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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
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36 {\small Copyright \copyright{} \number\year{} by Lawrence C. Paulson}
41 \index{Isabelle!overview} \index{Isabelle!object-logics supported}
42 Isabelle~\cite{paulson-natural,paulson-found,paulson700} is a generic theorem
43 prover. It has been instantiated to support reasoning in several
46 \item first-order logic, constructive and classical versions
47 \item higher-order logic, similar to that of Gordon's {\sc
48 hol}~\cite{mgordon-hol}
49 \item Zermelo-Fraenkel set theory~\cite{suppes72}
50 \item an extensional version of Martin-L\"of's Type Theory~\cite{nordstrom90}
51 \item the classical first-order sequent calculus, {\sc lk}
52 \item the modal logics $T$, $S4$, and $S43$
53 \item the Logic for Computable Functions~\cite{paulson87}
55 A logic's syntax and inference rules are specified declaratively; this
56 allows single-step proof construction. Isabelle provides control
57 structures for expressing search procedures. Isabelle also provides
58 several generic tools, such as simplifiers and classical theorem provers,
59 which can be applied to object-logics.
62 Isabelle is a large system, but beginners can get by with a small
63 repertoire of commands and a basic knowledge of how Isabelle works. Some
64 knowledge of Standard~\ML{} is essential, because \ML{} is Isabelle's user
65 interface. Advanced Isabelle theorem proving can involve writing \ML{}
66 code, possibly with Isabelle's sources at hand. My book
67 on~\ML{}~\cite{paulson-ml2} covers much material connected with Isabelle,
68 including a simple theorem prover. Users must be familiar with logic as
69 used in computer science; there are many good
70 texts~\cite{galton90,reeves90}.
73 {\sc lcf}, developed by Robin Milner and colleagues~\cite{mgordon79}, is an
74 ancestor of {\sc hol}, Nuprl, and several other systems. Isabelle borrows
75 ideas from {\sc lcf}: formulae are~\ML{} values; theorems belong to an
76 abstract type; tactics and tacticals support backward proof. But {\sc lcf}
77 represents object-level rules by functions, while Isabelle represents them
78 by terms. You may find my other writings~\cite{paulson87,paulson-handbook}
79 helpful in understanding the relationship between {\sc lcf} and Isabelle.
81 \index{Isabelle!release history} Isabelle was first distributed in 1986.
82 The 1987 version introduced a higher-order meta-logic with an improved
83 treatment of quantifiers. The 1988 version added limited polymorphism and
84 support for natural deduction. The 1989 version included a parser and
85 pretty printer generator. The 1992 version introduced type classes, to
86 support many-sorted and higher-order logics. The current version provides
87 greater support for theories and is much faster. Isabelle is still under
88 development and will continue to change.
90 \subsubsection*{Overview}
91 This manual consists of three parts. Part~I discusses the Isabelle's
92 foundations. Part~II, presents simple on-line sessions, starting with
93 forward proof. It also covers basic tactics and tacticals, and some
94 commands for invoking them. Part~III contains further examples for users
95 with a bit of experience. It explains how to derive rules define theories,
96 and concludes with an extended example: a Prolog interpreter.
98 Isabelle's Reference Manual and Object-Logics manual contain more details.
99 They assume familiarity with the concepts presented here.
102 \subsubsection*{Acknowledgements}
103 Tobias Nipkow contributed most of the section on defining theories.
104 Stefan Berghofer and Sara Kalvala suggested improvements.
106 Tobias Nipkow has made immense contributions to Isabelle, including the parser
107 generator, type classes, and the simplifier. Carsten Clasohm and Markus
108 Wenzel made major contributions; Sonia Mahjoub and Karin Nimmermann also
109 helped. Isabelle was developed using Dave Matthews's Standard~{\sc ml}
110 compiler, Poly/{\sc ml}. Many people have contributed to Isabelle's standard
111 object-logics, including Martin Coen, Philippe de Groote, Philippe No\"el.
112 The research has been funded by the EPSRC (grants GR/G53279, GR/H40570,
113 GR/K57381, GR/K77051, GR/M75440) and by ESPRIT (projects 3245: Logical
114 Frameworks, and 6453: Types), and by the DFG Schwerpunktprogramm
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126 You can only find truth with logic\\
127 if you have already found truth without it.}\\
130 G.K. Chesterton, {\em The Man who was Orthodox}
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