%% $Id$

\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 example 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 Isabelle system together with appropriate object-logics

--- otherwise see the \texttt{README} and \texttt{INSTALL} files in the

top-level directory of the distribution on how to do this.

\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

(usually {\HOL}) already pre-loaded.

Subsequently, we assume that the \texttt{isabelle} executable is determined

automatically by the shell, e.g.\ by adding {\tt \(\langle isabellehome

  \rangle\)/bin} to your search path.\footnote{Depending on your installation,

  there might be also stand-alone binaries located in some global directory

  such as \texttt{/usr/bin}.  Do not attempt to copy {\tt \(\langle

    isabellehome \rangle\)/bin/isabelle}, though!  See \texttt{isatool

    install} in \emph{The Isabelle System Manual} of how to do this properly.}

\medskip

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 an image of {\FOL} has been pre-built).

\index{saving your session|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 may 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 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 plain \HOL:

\begin{ttbox}

isabelle HOL 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}

\medskip Saving the {\ML} 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, these sources will be somewhat

intelligible to others as a formal description of your work.

It is good practice to put all source files that constitute a separate

Isabelle session into an individual directory, together with an {\ML} file

called \texttt{ROOT.ML} that contains appropriate commands to load all other

files required.  Running \texttt{isabelle} with option \texttt{-u}

automatically loads \texttt{ROOT.ML} on entering the session.  The

\texttt{isatool usedir} utility provides some more options to manage Isabelle

sessions, such as automatic generation of theory browsing information.

\medskip More details about the \texttt{isabelle} and \texttt{isatool}

commands may be found in \emph{The Isabelle System Manual}.

\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.

Again, see \emph{The Isabelle System Manual} for more information.

\section{Ending a session}

\begin{ttbox} 

quit    : unit -> unit

exit    : int -> unit

commit  : unit -> bool

\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;

  return value {\tt false} indicates an error.

\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 (e.g.\ \texttt{\$ISABELLE_HOME}) that are

expanded appropriately.  Note that \texttt{\~\relax} abbreviates

\texttt{\$HOME}, and \texttt{\~\relax\~\relax} abbreviates

\texttt{\$ISABELLE_HOME}\index{*\$ISABELLE_HOME}.  The syntax for path

specifications follows Unix conventions.

\section{Reading theories}\label{sec:intro-theories}

\index{theories!reading}

In Isabelle, any kind of declarations, definitions, etc.\ are organized around

named \emph{theory} objects.  Logical reasoning always takes place within a

certain theory context, which may be switched at any time.  Theory $name$ is

defined by a theory file $name$\texttt{.thy}, containing declarations of

\texttt{consts}, \texttt{types}, \texttt{defs}, etc.\ (see

\S\ref{sec:ref-defining-theories} for more details on concrete syntax).

Furthermore, there may be an associated {\ML} file $name$\texttt{.ML} with

proof scripts that are to be run in the context of the theory.

\begin{ttbox}

context      : theory -> unit

the_context  : unit -> theory

theory       : string -> theory

use_thy      : string -> unit

time_use_thy : string -> unit

update_thy   : string -> unit

\end{ttbox}

\begin{ttdescription}

\item[\ttindexbold{context} $thy$;] switches the current theory context.  Any

  subsequent command with ``implicit theory argument'' (e.g.\ \texttt{Goal})

  will refer to $thy$ as its theory.

\item[\ttindexbold{the_context}();] obtains the current theory context, or

  raises an error if absent.

\item[\ttindexbold{theory} "$name$";] retrieves the theory called $name$ from

  the internal database of loaded theories, raising an error if absent.

\item[\ttindexbold{use_thy} "$name$";] reads theory $name$ from the file

  system, looking for $name$\texttt{.thy} and $name$\texttt{.ML} (the latter

  being optional).  It also ensures that all parent theories are loaded as

  well.  In case some older versions have already been present,

  \texttt{use_thy} only tries to reload $name$ itself, but is content with any

  version of its ancestors.

\item[\ttindexbold{time_use_thy} "$name$";] same as \texttt{use_thy}, but

  reports the time taken to process the actual theory parts and {\ML} files

  separately.

\item[\ttindexbold{update_thy} "$name$";] is similar to \texttt{use_thy}, but

  ensures that theory $name$ is fully up-to-date with respect to the file

  system --- apart from $name$ itself any of its ancestors may be reloaded as

  well.

\end{ttdescription}

Note that theories of pre-built logic images (e.g.\ {\HOL}) are marked as

\emph{finished} and cannot be updated any more.  See \S\ref{sec:more-theories}

for further information on Isabelle's theory loader.

\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 the 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_tags     : bool ref \hfill{\bf initially false}

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_tags};] makes Isabelle show tags of theorems

  (which are basically just comments that may be attached by some tools).

\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.

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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