3 <!-- Copyright (C) 2000, HELM Team -->
5 <!-- This file is part of HELM, an Hypertextual, Electronic -->
6 <!-- Library of Mathematics, developed at the Computer Science -->
7 <!-- Department, University of Bologna, Italy. -->
9 <!-- HELM is free software; you can redistribute it and/or -->
10 <!-- modify it under the terms of the GNU General Public License -->
11 <!-- as published by the Free Software Foundation; either version 2 -->
12 <!-- of the License, or (at your option) any later version. -->
14 <!-- HELM is distributed in the hope that it will be useful, -->
15 <!-- but WITHOUT ANY WARRANTY; without even the implied warranty of -->
16 <!-- MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -->
17 <!-- GNU General Public License for more details. -->
19 <!-- You should have received a copy of the GNU General Public License -->
20 <!-- along with HELM; if not, write to the Free Software -->
21 <!-- Foundation, Inc., 59 Temple Place - Suite 330, Boston, -->
22 <!-- MA 02111-1307, USA. -->
24 <!-- For details, see the HELM World-Wide-Web page, -->
25 <!-- http://cs.unibo.it/helm/. -->
27 <!--******************************************************************-->
29 <!-- (completely) Revisited: february 2001, Andrea Asperti -->
30 <!-- HELM Group: Asperti, Padovani, Sacerdoti, Schena -->
31 <!--******************************************************************-->
33 <xsl:stylesheet version="1.0" xmlns:xsl="http://www.w3.org/1999/XSL/Transform"
34 xmlns:m="http://www.w3.org/1998/Math/MathML"
35 xmlns:helm="http://www.cs.unibo.it/helm">
37 <!-- ************************* LOGIC *********************************-->
39 <!-- Proof objects -->
41 <!-- <xsl:key name="typeid" use="@of" match="TYPE"/> -->
43 <!-- ALL this elements does not have inner type -->
44 <xsl:template match="LETIN|PROD|REL|SORT|VAR|META|CONST|MUTIND|MUTCONSTRUCT" mode="noannot">
45 <xsl:apply-templates select="." mode="pure"/>
48 <!-- ALL ELEMENTS WITH A TYPE ARE TRANSLATED AS A PROOF-ELEMENT -->
50 <!-- LAMBDA has inner type only if it is not nested inside another lambda -->
51 <xsl:template match="LAMBDA" mode="noannot">
52 <xsl:variable name="id" select="@id"/>
54 <xsl:when test="$naturalLanguage='yes' and @sort='Prop' and name(../..) != 'LAMBDA'">
55 <m:apply helm:xref="{@id}">
56 <m:csymbol>proof</m:csymbol>
57 <xsl:apply-templates mode="proof_transform" select="."/>
58 <xsl:apply-templates mode="pure" select="$InnerTypes/InnerTypes/TYPE[@of=$id]/*"/>
62 <xsl:apply-templates select="." mode="pure"/>
67 <!-- ALL these elements have inner type -->
68 <xsl:template match="CAST|APPLY|MUTCASE|FIX|COFIX" mode="noannot">
69 <xsl:variable name="id" select="@id"/>
71 <xsl:when test="$naturalLanguage='yes' and @sort='Prop'">
72 <m:apply helm:xref="{@id}">
73 <m:csymbol>proof</m:csymbol>
74 <xsl:apply-templates mode="proof_transform" select="."/>
75 <!-- <xsl:apply-templates mode="try_inductive" select="."/> -->
76 <xsl:apply-templates mode="pure" select="$InnerTypes/InnerTypes/TYPE[@of=$id]/*"/>
81 <xsl:when test="name()='APPLY'">
82 <xsl:apply-templates select="." mode="letin"/>
85 <xsl:apply-templates select="." mode="pure"/>
92 <!-- si presuppone che il tipo induttivo non sia mutuamente
93 induttivo. Bisognerebbe andare a vedere l'utlimo parametro
94 del presunto "principio di induzione", tirare fuori il tipo induttivo
95 e vedere se il suo nome coincide con il prefisso di _ind.
96 Ad esempio nat_double_ind e' definito dall'utente. L'ultimo
97 parametro di nat_double_ind e' di tipo nat, e nat e' diverso
98 da nat_double. Per ora, verifico solo l'esistenza di nat_double,
99 ma questo, benche' non porti ad errore, non copre tutti i
100 casi per quelli mutuamente induttivi -->
102 <xsl:template mode="try_inductive" match="APPLY">
103 <xsl:variable name="id" select="@id"/>
105 <xsl:when test="CONST[1]">
106 <xsl:variable name="uri" select="CONST[1]/@uri"/>
108 <xsl:when test="contains($uri,'_ind.con')">
109 <xsl:variable name="ind_uri"
110 select="concat(substring-before($uri,'_ind.con'),'.ind')"/>
111 <xsl:variable name="inductive_def"
112 select="document(concat(string($absPath),$ind_uri))/InductiveDefinition"/>
113 <!-- check if the corresponding inductive definition actually
116 <xsl:when test="$inductive_def">
117 <xsl:variable name="ind_name">
118 <xsl:call-template name="get_name">
119 <xsl:with-param name="uri" select="$uri"/>
122 <xsl:variable name="no_params">
123 <xsl:call-template name="get_no_params">
124 <xsl:with-param name="first_uri" select="$CICURI"/>
125 <xsl:with-param name="second_uri" select="$uri"/>
128 <xsl:apply-templates mode="inductive" select=".">
129 <xsl:with-param name="inductive_def_uri"
131 <xsl:with-param name="inductive_def"
132 select="$inductive_def"/>
133 <xsl:with-param name="section_params" select="$no_params"/>
134 <xsl:with-param name="inductive_def_index" select="1"/>
135 <xsl:with-param name="inductive_def_name" select="$ind_name"/>
136 </xsl:apply-templates>
139 <xsl:apply-templates mode="letin" select="."/>
144 <xsl:apply-templates mode="letin" select="."/>
149 <xsl:apply-templates mode="letin" select="."/>
155 <xsl:template mode="proof_transform" match="*">
157 <xsl:when test="name()='APPLY'">
158 <xsl:variable name="id" select="@id"/>
160 <!-- NATIND 3 parametri -->
161 <xsl:when test="CONST[attribute::uri='cic:/Coq/Init/Datatypes/nat_ind.con'] and count(child::*) = 4">
163 <m:csymbol>nat_ind</m:csymbol>
164 <xsl:apply-templates mode="noannot" select="*[3]"/>
165 <xsl:apply-templates mode="noannot" select="*[4]"/>
168 <!-- NATIND 4 parametri (nuova versione) -->
170 <xsl:when test="CONST[
171 attribute::uri='cic:/Coq/Init/Datatypes/nat_ind.con']
172 and count(child::*) = 5
173 and name(*[4])='LAMBDA'
174 and name(*[4]/target/*[1])='LAMBDA'">
176 <m:csymbol>nat_ind_complete</m:csymbol>
177 <xsl:apply-templates mode="noannot" select="*[5]"/>
178 <xsl:apply-templates mode="noannot" select="*[3]"/>
179 <m:ci><xsl:value-of select="*[4]/target/@binder"/></m:ci>
180 <m:ci><xsl:value-of select="*[4]/target/*[1]/target/@binder"/></m:ci>
181 <xsl:apply-templates mode="noannot" select="*[4]/target/*[1]/source/*"/>
182 <xsl:apply-templates mode="noannot" select="*[4]/target/*[1]/target/*"/>
187 <xsl:when test="CONST[
188 attribute::uri='cic:/Coq/Init/Logic/Equality/eq_ind.con' or
189 attribute::uri='cic:/Coq/Init/Logic/Logic_lemmas/eq_ind_r.con' or
190 attribute::uri='cic:/Coq/Init/Logic_Type/eqT_ind.con' or
191 attribute::uri='cic:/Coq/Init/Logic_Type/eqT_ind_r.con' or
192 attribute::uri='cic:/Coq/Zarith/auxiliary/eqT_ind_r.con'] and count(child::*) = 7">
194 <m:csymbol>rw_step</m:csymbol>
195 <xsl:apply-templates mode="noannot" select="*[5]"/>
196 <xsl:apply-templates mode="pure" select="*[3]"/>
197 <xsl:apply-templates mode="pure" select="*[6]"/>
198 <xsl:apply-templates mode="proof_transform" select="*[7]"/>
201 <!-- EQUALITY with extra-parameters -->
202 <xsl:when test="CONST[
203 attribute::uri='cic:/Coq/Init/Logic/Equality/eq_ind.con' or
204 attribute::uri='cic:/Coq/Init/Logic/Logic_lemmas/eq_ind_r.con' or
205 attribute::uri='cic:/Coq/Init/Logic_Type/eqT_ind.con' or
206 attribute::uri='cic:/Coq/Init/Logic_Type/eqT_ind_r.con' or
207 attribute::uri='cic:/Coq/Zarith/auxiliary/eqT_ind_r.con'] and count(child::*) > 7">
208 <xsl:variable name="no_extraproofs" select="count(*[position()>7 and @sort='Prop' and (name(.)='LAMBDA' or name(.)='LETIN' or name(.)='APPLY' or name(.)='MUTCASE' or name(.)='FIX' or name(.)='COFIX')])"/>
210 <xsl:when test="$no_extraproofs=0">
212 <m:csymbol>rewrite_and_apply</m:csymbol>
214 <m:csymbol>rw_step</m:csymbol>
215 <xsl:apply-templates mode="noannot" select="*[5]"/>
216 <xsl:apply-templates mode="pure" select="*[3]"/>
217 <xsl:apply-templates mode="pure" select="*[6]"/>
218 <xsl:apply-templates mode="pure" select="*[7]"/>
220 <xsl:apply-templates mode="noannot" select="*[position()>7]"/>
225 <xsl:when test="*[5]/@sort='Prop'">
226 <m:apply helm:xref="{@id}">
227 <m:csymbol>letin</m:csymbol>
229 <m:csymbol>let</m:csymbol>
231 <xsl:call-template name="insert_subscript">
232 <xsl:with-param name="node_value" select="'h1'"/>
235 <xsl:apply-templates mode="noannot" select="*[5]"/>
237 <xsl:call-template name="gen_let">
238 <xsl:with-param name="init_pos" select="1"/>
239 <xsl:with-param name="from" select="7"/>
242 <m:csymbol>rewrite_and_apply</m:csymbol>
244 <m:csymbol>rw_step</m:csymbol>
246 <xsl:call-template name="insert_subscript">
247 <xsl:with-param name="node_value" select="'h1'"/>
250 <xsl:apply-templates mode="pure" select="*[3]"/>
251 <xsl:apply-templates mode="pure" select="*[6]"/>
252 <xsl:apply-templates mode="pure" select="*[7]"/>
254 <xsl:apply-templates mode="flat" select="*[8]">
255 <xsl:with-param name="n">
256 <xsl:value-of select="2"/>
258 </xsl:apply-templates>
263 <m:apply helm:xref="{@id}">
264 <m:csymbol>letin</m:csymbol>
265 <xsl:call-template name="gen_let">
266 <xsl:with-param name="init_pos" select="0"/>
267 <xsl:with-param name="form" select="7"/>
270 <m:csymbol>rewrite_and_apply</m:csymbol>
272 <m:csymbol>rw_step</m:csymbol>
273 <xsl:apply-templates mode="pure" select="*[5]"/>
274 <xsl:apply-templates mode="pure" select="*[3]"/>
275 <xsl:apply-templates mode="pure" select="*[6]"/>
276 <xsl:apply-templates mode="pure" select="*[7]"/>
278 <xsl:apply-templates mode="flat" select="*[8]">
279 <xsl:with-param name="n">
280 <xsl:value-of select="1"/>
282 </xsl:apply-templates>
291 <xsl:when test="CONST[
292 attribute::uri='cic:/Coq/Init/Logic/False_ind.con'] and
293 count(child::*) = 3">
294 <m:apply helm:xref="{@id}">
295 <m:csymbol>false_ind</m:csymbol>
296 <m:ci>cic:/Coq/Init/Logic/False_ind.con</m:ci>
297 <xsl:apply-templates mode="noannot" select="*[3]"/>
300 <!-- gestire meglio il caso di and_ind quando la prova
301 non e' della forma \x.\y.M -->
302 <xsl:when test="CONST[
303 attribute::uri='cic:/Coq/Init/Logic/Conjunction/and_ind.con']
304 and count(child::*) = 6
305 and name(*[5])='LAMBDA'
306 and name(*[5]/target/*[1])='LAMBDA'">
307 <m:apply helm:xref="{@id}">
308 <m:csymbol>and_ind</m:csymbol>
309 <xsl:apply-templates mode="noannot" select="*[6]"/>
310 <m:ci><xsl:call-template name="insert_subscript"><xsl:with-param name="node_value"><xsl:value-of select="*[5]/target/@binder"/></xsl:with-param></xsl:call-template></m:ci>
311 <xsl:apply-templates mode="pure" select="*[5]/source/*"/>
312 <m:ci><xsl:call-template name="insert_subscript"><xsl:with-param name="node_value"><xsl:value-of select="*[5]/target/LAMBDA/target/@binder"/></xsl:with-param></xsl:call-template></m:ci>
313 <xsl:apply-templates mode="pure" select="*[5]/target/LAMBDA/source/*"/>
314 <xsl:apply-templates mode="proof_transform" select="*[5]/target/LAMBDA/target/*"/>
317 <xsl:when test="CONST[
318 attribute::uri='cic:/Coq/Init/Logic/Disjunction/or_ind.con']
319 and count(child::*) = 7">
321 <xsl:when test="name(*[5])='LAMBDA'
322 and name(*[6])='LAMBDA'">
323 <xsl:variable name="definition_url"
324 select="'cic:/Coq/Init/Logic/Disjunction/or.ind'"/>
325 <m:apply helm:xref="{@id}">
326 <m:csymbol>full_or_ind</m:csymbol>
327 <xsl:apply-templates mode="noannot" select="*[7]"/>
328 <xsl:apply-templates mode="pure"
329 select="$InnerTypes/InnerTypes/TYPE[@of=$id]/*"/>
331 <m:csymbol>left_case</m:csymbol>
334 <xsl:value-of select="*[5]/target/@binder"/>
337 <xsl:apply-templates mode="pure" select="*[5]/source/*[1]"/>
340 <xsl:apply-templates mode="noannot" select="*[5]/target/*[1]"/>
343 <m:csymbol>right_case</m:csymbol>
346 <xsl:apply-templates mode="pure" select="*[6]/target/@binder"/>
349 <xsl:apply-templates mode="pure" select="*[6]/source/*[1]"/>
352 <xsl:apply-templates mode="noannot" select="*[6]/target/*[1]"/>
357 <m:apply helm:xref="{@id}">
358 <m:csymbol>or_ind</m:csymbol>
359 <xsl:apply-templates mode="noannot" select="*[7]"/>
360 <xsl:apply-templates mode="pure"
361 select="$InnerTypes/InnerTypes/TYPE[@of=$id]/*"/>
362 <xsl:apply-templates mode="pure" select="*[5]"/>
363 <xsl:apply-templates mode="pure" select="*[6]"/>
368 <!-- ex_ind, exT_ind -->
369 <xsl:when test="(CONST[attribute::uri='cic:/Coq/Init/Logic_Type/exT_ind.con'] or
370 CONST[attribute::uri='cic:/Coq/Init/Logic/First_order_quantifiers/ex_ind.con'])
371 and count(child::*) = 6
372 and name(*[5])='LAMBDA'
373 and name(*[5]/target/*[1])='LAMBDA'">
374 <m:apply helm:xref="{@id}">
375 <m:csymbol>ex_ind</m:csymbol>
376 <xsl:apply-templates mode="noannot" select="*[6]"/>
377 <m:ci><xsl:call-template name="insert_subscript"><xsl:with-param name="node_value"><xsl:value-of select="*[5]/target/@binder"/></xsl:with-param></xsl:call-template></m:ci>
378 <xsl:apply-templates mode="pure" select="*[5]/source/*"/>
379 <m:ci><xsl:call-template name="insert_subscript"><xsl:with-param name="node_value"><xsl:value-of select="*[5]/target/LAMBDA/target/@binder"/></xsl:with-param></xsl:call-template></m:ci>
380 <xsl:apply-templates mode="pure" select="*[5]/target/LAMBDA/source/*"/>
381 <xsl:apply-templates mode="proof_transform" select="*[5]/target/LAMBDA/target/*"/>
384 <xsl:when test="name(*[1])='CONST'">
385 <xsl:apply-templates mode="try_inductive" select="."/>
387 <!-- patch temporanea per la gestione di redex -->
388 <xsl:when test="name(*[1])='LAMBDA' and count(child::*)=2
389 and *[2]/@sort='Prop'">
390 <m:apply helm:xref="{@id}">
391 <m:csymbol>letin</m:csymbol>
393 <m:csymbol>let</m:csymbol>
395 <xsl:call-template name="insert_subscript">
396 <xsl:with-param name="node_value">
397 <xsl:value-of select="*[1]/target/@binder"/>
401 <xsl:apply-templates mode="noannot" select="*[2]"/>
403 <xsl:apply-templates mode="proof_transform" select="*[1]/target/*[1]"/>
407 <xsl:apply-templates select="." mode="letin"/>
411 <xsl:when test="name()='LAMBDA'">
413 <xsl:when test="(name(target/*[1])='APPLY' and
414 name(target/*[1]/*[1])='CONST' and
415 (target/*[1]/*[1]/@uri='cic:/Coq/Init/Logic_Type/eqT_ind.con' or
416 target/*[1]/*[1]/@uri='cic:/Coq/Init/Logic_Type/eqT_ind_r.con' or
417 target/*[1]/*[1]/@uri='cic:/Coq/Zarith/auxiliary/eqT_ind_r.con')
418 and count(target/*[1]/*) = 8
419 and name(target/*[1]/*[8])='REL'
420 and target/@binder = target/*[1]/*[8]/@binder )">
422 <m:csymbol>rw_step</m:csymbol>
423 <xsl:apply-templates mode="noannot" select="target/*[1]/*[5]"/>
424 <xsl:apply-templates mode="pure" select="target/*[1]/*[3]"/>
425 <xsl:apply-templates mode="pure" select="target/*[1]/*[6]"/>
426 <xsl:apply-templates mode="proof_transform" select="target/*[1]/*[7]"/>
430 <xsl:apply-templates mode="pure" select="."/>
435 <xsl:apply-templates select="." mode="pure"/>
441 <xsl:template match="APPLY" mode="letin">
442 <xsl:variable name="no_subproofs" select="count(*[@sort='Prop' and (name(.)='LAMBDA' or name(.)='LETIN' or name(.)='APPLY' or name(.)='MUTCASE' or name(.)='FIX' or name(.)='COFIX')])"/>
443 <!-- <m:cn><xsl:value-of select="$no_subproofs"/></m:cn> -->
445 <xsl:when test="$naturalLanguage='yes' and ($no_subproofs = 1)">
446 <m:apply helm:xref="{@id}">
447 <m:csymbol>letin1</m:csymbol>
448 <xsl:apply-templates mode="noannot" select="*[@sort='Prop' and (name(.)='LAMBDA' or name(.)='LETIN' or name(.)='APPLY' or name(.)='MUTCASE' or name(.)='FIX' or name(.)='COFIX')]"/>
449 <!-- now re-process the application -->
450 <m:apply helm:xref="{@id}">
451 <m:csymbol>app</m:csymbol>
452 <!-- mode previous looks for siblings:
453 call with the first child -->
454 <xsl:apply-templates mode="previous" select="*[1]"/>
458 <xsl:when test="$naturalLanguage='yes' and ($no_subproofs > 1)">
459 <m:apply helm:xref="{@id}">
460 <m:csymbol>letin</m:csymbol>
461 <!-- first process all subproofs (let-in) -->
462 <xsl:call-template name="gen_let"/>
463 <!-- now re-process the application -->
464 <m:apply helm:xref="{@id}">
465 <m:csymbol>app</m:csymbol>
466 <!-- mode flat looks for siblings: call with the first child -->
467 <xsl:apply-templates mode="flat" select="*[1]"/>
473 <xsl:when test="@sort='Prop'">
475 <m:csymbol>app</m:csymbol>
476 <xsl:apply-templates mode="erase" select="*[1]"/>
480 <xsl:apply-templates mode="pure" select="."/>
487 <xsl:template name="gen_let">
488 <xsl:param name="init_pos" select="0"/>
489 <xsl:param name="from" select="0"/>
490 <xsl:for-each select="*[position()>$from and @sort='Prop' and (name(.)='LAMBDA' or name(.)='LETIN' or name(.)='APPLY' or name(.)='MUTCASE' or name(.)='FIX' or name(.)='COFIX')]">
492 <m:csymbol>let</m:csymbol>
493 <m:ci><xsl:call-template name="insert_subscript"><xsl:with-param name="node_value"><xsl:value-of select="concat('h',position()+$init_pos)"/></xsl:with-param></xsl:call-template></m:ci>
494 <xsl:apply-templates mode="noannot" select="."/>
499 <xsl:template match="*" mode="erase">
501 <xsl:when test="@sort='Prop' or $naturalLanguage='no'">
502 <xsl:apply-templates mode="pure" select="."/>
508 <xsl:apply-templates mode="previous" select="following-sibling::*[1]"/>
511 <xsl:template match="*" mode="previous">
513 <xsl:when test="$naturalLanguage='yes' and(@sort='Prop' and (name(.)='LAMBDA' or name(.)='LETIN' or name(.)='APPLY' or name(.)='MUTCASE' or name(.)='FIX' or name(.)='COFIX'))">
514 <m:ci>previous</m:ci>
518 <xsl:when test="@sort='Prop' or $naturalLanguage='no' ">
519 <xsl:apply-templates mode="pure" select="."/>
525 <!-- <xsl:apply-templates select="." mode="pure"/> -->
528 <xsl:apply-templates mode="previous" select="following-sibling::*[1]"/>
531 <xsl:template match="*" mode="flat">
532 <xsl:param name="n" select="1"/>
533 <xsl:variable name="id" select="@id"/>
535 <!-- <xsl:when test="key('typeid',@id)"> -->
536 <!-- <xsl:when test="$InnerTypes/InnerTypes/TYPE[@of=$id]"> -->
537 <xsl:when test="$naturalLanguage='yes' and @sort='Prop' and (name(.)='LAMBDA' or name(.)='LETIN' or name(.)='APPLY' or name(.)='MUTCASE' or name(.)='FIX' or name(.)='COFIX')">
539 <xsl:call-template name="insert_subscript"><xsl:with-param name="node_value"><xsl:value-of select="concat('h',$n)"/></xsl:with-param></xsl:call-template>
541 <xsl:apply-templates mode="flat" select="following-sibling::*[1]">
542 <xsl:with-param name="n" select="$n+1"/>
543 </xsl:apply-templates>
547 <xsl:when test="@sort='Prop' or $naturalLanguage='no'">
548 <xsl:apply-templates mode="pure" select="."/>
554 <!-- <xsl:apply-templates mode="pure" select="."/> -->
555 <xsl:apply-templates mode="flat" select="following-sibling::*[1]">
556 <xsl:with-param name="n" select="$n"/>
557 </xsl:apply-templates>
562 <!-- Auxiliary functions -->
563 <xsl:template name="get_name">
564 <xsl:param name="uri" select="''"/>
565 <xsl:variable name="sub_after" select="substring-after($uri,'/')"/>
567 <xsl:when test="contains($sub_after,'/')">
568 <xsl:call-template name="get_name">
569 <xsl:with-param name="uri" select="$sub_after"/>
573 <xsl:value-of select="substring-before($sub_after,'_ind.con')"/>
578 <!-- <xsl:template match="APPLY[CONST[
579 attribute::uri='cic:/Coq/Init/Logic/Conjunction/and_ind.con']]" mode="appflat">
581 <xsl:when test="count(child::*) > 4">
582 <m:apply helm:xref="{@id}">
583 <m:csymbol>app</m:csymbol>
584 <xsl:apply-templates mode="pure" select="*[1]"/>
588 <xsl:apply-templates mode="flat" select="*[5]"/>
592 <m:apply helm:xref="{@id}">
593 <m:csymbol>app</m:csymbol>
594 <xsl:apply-templates mode="flat" select="*[1]"/>