--- a/doc-src/IsarRef/Thy/intro.thy Mon Jun 02 13:21:06 2008 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
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-(* $Id$ *)
-
-theory intro
-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