doc-src/preface.tex
 author haftmann Tue Sep 19 15:31:32 2006 +0200 (2006-09-19) changeset 20607 926a76a84e97 parent 14379 ea10a8c3e9cf permissions -rw-r--r--
Operational Equality
     1 \chapter*{Preface}

     2 \markboth{Preface}{Preface}   %or Preface ?

     3 %%\addcontentsline{toc}{chapter}{Preface}

     4

     5 Most theorem provers support a fixed logic, such as first-order or

     6 equational logic.  They bring sophisticated proof procedures to bear upon

     7 the conjectured formula.  The resolution prover Otter~\cite{wos-bledsoe} is

     8 an impressive example.

     9

    10 {\sc alf}~\cite{alf}, Coq~\cite{coq} and Nuprl~\cite{constable86} each

    11 support a fixed logic too.  These are higher-order type theories,

    12 explicitly concerned with computation and capable of expressing

    13 developments in constructive mathematics.  They are far removed from

    14 classical first-order logic.

    15

    16 A diverse collection of logics --- type theories, process calculi,

    17 $\lambda$-calculi --- may be found in the Computer Science literature.

    18 Such logics require proof support.  Few proof procedures are known for

    19 them, but the theorem prover can at least automate routine steps.

    20

    21 A {\bf generic} theorem prover is one that supports a variety of logics.

    22 Some generic provers are noteworthy for their user interfaces

    23 \cite{dawson90,mural,sawamura92}.  Most of them work by implementing a

    24 syntactic framework that can express typical inference rules.  Isabelle's

    25 distinctive feature is its representation of logics within a fragment of

    26 higher-order logic, called the meta-logic.  The proof theory of

    27 higher-order logic may be used to demonstrate that the representation is

    28 correct~\cite{paulson89}.  The approach has much in common with the

    29 Edinburgh Logical Framework~\cite{harper-jacm} and with

    30 Felty's~\cite{felty93} use of $\lambda$Prolog to implement logics.

    31

    32 An inference rule in Isabelle is a generalized Horn clause.  Rules are

    33 joined to make proofs by resolving such clauses.  Logical variables in

    34 goals can be instantiated incrementally.  But Isabelle is not a resolution

    35 theorem prover like Otter.  Isabelle's clauses are drawn from a richer

    36 language and a fully automatic search would be impractical.  Isabelle does

    37 not resolve clauses automatically, but under user direction.  You can

    38 conduct single-step proofs, use Isabelle's built-in proof procedures, or

    39 develop new proof procedures using tactics and tacticals.

    40

    41 Isabelle's meta-logic is higher-order, based on the simply typed

    42 $\lambda$-calculus.  So resolution cannot use ordinary unification, but

    43 higher-order unification~\cite{huet75}.  This complicated procedure gives

    44 Isabelle strong support for many logical formalisms involving variable

    45 binding.

    46

    47 The diagram below illustrates some of the logics distributed with Isabelle.

    48 These include first-order logic (intuitionistic and classical), the sequent

    49 calculus, higher-order logic, Zermelo-Fraenkel set theory~\cite{suppes72},

    50 a version of Constructive Type Theory~\cite{nordstrom90}, several modal

    51 logics, and a Logic for Computable Functions~\cite{paulson87}.  Several

    52 experimental logics are being developed, such as linear logic.

    53

    54 \centerline{\epsfbox{gfx/Isa-logics.eps}}

    55

    56

    57 \section*{How to read this book}

    58 Isabelle is a complex system, but beginners can get by with a few commands

    59 and a basic knowledge of how Isabelle works.  Some knowledge of

    60 Standard~\ML{} is essential because \ML{} is Isabelle's user interface.

    61 Advanced Isabelle theorem proving can involve writing \ML{} code, possibly

    62 with Isabelle's sources at hand.  My book on~\ML{}~\cite{paulson91} covers

    63 much material connected with Isabelle, including a simple theorem prover.

    64

    65 The Isabelle documentation is divided into three parts, which serve

    66 distinct purposes:

    67 \begin{itemize}

    68 \item {\em Introduction to Isabelle\/} describes the basic features of

    69   Isabelle.  This part is intended to be read through.  If you are

    70   impatient to get started, you might skip the first chapter, which

    71   describes Isabelle's meta-logic in some detail.  The other chapters

    72   present on-line sessions of increasing difficulty.  It also explains how

    73   to derive rules define theories, and concludes with an extended example:

    74   a Prolog interpreter.

    75

    76 \item {\em The Isabelle Reference Manual\/} provides detailed information

    77   about Isabelle's facilities, excluding the object-logics.  This part

    78   would make boring reading, though browsing might be useful.  Mostly you

    79   should use it to locate facts quickly.

    80

    81 \item {\em Isabelle's Object-Logics\/} describes the various logics

    82   distributed with Isabelle.  The chapters are intended for reference only;

    83   they overlap somewhat so that each chapter can be read in isolation.

    84 \end{itemize}

    85 This book should not be read from start to finish.  Instead you might read

    86 a couple of chapters from {\em Introduction to Isabelle}, then try some

    87 examples referring to the other parts, return to the {\em Introduction},

    88 and so forth.  Starred sections discuss obscure matters and may be skipped

    89 on a first reading.

    90

    91

    92

    93 \section*{Releases of Isabelle}

    94 Isabelle was first distributed in 1986.  The 1987 version introduced a

    95 higher-order meta-logic with an improved treatment of quantifiers.  The

    96 1988 version added limited polymorphism and support for natural deduction.

    97 The 1989 version included a parser and pretty printer generator.  The 1992

    98 version introduced type classes, to support many-sorted and higher-order

    99 logics.  The 1993 version provides greater support for theories and is

   100 much faster.

   101

   102 Isabelle is still under development.  Projects under consideration include

   103 better support for inductive definitions, some means of recording proofs, a

   104 graphical user interface, and developments in the standard object-logics.

   105 I hope but cannot promise to maintain upwards compatibility.

   106

   107 Isabelle can be downloaded from .

   108 \begin{quote}

   109 {\tt http://www.cl.cam.ac.uk/Research/HVG/Isabelle/dist/}

   110 \end{quote}

   111 The electronic distribution list {\tt isabelle-users\at cl.cam.ac.uk}

   112 provides a forum for discussing problems and applications involving

   113 Isabelle.  To join, send me a message via {\tt lcp\at cl.cam.ac.uk}.

   114 Please notify me of any errors you find in this book.

   115

   116 \section*{Acknowledgements}

   117 Tobias Nipkow has made immense contributions to Isabelle, including the

   118 parser generator, type classes, the simplifier, and several object-logics.

   119 He also arranged for several of his students to help.  Carsten Clasohm

   120 implemented the theory database; Markus Wenzel implemented macros; Sonia

   121 Mahjoub and Karin Nimmermann also contributed.

   122

   123 Nipkow and his students wrote much of the documentation underlying this

   124 book.  Nipkow wrote the first versions of \S\ref{sec:defining-theories},

   125 \S\ref{sec:ref-defining-theories}, Chap.\ts\ref{Defining-Logics},

   126 Chap.\ts\ref{simp-chap} and App.\ts\ref{app:TheorySyntax}\@.  Carsten

   127 Clasohm contributed to Chap.\ts\ref{theories}.  Markus Wenzel contributed

   128 to Chap.\ts\ref{chap:syntax}.  Nipkow also provided the quotation at

   129 the front.

   130

   131 David Aspinall, Sara Kalvala, Ina Kraan, Chris Owens, Zhenyu Qian, Norbert

   132 V{\"o}lker and Markus Wenzel suggested changes and corrections to the

   133 documentation.

   134

   135 Martin Coen, Rajeev Gor\'e, Philippe de Groote and Philippe No\"el helped

   136 to develop Isabelle's standard object-logics.  David Aspinall performed

   137 some useful research into theories and implemented an Isabelle Emacs mode.

   138 Isabelle was developed using Dave Matthews's Standard~{\sc ml} compiler,

   139 Poly/{\sc ml}.

   140

   141 The research has been funded by numerous SERC grants dating from the Alvey

   142 programme (grants GR/E0355.7, GR/G53279, GR/H40570) and by ESPRIT (projects

   143 3245: Logical Frameworks and 6453: Types).