+++ /dev/null
-<?xml version="1.0"?>
-
-<!-- Copyright (C) 2000, HELM Team -->
-<!-- -->
-<!-- This file is part of HELM, an Hypertextual, Electronic -->
-<!-- Library of Mathematics, developed at the Computer Science -->
-<!-- Department, University of Bologna, Italy. -->
-<!-- -->
-<!-- HELM is free software; you can redistribute it and/or -->
-<!-- modify it under the terms of the GNU General Public License -->
-<!-- as published by the Free Software Foundation; either version 2 -->
-<!-- of the License, or (at your option) any later version. -->
-<!-- -->
-<!-- HELM is distributed in the hope that it will be useful, -->
-<!-- but WITHOUT ANY WARRANTY; without even the implied warranty of -->
-<!-- MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -->
-<!-- GNU General Public License for more details. -->
-<!-- -->
-<!-- You should have received a copy of the GNU General Public License -->
-<!-- along with HELM; if not, write to the Free Software -->
-<!-- Foundation, Inc., 59 Temple Place - Suite 330, Boston, -->
-<!-- MA 02111-1307, USA. -->
-<!-- -->
-<!-- For details, see the HELM World-Wide-Web page, -->
-<!-- http://cs.unibo.it/helm/. -->
-
-<!--******************************************************************-->
-<!-- XSLT version 0.1 of CIC inductive objects to MathML content: -->
-<!-- Completely revisited: November 2002, Andrea asperti -->
-<!-- First draft: March 2001, Andrea asperti -->
-<!--******************************************************************-->
-
-
-<xsl:stylesheet version="1.0" xmlns:xsl="http://www.w3.org/1999/XSL/Transform"
- xmlns:m="http://www.w3.org/1998/Math/MathML"
- xmlns:helm="http://www.cs.unibo.it/helm">
-
-<!-- try_inductive essentially checks if the head constant is an
- invocation of an induction principle.
- Si presuppone che il tipo induttivo non sia mutuamente
- induttivo. Bisognerebbe andare a vedere l'utlimo parametro
- del presunto "principio di induzione", tirare fuori il tipo induttivo
- e vedere se il suo nome coincide con il prefisso di _ind.
- Ad esempio nat_double_ind e' definito dall'utente. L'ultimo
- parametro di nat_double_ind e' di tipo nat, e nat e' diverso
- da nat_double. Per ora, verifico solo l'esistenza di nat_double,
- ma questo, benche' non porti ad errore, non copre tutti i
- casi per quelli mutuamente induttivi -->
-
-
-<xsl:template mode="try_inductive" match="APPLY">
- <xsl:variable name="id" select="@id"/>
- <xsl:variable name="uri">
- <xsl:choose>
- <xsl:when test="name(*[1])='CONST'">
- <xsl:value-of select="*[1]/@uri"/>
- </xsl:when>
- <xsl:otherwise>
- <!-- instantiate -->
- <xsl:value-of select="*[1]/CONST[1]/@uri"/>
- </xsl:otherwise>
- </xsl:choose>
- </xsl:variable>
- <xsl:choose>
- <xsl:when test="contains($uri,'_ind.con')">
- <xsl:variable name="ind_uri"
- select="concat(substring-before($uri,'_ind.con'),'.ind')"/>
- <xsl:variable name="InductiveTypeUrl"><xsl:call-template name="URLofURI4getter"><xsl:with-param name="uri" select="$ind_uri"/></xsl:call-template></xsl:variable>
- <xsl:variable name="inductive_def"
- select="document($InductiveTypeUrl)/InductiveDefinition"/>
- <xsl:choose>
- <xsl:when test="$inductive_def">
- <xsl:variable name="ind_name">
- <xsl:call-template name="get_name">
- <xsl:with-param name="uri" select="$uri"/>
- </xsl:call-template>
- </xsl:variable>
- <xsl:apply-templates mode="inductive" select=".">
- <xsl:with-param name="uri" select="$uri"/>
- <xsl:with-param name="inductive_def_uri"
- select="$ind_uri"/>
- <xsl:with-param name="inductive_def" select="$inductive_def"/>
- <xsl:with-param name="inductive_def_index" select="1"/>
- <xsl:with-param name="inductive_def_name" select="$ind_name"/>
- </xsl:apply-templates>
- </xsl:when>
- <xsl:otherwise>
- <xsl:apply-templates select="." mode="letin"/>
- </xsl:otherwise>
- </xsl:choose>
- </xsl:when>
- <xsl:otherwise>
- <xsl:apply-templates select="." mode="letin"/>
- </xsl:otherwise>
- </xsl:choose>
-</xsl:template>
-
-
-<xsl:template mode="inductive" match="APPLY">
- <xsl:param name="uri" select="''"/>
- <xsl:param name="inductive_def_uri" select="''"/>
- <xsl:param name="inductive_def" select="/.."/>
- <xsl:param name="inductive_def_index" select="1"/>
- <xsl:param name="inductive_def_name" select="''"/>
- <xsl:variable name="InductiveTypeUrl"><xsl:call-template name="URLofURI4getter"><xsl:with-param name="uri" select="$uri"/></xsl:call-template></xsl:variable>
- <!-- expected_args_type contains the types of the arguments expected by
- the induction principle -->
- <xsl:variable name="expected_args_types"
- select="document($InductiveTypeUrl)/ConstantType/PROD/decl/*[1]"/>
- <xsl:variable name="no_expected_args" select="count($expected_args_types)"/>
- <xsl:variable name="actual_arguments" select="*[position()>1]"/>
- <!-- First check that the induction principle is applied to the
- expected number of arguments -->
- <xsl:choose>
- <xsl:when test="$no_expected_args = count($actual_arguments)">
- <!-- Now check that each actual argument starts with the
- expected number of lambda abstractions -->
- <xsl:variable name="argsOK">
- <xsl:call-template name="check_args">
- <xsl:with-param name="arg_types" select="$expected_args_types"/>
- <xsl:with-param name="actual_args" select="$actual_arguments"/>
- </xsl:call-template>
- </xsl:variable>
- <xsl:choose>
- <!-- il semplice test $argsOK non funziona -->
- <xsl:when test="string($argsOK) = 'true'">
- <!-- arguments are in the expected form: we create a
- "by_induction" content element -->
- <!-- no_params is the number of parameters in square brackets -->
- <xsl:variable name="no_params"
- select="$inductive_def/@noParams"/>
- <!-- the inductive property is the first argument following
- the parameters -->
- <xsl:variable name="inductive_property"
- select="$actual_arguments[1 + $no_params]"/>
- <xsl:variable name="tail_args"
- select="$actual_arguments[position()> (1 + $no_params)]"/>
- <!-- inductive_type contains the right inductive type in the
- mutual inductive definition -->
- <xsl:variable name="inductive_type"
- select="$inductive_def/InductiveType[position()=$inductive_def_index]"/>
- <xsl:variable name="no_constructors"
- select="count($inductive_type/Constructor)"/>
- <!-- each case has a single argument -->
- <xsl:variable name="args_for_cases"
- select="$tail_args[($no_constructors + 1) > position()]"/>
- <!-- extra_args contains the remaining arguments; the LAST one
- of them is the argument we are inductively arguing on -->
- <xsl:variable name="extra_args"
- select="$tail_args[position()> $no_constructors]"/>
- <m:apply>
- <m:csymbol>by_induction</m:csymbol>
- <!-- the first (i.e. second) argument of by_induction
- is the uri of the inductive definition -->
- <m:ci><xsl:value-of select="$inductive_def_uri"/></m:ci>
- <!-- next, we have the inductive property, currently not
- used for rendering (it could be omitted ??) -->
- <xsl:apply-templates mode="pure" select="$inductive_property"/>
- <!-- each case has its own "inductive_case" element -->
- <!-- the inductive case element is composed by:
- * "case_lhs" element, containing the constructor name applied
- to its arguments. The arguments are abstraction variables
- (with types) got form the initial lambdas of the argument
- for the case.
- * "induction_hypothesis" element, containg the induction
- hypothesis. Again, these are abstraction variables
- (with types) got form the initial lambdas of the argument
- for the case.
- * body of the case, without specific markup.
- -->
- <xsl:for-each select="$inductive_type/Constructor">
- <xsl:variable name="pos" select="position()"/>
- <xsl:variable name="current_arg"
- select="$args_for_cases[position()=$pos]"/>
- <m:apply>
- <m:csymbol>inductive_case</m:csymbol>
- <m:apply>
- <m:csymbol>case_lhs</m:csymbol>
- <m:ci definitionURL="{$inductive_def_uri}">
- <xsl:value-of select="@name"/>
- </m:ci>
- <xsl:call-template name="get_constructor_args">
- <xsl:with-param name="constructor_args"
- select="PROD/decl[position()> $no_params]"/>
- <xsl:with-param name="actual_args"
- select="$current_arg/decl"/>
- <xsl:with-param name="inductive_def_uri"
- select="$inductive_def_uri"/>
- </xsl:call-template>
- </m:apply>
- <m:apply>
- <m:csymbol>induction_hypothesis</m:csymbol>
- <xsl:call-template name="get_induction_hypothesis">
- <xsl:with-param name="constructor_args"
- select="PROD/decl[position()> $no_params]"/>
- <xsl:with-param name="actual_args"
- select="$current_arg/decl"/>
- <xsl:with-param name="inductive_def_uri"
- select="$inductive_def_uri"/>
- </xsl:call-template>
- </m:apply>
- <xsl:choose>
- <xsl:when test="count(PROD/decl) > $no_params">
- <!-- in this case the actual_arg must be a LAMBDA -->
- <xsl:call-template name="get_body">
- <xsl:with-param name="constructor_args"
- select="PROD/decl[position()>$no_params]"/>
- <xsl:with-param name="actual_args" select="$current_arg/decl"/>
- <xsl:with-param name="inductive_def_uri"
- select="$inductive_def_uri"/>
- <xsl:with-param name="target"
- select="$current_arg/target/*[1]"/>
- </xsl:call-template>
- </xsl:when>
- <xsl:otherwise>
- <xsl:apply-templates mode="noannot" select="$current_arg"/>
- </xsl:otherwise>
- </xsl:choose>
- </m:apply>
- </xsl:for-each>
- <!-- the inductive argument is the last argument of extra-args -->
- <m:apply>
- <m:csymbol>extra_args</m:csymbol>
- <xsl:apply-templates mode="pure" select="$extra_args"/>
- </m:apply>
- </m:apply>
- </xsl:when>
- <xsl:otherwise>
- <xsl:apply-templates mode="letin" select="."/>
- </xsl:otherwise>
- </xsl:choose>
- </xsl:when>
- <xsl:otherwise>
- <xsl:apply-templates mode="letin" select="."/>
- </xsl:otherwise>
- </xsl:choose>
-</xsl:template>
-
-<!-- check_args checks that the number of lambda abstractions
- of each actual parameter is GREATER OR EQUAL to the number
- or products of the corresponding formal parameter of the
- induction principles. That is, that each argument is
- sufficiently eta-expanded.
- If this is not the case, not good rendering looks possible.
- Check_args returns a boolean.
- -->
-
-
-<xsl:template name="check_args">
- <xsl:param name="arg_types" select="/.."/>
- <xsl:param name="actual_args" select="/.."/>
- <xsl:param name="bool_var" select="true()"/>
- <!-- <xsl:value-of select="false()"/> -->
- <xsl:choose>
- <xsl:when test="count($arg_types) = 0">
- <xsl:value-of select="$bool_var"/>
- </xsl:when>
- <xsl:otherwise>
- <xsl:variable name="no_expected_arg_of_arg"
- select="count($arg_types[1]/decl)"/>
- <xsl:variable name="no_actual_abst_of_arg"
- select="count($actual_args[1]/decl)"/>
- <xsl:variable name="test_arg"
- select="($no_actual_abst_of_arg >= $no_expected_arg_of_arg)"/>
- <xsl:call-template name="check_args">
- <xsl:with-param name="arg_types" select="$arg_types[position()>1]"/>
- <xsl:with-param name="actual_args" select="$actual_args[position()>1]"/>
- <xsl:with-param name="bool_var" select="($bool_var and $test_arg)"/>
- </xsl:call-template>
- </xsl:otherwise>
- </xsl:choose>
-</xsl:template>
-
-
-<!-- The following three functions are essentially identical
- in their recursive structure.
- The problem is that of decomposing an actual argument for
- a case in three parts:
- * constructor variables
- * induction hypothesis
- * body
- To this aim we must proceed in parallel with the type of
- the constructor: if the type contains a prod, then the
- the corresponding lambda of the argument provides the
- constructor variable. Moreover, if the source type of the
- prod contains a reference to the inductive type, it is a
- recursive argument and the NEXT lambda of the argument
- provides an induction hypothesis.
- Unfortunately the three functions cannot be merged into a
- single one without a conversion from document tree fragments
- to node-sets.
--->
-
-<xsl:template name="get_constructor_args">
- <xsl:param name="constructor_args" select="/.."/>
- <xsl:param name="actual_args" select="/.."/>
- <xsl:param name="inductive_def_uri" select="''"/>
- <xsl:if test="$constructor_args">
- <m:bvar>
- <m:ci><xsl:value-of select="$actual_args[1]/@binder"/></m:ci>
- <m:type>
- <xsl:apply-templates mode="pure" select="$actual_args[1]/*"/>
- </m:type>
- </m:bvar>
- <xsl:choose>
- <xsl:when test="$constructor_args[1]//MUTIND[@uri=$inductive_def_uri]">
- <xsl:call-template name="get_constructor_args">
- <xsl:with-param name="constructor_arity"
- select="$constructor_args[position()>1]"/>
- <xsl:with-param name="actual_args"
- select="$actual_args[position()>2]"/>
- <xsl:with-param name="inductive_def_uri"
- select="$inductive_def_uri"/>
- </xsl:call-template>
- </xsl:when>
- <xsl:otherwise>
- <xsl:call-template name="get_constructor_args">
- <xsl:with-param name="constructor_args"
- select="$constructor_args[position()>1]"/>
- <xsl:with-param name="actual_args"
- select="$actual_args[position()>1]"/>
- <xsl:with-param name="inductive_def_uri"
- select="$inductive_def_uri"/>
- </xsl:call-template>
- </xsl:otherwise>
- </xsl:choose>
- </xsl:if>
-</xsl:template>
-
-<xsl:template name="get_induction_hypothesis">
- <xsl:param name="constructor_args" select="/.."/>
- <xsl:param name="actual_args" select="/.."/>
- <xsl:param name="inductive_def_uri" select="''"/>
- <xsl:if test="$constructor_args">
- <xsl:choose>
- <xsl:when test="$constructor_args[1]//MUTIND[@uri=$inductive_def_uri]">
- <m:bvar>
- <m:ci>
- <xsl:value-of select="$actual_args[2]/@binder"/>
- </m:ci>
- <m:type>
- <xsl:apply-templates mode="pure"
- select="$actual_args[2]/*"/>
- </m:type>
- </m:bvar>
- <xsl:call-template name="get_induction_hypothesis">
- <xsl:with-param name="constructor_args"
- select="$constructor_args[position()>1]"/>
- <xsl:with-param name="actual_args"
- select="$actual_args[position()>2]"/>
- <xsl:with-param name="inductive_def_uri"
- select="$inductive_def_uri"/>
- </xsl:call-template>
- </xsl:when>
- <xsl:otherwise>
- <xsl:call-template name="get_induction_hypothesis">
- <xsl:with-param name="constructor_args"
- select="$constructor_args[position()>1]"/>
- <xsl:with-param name="actual_args"
- select="$actual_args[position()>1]"/>
- <xsl:with-param name="inductive_def_uri"
- select="$inductive_def_uri"/>
- </xsl:call-template>
- </xsl:otherwise>
- </xsl:choose>
- </xsl:if>
-</xsl:template>
-
-<xsl:template name="get_body">
- <xsl:param name="constructor_args" select="/.."/>
- <xsl:param name="actual_args" select="/.."/>
- <xsl:param name="inductive_def_uri" select="''"/>
- <xsl:param name="target" select="/.."/>
- <xsl:choose>
- <xsl:when test="$constructor_args">
- <xsl:choose>
- <xsl:when test="$constructor_args[1]//MUTIND[@uri=$inductive_def_uri]">
- <xsl:call-template name="get_body">
- <xsl:with-param name="constructor_args"
- select="$constructor_args[position()> 1]"/>
- <xsl:with-param name="actual_args"
- select="$actual_args[position()> 2]"/>
- <xsl:with-param name="inductive_def_uri"
- select="$inductive_def_uri"/>
- <xsl:with-param name="target"
- select="$target"/>
- </xsl:call-template>
- </xsl:when>
- <xsl:otherwise>
- <xsl:call-template name="get_body">
- <xsl:with-param name="constructor_args"
- select="$constructor_args[position()> 1]"/>
- <xsl:with-param name="actual_args"
- select="$actual_args[position()> 1]"/>
- <xsl:with-param name="inductive_def_uri"
- select="$inductive_def_uri"/>
- <xsl:with-param name="target"
- select="$target"/>
- </xsl:call-template>
- </xsl:otherwise>
- </xsl:choose>
- </xsl:when>
- <xsl:otherwise>
- <xsl:choose>
- <xsl:when test="$actual_args">
- <xsl:apply-templates select="$actual_args[1]" mode="lambda_prop"/>
- </xsl:when>
- <xsl:otherwise>
- <xsl:apply-templates mode="noannot" select="$target"/>
- </xsl:otherwise>
- </xsl:choose>
- </xsl:otherwise>
- </xsl:choose>
-</xsl:template>
-
-</xsl:stylesheet>
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