doc-src/Ref/introduction.tex
author wenzelm
Mon May 03 18:35:48 1999 +0200 (1999-05-03)
changeset 6568 b38bc78d9a9d
parent 6343 97c697a32b73
child 6569 66c941ea1f01
permissions -rw-r--r--
theory loader stuff updated and improved;
wenzelm@3200
     1
lcp@104
     2
%% $Id$
wenzelm@3108
     3
lcp@286
     4
\chapter{Basic Use of Isabelle}\index{sessions|(} 
wenzelm@3108
     5
The Reference Manual is a comprehensive description of Isabelle
wenzelm@3108
     6
proper, including all \ML{} commands, functions and packages.  It
wenzelm@3108
     7
really is intended for reference, perhaps for browsing, but not for
wenzelm@3108
     8
reading through.  It is not a tutorial, but assumes familiarity with
wenzelm@3108
     9
the basic logical concepts of Isabelle.
lcp@104
    10
lcp@286
    11
When you are looking for a way of performing some task, scan the Table of
lcp@286
    12
Contents for a relevant heading.  Functions are organized by their purpose,
lcp@286
    13
by their operands (subgoals, tactics, theorems), and by their usefulness.
lcp@286
    14
In each section, basic functions appear first, then advanced functions, and
lcp@322
    15
finally esoteric functions.  Use the Index when you are looking for the
lcp@322
    16
definition of a particular Isabelle function.
lcp@104
    17
wenzelm@6568
    18
A few examples are presented.  Many example files are distributed with
lcp@286
    19
Isabelle, however; please experiment interactively.
lcp@104
    20
lcp@104
    21
lcp@104
    22
\section{Basic interaction with Isabelle}
paulson@2225
    23
\index{starting up|bold}\nobreak
paulson@2225
    24
%
wenzelm@6568
    25
We assume that your local Isabelle administrator (this might be you!) has
wenzelm@6568
    26
already installed the Isabelle system together with appropriate object-logics
wenzelm@6568
    27
--- otherwise see the \texttt{README} and \texttt{INSTALL} files in the
wenzelm@6568
    28
top-level directory of the distribution on how to do this.
wenzelm@3108
    29
wenzelm@3108
    30
\medskip Let $\langle isabellehome \rangle$ denote the location where
paulson@3485
    31
the distribution has been installed.  To run Isabelle from a the shell
wenzelm@4317
    32
prompt within an ordinary text terminal session, simply type
wenzelm@3108
    33
\begin{ttbox}
wenzelm@3108
    34
\({\langle}isabellehome{\rangle}\)/bin/isabelle
wenzelm@3108
    35
\end{ttbox}
wenzelm@6568
    36
This should start an interactive \ML{} session with the default object-logic
wenzelm@6568
    37
(usually {\HOL}) already pre-loaded.
wenzelm@3108
    38
wenzelm@6568
    39
Subsequently, we assume that the \texttt{isabelle} executable is determined
wenzelm@6568
    40
automatically by the shell, e.g.\ by adding {\tt \(\langle isabellehome
wenzelm@6568
    41
  \rangle\)/bin} to your search path.\footnote{Depending on your installation,
wenzelm@6568
    42
  there might be also stand-alone binaries located in some global directory
wenzelm@6568
    43
  such as \texttt{/usr/bin}.  Do not attempt to copy {\tt \(\langle
wenzelm@6568
    44
    isabellehome \rangle\)/bin/isabelle}, though!  See \texttt{isatool
wenzelm@6568
    45
    install} in \emph{The Isabelle System Manual} of how to do this properly.}
wenzelm@3108
    46
wenzelm@6568
    47
The object-logic image to load may be also specified explicitly as an argument
wenzelm@6568
    48
to the {\tt isabelle} command, e.g.
wenzelm@3108
    49
\begin{ttbox}
wenzelm@3108
    50
isabelle FOL
wenzelm@3108
    51
\end{ttbox}
wenzelm@6568
    52
This should put you into the world of polymorphic first-order logic (assuming
wenzelm@6568
    53
that an image of {\FOL} has been pre-built).
paulson@2225
    54
wenzelm@6568
    55
\index{saving your session|bold} Isabelle provides no means of storing
wenzelm@6568
    56
theorems or internal proof objects on files.  Theorems are simply part of the
wenzelm@6568
    57
\ML{} state.  To save your work between sessions, you may dump the \ML{}
wenzelm@6568
    58
system state to a file.  This is done automatically when ending the session
wenzelm@6568
    59
normally (e.g.\ by typing control-D), provided that the image has been opened
wenzelm@6568
    60
\emph{writable} in the first place.  The standard object-logic images are
wenzelm@6568
    61
usually read-only, so you have to create a private working copy first.  For
wenzelm@6568
    62
example, the following shell command puts you into a writable Isabelle session
wenzelm@6568
    63
of name \texttt{Foo} that initially contains just plain \HOL:
wenzelm@3108
    64
\begin{ttbox}
wenzelm@6568
    65
isabelle HOL Foo
wenzelm@3108
    66
\end{ttbox}
wenzelm@3108
    67
Ending the \texttt{Foo} session with control-D will cause the complete
wenzelm@6568
    68
\ML-world to be saved somewhere in your home directory\footnote{The default
wenzelm@6568
    69
  location is in \texttt{\~\relax/isabelle/heaps}, but this depends on your
wenzelm@6568
    70
  local configuration.}.  Make sure there is enough space available! Then one
wenzelm@6568
    71
may later continue at exactly the same point by running
wenzelm@3108
    72
\begin{ttbox}
wenzelm@3108
    73
isabelle Foo  
wenzelm@3108
    74
\end{ttbox}
lcp@104
    75
wenzelm@6568
    76
\medskip Saving the {\ML} state is not enough.  Record, on a file, the
wenzelm@6568
    77
top-level commands that generate your theories and proofs.  Such a record
wenzelm@6568
    78
allows you to replay the proofs whenever required, for instance after making
wenzelm@6568
    79
minor changes to the axioms.  Ideally, your these sources will be somewhat
wenzelm@6568
    80
intelligible to others as a formal description of your work.
wenzelm@3108
    81
wenzelm@6568
    82
It is good practice to put all source files that constitute a separate
wenzelm@6568
    83
Isabelle session into an individual directory, together with an {\ML} file
wenzelm@6568
    84
called \texttt{ROOT.ML} that contains appropriate commands to load all other
wenzelm@6568
    85
files required.  Running \texttt{isabelle} with option \texttt{-u}
wenzelm@6568
    86
automatically loads \texttt{ROOT.ML} on entering the session.  The
wenzelm@6568
    87
\texttt{isatool usedir} utility provides some more options to manage your
wenzelm@6568
    88
sessions, such as automatic generation of theory browsing information.
lcp@104
    89
wenzelm@6568
    90
\medskip More details about the \texttt{isabelle} and \texttt{isatool}
wenzelm@6568
    91
commands may be found in \emph{The Isabelle System Manual}.
wenzelm@6568
    92
wenzelm@6568
    93
\medskip There are more comfortable user interfaces than the bare-bones \ML{}
wenzelm@6568
    94
top-level run from a text terminal.  The \texttt{Isabelle} executable (note
wenzelm@6568
    95
the capital I) runs one such interface, depending on your local configuration.
wenzelm@6568
    96
Again, see \emph{The Isabelle System Manual} for more information.
lcp@104
    97
lcp@104
    98
lcp@104
    99
\section{Ending a session}
lcp@104
   100
\begin{ttbox} 
wenzelm@3108
   101
quit    : unit -> unit
wenzelm@3108
   102
exit    : int -> unit
wenzelm@6067
   103
commit  : unit -> bool
lcp@104
   104
\end{ttbox}
lcp@322
   105
\begin{ttdescription}
wenzelm@3108
   106
\item[\ttindexbold{quit}();] ends the Isabelle session, without saving
wenzelm@3108
   107
  the state.
wenzelm@4317
   108
  
wenzelm@4317
   109
\item[\ttindexbold{exit} \(i\);] similar to {\tt quit}, passing return
wenzelm@4317
   110
  code \(i\) to the operating system.
lcp@104
   111
wenzelm@3108
   112
\item[\ttindexbold{commit}();] saves the current state without ending
wenzelm@6067
   113
  the session, provided that the logic image is opened read-write;
wenzelm@6067
   114
  return value {\tt false} indicates an error.
lcp@322
   115
\end{ttdescription}
lcp@104
   116
wenzelm@3108
   117
Typing control-D also finishes the session in essentially the same way
wenzelm@3108
   118
as the sequence {\tt commit(); quit();} would.
lcp@104
   119
lcp@104
   120
lcp@322
   121
\section{Reading ML files}
lcp@322
   122
\index{files!reading}
lcp@104
   123
\begin{ttbox} 
clasohm@138
   124
cd              : string -> unit
clasohm@884
   125
pwd             : unit -> string
clasohm@138
   126
use             : string -> unit
clasohm@138
   127
time_use        : string -> unit
lcp@104
   128
\end{ttbox}
lcp@322
   129
\begin{ttdescription}
wenzelm@4317
   130
\item[\ttindexbold{cd} "{\it dir}";] changes the current directory to
wenzelm@4317
   131
  {\it dir}.  This is the default directory for reading files.
wenzelm@4317
   132
  
wenzelm@4317
   133
\item[\ttindexbold{pwd}();] returns the full path of the current
wenzelm@4317
   134
  directory.
clasohm@884
   135
lcp@322
   136
\item[\ttindexbold{use} "$file$";]  
lcp@104
   137
reads the given {\it file} as input to the \ML{} session.  Reading a file
lcp@104
   138
of Isabelle commands is the usual way of replaying a proof.
lcp@104
   139
lcp@322
   140
\item[\ttindexbold{time_use} "$file$";]  
lcp@104
   141
performs {\tt use~"$file$"} and prints the total execution time.
lcp@322
   142
\end{ttdescription}
lcp@104
   143
wenzelm@6343
   144
The $dir$ and $file$ specifications of the \texttt{cd} and \texttt{use}
wenzelm@6343
   145
commands may contain path variables (e.g.\ \texttt{\$ISABELLE_HOME}) that are
wenzelm@6343
   146
expanded appropriately.  Note that \texttt{\~\relax} abbreviates
wenzelm@6343
   147
\texttt{\$HOME}, and \texttt{\~\relax\~\relax} abbreviates
wenzelm@6568
   148
\texttt{\$ISABELLE_HOME}.
wenzelm@6568
   149
wenzelm@6568
   150
wenzelm@6568
   151
\section{Reading theories}\label{sec:intro-theories}
wenzelm@6568
   152
\index{theories!reading}
wenzelm@6568
   153
wenzelm@6568
   154
In Isabelle, any kind of declarations, definitions, etc.\ are organized around
wenzelm@6568
   155
named \emph{theory} objects.  Logical reasoning always takes place within a
wenzelm@6568
   156
certain theory context, which may be switched at any time.  Theory $name$ is
wenzelm@6568
   157
defined by a theory file $name$\texttt{.thy}, containing declarations of
wenzelm@6568
   158
\texttt{consts}, \texttt{types}, \texttt{defs}, etc.\ (see
wenzelm@6568
   159
\S\ref{sec:ref-defining-theories} for more details on concrete syntax).
wenzelm@6568
   160
Furthermore, there may be an associated {\ML} file $name$\texttt{.ML} with
wenzelm@6568
   161
proof scripts that are to be run in the context of the theory.
wenzelm@6568
   162
wenzelm@6568
   163
\begin{ttbox}
wenzelm@6568
   164
context      : theory -> unit
wenzelm@6568
   165
the_context  : unit -> theory
wenzelm@6568
   166
theory       : string -> theory
wenzelm@6568
   167
use_thy      : string -> unit
wenzelm@6568
   168
time_use_thy : string -> unit
wenzelm@6568
   169
\end{ttbox}
wenzelm@6568
   170
wenzelm@6568
   171
\begin{ttdescription}
wenzelm@6568
   172
  
wenzelm@6568
   173
\item[\ttindexbold{context} $thy$;] switches the current theory context.  Any
wenzelm@6568
   174
  subsequent command with ``implicit theory argument'' (e.g.\ \texttt{Goal})
wenzelm@6568
   175
  will refer to $thy$ as its theory.
wenzelm@6568
   176
  
wenzelm@6568
   177
\item[\ttindexbold{the_context}();] obtains the current theory context, or
wenzelm@6568
   178
  raises an error if absent.
wenzelm@6568
   179
  
wenzelm@6568
   180
\item[\ttindexbold{theory} $name$;] retrieves the theory called $name$ from
wenzelm@6568
   181
  the internal database of loaded theories, raising an error if absent.
wenzelm@6568
   182
  
wenzelm@6568
   183
\item[\ttindexbold{use_thy} $name$;] reads theory $name$ from the file system,
wenzelm@6568
   184
  looking for $name$\texttt{.thy} and (optionally) $name$\texttt{.ML}; also
wenzelm@6568
   185
  makes sure that all parent theories are loaded as well.  In case some older
wenzelm@6568
   186
  versions have already been present, \texttt{use_thy} only tries to reload
wenzelm@6568
   187
  $name$ itself, but is content with any version of its parents.
wenzelm@6568
   188
  
wenzelm@6568
   189
\item[\ttindexbold{time_use_thy} $name$;] same as \texttt{use_thy}, but
wenzelm@6568
   190
  reports the time taken to process the actual theory parts and {\ML} files
wenzelm@6568
   191
  separately.
wenzelm@6568
   192
  
wenzelm@6568
   193
\end{ttdescription}
wenzelm@6568
   194
wenzelm@6568
   195
See \S\ref{sec:more-theories} for further information on Isabelle's theory
wenzelm@6568
   196
loader.
wenzelm@4274
   197
lcp@104
   198
wenzelm@3108
   199
\section{Setting flags}
wenzelm@3108
   200
\begin{ttbox}
wenzelm@3108
   201
set     : bool ref -> bool
wenzelm@3108
   202
reset   : bool ref -> bool
wenzelm@3108
   203
toggle  : bool ref -> bool
wenzelm@3108
   204
\end{ttbox}\index{*set}\index{*reset}\index{*toggle}
paulson@3485
   205
These are some shorthands for manipulating boolean references.  The new
wenzelm@3108
   206
value is returned.
wenzelm@3108
   207
wenzelm@3108
   208
lcp@508
   209
\section{Printing of terms and theorems}\label{sec:printing-control}
lcp@322
   210
\index{printing control|(}
lcp@104
   211
Isabelle's pretty printer is controlled by a number of parameters.
lcp@104
   212
lcp@104
   213
\subsection{Printing limits}
lcp@104
   214
\begin{ttbox} 
lcp@104
   215
Pretty.setdepth  : int -> unit
lcp@104
   216
Pretty.setmargin : int -> unit
lcp@104
   217
print_depth      : int -> unit
lcp@104
   218
\end{ttbox}
wenzelm@4317
   219
These set limits for terminal output.  See also {\tt goals_limit},
wenzelm@4317
   220
which limits the number of subgoals printed
wenzelm@4317
   221
(\S\ref{sec:goals-printing}).
lcp@104
   222
lcp@322
   223
\begin{ttdescription}
lcp@322
   224
\item[\ttindexbold{Pretty.setdepth} \(d\);]  
lcp@322
   225
  tells Isabelle's pretty printer to limit the printing depth to~$d$.  This
lcp@322
   226
  affects Isabelle's display of theorems and terms.  The default value
lcp@322
   227
  is~0, which permits printing to an arbitrary depth.  Useful values for
lcp@322
   228
  $d$ are~10 and~20.
lcp@104
   229
lcp@322
   230
\item[\ttindexbold{Pretty.setmargin} \(m\);]  
lcp@322
   231
  tells Isabelle's pretty printer to assume a right margin (page width)
wenzelm@4317
   232
  of~$m$.  The initial margin is~76.
lcp@104
   233
lcp@322
   234
\item[\ttindexbold{print_depth} \(n\);]  
lcp@322
   235
  limits the printing depth of complex \ML{} values, such as theorems and
lcp@322
   236
  terms.  This command affects the \ML{} top level and its effect is
lcp@322
   237
  compiler-dependent.  Typically $n$ should be less than~10.
lcp@322
   238
\end{ttdescription}
lcp@104
   239
lcp@104
   240
wenzelm@4317
   241
\subsection{Printing of hypotheses, brackets, types etc.}
lcp@322
   242
\index{meta-assumptions!printing of}
lcp@322
   243
\index{types!printing of}\index{sorts!printing of}
lcp@104
   244
\begin{ttbox} 
lcp@508
   245
show_hyps     : bool ref \hfill{\bf initially true}
wenzelm@6343
   246
show_tags     : bool ref \hfill{\bf initially false}
lcp@508
   247
show_brackets : bool ref \hfill{\bf initially false}
lcp@508
   248
show_types    : bool ref \hfill{\bf initially false}
lcp@508
   249
show_sorts    : bool ref \hfill{\bf initially false}
wenzelm@4317
   250
show_consts   : bool ref \hfill{\bf initially false}
wenzelm@4543
   251
long_names    : bool ref \hfill{\bf initially false}
lcp@104
   252
\end{ttbox}
lcp@322
   253
These flags allow you to control how much information is displayed for
wenzelm@4317
   254
types, terms and theorems.  The hypotheses of theorems \emph{are}
wenzelm@4317
   255
normally shown.  Superfluous parentheses of types and terms are not.
wenzelm@4317
   256
Types and sorts of variables are normally hidden.
wenzelm@4317
   257
wenzelm@4317
   258
Note that displaying types and sorts may explain why a polymorphic
wenzelm@4317
   259
inference rule fails to resolve with some goal, or why a rewrite rule
wenzelm@4317
   260
does not apply as expected.
lcp@104
   261
lcp@322
   262
\begin{ttdescription}
wenzelm@4543
   263
wenzelm@4317
   264
\item[reset \ttindexbold{show_hyps};] makes Isabelle show each
wenzelm@4317
   265
  meta-level hypothesis as a dot.
wenzelm@4317
   266
  
wenzelm@6343
   267
\item[set \ttindexbold{show_tags};] makes Isabelle show tags of theorems
wenzelm@6343
   268
  (which are basically just comments that may be attached by some tools).
wenzelm@6343
   269
  
wenzelm@4317
   270
\item[set \ttindexbold{show_brackets};] makes Isabelle show full
wenzelm@4317
   271
  bracketing.  In particular, this reveals the grouping of infix
wenzelm@4317
   272
  operators.
wenzelm@4317
   273
  
wenzelm@4317
   274
\item[set \ttindexbold{show_types};] makes Isabelle show types when
wenzelm@4317
   275
  printing a term or theorem.
wenzelm@4317
   276
  
wenzelm@4317
   277
\item[set \ttindexbold{show_sorts};] makes Isabelle show both types
wenzelm@4317
   278
  and the sorts of type variables, independently of the value of
wenzelm@4317
   279
  \texttt{show_types}.
wenzelm@4543
   280
wenzelm@4317
   281
\item[set \ttindexbold{show_consts};] makes Isabelle show types of
wenzelm@4317
   282
  constants, provided that showing of types is enabled at all.  This
wenzelm@4317
   283
  is supported for printing of proof states only.  Note that the
wenzelm@4317
   284
  output can be enormous as polymorphic constants often occur at
wenzelm@4317
   285
  several different type instances.
lcp@508
   286
wenzelm@4543
   287
\item[set \ttindexbold{long_names};] forces names of all objects
wenzelm@4543
   288
  (types, constants, theorems, etc.) to be printed in their fully
wenzelm@4543
   289
  qualified internal form.
wenzelm@4543
   290
lcp@322
   291
\end{ttdescription}
lcp@104
   292
lcp@104
   293
lcp@104
   294
\subsection{$\eta$-contraction before printing}
lcp@104
   295
\begin{ttbox} 
lcp@104
   296
eta_contract: bool ref \hfill{\bf initially false}
lcp@104
   297
\end{ttbox}
lcp@104
   298
The {\bf $\eta$-contraction law} asserts $(\lambda x.f(x))\equiv f$,
lcp@104
   299
provided $x$ is not free in ~$f$.  It asserts {\bf extensionality} of
lcp@104
   300
functions: $f\equiv g$ if $f(x)\equiv g(x)$ for all~$x$.  Higher-order
lcp@332
   301
unification frequently puts terms into a fully $\eta$-expanded form.  For
lcp@158
   302
example, if $F$ has type $(\tau\To\tau)\To\tau$ then its expanded form is
lcp@158
   303
$\lambda h.F(\lambda x.h(x))$.  By default, the user sees this expanded
lcp@158
   304
form.
lcp@104
   305
lcp@322
   306
\begin{ttdescription}
wenzelm@4317
   307
\item[set \ttindexbold{eta_contract};]
lcp@104
   308
makes Isabelle perform $\eta$-contractions before printing, so that
lcp@104
   309
$\lambda h.F(\lambda x.h(x))$ appears simply as~$F$.  The
lcp@104
   310
distinction between a term and its $\eta$-expanded form occasionally
lcp@104
   311
matters.
lcp@322
   312
\end{ttdescription}
lcp@322
   313
\index{printing control|)}
lcp@104
   314
wenzelm@4317
   315
\section{Diagnostic messages}
wenzelm@4317
   316
\index{error messages}
wenzelm@4317
   317
\index{warnings}
wenzelm@4317
   318
wenzelm@6568
   319
Isabelle conceptually provides three output channels for different kinds of
wenzelm@6568
   320
messages: ordinary text, warnings, errors.  Depending on the user interface
wenzelm@6568
   321
involved, these messages may appear in different text styles or colours.
wenzelm@4317
   322
wenzelm@4317
   323
The default setup of an \texttt{isabelle} terminal session is as
wenzelm@4317
   324
follows: plain output of ordinary text, warnings prefixed by
wenzelm@4317
   325
\texttt{\#\#\#}'s, errors prefixed by \texttt{***}'s.  For example, a
wenzelm@4317
   326
typical warning would look like this:
wenzelm@4317
   327
\begin{ttbox}
wenzelm@4317
   328
\#\#\# Beware the Jabberwock, my son!
wenzelm@4317
   329
\#\#\# The jaws that bite, the claws that catch!
wenzelm@4317
   330
\#\#\# Beware the Jubjub Bird, and shun
wenzelm@4317
   331
\#\#\# The frumious Bandersnatch!
wenzelm@4317
   332
\end{ttbox}
wenzelm@4317
   333
wenzelm@4317
   334
\texttt{ML} programs may output diagnostic messages using the
wenzelm@4317
   335
following functions:
wenzelm@4317
   336
\begin{ttbox}
wenzelm@4317
   337
writeln : string -> unit
wenzelm@4317
   338
warning : string -> unit
wenzelm@4317
   339
error   : string -> 'a
wenzelm@4317
   340
\end{ttbox}
wenzelm@4317
   341
Note that \ttindex{error} fails by raising exception \ttindex{ERROR}
wenzelm@4317
   342
after having output the text, while \ttindex{writeln} and
wenzelm@4317
   343
\ttindex{warning} resume normal program execution.
wenzelm@4317
   344
lcp@104
   345
lcp@104
   346
\section{Displaying exceptions as error messages}
lcp@322
   347
\index{exceptions!printing of}
lcp@104
   348
\begin{ttbox} 
lcp@104
   349
print_exn: exn -> 'a
lcp@104
   350
\end{ttbox}
lcp@104
   351
Certain Isabelle primitives, such as the forward proof functions {\tt RS}
lcp@104
   352
and {\tt RSN}, are called both interactively and from programs.  They
lcp@104
   353
indicate errors not by printing messages, but by raising exceptions.  For
wenzelm@4317
   354
interactive use, \ML's reporting of an uncaught exception may be
lcp@322
   355
uninformative.  The Poly/ML function {\tt exception_trace} can generate a
lcp@322
   356
backtrace.\index{Poly/{\ML} compiler}
lcp@104
   357
lcp@322
   358
\begin{ttdescription}
lcp@104
   359
\item[\ttindexbold{print_exn} $e$] 
lcp@104
   360
displays the exception~$e$ in a readable manner, and then re-raises~$e$.
lcp@322
   361
Typical usage is~\hbox{\tt $EXP$ handle e => print_exn e;}, where
lcp@322
   362
$EXP$ is an expression that may raise an exception.
lcp@104
   363
lcp@104
   364
{\tt print_exn} can display the following common exceptions, which concern
lcp@104
   365
types, terms, theorems and theories, respectively.  Each carries a message
lcp@104
   366
and related information.
lcp@104
   367
\begin{ttbox} 
lcp@104
   368
exception TYPE   of string * typ list * term list
lcp@104
   369
exception TERM   of string * term list
lcp@104
   370
exception THM    of string * int * thm list
lcp@104
   371
exception THEORY of string * theory list
lcp@104
   372
\end{ttbox}
lcp@322
   373
\end{ttdescription}
lcp@322
   374
\begin{warn}
lcp@322
   375
  {\tt print_exn} prints terms by calling \ttindex{prin}, which obtains
lcp@322
   376
  pretty printing information from the proof state last stored in the
lcp@322
   377
  subgoal module.  The appearance of the output thus depends upon the
lcp@322
   378
  theory used in the last interactive proof.
lcp@322
   379
\end{warn}
lcp@104
   380
lcp@104
   381
\index{sessions|)}
wenzelm@5371
   382
wenzelm@5371
   383
wenzelm@5371
   384
%%% Local Variables: 
wenzelm@5371
   385
%%% mode: latex
wenzelm@5371
   386
%%% TeX-master: "ref"
wenzelm@5371
   387
%%% End: