\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 a 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 text 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.\footnote{There is also a \texttt{ProofGeneral/isa} interface, for

  classic Isabelle tactic scripts.}  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="-u false -p emacs"

\end{ttbox}

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.}

\medskip

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, such as ``\texttt{c-c return}'' or

``\texttt{c-c u}''.

\section{Isabelle/Isar theories}

Isabelle/Isar offers two main improvements over classic Isabelle:

\begin{enumerate}

\item A new \emph{theory format}, occasionally referred to as ``new-style

  theories'', 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 mathematical practice.

\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 $\THEOREMNAME$ or

$\LEMMANAME$ at the theory level, and left again with the final conclusion

(e.g.\ via $\QEDNAME$).  A few theory extension mechanisms require proof as

well, such as the HOL $\isarkeyword{typedef}$ which demands non-emptiness of

the representing sets.

New-style theory files may still be associated with separate ML files

consisting of plain old tactic scripts.  There is no longer any ML binding

generated for the theory and theorems, though.  ML functions \texttt{theory},

\texttt{thm}, and \texttt{thms} retrieve this information \cite{isabelle-ref}.

Nevertheless, migration between classic Isabelle and Isabelle/Isar is

relatively easy.  Thus users may start to benefit from interactive theory

development even before they have any idea of the Isar proof language at all.

\begin{warn}

  Currently Proof~General does \emph{not} support mixed interactive

  development of classic Isabelle theory files or tactic scripts, together

  with Isar documents.  The ``\texttt{isa}'' and ``\texttt{isar}'' versions of

  Proof~General are handled as two different theorem proving systems, only one

  of these may be active at the same time.

\end{warn}

Porting of existing tactic scripts is best done by running two separate

Proof~General sessions, one for replaying the old script and the other for the

emerging Isabelle/Isar document.

\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.  See also \cite{Wenzel:1999:TPHOL} for further background information

on Isar.

\medskip This really is a \emph{reference manual}.  Nevertheless, we will also

give some clues of how the concepts introduced here may be put into practice.

Appendix~\ref{ap:refcard} provides a quick reference card of the most common

Isabelle/Isar language elements.  There are several examples distributed with

Isabelle, and available via the Isabelle WWW 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}

See \texttt{HOL/Isar_examples} for a collection of introductory examples, and

\texttt{HOL/HOL-Real/HahnBanach} is a big mathematics application.  Apart from

browsable HTML sources, both sessions provide actual documents (in PDF).

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