doc-src/Ref/introduction.tex

New equivalence proofs

%% $Id$

\chapter{Basic Use of Isabelle}\index{sessions|(} 
The Reference Manual is a comprehensive description of Isabelle
proper, including all \ML{} commands, functions and packages.  It
really is intended for reference, perhaps for browsing, but not for
reading through.  It is not a tutorial, but assumes familiarity with
the basic logical concepts of Isabelle.

When you are looking for a way of performing some task, scan the Table of
Contents for a relevant heading.  Functions are organized by their purpose,
by their operands (subgoals, tactics, theorems), and by their usefulness.
In each section, basic functions appear first, then advanced functions, and
finally esoteric functions.  Use the Index when you are looking for the
definition of a particular Isabelle function.

A few examples are presented.  Many examples files are distributed with
Isabelle, however; please experiment interactively.


\section{Basic interaction with Isabelle}
\index{starting up|bold}\nobreak
%
We assume that your local Isabelle administrator (this might be you!)
has already installed the \Pure\ system and several object-logics
properly --- otherwise see the {\tt INSTALL} file in the top-level
directory of the distribution on how to build it.

\medskip Let $\langle isabellehome \rangle$ denote the location where
the distribution has been installed. To run Isabelle from a the shell
prompt within an ordinary text terminal session, simply type:
\begin{ttbox}
\({\langle}isabellehome{\rangle}\)/bin/isabelle
\end{ttbox}
This should start an interactive \ML{} session with the default
object-logic already preloaded. All Isabelle commands are bound to
\ML{} identifiers.

Subsequently we assume that {\tt \(\langle isabellehome \rangle\)/bin}
has been added to your shell's search path, in order to avoid typing
full path specifications of the executable files.

The object-logic image to load may be also specified explicitly as an
argument to the {\tt isabelle} command, e.g.:
\begin{ttbox}
isabelle FOL
\end{ttbox}
This should put you into the world of polymorphic first-order logic
(assuming that {\FOL} has been pre-built).

\index{saving your work|bold} Isabelle provides no means of storing
theorems or proofs on files.  Theorems are simply part of the \ML{}
state and are named by \ML{} identifiers.  To save your work between
sessions, you must dump the \ML{} system state to a file. This is done
automatically when ending the session normally (e.g.\ by typing
control-D), provided that the image has been opened \emph{writable} in
the first place. The standard object-logics are usually read-only, so
you probably have to create a private working copy first. For example,
the following shell command puts you into a writable Isabelle session
of name \texttt{Foo} that initially contains just \FOL:
\begin{ttbox}
isabelle FOL Foo
\end{ttbox}
Ending the \texttt{Foo} session with control-D will cause the complete
\ML{} world to be saved somewhere in your home directory\footnote{The
  default location is in \texttt{\~\relax/isabelle/heaps}, but this
  depends on your local configuration.}. Make sure there is enough
space available! Then one may later continue at exactly the same point
by running
\begin{ttbox}
isabelle Foo  
\end{ttbox}

%FIXME not yet
%More details about \texttt{isabelle} may be found in the \emph{System
%  Manual}.

\medskip Saving the state is not enough.  Record, on a file, the
top-level commands that generate your theories and proofs.  Such a
record allows you to replay the proofs whenever required, for instance
after making minor changes to the axioms.  Ideally, your record will
be somewhat intelligible to others as a formal description of your
work.

\medskip There are more comfortable user interfaces than the
bare-bones \ML{} top-level run from a text terminal. The
\texttt{Isabelle} executable (note the capital I) runs one such
interface, depending on your local configuration.  Furthermore there
are a number of external utilities available. These are started
uniformly via the \texttt{isatool} wrapper.

%FIXME not yet
%Again, see the \emph{System Manual} for more information user
%interfaces and utilities.


\section{Ending a session}
\begin{ttbox} 
quit    : unit -> unit
exit    : int -> unit
commit  : unit -> unit
\end{ttbox}
\begin{ttdescription}
\item[\ttindexbold{quit}();] ends the Isabelle session, without saving
  the state.

\item[\ttindexbold{exit}();] same as {\tt quit}, passing a return code
  to the operating system.

\item[\ttindexbold{commit}();] saves the current state without ending
  the session, provided that the logic image is opened read-write.
\end{ttdescription}

Typing control-D also finishes the session in essentially the same way
as the sequence {\tt commit(); quit();} would.


\section{Reading ML files}
\index{files!reading}
\begin{ttbox} 
cd              : string -> unit
pwd             : unit -> string
use             : string -> unit
time_use        : string -> unit
\end{ttbox}
Section~\ref{LoadingTheories} describes commands for loading theory files.
\begin{ttdescription}
\item[\ttindexbold{cd} "{\it dir}";]
  changes the current directory to {\it dir}.  This is the default directory
  for reading files and for writing temporary files.

\item[\ttindexbold{pwd}();] returns the path of the current directory.

\item[\ttindexbold{use} "$file$";]  
reads the given {\it file} as input to the \ML{} session.  Reading a file
of Isabelle commands is the usual way of replaying a proof.

\item[\ttindexbold{time_use} "$file$";]  
performs {\tt use~"$file$"} and prints the total execution time.
\end{ttdescription}


\section{Setting flags}
\begin{ttbox}
set     : bool ref -> bool
reset   : bool ref -> bool
toggle  : bool ref -> bool
\end{ttbox}\index{*set}\index{*reset}\index{*toggle}
These are some shorthands for manipulating boolean references. The new
value is returned.


\section{Printing of terms and theorems}\label{sec:printing-control}
\index{printing control|(}
Isabelle's pretty printer is controlled by a number of parameters.

\subsection{Printing limits}
\begin{ttbox} 
Pretty.setdepth  : int -> unit
Pretty.setmargin : int -> unit
print_depth      : int -> unit
\end{ttbox}
These set limits for terminal output.  See also {\tt goals_limit}, which
limits the number of subgoals printed (page~\pageref{sec:goals-printing}).

\begin{ttdescription}
\item[\ttindexbold{Pretty.setdepth} \(d\);]  
  tells Isabelle's pretty printer to limit the printing depth to~$d$.  This
  affects Isabelle's display of theorems and terms.  The default value
  is~0, which permits printing to an arbitrary depth.  Useful values for
  $d$ are~10 and~20.

\item[\ttindexbold{Pretty.setmargin} \(m\);]  
  tells Isabelle's pretty printer to assume a right margin (page width)
  of~$m$.  The initial margin is~80.

\item[\ttindexbold{print_depth} \(n\);]  
  limits the printing depth of complex \ML{} values, such as theorems and
  terms.  This command affects the \ML{} top level and its effect is
  compiler-dependent.  Typically $n$ should be less than~10.
\end{ttdescription}


\subsection{Printing of hypotheses, brackets, types and sorts}
\index{meta-assumptions!printing of}
\index{types!printing of}\index{sorts!printing of}
\begin{ttbox} 
show_hyps     : bool ref \hfill{\bf initially true}
show_brackets : bool ref \hfill{\bf initially false}
show_types    : bool ref \hfill{\bf initially false}
show_sorts    : bool ref \hfill{\bf initially false}
\end{ttbox}
These flags allow you to control how much information is displayed for
terms and theorems.  The hypotheses are normally shown; superfluous
parentheses are not.  Types and sorts are normally hidden.  Displaying
types and sorts may explain why a polymorphic inference rule fails to
resolve with some goal.

\begin{ttdescription}
\item[\ttindexbold{show_hyps} := false;]   
makes Isabelle show each meta-level hypothesis as a dot.

\item[\ttindexbold{show_brackets} := true;] 
  makes Isabelle show full bracketing.  This reveals the
  grouping of infix operators.

\item[\ttindexbold{show_types} := true;]
makes Isabelle show types when printing a term or theorem.

\item[\ttindexbold{show_sorts} := true;]
makes Isabelle show both types and the sorts of type variables.  It does not
matter whether {\tt show_types} is also~{\tt true}. 
\end{ttdescription}


\subsection{$\eta$-contraction before printing}
\begin{ttbox} 
eta_contract: bool ref \hfill{\bf initially false}
\end{ttbox}
The {\bf $\eta$-contraction law} asserts $(\lambda x.f(x))\equiv f$,
provided $x$ is not free in ~$f$.  It asserts {\bf extensionality} of
functions: $f\equiv g$ if $f(x)\equiv g(x)$ for all~$x$.  Higher-order
unification frequently puts terms into a fully $\eta$-expanded form.  For
example, if $F$ has type $(\tau\To\tau)\To\tau$ then its expanded form is
$\lambda h.F(\lambda x.h(x))$.  By default, the user sees this expanded
form.

\begin{ttdescription}
\item[\ttindexbold{eta_contract} := true;]
makes Isabelle perform $\eta$-contractions before printing, so that
$\lambda h.F(\lambda x.h(x))$ appears simply as~$F$.  The
distinction between a term and its $\eta$-expanded form occasionally
matters.
\end{ttdescription}
\index{printing control|)}


\section{Displaying exceptions as error messages}
\index{exceptions!printing of}
\begin{ttbox} 
print_exn: exn -> 'a
\end{ttbox}
Certain Isabelle primitives, such as the forward proof functions {\tt RS}
and {\tt RSN}, are called both interactively and from programs.  They
indicate errors not by printing messages, but by raising exceptions.  For
interactive use, \ML's reporting of an uncaught exception is 
uninformative.  The Poly/ML function {\tt exception_trace} can generate a
backtrace.\index{Poly/{\ML} compiler}

\begin{ttdescription}
\item[\ttindexbold{print_exn} $e$] 
displays the exception~$e$ in a readable manner, and then re-raises~$e$.
Typical usage is~\hbox{\tt $EXP$ handle e => print_exn e;}, where
$EXP$ is an expression that may raise an exception.

{\tt print_exn} can display the following common exceptions, which concern
types, terms, theorems and theories, respectively.  Each carries a message
and related information.
\begin{ttbox} 
exception TYPE   of string * typ list * term list
exception TERM   of string * term list
exception THM    of string * int * thm list
exception THEORY of string * theory list
\end{ttbox}
\end{ttdescription}
\begin{warn}
  {\tt print_exn} prints terms by calling \ttindex{prin}, which obtains
  pretty printing information from the proof state last stored in the
  subgoal module.  The appearance of the output thus depends upon the
  theory used in the last interactive proof.
\end{warn}

%FIXME remove
%\section{Shell scripts}\label{sec:shell-scripts}
%\index{shell scripts|bold} The following files are distributed with
%Isabelle, and work under Unix$^{\rm TM}$.  They can be executed as commands
%to the Unix shell.  Some of them depend upon shell environment variables.
%\begin{ttdescription}
%\item[make-all $switches$] \index{*make-all shell script}
%  compiles the Isabelle system, when executed on the source directory.
%  Environment variables specify which \ML{} compiler to use.  These
%  variables, and the {\it switches}, are documented on the file itself.
%
%\item[teeinput $program$] \index{*teeinput shell script}
%  executes the {\it program}, while piping the standard input to a log file
%  designated by the \verb|$LISTEN| environment variable.  Normally the
%  program is Isabelle, and the log file receives a copy of all the Isabelle
%  commands.
%
%\item[xlisten $program$] \index{*xlisten shell script}
%  is a trivial `user interface' for the X Window System.  It creates two
%  windows using {\tt xterm}.  One executes an interactive session via
%  \hbox{\tt teeinput $program$}, while the other displays the log file.  To
%  make a proof record, simply paste lines from the log file into an editor
%  window.
%
%\item[expandshort $files$]  \index{*expandshort shell script}
%  reads the {\it files\/} and replaces all occurrences of the shorthand
%  commands {\tt br}, {\tt be}, {\tt brs}, {\tt bes}, etc., with the
%  corresponding full commands.  Shorthand commands should appear one
%  per line.  The old versions of the files
%  are renamed to have the suffix~\verb'~~'.
%\end{ttdescription}

\index{sessions|)}