%% $Id$
\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.
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 internal proof objects on files. Theorems are simply part
of the \ML{} state. 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-logic images 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}
More details about the \texttt{isabelle} command 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. 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} \(i\);] similar to {\tt quit}, passing return
code \(i\) 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}
\begin{ttdescription}
\item[\ttindexbold{cd} "{\it dir}";] changes the current directory to
{\it dir}. This is the default directory for reading files.
\item[\ttindexbold{pwd}();] returns the full 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}
The $dir$ and $file$ specifications of the \texttt{cd} and
\texttt{use} commands may contain path variables that are expanded
appropriately, e.g.\ \texttt{\$ISABELLE_HOME} or \texttt{\~\relax}
(which abbreviates \texttt{\$HOME}). Section~\ref{LoadingTheories}
describes commands for loading theory files.
\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
(\S\ref{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~76.
\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 etc.}
\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}
show_consts : bool ref \hfill{\bf initially false}
long_names : bool ref \hfill{\bf initially false}
\end{ttbox}
These flags allow you to control how much information is displayed for
types, terms and theorems. The hypotheses of theorems \emph{are}
normally shown. Superfluous parentheses of types and terms are not.
Types and sorts of variables are normally hidden.
Note that displaying types and sorts may explain why a polymorphic
inference rule fails to resolve with some goal, or why a rewrite rule
does not apply as expected.
\begin{ttdescription}
\item[reset \ttindexbold{show_hyps};] makes Isabelle show each
meta-level hypothesis as a dot.
\item[set \ttindexbold{show_brackets};] makes Isabelle show full
bracketing. In particular, this reveals the grouping of infix
operators.
\item[set \ttindexbold{show_types};] makes Isabelle show types when
printing a term or theorem.
\item[set \ttindexbold{show_sorts};] makes Isabelle show both types
and the sorts of type variables, independently of the value of
\texttt{show_types}.
\item[set \ttindexbold{show_consts};] makes Isabelle show types of
constants, provided that showing of types is enabled at all. This
is supported for printing of proof states only. Note that the
output can be enormous as polymorphic constants often occur at
several different type instances.
\item[set \ttindexbold{long_names};] forces names of all objects
(types, constants, theorems, etc.) to be printed in their fully
qualified internal form.
\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[set \ttindexbold{eta_contract};]
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{Diagnostic messages}
\index{error messages}
\index{warnings}
Isabelle conceptually provides three output channels for different
kinds of messages: ordinary text, warnings, errors. Depending on the
user interface involved, these messages may appear in different text
styles or colours, even within separate windows.
The default setup of an \texttt{isabelle} terminal session is as
follows: plain output of ordinary text, warnings prefixed by
\texttt{\#\#\#}'s, errors prefixed by \texttt{***}'s. For example, a
typical warning would look like this:
\begin{ttbox}
\#\#\# Beware the Jabberwock, my son!
\#\#\# The jaws that bite, the claws that catch!
\#\#\# Beware the Jubjub Bird, and shun
\#\#\# The frumious Bandersnatch!
\end{ttbox}
\texttt{ML} programs may output diagnostic messages using the
following functions:
\begin{ttbox}
writeln : string -> unit
warning : string -> unit
error : string -> 'a
\end{ttbox}
Note that \ttindex{error} fails by raising exception \ttindex{ERROR}
after having output the text, while \ttindex{writeln} and
\ttindex{warning} resume normal program execution.
\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 may be
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}
\index{sessions|)}
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