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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}

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}

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

18 \underscoreoff

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

22 \sloppy

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

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

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

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

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35 which is largely superseded by the Isabelle/HOL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.

44 \thispagestyle{empty}

45 \vfill

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

47 \end{titlepage}

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.

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}.

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.

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.

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.

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

112 They assume familiarity with the concepts presented here.

115 \subsubsection*{Acknowledgements}

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

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

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}.

130 \newpage

131 \pagestyle{plain} \tableofcontents

132 \newpage

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

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

144 \end{quote}

146 \clearfirst \pagestyle{headings}

147 \include{foundations}

148 \include{getting}

149 \include{advanced}

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

152 \bibliography{../manual}

154 \printindex

155 \end{document}