1 \documentclass[12pt,a4paper]{article}
2 \usepackage{graphicx,../iman,../extra,../ttbox,../proof,../pdfsetup}
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8 %{\\out \(.*\)} {\\out val it = "\1" : thm}
10 \title{\includegraphics[scale=0.5]{isabelle} \\[4ex] Old 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
20 \setcounter{secnumdepth}{2} \setcounter{tocdepth}{2}
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{\#}}
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35 which is largely superseded by the Isabelle/HOL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.
46 {\small Copyright \copyright{} \number\year{} by Lawrence C. Paulson}
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
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}
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{};
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}.
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
131 \pagestyle{plain} \tableofcontents
134 \newfont{\sanssi}{cmssi12}
139 You can only find truth with logic\\
140 if you have already found truth without it.}\\
143 G.K. Chesterton, {\em The Man who was Orthodox}
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147 \include{foundations}
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152 \bibliography{../manual}