manpages.tex 17 KB
Newer Older
1
\chapter{Reference manuals for the \why\ tools}
MARCHE Claude's avatar
MARCHE Claude committed
2
\label{chap:manpages}
MARCHE Claude's avatar
doc    
MARCHE Claude committed
3
4

\section{Compilation, Installation}
MARCHE Claude's avatar
MARCHE Claude committed
5
\label{sec:install}
MARCHE Claude's avatar
doc    
MARCHE Claude committed
6

7
Compilation of \why\ must start with a configuration phase which is run as
MARCHE Claude's avatar
MARCHE Claude committed
8
9
10
11
12
13
\begin{verbatim}
./configure
\end{verbatim}
This analyzes you current configuration and check if requirements hold.
Compilation requires:
\begin{itemize}
MARCHE Claude's avatar
MARCHE Claude committed
14
15
16
\item The Objective Caml compiler, version 3.10 or higher. It is
  available as a binary package for most Unix distributions. For
  debian-based Linux distributions, you can install the packages
MARCHE Claude's avatar
MARCHE Claude committed
17
18
19
20
21
\begin{verbatim}
ocaml ocaml-native-compilers
\end{verbatim}
It is also installable from sources, downloadable from the Web site
\url{http://caml.inria.fr/ocaml/}
MARCHE Claude's avatar
add    
MARCHE Claude committed
22
\end{itemize}
MARCHE Claude's avatar
MARCHE Claude committed
23

MARCHE Claude's avatar
add    
MARCHE Claude committed
24
25
For the IDE, additional Ocaml libraries are needed:
\begin{itemize}
MARCHE Claude's avatar
MARCHE Claude committed
26
27
28
29
30
31
32
\item The Lablgtk2 library for Ocaml bindings of the gtk2 graphical library.
 For debian-based Linux distributions, you can install the packages
\begin{verbatim}
liblablgtk2-ocaml-dev liblablgtksourceview2-ocaml-dev
\end{verbatim}
It is also installable from sources, available from the site \url{http://wwwfun.kurims.kyoto-u.ac.jp/soft/olabl/lablgtk.html}

MARCHE Claude's avatar
MARCHE Claude committed
33
34
35
36
37
38
39
\item The Ocaml bindings of the sqlite3 library
For debian-based Linux distributions, you can install the package
\begin{verbatim}
libsqlite3-ocaml-dev
\end{verbatim}
It is also installable from sources, available from the site
\url{http://ocaml.info/home/ocaml_sources.html#ocaml-sqlite3}
MARCHE Claude's avatar
MARCHE Claude committed
40
41
\end{itemize}

MARCHE Claude's avatar
add    
MARCHE Claude committed
42
43
\subsection{Local use, without installation}

44
It is not mandatory to install \why\ to use it. Local use is obtained via
MARCHE Claude's avatar
add    
MARCHE Claude committed
45
46
47
48
\begin{verbatim}
./configure --enable-local
make
\end{verbatim}
49
The \why\ executables are then available in subdirectory \texttt{bin/}.
MARCHE Claude's avatar
add    
MARCHE Claude committed
50

51
\subsection{Installation of the \why\ library}
MARCHE Claude's avatar
MARCHE Claude committed
52
53
\label{sec:installlib}

54
By default, the \why\ library is not installed. It can be installed using
55
56
57
58
\begin{verbatim}
make byte opt
make install_lib
\end{verbatim}
MARCHE Claude's avatar
MARCHE Claude committed
59

MARCHE Claude's avatar
MARCHE Claude committed
60
\section{Installation of external provers}
MARCHE Claude's avatar
doc    
MARCHE Claude committed
61

62
63
\why\ can use a wide range of external theorem provers. These need to
be installed separately, and then \why\ needs to be configured to use
MARCHE Claude's avatar
MARCHE Claude committed
64
65
them. There is no need to install these provers before compiling and
installing Why. 
MARCHE Claude's avatar
add    
MARCHE Claude committed
66

MARCHE Claude's avatar
MARCHE Claude committed
67
68
For installation of external provers, please look at the Why provers
tips page \url{http://why.lri.fr/provers.en.html}.
MARCHE Claude's avatar
add    
MARCHE Claude committed
69

70
For configuring \why\ to use the provers, follow intructions given in
MARCHE Claude's avatar
MARCHE Claude committed
71
Section~\ref{sec:why3config}.
MARCHE Claude's avatar
add    
MARCHE Claude committed
72

MARCHE Claude's avatar
MARCHE Claude committed
73
74
\section{The \texttt{why3config} command-line tool}
\label{sec:why3config}.
MARCHE Claude's avatar
add    
MARCHE Claude committed
75

76
\why\ must be configured to access external provers. Typically, this is done
MARCHE Claude's avatar
MARCHE Claude committed
77
78
79
80
81
82
83
84
85
86
87
88
by running either the command line tool
\begin{verbatim}
why3config
\end{verbatim}
or using the menu
\begin{verbatim}
File/Detect provers
\end{verbatim}
of the IDE. This must be done again each time a new prover is installed.

The set of all provers which are attempted to detect is described in
the readable configuration file \texttt{provers-detection-data.conf}
89
of the \why\ data directory (\eg{}
MARCHE Claude's avatar
MARCHE Claude committed
90
91
92
93
94
95
96
97
98
99
100
101
102
\texttt{/usr/local/share/why3}). Advanced users may try to modify this
file to add support for detection of other provers. (In that case,
please consider submitting a new prover configuration on the bug
tracking system).

The result of the prover detection is stored in the user's
configuration file (\eg{} \texttt{~/.why.conf}). Again, this file is
human readable, and advanced users may modify it in order to
experiment different ways of calling provers, \eg{} different versions
of the same prover, or with different options.

The provers which are typically attemped for detection are
\begin{itemize}
MARCHE Claude's avatar
MARCHE Claude committed
103
104
105
106
107
108
109
110
111
112
\item Alt-Ergo~\cite{conchon08smt,ergo}: \url{http://alt-ergo.lri.fr}
\item CVC3~\cite{BarTin-CAV-07}: \url{http://cs.nyu.edu/acsys/cvc3/}
\item Coq~\cite{CoqArt}: \url{http://coq.inria.fr}
\item Eprover~\cite{schulz04ijcar}: \url{http://www4.informatik.tu-muenchen.de/~schulz/WORK/eprover.html}
\item Gappa~\cite{melquiond08rnc}: \url{http://gappa.gforge.inria.fr/}
\item Simplify~\cite{simplify05}: \url{http://secure.ucd.ie/products/opensource/Simplify/}
\item Spass~: \url{http://www.spass-prover.org/}
\item veriT~: \url{http://www.verit-solver.org/}
\item Yices~\cite{DM06}: \url{http://yices.csl.sri.com/}
\item Z3~\cite{z3}: \url{http://research.microsoft.com/en-us/um/redmond/projects/z3/}
MARCHE Claude's avatar
MARCHE Claude committed
113
\end{itemize}
MARCHE Claude's avatar
add    
MARCHE Claude committed
114

115
\texttt{why3config} also detects the plugins installed in the \why\
116
117
118
119
120
121
plugins directory (\eg{} \texttt{/usr/local/lib/why3/plugins}). A
plugin must register itself as a parser, a transformation or a
printer, as explained in the corresponding section.

If the user's configuration file is already present,
\texttt{why3config} will only reset unset variables to default value.
MARCHE Claude's avatar
MARCHE Claude committed
122
The option \texttt{--autodetect-provers} will detect again the available
123
provers and will replace them in the file configuration.
MARCHE Claude's avatar
MARCHE Claude committed
124
\texttt{--autodetect-plugins} will do the same for plugins.
125

MARCHE Claude's avatar
doc    
MARCHE Claude committed
126
\section{The \texttt{why3} command-line tool}
MARCHE Claude's avatar
MARCHE Claude committed
127
\label{sec:why3ref}
MARCHE Claude's avatar
doc    
MARCHE Claude committed
128

129
\why\ is primarily used to call provers on goals contains by file in
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
why3 format \texttt{.why} extension. However plugins can register
parser which can extend the known format. \texttt{why3ml} apply the
following steps :
\begin{enumerate}
\item Parse the command line and report error if needed
\item Read the configuration file using the priority defined in
  section\ref{sec:whyconffile}
\item Load the plugins mentionned in the configuration. It will not
  stop if a plugin fail to load.
\item Parse and type the given files using the correct parser in order
  to obtain a set of why theory for each files. It uses
  the filename extension or the \texttt{--format} options to choose
  among the available parsers. \texttt{--list-format} gives the list
  of them.
\item Extract the selected goals inside each selected theories into
  tasks. The goals and theories are selected using the options
  \texttt{-G/--goal} and \texttt{-T/--theory}. One
  \texttt{-T/--theory} applies to the last file appearing on the
  commandline, one \texttt{-G/--goal} applies to the last theory
  appearing on the commandline. If none theories are selected in one
  file, they are all selected. If none goals are selected inside one
  selected theory, they are all selected.
\item Apply the transformation requested
  with \texttt{-a/--apply-transform} in the order they appear on the
  command line. \texttt{--list-transforms} list the known
  transformations, plugins can add more of them.
\item Apply the driver selected with the \texttt{-D/--driver} option,
  or the driver of the prover selected with \texttt{-P/--prover}
  option. \texttt{--list-provers} lists the known provers, ie the one
  which appear in the configuration file.
\item Print the result of the standard output if \texttt{-D/--driver}
  is used or call the prover and print the result if
  \texttt{-P/--prover} is used.
\end{enumerate}

MARCHE Claude's avatar
roadmap    
MARCHE Claude committed
165
166
167
168
169
170
171
172
173
174
% \texttt{why3} call the prover sequentially, use \texttt{why3bench} if *)
% you want to call the provers concurrently.  *)

% \why\ can also be *)
% used to provide other informations : *)
% \begin{itemize} *)
% \item \texttt{print-namespace} print the namespace of the selected *)
%   theories *)
% \item TO BE COMPLETED *)
% \end{itemize} *)
175

176
\section{The \texttt{why3ide} GUI}
MARCHE Claude's avatar
MARCHE Claude committed
177
178
\label{sec:ideref}

179
180
181
182
The basic usage of the GUI is described by the tutorial of
Section~\ref{sec:gui}. We describe here the command-line options and
the actions of the various menus and buttons of the interface.

MARCHE Claude's avatar
MARCHE Claude committed
183
184
185
186
187
188
\subsection{Command-line options}

\begin{description}
\item[-I] $d$: adds $d$ in the load path, to search for theories.
\end{description}

MARCHE Claude's avatar
MARCHE Claude committed
189
\subsection{Left toolbar actions}
MARCHE Claude's avatar
MARCHE Claude committed
190
191

\begin{description}
MARCHE Claude's avatar
MARCHE Claude committed
192
193
194
195
196
197
\item[Context] The context in which the other tools below will
  apply. If ``only unproved goals'' is selected, no action will ever
  be applied to an already proved goal.  If ``all goals'', then
  actions are performed even if the goal is already proved. The second
  choice allows to compare provers on the same goal.

MARCHE Claude's avatar
MARCHE Claude committed
198
199
200
201
\item[Provers] To each detected prover corresponds to a button in this
  prover framed box. Clicking on this button starts the prover on the
  selected goal(s).

MARCHE Claude's avatar
MARCHE Claude committed
202
203
204
205
206
207
\item[Split] This splits the current goal into subgoals if it is a
  conjunction of two or more goals.

\item[Inline] If the goal is headed by a defined predicate symbol,
  expands it with this definition. [NOT YET AVAILABLE]

MARCHE Claude's avatar
MARCHE Claude committed
208
209
210
211
212
213
214
215
216
\item[Edit] Start an editor on the selected task.

  For automatic provers, this allows to see the file sent to the
  prover.

  For interactive provers, this also allows to add or modify the
  corresponding proof script. The modifications are saved, and can be
  retrieved later even if the goal was modified.

MARCHE Claude's avatar
MARCHE Claude committed
217
218
\item[Replay] replay all obsolete proofs [NOT YET AVAILABLE]

MARCHE Claude's avatar
MARCHE Claude committed
219
\item[Remove] Removes a proof attempt or a transformation. 
MARCHE Claude's avatar
MARCHE Claude committed
220
221
222
223
224
225

\end{description}

\subsection{Menus}

\begin{description}
MARCHE Claude's avatar
MARCHE Claude committed
226
227
\item[File/Detect provers] runs provers auto-detection
\item[File/Preferences] opens a window for modifying preferred configuration
MARCHE Claude's avatar
MARCHE Claude committed
228
\end{description}
MARCHE Claude's avatar
MARCHE Claude committed
229

MARCHE Claude's avatar
MARCHE Claude committed
230
231
\subsection{Preferences}

MARCHE Claude's avatar
MARCHE Claude committed
232
233
234
235
236
237
238
239
240
The preferences window allows you customize
\begin{itemize}
\item the default editor to use when the \textsf{Edit} button is
  pressed. This might be overidden for a specific prover (the only way
  to do that for the moment is to manually edit the config file)
\item the time limit given to provers, in seconds
\item the maximal number of simultaneous provers allowed to run in parallel. 
\end{itemize}

MARCHE Claude's avatar
MARCHE Claude committed
241
242
\subsection{Structure of the database file}

243
244
245
246
[TO BE COMPLETED LATER]

\section{The \texttt{why3ml} tool}

247
The \texttt{why3ml} is an additional layer on \why\ library for
248
249
250
251
252
253
254
255
256
generating verification conditions from WhyML programs. This tool and
the syntax of WhyML programs is intentionally left undocumented since
it might evolve significantly in the near future.

For those who want to experiment with it, examples are provided in
\texttt{examples/programs}. The files \texttt{*.mlw} can be loaded in
the GUI.

[TO BE COMPLETED LATER]
MARCHE Claude's avatar
doc    
MARCHE Claude committed
257

258
259
\section{The \texttt{why3bench} tool}

260
261
[TO BE COMPLETED LATER]

MARCHE Claude's avatar
MARCHE Claude committed
262
\section{The \texttt{why.conf} configuration file}
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
\label{sec:whyconffile}
One can defined more than one configuration file. \texttt{why3config}
and all the others \texttt{why3}'s tools use priorities for which
user's configuration file to consider:
\begin{itemize}
\item the file specified by the \texttt{-C} or \texttt{--config} options,
\item the file specified by the environment variable
  \texttt{\$WHY\_CONFIG} if set.
\item the file \texttt{why.conf} or \texttt{.why.conf} in the current
  directory.
\item the file \texttt{\$HOME/.why.conf} or \texttt{\$USERPROFILE/.why.conf}
\end{itemize}
If none of this file exists a built-in default configuration is used
which is saved in a default configuration filename, which is usually
\texttt{\$HOME/.why.conf}.

The configuration file is a human-readable text file, which is
composed by association pairs arranged by sections. Here an example of
a configuration file.

\begin{verbatim}
[main ]
datadir = "/usr/local/share/why3"
libdir = "/usr/local/lib/why3"
loadpath = "/usr/local/share/why3/theories"
memlimit = 0
running_provers_max = 2
timelimit = 10

[ide ]
default_editor = "emacs"
task_height = 384
tree_width = 438
verbose = 0
window_height = 779
window_width = 638

[prover coq]
command = "coqc %f"
driver = "/usr/local/share/why3/drivers/coq.drv"
editor = "coqide"
name = "Coq"
version = "8.2pl2"

[prover alt-ergo]
command = "why3-cpulimit %t %m alt-ergo %f"
driver = "/usr/local/share/why3/drivers/alt_ergo.drv"
editor = ""
name = "Alt-Ergo"
version = "0.91"
\end{verbatim}

A section begin with an header inside square brackets and end at the
next square brackets. Sections can't be nested. The header of a
section can be only one identifier, \texttt{main} and \texttt{ide} in
the example, or it can be composed by a family name and one family
argument, \texttt{prover} is one family name, \texttt{coq} and
\texttt{alt-ergo} are the family argument.

Inside a section, one key can be associated to an integer (.eg -555),
MARCHE Claude's avatar
roadmap    
MARCHE Claude committed
323
a boolean (true, false) or a string (\eg{} "emacs"). One key can appear
324
325
only once except if its a multi-value key. The order of apparition of
the keys inside a section matter only for the multi-value key.
MARCHE Claude's avatar
MARCHE Claude committed
326

MARCHE Claude's avatar
MARCHE Claude committed
327
\section{Drivers of external provers}
328
329
330
331
332
333
334

The drivers of external provers are readable files, in directory
\texttt{drivers}. Experimented users can modify them to change the way
the external provers are called, in particular which transformations
are applied to goals.

[TO BE COMPLETED LATER]
MARCHE Claude's avatar
MARCHE Claude committed
335
336

\section{Transformations}
MARCHE Claude's avatar
MARCHE Claude committed
337
\label{sec:transformations}
MARCHE Claude's avatar
MARCHE Claude committed
338

339
340
341
342
Here is a quick documentation of provided transformations. We give
first the non-splitting ones, \eg{} those which produce one goal as
result, and others which produces any number of goals.

MARCHE Claude's avatar
MARCHE Claude committed
343
344
345
\subsection{Non-splitting transformations}

\begin{description}
346

MARCHE Claude's avatar
MARCHE Claude committed
347
348
\item[eliminate\_algebraic] Replaces algebraic data types by first-order
definitions~\cite{paskevich09rr}
349

350
351
\item[eliminate\_builtin] Suppress definitions of symbols which are
  declared as builtin in the driver, i.e. with a ``syntax'' rule.
MARCHE Claude's avatar
MARCHE Claude committed
352
\item[eliminate\_definition\_func]
MARCHE Claude's avatar
roadmap    
MARCHE Claude committed
353
  Replaces all function definitions with axioms.
MARCHE Claude's avatar
MARCHE Claude committed
354
\item[eliminate\_definition\_pred]
MARCHE Claude's avatar
roadmap    
MARCHE Claude committed
355
356
357
358
359
360
361
  Replaces all predicate definitions with axioms.
\item[eliminate\_definition]
  Apply both transformations above.
\item[eliminate\_mutual\_recursion]
  Replaces mutually recursive definitions with axioms.
\item[eliminate\_recursion]
  Replaces all recursive definitions with axioms.
362

MARCHE Claude's avatar
roadmap    
MARCHE Claude committed
363
364
365
\item[eliminate\_if\_term] replaces terms of the form \texttt{if
    formula then t2 else t3} by lifting them at the level of formulas.
  This may introduce \texttt{if then else } in formulas.
366

MARCHE Claude's avatar
roadmap    
MARCHE Claude committed
367
368
369
\item[eliminate\_if\_fmla] replaces formulas of the form \texttt{if f1 then f2
  else f3} by an equivalent formula using implications and other
  connectives. 
370

MARCHE Claude's avatar
MARCHE Claude committed
371
\item[eliminate\_if]
MARCHE Claude's avatar
roadmap    
MARCHE Claude committed
372
  Apply both transformations above.
373

374
\item[eliminate\_inductive] replaces inductive predicates by
MARCHE Claude's avatar
roadmap    
MARCHE Claude committed
375
376
  (incomplete) axiomatic definitions, i.e. construction axioms and
  an inversion axiom.
377

MARCHE Claude's avatar
MARCHE Claude committed
378
\item[eliminate\_let\_fmla]
MARCHE Claude's avatar
roadmap    
MARCHE Claude committed
379
380
  Eliminates \texttt{let} by substitution, at the predicate level.

MARCHE Claude's avatar
MARCHE Claude committed
381
\item[eliminate\_let\_term]
MARCHE Claude's avatar
roadmap    
MARCHE Claude committed
382
383
  Eliminates \texttt{let} by substitution, at the term level.

384
\item[eliminate\_let]
MARCHE Claude's avatar
roadmap    
MARCHE Claude committed
385
  Apply both transformations above.
386

MARCHE Claude's avatar
roadmap    
MARCHE Claude committed
387
388
389
% \item[encoding\_decorate\_mono]

% \item[encoding\_enumeration]
390

MARCHE Claude's avatar
MARCHE Claude committed
391
\item[encoding\_smt]
392
393
  Encode polymorphic types into monomorphic type~\cite{conchon08smt}.

MARCHE Claude's avatar
MARCHE Claude committed
394
\item[encoding\_tptp]
MARCHE Claude's avatar
roadmap    
MARCHE Claude committed
395
  Encode theories into unsorted logic. %~\cite{cruanes10}.
396

MARCHE Claude's avatar
roadmap    
MARCHE Claude committed
397
398
399
400
401
402
403
404
% \item[filter\_trigger] *)

% \item[filter\_trigger\_builtin] *)

% \item[filter\_trigger\_no\_predicate] *)

% \item[hypothesis\_selection] *)
%   Filter hypothesis of goals~\cite{couchot07ftp,cruanes10}. *)
405

MARCHE Claude's avatar
MARCHE Claude committed
406
\item[inline\_all]
MARCHE Claude's avatar
roadmap    
MARCHE Claude committed
407
408
409
410
411
  expands all non-recursive definitions.

\item[inline\_goal] Expands all outermost symbols of the goal that
  have a non-recursive definition.

MARCHE Claude's avatar
MARCHE Claude committed
412
\item[inline\_trivial]
413
  removes definitions of the form
MARCHE Claude's avatar
roadmap    
MARCHE Claude committed
414

415
416
417
\begin{verbatim}
logic f x_1 .. x_n = (g e_1 .. e_k)
\end{verbatim}
MARCHE Claude's avatar
roadmap    
MARCHE Claude committed
418
419
420
421
422
when each $e_i$ is either a ground term or one of the $x_j$, and
each $x_1$ .. $x_n$ occur at most once in the $e_i$

\item[introduce\_premises] moves antecedents of implications and
  universal quantifications of the goal into the premises of the task.
423

MARCHE Claude's avatar
roadmap    
MARCHE Claude committed
424
425
% \item[remove\_triggers] *)
%   removes the triggers in all quantifications. *)
426

MARCHE Claude's avatar
roadmap    
MARCHE Claude committed
427
428
\item[simplify\_array] Automatically rewrites the task using the lemma
  \verb|Select_eq| of theory \verb|array.Array|.
429

MARCHE Claude's avatar
roadmap    
MARCHE Claude committed
430
431
\item[simplify\_formula] reduces trivial equalities $t=t$ to true and
  then simplifies propositional structure: removes true, false, ``f
432
  and f'' to ``f'', etc.
433
434
435

\item[simplify\_recursive\_definition] reduces mutually recursive
  definitions if they are not really mutually recursive, e.g.:
436
437
438
439
440
441
442
443
444
445
446
447
\begin{verbatim}
logic f : ... = .... g ...

with g : .. = e
\end{verbatim}
becomes
\begin{verbatim}
logic g : .. = e
logic f : ... = .... g ...
\end{verbatim}
if f does not occur in e

MARCHE Claude's avatar
MARCHE Claude committed
448
\item[simplify\_trivial\_quantification]
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
  simplifies quantifications of the form
\begin{verbatim}
  forall x, x=t -> P(x)
\end{verbatim}
or
\begin{verbatim}
  forall x, t=x -> P(x)
\end{verbatim}
  when x does not occur in t
  into 
\begin{verbatim}
P(t)
\end{verbatim}
  More generally, it applies this simplification whenever x=t appear
  in a negative position.
  
MARCHE Claude's avatar
MARCHE Claude committed
465
\item[simplify\_trivial\_quantification\_in\_goal]
MARCHE Claude's avatar
roadmap    
MARCHE Claude committed
466
  same as above but applies only in the goal.
467

MARCHE Claude's avatar
MARCHE Claude committed
468
\item[split\_premise]
MARCHE Claude's avatar
roadmap    
MARCHE Claude committed
469
  splits conjunctive premises.
470

MARCHE Claude's avatar
MARCHE Claude committed
471
472
473
474
475
\end{description}

\subsection{Splitting transformations}

\begin{description}
MARCHE Claude's avatar
roadmap    
MARCHE Claude committed
476
477
478
479
480
481
482
483
484
485
486

\item[full\_split\_all]
  composition of \texttt{split\_premise} and \texttt{full\_split\_goal}.

\item[full\_split\_goal] puts the goal in a conjunctive form,
  returns the corresponding set of subgoals. The number of subgoals
  generated may be exponential in the size of the initial goal.

\item[simplify\_formula\_and\_task] same as \texttt{simplify\_formula}
  but also removes the goal if it is equivalent to true.

MARCHE Claude's avatar
MARCHE Claude committed
487
\item[split\_all]
MARCHE Claude's avatar
roadmap    
MARCHE Claude committed
488
  composition of \texttt{split\_premise} and \texttt{split\_goal}.
489
490

\item[split\_goal] if the goal is a conjunction of goals, returns the
MARCHE Claude's avatar
roadmap    
MARCHE Claude committed
491
492
493
494
495
496
  corresponding set of subgoals. The number of subgoals generated is linear in
  the size of the initial goal.

\item[split\_intro]
  when a goal is an implication, moves the antecedents into the premises.

MARCHE Claude's avatar
MARCHE Claude committed
497
498
\end{description}

MARCHE Claude's avatar
MARCHE Claude committed
499

MARCHE Claude's avatar
doc    
MARCHE Claude committed
500
501
502
503
504
505

%%% Local Variables:
%%% mode: latex
%%% TeX-PDF-mode: t
%%% TeX-master: "manual"
%%% End: