doc-src/IsarRef/intro.tex

updated;

\chapter{Introduction}

\section{Quick start}

Isar is already part of Isabelle (as of version Isabelle99, or later).  The
\texttt{isabelle} binary provides option \texttt{-I} to run the Isar
interaction loop at startup, rather than the plain ML top-level.  Thus the
quickest way to do anything with Isabelle/Isar is as follows:
\begin{ttbox}
isabelle -I HOL\medskip
\out{> Welcome to Isabelle/HOL (Isabelle99)}\medskip
theory Foo = Main:
constdefs foo :: nat  "foo == 1";
lemma "0 < foo" by (simp add: foo_def);
end
\end{ttbox}
Note that any Isabelle/Isar command may be retracted by \texttt{undo}; the
\texttt{help} command prints the list of available language elements.

Plain TTY-based interaction like this used to be quite feasible with
traditional tactic based theorem proving, but developing Isar documents
demands some better user-interface support.  \emph{Proof~General}\index{Proof
  General} of LFCS Edinburgh \cite{proofgeneral} offers a generic Emacs-based
environment for interactive theorem provers that does all the cut-and-paste
and forward-backward walk through the document in a very neat way.  Note that
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 real production
work.

\medskip

The easiest way to use Proof~General is to make it the default Isabelle user
interface.  Just put something like this into your Isabelle settings file (see
also \cite{isabelle-sys}):
\begin{ttbox}
ISABELLE_INTERFACE=\$ISABELLE_HOME/contrib/ProofGeneral/isar/interface
PROOFGENERAL_OPTIONS="-u false"
\end{ttbox}
You may have to change \texttt{\$ISABELLE_HOME/contrib/ProofGeneral} to the
actual installation directory of Proof~General.  From now on, the capital
\texttt{Isabelle} executable refers to the \texttt{ProofGeneral/isar}
interface.  Its usage is as follows:
\begin{ttbox}
Usage: interface [OPTIONS] [FILES ...]

  Options are:
    -l NAME      logic image name (default $ISABELLE_LOGIC=HOL)
    -p NAME      Emacs program name (default xemacs)
    -u BOOL      use .emacs file (default true)
    -w BOOL      use window system (default true)

  Starts Proof General for Isabelle/Isar with proof documents FILES
  (default Scratch.thy).

  PROOFGENERAL_OPTIONS=
\end{ttbox} %$
Apart from the command line, the defaults for these options may be overridden
via the \texttt{PROOFGENERAL_OPTIONS} setting as well.  For example, plain GNU
Emacs may be configured as follows:
\begin{ttbox}
PROOFGENERAL_OPTIONS="-p emacs"
\end{ttbox}

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/BasicLogic.thy
\end{ttbox}
Users of XEmacs may note the tool bar for navigating forward and backward
through the text.  Consult the Proof~General documentation \cite{proofgeneral}
for further basic command sequences, like ``\texttt{c-c return}'' or
``\texttt{c-c u}''.

\medskip

Occasionally, a user's \texttt{.emacs} file contains material that is
incompatible with the version of (X)Emacs that Proof~General prefers.  Then
proper startup may be still achieved by using the \texttt{-u false}
option.\footnote{Any Emacs lisp file \texttt{proofgeneral-settings.el}
  occurring in \texttt{\$ISABELLE_HOME/etc} or
  \texttt{\$ISABELLE_HOME_USER/etc} is automatically loaded by the
  Proof~General interface script as well.}

\section{How to write Isar proofs anyway?}

This is one of the key questions, of course.  Isar offers a rather different
approach to formal proof documents than plain old tactic scripts.  Experienced
users of existing interactive theorem proving systems may have to learn
thinking differently in order to make effective use of Isabelle/Isar.  On the
other hand, Isabelle/Isar comes much closer to existing mathematical practice
of formal proof, so users with less experience in old-style tactical proving,
but a good understanding of mathematical proof, might cope with Isar even
better.

This document really is a \emph{reference manual}.  Nevertheless, we will give
some discussions of the general principles underlying Isar in
chapter~\ref{ch:basics}, and provide some clues of how these may be put into
practice.  Some more background information on Isar is given in
\cite{Wenzel:1999:TPHOL}.  While there is no proper tutorial on Isabelle/Isar
available yet, there are several examples distributed with Isabelle.  See
\texttt{HOL/Isar_examples} and \texttt{HOL/HOL-Real/HahnBanach} in the
Isabelle library:

\begin{center}\small
  \begin{tabular}{l}
    \url{http://www.cl.cam.ac.uk/Research/HVG/Isabelle/library/} \\
    \url{http://isabelle.in.tum.de/library/} \\
  \end{tabular}
\end{center}

Apart from browsable HTML sources, both Isabelle/Isar sessions also provide
actual documents (in PDF).

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