gordon's {\sc

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hol}~\cite{mgordonhol}

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\item ZermeloFraenkel set theory~\cite{suppes72}


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\item an extensional version of MartinL\"of's Type Theory~\cite{nordstrom90}


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\item the classical firstorder sequent calculus, {\sc lk}


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\item the modal logics $T$, $S4$, and $S43$


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\item the Logic for Computable Functions~\cite{paulson87}


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\end{itemize}


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A logic's syntax and inference rules are specified declaratively; this


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allows singlestep proof construction. Isabelle provides control


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structures for expressing search procedures. Isabelle also provides


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several generic tools, such as simplifiers and classical theorem provers,


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which can be applied to objectlogics.


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\index{ML}


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


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


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knowledge of Standard~\ML{} is essential, because \ML{} is Isabelle's user


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interface. Advanced Isabelle theorem proving can involve writing \ML{}


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code, possibly with Isabelle's sources at hand. My book


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on~\ML{}~\cite{paulson91} covers much material connected with Isabelle,


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including a simple theorem prover. Users must be familiar with logic as


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used in computer science; there are many good


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texts~\cite{galton90,reeves90}.


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\index{LCF}

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{\sc lcf}, developed by Robin Milner and colleagues~\cite{mgordon79}, is an

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ancestor of {\sc hol}, Nuprl, and several other systems. Isabelle borrows


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ideas from {\sc lcf}: formulae are~\ML{} values; theorems belong to an


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abstract type; tactics and tacticals support backward proof. But {\sc lcf}


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represents objectlevel rules by functions, while Isabelle represents them


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by terms. You may find my other writings~\cite{paulson87,paulsonhandbook}


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helpful in understanding the relationship between {\sc lcf} and Isabelle.


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\index{Isabelle!release history} Isabelle was first distributed in 1986.


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The 1987 version introduced a higherorder metalogic with an improved


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treatment of quantifiers. The 1988 version added limited polymorphism and


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support for natural deduction. The 1989 version included a parser and


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pretty printer generator. The 1992 version introduced type classes, to


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support manysorted and higherorder logics. The current version provides


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greater support for theories and is much faster. Isabelle is still under


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development and will continue to change.


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\subsubsection*{Overview}

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This manual consists of three parts. Part~I discusses the Isabelle's


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foundations. Part~II, presents simple online sessions, starting with


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forward proof. It also covers basic tactics and tacticals, and some


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commands for invoking them. Part~III contains further examples for users


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with a bit of experience. It explains how to derive rules define theories,


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and concludes with an extended example: a Prolog interpreter.

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Isabelle's Reference Manual and ObjectLogics manual contain more details.


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They assume familiarity with the concepts presented here.


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\subsubsection*{Acknowledgements}

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Tobias Nipkow contributed most of the section on defining theories.

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Stefan Berghofer, Sara Kalvala and Markus Wenzel suggested improvements.

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Tobias Nipkow has made immense contributions to Isabelle, including the

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


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Markus Wenzel made major contributions; Sonia Mahjoub and Karin Nimmermann


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also helped. Isabelle was developed using Dave Matthews's Standard~{\sc


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ml} compiler, Poly/{\sc ml}. Many people have contributed to Isabelle's


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standard objectlogics, including Martin Coen, Philippe de Groote, Philippe


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No\"el. The research has been funded by the SERC (grants GR/G53279,


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GR/H40570) and by ESPRIT (projects 3245: Logical Frameworks, and 6453:


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Types).

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\vspace*{2.5cm}


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\begin{quote}


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\raggedleft


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{\sanssi


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You can only find truth with logic\\


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if you have already found truth without it.}\\


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\bigskip


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


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\end{quote}


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