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16 \title{Introduction to Isabelle}
17 \author{{\em Lawrence C. Paulson}\\
18 Computer Laboratory \\ University of Cambridge \\
19 \texttt{lcp@cl.cam.ac.uk}\\[3ex]
20 With Contributions by Tobias Nipkow and Markus Wenzel
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42 {\small Copyright \copyright{} \number\year{} by Lawrence C. Paulson}
47 \index{Isabelle!overview} \index{Isabelle!object-logics supported}
48 Isabelle~\cite{paulson-natural,paulson-found,paulson700} is a generic theorem
49 prover. It has been instantiated to support reasoning in several
52 \item first-order logic, constructive and classical versions
53 \item higher-order logic, similar to that of Gordon's {\sc
54 hol}~\cite{mgordon-hol}
55 \item Zermelo-Fraenkel set theory~\cite{suppes72}
56 \item an extensional version of Martin-L\"of's Type Theory~\cite{nordstrom90}
57 \item the classical first-order sequent calculus, {\sc lk}
58 \item the modal logics $T$, $S4$, and $S43$
59 \item the Logic for Computable Functions~\cite{paulson87}
61 A logic's syntax and inference rules are specified declaratively; this
62 allows single-step proof construction. Isabelle provides control
63 structures for expressing search procedures. Isabelle also provides
64 several generic tools, such as simplifiers and classical theorem provers,
65 which can be applied to object-logics.
68 Isabelle is a large system, but beginners can get by with a small
69 repertoire of commands and a basic knowledge of how Isabelle works. Some
70 knowledge of Standard~\ML{} is essential, because \ML{} is Isabelle's user
71 interface. Advanced Isabelle theorem proving can involve writing \ML{}
72 code, possibly with Isabelle's sources at hand. My book
73 on~\ML{}~\cite{paulson91} covers much material connected with Isabelle,
74 including a simple theorem prover. Users must be familiar with logic as
75 used in computer science; there are many good
76 texts~\cite{galton90,reeves90}.
79 {\sc lcf}, developed by Robin Milner and colleagues~\cite{mgordon79}, is an
80 ancestor of {\sc hol}, Nuprl, and several other systems. Isabelle borrows
81 ideas from {\sc lcf}: formulae are~\ML{} values; theorems belong to an
82 abstract type; tactics and tacticals support backward proof. But {\sc lcf}
83 represents object-level rules by functions, while Isabelle represents them
84 by terms. You may find my other writings~\cite{paulson87,paulson-handbook}
85 helpful in understanding the relationship between {\sc lcf} and Isabelle.
87 \index{Isabelle!release history} Isabelle was first distributed in 1986.
88 The 1987 version introduced a higher-order meta-logic with an improved
89 treatment of quantifiers. The 1988 version added limited polymorphism and
90 support for natural deduction. The 1989 version included a parser and
91 pretty printer generator. The 1992 version introduced type classes, to
92 support many-sorted and higher-order logics. The current version provides
93 greater support for theories and is much faster. Isabelle is still under
94 development and will continue to change.
96 \subsubsection*{Overview}
97 This manual consists of three parts. Part~I discusses the Isabelle's
98 foundations. Part~II, presents simple on-line sessions, starting with
99 forward proof. It also covers basic tactics and tacticals, and some
100 commands for invoking them. Part~III contains further examples for users
101 with a bit of experience. It explains how to derive rules define theories,
102 and concludes with an extended example: a Prolog interpreter.
104 Isabelle's Reference Manual and Object-Logics manual contain more details.
105 They assume familiarity with the concepts presented here.
108 \subsubsection*{Acknowledgements}
109 Tobias Nipkow contributed most of the section on defining theories.
110 Stefan Berghofer and Sara Kalvala suggested improvements.
112 Tobias Nipkow has made immense contributions to Isabelle, including the
113 parser generator, type classes, and the simplifier. Carsten Clasohm and
114 Markus Wenzel made major contributions; Sonia Mahjoub and Karin Nimmermann
115 also helped. Isabelle was developed using Dave Matthews's Standard~{\sc
116 ml} compiler, Poly/{\sc ml}. Many people have contributed to Isabelle's
117 standard object-logics, including Martin Coen, Philippe de Groote, Philippe
118 No\"el. The research has been funded by the EPSRC (grants
119 GR/G53279, GR/H40570, GR/K57381, GR/K77051)
120 and by ESPRIT (projects 3245: Logical Frameworks, and 6453: Types).
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131 You can only find truth with logic\\
132 if you have already found truth without it.}\\
135 G.K. Chesterton, {\em The Man who was Orthodox}
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