doc-src/Intro/intro.tex
author lcp
Wed Nov 10 05:06:55 1993 +0100 (1993-11-10)
changeset 105 216d6ed87399
child 184 236b655114a1
permissions -rw-r--r--
Initial revision
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\documentstyle[a4,12pt,proof,iman,alltt]{article}
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%% $Id$
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%% run    bibtex intro         to prepare bibliography
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%% run    ../sedindex intro    to prepare index file
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%prth *(\(.*\));          \1;      
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%{\\out \(.*\)}          {\\out val it = "\1" : thm}
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\title{Introduction to Isabelle}   
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\author{{\em Lawrence C. Paulson}\\
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        Computer Laboratory \\ University of Cambridge \\[2ex]
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        {\small{\em Electronic mail\/}: {\tt lcp@cl.cam.ac.uk}}
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}
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\date{} 
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\makeindex
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\underscoreoff
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\setcounter{secnumdepth}{2} \setcounter{tocdepth}{2}
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\sloppy
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\binperiod     %%%treat . like a binary operator
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\newcommand\qeq{\stackrel{?}{\equiv}}  %for disagreement pairs in unification
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\newcommand{\nand}{\mathbin{\lnot\&}} 
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\newcommand{\xor}{\mathbin{\#}}
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\pagenumbering{roman} 
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\begin{document}
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\pagestyle{empty}
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\begin{titlepage}
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\maketitle 
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\thispagestyle{empty}
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\vfill
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{\small Copyright \copyright{} \number\year{} by Lawrence C. Paulson}
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\end{titlepage}
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\pagestyle{headings}
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\part*{Preface}
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\index{Isabelle!overview}
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\index{Isabelle!object-logics supported}
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Isabelle~\cite{paulson86,paulson89,paulson700} is a generic theorem prover.
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It has been instantiated to support reasoning in several object-logics:
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\begin{itemize}
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\item first-order logic, constructive and classical versions
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\item higher-order logic, similar to that of Gordon's {\sc
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hol}~\cite{gordon88a}
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\item Zermelo-Fraenkel set theory~\cite{suppes72}
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\item an extensional version of Martin-L\"of's Type Theory~\cite{nordstrom90}
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\item the classical first-order sequent calculus, {\sc lk}
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\item the modal logics $T$, $S4$, and $S43$
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\item the Logic for Computable Functions~\cite{paulson87}
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\end{itemize}
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A logic's syntax and inference rules are specified declaratively; this
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allows single-step proof construction.  Isabelle provides control
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structures for expressing search procedures.  Isabelle also provides
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several generic tools, such as simplifiers and classical theorem provers,
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which can be applied to object-logics.
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\index{ML}
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Isabelle is a large system, but beginners can get by with a small
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repertoire of commands and a basic knowledge of how Isabelle works.  Some
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knowledge of Standard~\ML{} is essential, because \ML{} is Isabelle's user
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interface.  Advanced Isabelle theorem proving can involve writing \ML{}
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code, possibly with Isabelle's sources at hand.  My book
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on~\ML{}~\cite{paulson91} covers much material connected with Isabelle,
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including a simple theorem prover.  Users must be familiar with logic as
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used in computer science; there are many good
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texts~\cite{galton90,reeves90}.
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\index{LCF}
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{\sc lcf}, developed by Robin Milner and colleagues~\cite{gordon79}, is an
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ancestor of {\sc hol}, Nuprl, and several other systems.  Isabelle borrows
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ideas from {\sc lcf}: formulae are~\ML{} values; theorems belong to an
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abstract type; tactics and tacticals support backward proof.  But {\sc lcf}
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represents object-level rules by functions, while Isabelle represents them
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by terms.  You may find my other writings~\cite{paulson87,paulson-handbook}
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helpful in understanding the relationship between {\sc lcf} and Isabelle.
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Isabelle does not keep a record of inference steps.  Each step is checked
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at run time to ensure that theorems can only be constructed by applying
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inference rules.  An Isabelle proof typically involves hundreds of
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primitive inferences, and would be unintelligible if displayed.
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Discarding proofs saves vast amounts of storage.  But can Isabelle be
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trusted?  If desired, object-logics can be formalized such that each
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theorem carries a proof term, which could be checked by another program.
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Proofs can also be traced.
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\index{Isabelle!release history} Isabelle was first distributed in 1986.
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The 1987 version introduced a higher-order meta-logic with an improved
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treatment of quantifiers.  The 1988 version added limited polymorphism and
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support for natural deduction.  The 1989 version included a parser and
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pretty printer generator.  The 1992 version introduced type classes, to
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support many-sorted and higher-order logics.  The current version provides
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greater support for theories and is much faster.  Isabelle is still under
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development and will continue to change.
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\subsubsection*{Overview} 
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This manual consists of three parts.  
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Part~I discusses the Isabelle's foundations.
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Part~II, presents simple on-line sessions, starting with forward proof.
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It also covers basic tactics and tacticals, and some commands for invoking
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Part~III contains further examples for users with a bit of experience.
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It explains how to derive rules define theories, and concludes with an
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extended example: a Prolog interpreter.
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Isabelle's Reference Manual and Object-Logics manual contain more details.
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They assume familiarity with the concepts presented here.
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\subsubsection*{Acknowledgements} 
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Tobias Nipkow contributed most of the section on ``Defining Theories''.
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Sara Kalvala and Markus Wenzel suggested improvements.
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Tobias Nipkow has made immense contributions to Isabelle, including the
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parser generator, type classes, and the simplifier.  Carsten Clasohm, Sonia
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Mahjoub, Karin Nimmermann and Markus Wenzel also made improvements.
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Isabelle was developed using Dave Matthews's Standard~{\sc ml} compiler,
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Poly/{\sc ml}.  Many people have contributed to Isabelle's standard
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object-logics, including Martin Coen, Philippe de Groote, Philippe No\"el.
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The research has been funded by the SERC (grants GR/G53279, GR/H40570) and
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by ESPRIT (projects 3245: Logical Frameworks, and 6453: Types).
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\newpage
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\pagestyle{plain} \tableofcontents 
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\newpage
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\newfont{\sanssi}{cmssi12}
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\vspace*{2.5cm}
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\begin{quote}
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\raggedleft
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{\sanssi
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You can only find truth with logic\\
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if you have already found truth without it.}\\
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\bigskip
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G.K. Chesterton, {\em The Man who was Orthodox}
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\end{quote}
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\clearfirst  \pagestyle{headings}
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\include{foundations}
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\include{getting}
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\include{advanced}
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\bibliographystyle{plain} \small\raggedright\frenchspacing
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\bibliography{atp,funprog,general,logicprog,theory}
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\input{intro.ind}
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\end{document}