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="$ind_name"/>
136 </xsl:apply-templates>
139 <xsl:apply-templates mode="letin" select="."/>
144 <xsl:apply-templates mode="letin" select="."/>
149 <xsl:apply-templates mode="letin" select="."/>
155 <xsl:template mode="proof_transform" match="*">
157 <xsl:when test="name()='APPLY'">
158 <xsl:variable name="id" select="@id"/>
161 <xsl:when test="CONST[
162 attribute::uri='cic:/Coq/Init/Logic/Equality/eq_ind.con' or
163 attribute::uri='cic:/Coq/Init/Logic/Logic_lemmas/eq_ind_r.con' or
164 attribute::uri='cic:/Coq/Init/Logic_Type/eqT_ind.con' or
165 attribute::uri='cic:/Coq/Init/Logic_Type/eqT_ind_r.con' or
166 attribute::uri='cic:/Coq/Zarith/auxiliary/eqT_ind_r.con'] and count(child::*) = 7">
168 <m:csymbol>rw_step</m:csymbol>
169 <xsl:apply-templates mode="noannot" select="*[5]"/>
170 <xsl:apply-templates mode="pure" select="*[3]"/>
171 <xsl:apply-templates mode="pure" select="*[6]"/>
172 <xsl:apply-templates mode="proof_transform" select="*[7]"/>
175 <!-- EQUALITY with extra-parameters -->
176 <xsl:when test="CONST[
177 attribute::uri='cic:/Coq/Init/Logic/Equality/eq_ind.con' or
178 attribute::uri='cic:/Coq/Init/Logic/Logic_lemmas/eq_ind_r.con' or
179 attribute::uri='cic:/Coq/Init/Logic_Type/eqT_ind.con' or
180 attribute::uri='cic:/Coq/Init/Logic_Type/eqT_ind_r.con' or
181 attribute::uri='cic:/Coq/Zarith/auxiliary/eqT_ind_r.con'] and count(child::*) > 7">
182 <xsl:variable name="no_extraproofs" select="count(*[position()>7 and @sort='Prop' and (name(.)='LAMBDA' or name(.)='LETIN' or name(.)='APPLY' or name(.)='MUTCASE' or name(.)='FIX' or name(.)='COFIX')])"/>
184 <xsl:when test="$no_extraproofs=0">
186 <m:csymbol>rewrite_and_apply</m:csymbol>
188 <m:csymbol>rw_step</m:csymbol>
189 <xsl:apply-templates mode="noannot" select="*[5]"/>
190 <xsl:apply-templates mode="pure" select="*[3]"/>
191 <xsl:apply-templates mode="pure" select="*[6]"/>
192 <xsl:apply-templates mode="pure" select="*[7]"/>
194 <xsl:apply-templates mode="noannot" select="*[position()>7]"/>
199 <xsl:when test="*[5]/@sort='Prop'">
200 <m:apply helm:xref="{@id}">
201 <m:csymbol>letin</m:csymbol>
203 <m:csymbol>let</m:csymbol>
205 <xsl:call-template name="insert_subscript">
206 <xsl:with-param name="node_value" select="'h1'"/>
209 <xsl:apply-templates mode="noannot" select="*[5]"/>
211 <xsl:call-template name="gen_let">
212 <xsl:with-param name="init_pos" select="1"/>
213 <xsl:with-param name="from" select="7"/>
216 <m:csymbol>rewrite_and_apply</m:csymbol>
218 <m:csymbol>rw_step</m:csymbol>
220 <xsl:call-template name="insert_subscript">
221 <xsl:with-param name="node_value" select="'h1'"/>
224 <xsl:apply-templates mode="pure" select="*[3]"/>
225 <xsl:apply-templates mode="pure" select="*[6]"/>
226 <xsl:apply-templates mode="pure" select="*[7]"/>
228 <xsl:apply-templates mode="flat" select="*[8]">
229 <xsl:with-param name="n">
230 <xsl:value-of select="2"/>
232 </xsl:apply-templates>
237 <m:apply helm:xref="{@id}">
238 <m:csymbol>letin</m:csymbol>
239 <xsl:call-template name="gen_let">
240 <xsl:with-param name="init_pos" select="0"/>
241 <xsl:with-param name="form" select="7"/>
244 <m:csymbol>rewrite_and_apply</m:csymbol>
246 <m:csymbol>rw_step</m:csymbol>
247 <xsl:apply-templates mode="pure" select="*[5]"/>
248 <xsl:apply-templates mode="pure" select="*[3]"/>
249 <xsl:apply-templates mode="pure" select="*[6]"/>
250 <xsl:apply-templates mode="pure" select="*[7]"/>
252 <xsl:apply-templates mode="flat" select="*[8]">
253 <xsl:with-param name="n">
254 <xsl:value-of select="1"/>
256 </xsl:apply-templates>
265 <xsl:when test="CONST[
266 attribute::uri='cic:/Coq/Init/Logic/False_ind.con'] and
267 count(child::*) = 3">
268 <m:apply helm:xref="{@id}">
269 <m:csymbol>false_ind</m:csymbol>
270 <m:ci>cic:/Coq/Init/Logic/False_ind.con</m:ci>
271 <xsl:apply-templates mode="noannot" select="*[3]"/>
274 <!-- gestire meglio il caso di and_ind quando la prova
275 non e' della forma \x.\y.M -->
276 <xsl:when test="CONST[
277 attribute::uri='cic:/Coq/Init/Logic/Conjunction/and_ind.con']
278 and count(child::*) = 6
279 and name(*[5])='LAMBDA'
280 and name(*[5]/target/*[1])='LAMBDA'">
281 <m:apply helm:xref="{@id}">
282 <m:csymbol>and_ind</m:csymbol>
283 <xsl:apply-templates mode="noannot" select="*[6]"/>
284 <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>
285 <xsl:apply-templates mode="pure" select="*[5]/source/*"/>
286 <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>
287 <xsl:apply-templates mode="pure" select="*[5]/target/LAMBDA/source/*"/>
288 <xsl:apply-templates mode="proof_transform" select="*[5]/target/LAMBDA/target/*"/>
291 <xsl:when test="CONST[
292 attribute::uri='cic:/Coq/Init/Logic/Disjunction/or_ind.con']
293 and count(child::*) = 7">
295 <xsl:when test="name(*[5])='LAMBDA'
296 and name(*[6])='LAMBDA'">
297 <xsl:variable name="definition_url"
298 select="'cic:/Coq/Init/Logic/Disjunction/or.ind'"/>
299 <m:apply helm:xref="{@id}">
300 <m:csymbol>full_or_ind</m:csymbol>
301 <xsl:apply-templates mode="noannot" select="*[7]"/>
302 <xsl:apply-templates mode="pure"
303 select="$InnerTypes/InnerTypes/TYPE[@of=$id]/*"/>
305 <m:csymbol>left_case</m:csymbol>
308 <xsl:value-of select="*[5]/target/@binder"/>
311 <xsl:apply-templates mode="pure" select="*[5]/source/*[1]"/>
314 <xsl:apply-templates mode="noannot" select="*[5]/target/*[1]"/>
317 <m:csymbol>right_case</m:csymbol>
320 <xsl:apply-templates mode="pure" select="*[6]/target/@binder"/>
323 <xsl:apply-templates mode="pure" select="*[6]/source/*[1]"/>
326 <xsl:apply-templates mode="noannot" select="*[6]/target/*[1]"/>
331 <m:apply helm:xref="{@id}">
332 <m:csymbol>or_ind</m:csymbol>
333 <xsl:apply-templates mode="noannot" select="*[7]"/>
334 <xsl:apply-templates mode="pure"
335 select="$InnerTypes/InnerTypes/TYPE[@of=$id]/*"/>
336 <xsl:apply-templates mode="pure" select="*[5]"/>
337 <xsl:apply-templates mode="pure" select="*[6]"/>
342 <!-- ex_ind, exT_ind -->
343 <xsl:when test="(CONST[attribute::uri='cic:/Coq/Init/Logic_Type/exT_ind.con'] or
344 CONST[attribute::uri='cic:/Coq/Init/Logic/First_order_quantifiers/ex_ind.con'])
345 and count(child::*) = 6
346 and name(*[5])='LAMBDA'
347 and name(*[5]/target/*[1])='LAMBDA'">
348 <m:apply helm:xref="{@id}">
349 <m:csymbol>ex_ind</m:csymbol>
350 <xsl:apply-templates mode="noannot" select="*[6]"/>
351 <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>
352 <xsl:apply-templates mode="pure" select="*[5]/source/*"/>
353 <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>
354 <xsl:apply-templates mode="pure" select="*[5]/target/LAMBDA/source/*"/>
355 <xsl:apply-templates mode="proof_transform" select="*[5]/target/LAMBDA/target/*"/>
358 <xsl:when test="name(*[1])='CONST'">
359 <xsl:apply-templates mode="try_inductive" select="."/>
361 <!-- patch temporanea per la gestione di redex -->
362 <xsl:when test="name(*[1])='LAMBDA' and count(child::*)=2
363 and *[2]/@sort='Prop'">
364 <m:apply helm:xref="{@id}">
365 <m:csymbol>letin</m:csymbol>
367 <m:csymbol>let</m:csymbol>
369 <xsl:call-template name="insert_subscript">
370 <xsl:with-param name="node_value">
371 <xsl:value-of select="*[1]/target/@binder"/>
375 <xsl:apply-templates mode="noannot" select="*[2]"/>
377 <xsl:apply-templates mode="proof_transform" select="*[1]/target/*[1]"/>
381 <xsl:apply-templates select="." mode="letin"/>
385 <xsl:when test="name()='LAMBDA'">
387 <xsl:when test="(name(target/*[1])='APPLY' and
388 name(target/*[1]/*[1])='CONST' and
389 (target/*[1]/*[1]/@uri='cic:/Coq/Init/Logic_Type/eqT_ind.con' or
390 target/*[1]/*[1]/@uri='cic:/Coq/Init/Logic_Type/eqT_ind_r.con' or
391 target/*[1]/*[1]/@uri='cic:/Coq/Zarith/auxiliary/eqT_ind_r.con')
392 and count(target/*[1]/*) = 8
393 and name(target/*[1]/*[8])='REL'
394 and target/@binder = target/*[1]/*[8]/@binder )">
396 <m:csymbol>rw_step</m:csymbol>
397 <xsl:apply-templates mode="noannot" select="target/*[1]/*[5]"/>
398 <xsl:apply-templates mode="pure" select="target/*[1]/*[3]"/>
399 <xsl:apply-templates mode="pure" select="target/*[1]/*[6]"/>
400 <xsl:apply-templates mode="proof_transform" select="target/*[1]/*[7]"/>
404 <xsl:apply-templates mode="pure" select="."/>
409 <xsl:apply-templates select="." mode="pure"/>
415 <xsl:template match="APPLY" mode="letin">
416 <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')])"/>
417 <!-- <m:cn><xsl:value-of select="$no_subproofs"/></m:cn> -->
419 <xsl:when test="$naturalLanguage='yes' and ($no_subproofs = 1)">
420 <m:apply helm:xref="{@id}">
421 <m:csymbol>letin1</m:csymbol>
422 <xsl:apply-templates mode="noannot" select="*[@sort='Prop' and (name(.)='LAMBDA' or name(.)='LETIN' or name(.)='APPLY' or name(.)='MUTCASE' or name(.)='FIX' or name(.)='COFIX')]"/>
423 <!-- now re-process the application -->
424 <m:apply helm:xref="{@id}">
425 <m:csymbol>app</m:csymbol>
426 <!-- mode previous looks for siblings:
427 call with the first child -->
428 <xsl:apply-templates mode="previous" select="*[1]"/>
432 <xsl:when test="$naturalLanguage='yes' and ($no_subproofs > 1)">
433 <m:apply helm:xref="{@id}">
434 <m:csymbol>letin</m:csymbol>
435 <!-- first process all subproofs (let-in) -->
436 <xsl:call-template name="gen_let"/>
437 <!-- now re-process the application -->
438 <m:apply helm:xref="{@id}">
439 <m:csymbol>app</m:csymbol>
440 <!-- mode flat looks for siblings: call with the first child -->
441 <xsl:apply-templates mode="flat" select="*[1]"/>
447 <xsl:when test="@sort='Prop'">
449 <m:csymbol>app</m:csymbol>
450 <xsl:apply-templates mode="erase" select="*[1]"/>
454 <xsl:apply-templates mode="pure" select="."/>
461 <xsl:template name="gen_let">
462 <xsl:param name="init_pos" select="0"/>
463 <xsl:param name="from" select="0"/>
464 <xsl:for-each select="*[position()>$from and @sort='Prop' and (name(.)='LAMBDA' or name(.)='LETIN' or name(.)='APPLY' or name(.)='MUTCASE' or name(.)='FIX' or name(.)='COFIX')]">
466 <m:csymbol>let</m:csymbol>
467 <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>
468 <xsl:apply-templates mode="noannot" select="."/>
473 <xsl:template match="*" mode="erase">
475 <xsl:when test="@sort='Prop' or $naturalLanguage='no'">
476 <xsl:apply-templates mode="pure" select="."/>
482 <xsl:apply-templates mode="previous" select="following-sibling::*[1]"/>
485 <xsl:template match="*" mode="previous">
487 <xsl:when test="$naturalLanguage='yes' and(@sort='Prop' and (name(.)='LAMBDA' or name(.)='LETIN' or name(.)='APPLY' or name(.)='MUTCASE' or name(.)='FIX' or name(.)='COFIX'))">
488 <m:ci>previous</m:ci>
492 <xsl:when test="@sort='Prop' or $naturalLanguage='no' ">
493 <xsl:apply-templates mode="pure" select="."/>
499 <!-- <xsl:apply-templates select="." mode="pure"/> -->
502 <xsl:apply-templates mode="previous" select="following-sibling::*[1]"/>
505 <xsl:template match="*" mode="flat">
506 <xsl:param name="n" select="1"/>
507 <xsl:variable name="id" select="@id"/>
509 <!-- <xsl:when test="key('typeid',@id)"> -->
510 <!-- <xsl:when test="$InnerTypes/InnerTypes/TYPE[@of=$id]"> -->
511 <xsl:when test="$naturalLanguage='yes' and @sort='Prop' and (name(.)='LAMBDA' or name(.)='LETIN' or name(.)='APPLY' or name(.)='MUTCASE' or name(.)='FIX' or name(.)='COFIX')">
513 <xsl:call-template name="insert_subscript"><xsl:with-param name="node_value"><xsl:value-of select="concat('h',$n)"/></xsl:with-param></xsl:call-template>
515 <xsl:apply-templates mode="flat" select="following-sibling::*[1]">
516 <xsl:with-param name="n" select="$n+1"/>
517 </xsl:apply-templates>
521 <xsl:when test="@sort='Prop' or $naturalLanguage='no'">
522 <xsl:apply-templates mode="pure" select="."/>
528 <!-- <xsl:apply-templates mode="pure" select="."/> -->
529 <xsl:apply-templates mode="flat" select="following-sibling::*[1]">
530 <xsl:with-param name="n" select="$n"/>
531 </xsl:apply-templates>
536 <!-- Auxiliary functions -->
537 <!-- OMDOC: now we have name_of_uri generalized on the extension that -->
538 <!-- can replace the next template -->
539 <xsl:template name="get_name">
540 <xsl:param name="uri" select="''"/>
541 <xsl:variable name="sub_after" select="substring-after($uri,'/')"/>
543 <xsl:when test="contains($sub_after,'/')">
544 <xsl:call-template name="get_name">
545 <xsl:with-param name="uri" select="$sub_after"/>
549 <xsl:value-of select="substring-before($sub_after,'_ind.con')"/>
554 <!-- <xsl:template match="APPLY[CONST[
555 attribute::uri='cic:/Coq/Init/Logic/Conjunction/and_ind.con']]" mode="appflat">
557 <xsl:when test="count(child::*) > 4">
558 <m:apply helm:xref="{@id}">
559 <m:csymbol>app</m:csymbol>
560 <xsl:apply-templates mode="pure" select="*[1]"/>
564 <xsl:apply-templates mode="flat" select="*[5]"/>
568 <m:apply helm:xref="{@id}">
569 <m:csymbol>app</m:csymbol>
570 <xsl:apply-templates mode="flat" select="*[1]"/>