doc-src/Intro/intro.tex
 author wenzelm Mon Oct 01 21:19:50 2007 +0200 (2007-10-01) changeset 24803 38577b4b1fde parent 14148 6580d374a509 child 30118 df610709eda5 permissions -rw-r--r--
Norbert Schirmer: record improvements;
     1 \documentclass[12pt,a4paper]{article}

     2 \usepackage{graphicx,../iman,../extra,../ttbox,../proof,../pdfsetup}

     3

     4 %% $Id$

     5 %% run    bibtex intro         to prepare bibliography

     6 %% run    ../sedindex intro    to prepare index file

     7 %prth *($$.*$$);          \1;

     8 %{\\out $$.*$$}          {\\out val it = "\1" : thm}

     9

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

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

    12         Computer Laboratory \\ University of Cambridge \\

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

    14         With Contributions by Tobias Nipkow and Markus Wenzel

    15 }

    16 \makeindex

    17

    18 \underscoreoff

    19

    20 \setcounter{secnumdepth}{2} \setcounter{tocdepth}{2}

    21

    22 \sloppy

    23 \binperiod     %%%treat . like a binary operator

    24

    25 \newcommand\qeq{\stackrel{?}{\equiv}}  %for disagreement pairs in unification

    26 \newcommand{\nand}{\mathbin{\lnot\&}}

    27 \newcommand{\xor}{\mathbin{\#}}

    28

    29 \pagenumbering{roman}

    30 \begin{document}

    31 \pagestyle{empty}

    32 \begin{titlepage}

    33 \maketitle

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

    35 which is largely superseded by the Isabelle/HOL

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

    37 syntax and shows how to conduct proofs using the

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

    39 most Isabelle proofs are now written using the Isar

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

    41 information that is not available elsewhere. Its examples are based

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

    43

    44 \thispagestyle{empty}

    45 \vfill

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

    47 \end{titlepage}

    48

    49 \pagestyle{headings}

    50 \part*{Preface}

    51 \index{Isabelle!overview} \index{Isabelle!object-logics supported}

    52 Isabelle~\cite{paulson-natural,paulson-found,paulson700} is a generic theorem

    53 prover.  It has been instantiated to support reasoning in several

    54 object-logics:

    55 \begin{itemize}

    56 \item first-order logic, constructive and classical versions

    57 \item higher-order logic, similar to that of Gordon's {\sc

    58 hol}~\cite{mgordon-hol}

    59 \item Zermelo-Fraenkel set theory~\cite{suppes72}

    60 \item an extensional version of Martin-L\"of's Type Theory~\cite{nordstrom90}

    61 \item the classical first-order sequent calculus, {\sc lk}

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

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

    64 \end{itemize}

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

    66 allows single-step proof construction.  Isabelle provides control

    67 structures for expressing search procedures.  Isabelle also provides

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

    69 which can be applied to object-logics.

    70

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

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

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

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

    75 \index{ML}

    76 if you are prepared to writing \ML{}

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

    78 on~\ML{}~\cite{paulson-ml2} covers much material connected with Isabelle,

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

    80 used in computer science; there are many good

    81 texts~\cite{galton90,reeves90}.

    82

    83 \index{LCF}

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

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

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

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

    88 represents object-level rules by functions, while Isabelle represents them

    89 by terms.  You may find my other writings~\cite{paulson87,paulson-handbook}

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

    91

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

    93 The 1987 version introduced a higher-order meta-logic with an improved

    94 treatment of quantifiers.  The 1988 version added limited polymorphism and

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

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

    97 support many-sorted and higher-order logics.  The 1994 version introduced

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

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

   100 Isabelle is still under

   101 development and will continue to change.

   102

   103 \subsubsection*{Overview}

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

   105 foundations.  Part~II, presents simple on-line sessions, starting with

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

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

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

   109 and concludes with an extended example: a Prolog interpreter.

   110

   111 Isabelle's Reference Manual and Object-Logics manual contain more details.

   112 They assume familiarity with the concepts presented here.

   113

   114

   115 \subsubsection*{Acknowledgements}

   116 Tobias Nipkow contributed most of the section on defining theories.

   117 Stefan Berghofer, Sara Kalvala and Viktor Kuncak suggested improvements.

   118

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

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

   121 Wenzel made major contributions; Sonia Mahjoub and Karin Nimmermann also

   122 helped.  Isabelle was developed using Dave Matthews's Standard~{\sc ml}

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

   124 object-logics, including Martin Coen, Philippe de Groote, Philippe No\"el.

   125 The research has been funded by the EPSRC (grants GR/G53279, GR/H40570,

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

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

   128 \emph{Deduktion}.

   129

   130 \newpage

   131 \pagestyle{plain} \tableofcontents

   132 \newpage

   133

   134 \newfont{\sanssi}{cmssi12}

   135 \vspace*{2.5cm}

   136 \begin{quote}

   137 \raggedleft

   138 {\sanssi

   139 You can only find truth with logic\\

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

   141 \bigskip

   142

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

   144 \end{quote}

   145

   146 \clearfirst  \pagestyle{headings}

   147 \include{foundations}

   148 \include{getting}

   149 \include{advanced}

   150

   151 \bibliographystyle{plain} \small\raggedright\frenchspacing

   152 \bibliography{../manual}

   153

   154 \printindex

   155 \end{document}