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+++ b/doc-src/IsarRef/Thy/Introduction.thy Mon Jun 02 21:01:42 2008 +0200
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+(* $Id$ *)
+
+theory Introduction
+imports Pure
+begin
+
+chapter {* Introduction *}
+
+section {* Overview *}
+
+text {*
+ The \emph{Isabelle} system essentially provides a generic
+ infrastructure for building deductive systems (programmed in
+ Standard ML), with a special focus on interactive theorem proving in
+ higher-order logics. In the olden days even end-users would refer
+ to certain ML functions (goal commands, tactics, tacticals etc.) to
+ pursue their everyday theorem proving tasks
+ \cite{isabelle-intro,isabelle-ref}.
+
+ In contrast \emph{Isar} provides an interpreted language environment
+ of its own, which has been specifically tailored for the needs of
+ theory and proof development. Compared to raw ML, the Isabelle/Isar
+ top-level provides a more robust and comfortable development
+ platform, with proper support for theory development graphs,
+ single-step transactions with unlimited undo, etc. The
+ Isabelle/Isar version of the \emph{Proof~General} user interface
+ \cite{proofgeneral,Aspinall:TACAS:2000} provides an adequate
+ front-end for interactive theory and proof development in this
+ advanced theorem proving environment.
+
+ \medskip Apart from the technical advances over bare-bones ML
+ programming, the main purpose of the Isar language is to provide a
+ conceptually different view on machine-checked proofs
+ \cite{Wenzel:1999:TPHOL,Wenzel-PhD}. ``Isar'' stands for
+ ``Intelligible semi-automated reasoning''. Drawing from both the
+ traditions of informal mathematical proof texts and high-level
+ programming languages, Isar offers a versatile environment for
+ structured formal proof documents. Thus properly written Isar
+ proofs become accessible to a broader audience than unstructured
+ tactic scripts (which typically only provide operational information
+ for the machine). Writing human-readable proof texts certainly
+ requires some additional efforts by the writer to achieve a good
+ presentation, both of formal and informal parts of the text. On the
+ other hand, human-readable formal texts gain some value in their own
+ right, independently of the mechanic proof-checking process.
+
+ Despite its grand design of structured proof texts, Isar is able to
+ assimilate the old tactical style as an ``improper'' sub-language.
+ This provides an easy upgrade path for existing tactic scripts, as
+ well as additional means for interactive experimentation and
+ debugging of structured proofs. Isabelle/Isar supports a broad
+ range of proof styles, both readable and unreadable ones.
+
+ \medskip The Isabelle/Isar framework is generic and should work
+ reasonably well for any Isabelle object-logic that conforms to the
+ natural deduction view of the Isabelle/Pure framework. Major
+ Isabelle logics like HOL \cite{isabelle-HOL}, HOLCF
+ \cite{MuellerNvOS99}, FOL \cite{isabelle-logics}, and ZF
+ \cite{isabelle-ZF} have already been set up for end-users.
+*}
+
+
+section {* Quick start *}
+
+subsection {* Terminal sessions *}
+
+text {*
+ Isar is already part of Isabelle. The low-level @{verbatim
+ isabelle} binary provides option @{verbatim "-I"} to run the
+ Isabelle/Isar interaction loop at startup, rather than the raw ML
+ top-level. So the most basic way to do anything with Isabelle/Isar
+ is as follows: % FIXME update
+\begin{ttbox}
+isabelle -I HOL\medskip
+\out{> Welcome to Isabelle/HOL (Isabelle2005)}\medskip
+theory Foo imports Main begin;
+definition foo :: nat where "foo == 1";
+lemma "0 < foo" by (simp add: foo_def);
+end;
+\end{ttbox}
+
+ Note that any Isabelle/Isar command may be retracted by @{command
+ "undo"}. See the Isabelle/Isar Quick Reference
+ (\appref{ap:refcard}) for a comprehensive overview of available
+ commands and other language elements.
+*}
+
+
+subsection {* Proof General *}
+
+text {*
+ Plain TTY-based interaction as above used to be quite feasible with
+ traditional tactic based theorem proving, but developing Isar
+ documents really demands some better user-interface support. The
+ Proof~General environment by David Aspinall
+ \cite{proofgeneral,Aspinall:TACAS:2000} offers a generic Emacs
+ interface for interactive theorem provers that organizes all the
+ cut-and-paste and forward-backward walk through the text in a very
+ neat way. In Isabelle/Isar, the current position within a partial
+ proof document is equally important than the actual proof state.
+ Thus Proof~General provides the canonical working environment for
+ Isabelle/Isar, both for getting acquainted (e.g.\ by replaying
+ existing Isar documents) and for production work.
+*}
+
+
+subsubsection{* Proof~General as default Isabelle interface *}
+
+text {*
+ The Isabelle interface wrapper script provides an easy way to invoke
+ Proof~General (including XEmacs or GNU Emacs). The default
+ configuration of Isabelle is smart enough to detect the
+ Proof~General distribution in several canonical places (e.g.\
+ @{verbatim "$ISABELLE_HOME/contrib/ProofGeneral"}). Thus the
+ capital @{verbatim Isabelle} executable would already refer to the
+ @{verbatim "ProofGeneral/isar"} interface without further ado. The
+ Isabelle interface script provides several options; pass @{verbatim
+ "-?"} to see its usage.
+
+ With the proper Isabelle interface setup, Isar documents may now be edited by
+ visiting appropriate theory files, e.g.\
+\begin{ttbox}
+Isabelle \({\langle}isabellehome{\rangle}\)/src/HOL/Isar_examples/Summation.thy
+\end{ttbox}
+ Beginners may note the tool bar for navigating forward and backward
+ through the text (this depends on the local Emacs installation).
+ Consult the Proof~General documentation \cite{proofgeneral} for
+ further basic command sequences, in particular ``@{verbatim "C-c C-return"}''
+ and ``@{verbatim "C-c u"}''.
+
+ \medskip Proof~General may be also configured manually by giving
+ Isabelle settings like this (see also \cite{isabelle-sys}):
+
+\begin{ttbox}
+ISABELLE_INTERFACE=\$ISABELLE_HOME/contrib/ProofGeneral/isar/interface
+PROOFGENERAL_OPTIONS=""
+\end{ttbox}
+ You may have to change @{verbatim
+ "$ISABELLE_HOME/contrib/ProofGeneral"} to the actual installation
+ directory of Proof~General.
+
+ \medskip Apart from the Isabelle command line, defaults for
+ interface options may be given by the @{verbatim PROOFGENERAL_OPTIONS}
+ setting. For example, the Emacs executable to be used may be
+ configured in Isabelle's settings like this:
+\begin{ttbox}
+PROOFGENERAL_OPTIONS="-p xemacs-mule"
+\end{ttbox}
+
+ Occasionally, a user's @{verbatim "~/.emacs"} file contains code
+ that is incompatible with the (X)Emacs version used by
+ Proof~General, causing the interface startup to fail prematurely.
+ Here the @{verbatim "-u false"} option helps to get the interface
+ process up and running. Note that additional Lisp customization
+ code may reside in @{verbatim "proofgeneral-settings.el"} of
+ @{verbatim "$ISABELLE_HOME/etc"} or @{verbatim
+ "$ISABELLE_HOME_USER/etc"}.
+*}
+
+
+subsubsection {* The X-Symbol package *}
+
+text {*
+ Proof~General incorporates a version of the Emacs X-Symbol package
+ \cite{x-symbol}, which handles proper mathematical symbols displayed
+ on screen. Pass option @{verbatim "-x true"} to the Isabelle
+ interface script, or check the appropriate Proof~General menu
+ setting by hand. The main challenge of getting X-Symbol to work
+ properly is the underlying (semi-automated) X11 font setup.
+
+ \medskip Using proper mathematical symbols in Isabelle theories can
+ be very convenient for readability of large formulas. On the other
+ hand, the plain ASCII sources easily become somewhat unintelligible.
+ For example, @{text "\<Longrightarrow>"} would appear as @{verbatim "\<Longrightarrow>"} according
+ the default set of Isabelle symbols. Nevertheless, the Isabelle
+ document preparation system (see \secref{sec:document-prep}) will be
+ happy to print non-ASCII symbols properly. It is even possible to
+ invent additional notation beyond the display capabilities of Emacs
+ and X-Symbol.
+*}
+
+
+section {* Isabelle/Isar theories *}
+
+text {*
+ Isabelle/Isar offers the following main improvements over classic
+ Isabelle.
+
+ \begin{enumerate}
+
+ \item A \emph{theory format} that integrates specifications and
+ proofs, supporting interactive development and unlimited undo
+ operation.
+
+ \item A \emph{formal proof document language} designed to support
+ intelligible semi-automated reasoning. Instead of putting together
+ unreadable tactic scripts, the author is enabled to express the
+ reasoning in way that is close to usual mathematical practice. The
+ old tactical style has been assimilated as ``improper'' language
+ elements.
+
+ \item A simple document preparation system, for typesetting formal
+ developments together with informal text. The resulting
+ hyper-linked PDF documents are equally well suited for WWW
+ presentation and as printed copies.
+
+ \end{enumerate}
+
+ The Isar proof language is embedded into the new theory format as a
+ proper sub-language. Proof mode is entered by stating some
+ @{command "theorem"} or @{command "lemma"} at the theory level, and
+ left again with the final conclusion (e.g.\ via @{command "qed"}).
+ A few theory specification mechanisms also require some proof, such
+ as HOL's @{command "typedef"} which demands non-emptiness of the
+ representing sets.
+*}
+
+
+subsection {* Document preparation \label{sec:document-prep} *}
+
+text {*
+ Isabelle/Isar provides a simple document preparation system based on
+ existing {PDF-\LaTeX} technology, with full support of hyper-links
+ (both local references and URLs) and bookmarks. Thus the results
+ are equally well suited for WWW browsing and as printed copies.
+
+ \medskip Isabelle generates {\LaTeX} output as part of the run of a
+ \emph{logic session} (see also \cite{isabelle-sys}). Getting
+ started with a working configuration for common situations is quite
+ easy by using the Isabelle @{verbatim mkdir} and @{verbatim make}
+ tools. First invoke
+\begin{ttbox}
+ isatool mkdir Foo
+\end{ttbox}
+ to initialize a separate directory for session @{verbatim Foo} ---
+ it is safe to experiment, since @{verbatim "isatool mkdir"} never
+ overwrites existing files. Ensure that @{verbatim "Foo/ROOT.ML"}
+ holds ML commands to load all theories required for this session;
+ furthermore @{verbatim "Foo/document/root.tex"} should include any
+ special {\LaTeX} macro packages required for your document (the
+ default is usually sufficient as a start).
+
+ The session is controlled by a separate @{verbatim IsaMakefile}
+ (with crude source dependencies by default). This file is located
+ one level up from the @{verbatim Foo} directory location. Now
+ invoke
+\begin{ttbox}
+ isatool make Foo
+\end{ttbox}
+ to run the @{verbatim Foo} session, with browser information and
+ document preparation enabled. Unless any errors are reported by
+ Isabelle or {\LaTeX}, the output will appear inside the directory
+ @{verbatim ISABELLE_BROWSER_INFO}, as reported by the batch job in
+ verbose mode.
+
+ \medskip You may also consider to tune the @{verbatim usedir}
+ options in @{verbatim IsaMakefile}, for example to change the output
+ format from @{verbatim pdf} to @{verbatim dvi}, or activate the
+ @{verbatim "-D"} option to retain a second copy of the generated
+ {\LaTeX} sources.
+
+ \medskip See \emph{The Isabelle System Manual} \cite{isabelle-sys}
+ for further details on Isabelle logic sessions and theory
+ presentation. The Isabelle/HOL tutorial \cite{isabelle-hol-book}
+ also covers theory presentation issues.
+*}
+
+
+subsection {* How to write Isar proofs anyway? \label{sec:isar-howto} *}
+
+text {*
+ This is one of the key questions, of course. First of all, the
+ tactic script emulation of Isabelle/Isar essentially provides a
+ clarified version of the very same unstructured proof style of
+ classic Isabelle. Old-time users should quickly become acquainted
+ with that (slightly degenerative) view of Isar.
+
+ Writing \emph{proper} Isar proof texts targeted at human readers is
+ quite different, though. Experienced users of the unstructured
+ style may even have to unlearn some of their habits to master proof
+ composition in Isar. In contrast, new users with less experience in
+ old-style tactical proving, but a good understanding of mathematical
+ proof in general, often get started easier.
+
+ \medskip The present text really is only a reference manual on
+ Isabelle/Isar, not a tutorial. Nevertheless, we will attempt to
+ give some clues of how the concepts introduced here may be put into
+ practice. Especially note that \appref{ap:refcard} provides a quick
+ reference card of the most common Isabelle/Isar language elements.
+
+ Further issues concerning the Isar concepts are covered in the
+ literature
+ \cite{Wenzel:1999:TPHOL,Wiedijk:2000:MV,Bauer-Wenzel:2000:HB,Bauer-Wenzel:2001}.
+ The author's PhD thesis \cite{Wenzel-PhD} presently provides the
+ most complete exposition of Isar foundations, techniques, and
+ applications. A number of example applications are distributed with
+ Isabelle, and available via the Isabelle WWW library (e.g.\
+ \url{http://isabelle.in.tum.de/library/}). The ``Archive of Formal
+ Proofs'' \url{http://afp.sourceforge.net/} also provides plenty of
+ examples, both in proper Isar proof style and unstructured tactic
+ scripts.
+*}
+
+end