--- /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: -->
+<!-- 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">
+
+
+<xsl:template mode="inductive" match="APPLY">
+ <xsl:param name="inductive_def_uri" select="/.."/>
+ <xsl:param name="inductive_def_index" select="1"/>
+ <xsl:param name="inductive_def_name" select="''"/>
+ <xsl:param name="section_params" select="0"/>
+ <!-- expected_args_type contains the types of the arguments expected by
+ the induction principle -->
+ <xsl:variable name="expected_args_types"
+ select="document(concat(string($absPath),*[1]/@uri))/Definition/type//PROD[not(ancestor::source)]/source/*[1]"/>
+ <xsl:variable name="no_expected_args" select="count($expected_args_types)"/>
+ <xsl:variable name="actual_arguments" select="*[position()>(1+$section_params)]"/>
+ <!-- First check that the induction principle is applied to the
+ expected number of arguments -->
+ <xsl:choose>
+ <xsl:when test="$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 -->
+ <!-- inductive_def contains the inductive definition -->
+ <xsl:variable name="inductive_def"
+ select="document(concat(string($absPath),$inductive_def_uri))/InductiveDefinition"/>
+ <!-- no_params is the number of paramters 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="{$inductive_def_uri}">
+ <xsl:value-of select="@name"/>
+ </m:ci>
+ <xsl:call-template name="get_constructor_args">
+ <xsl:with-param name="no_params"
+ select="$no_params"/>
+ <xsl:with-param name="constructor_arity"
+ select="*[1]"/>
+ <xsl:with-param name="actual_arg"
+ select="$current_arg"/>
+ <xsl:with-param name="inductive_def_name"
+ select="$inductive_def_name"/>
+ </xsl:call-template>
+ </m:apply>
+ <m:apply>
+ <m:csymbol>induction_hypothesis</m:csymbol>
+ <xsl:call-template name="get_induction_hypothesis">
+ <xsl:with-param name="no_params"
+ select="$no_params"/>
+ <xsl:with-param name="constructor_arity"
+ select="*[1]"/>
+ <xsl:with-param name="actual_arg"
+ select="$current_arg"/>
+ <xsl:with-param name="inductive_def_name"
+ select="$inductive_def_name"/>
+ </xsl:call-template>
+ </m:apply>
+ <xsl:call-template name="get_body">
+ <xsl:with-param name="no_params"
+ select="$no_params"/>
+ <xsl:with-param name="constructor_arity"
+ select="*[1]"/>
+ <xsl:with-param name="actual_arg" select="$current_arg"/>
+ <xsl:with-param name="inductive_def_name"
+ select="$inductive_def_name"/>
+ </xsl:call-template>
+ </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="$extra_args"/>
+ </m:apply>
+ </m:apply>
+ </xsl:when>
+ <xsl:otherwise>
+ <xsl:apply-templates mode="letin" select="."/>
+ </xsl:otherwise>
+ </xsl:choose>
+ </xsl:when>
+ <xsl:otherwise>
+ <xsl:apply-templates mode="letin" select="."/>
+ </xsl:otherwise>
+ </xsl:choose>
+</xsl:template>
+
+<!-- check_args checks that the number of lambda abstractions
+ of each actual parameter is GREATER OR EQUAL to the number
+ or products of the corresponding formal parameter of the
+ induction principles. That is, that each argument is
+ sufficiently eta-expanded.
+ If this is not the case, not good rendering looks possible.
+ Check_args returns a boolean.
+ -->
+<xsl:template name="check_args">
+ <xsl:param name="arg_types" select="/.."/>
+ <xsl:param name="actual_args" select="/.."/>
+ <xsl:param name="bool_var" select="true()"/>
+ <xsl:choose>
+ <xsl:when test="count($arg_types) = 0">
+ <xsl:value-of select="$bool_var"/>
+ </xsl:when>
+ <xsl:otherwise>
+ <xsl:variable name="no_expected_arg_of_arg">
+ <xsl:apply-templates mode="count_arity" select="$arg_types[1]">
+ <xsl:with-param name="what" select="'PROD'"/>
+ </xsl:apply-templates>
+ </xsl:variable>
+ <xsl:variable name="no_actual_abst_of_arg">
+ <xsl:apply-templates mode="count_arity" select="$actual_args[1]">
+ <xsl:with-param name="what" select="'LAMBDA'"/>
+ </xsl:apply-templates>
+ </xsl:variable>
+ <!-- REPLACE WITH EQUALITY ???? -->
+ <xsl:variable name="test_arg"
+ select="$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>
+
+<!-- count_arity counts the number of head lambda (or prod) -->
+<xsl:template mode="count_arity" match="*">
+ <xsl:param name="what" select="'LAMBDA'"/>
+ <xsl:param name="num" select="0"/>
+ <!-- MANCANO I CAST ??? -->
+ <xsl:choose>
+ <xsl:when test="name(.) = $what">
+ <xsl:apply-templates mode="count_arity" select="target/*[1]">
+ <xsl:with-param name="what" select="$what"/>
+ <xsl:with-param name="num" select="$num+1"/>
+ </xsl:apply-templates>
+ </xsl:when>
+ <xsl:otherwise>
+ <xsl:value-of select="$num"/>
+ </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="no_params" select="0"/>
+ <xsl:param name="constructor_arity" select="/.."/>
+ <xsl:param name="actual_arg" select="/.."/>
+ <xsl:param name="inductive_def_name" select="''"/>
+ <xsl:choose>
+ <xsl:when test="$no_params = 0">
+ <xsl:if test="name($constructor_arity)='PROD'">
+ <m:bvar>
+ <m:ci><xsl:value-of select="$actual_arg/target/@binder"/></m:ci>
+ <m:type>
+ <xsl:apply-templates mode="pure" select="$actual_arg/source/*[1]"/>
+ </m:type>
+ </m:bvar>
+ <xsl:choose>
+ <xsl:when test="$constructor_arity/source//REL[@binder=$inductive_def_name]">
+ <xsl:call-template name="get_constructor_args">
+ <xsl:with-param name="constructor_arity"
+ select="$constructor_arity/target/*[1]"/>
+ <xsl:with-param name="actual_arg"
+ select="$actual_arg/target/LAMBDA/target/*[1]"/>
+ <xsl:with-param name="inductive_def_name"
+ select="$inductive_def_name"/>
+ </xsl:call-template>
+ </xsl:when>
+ <xsl:otherwise>
+ <xsl:call-template name="get_constructor_args">
+ <xsl:with-param name="constructor_arity"
+ select="$constructor_arity/target/*[1]"/>
+ <xsl:with-param name="actual_arg"
+ select="$actual_arg/target/*[1]"/>
+ <xsl:with-param name="inductive_def_name"
+ select="$inductive_def_name"/>
+ </xsl:call-template>
+ </xsl:otherwise>
+ </xsl:choose>
+ </xsl:if>
+ </xsl:when>
+ <xsl:otherwise>
+ <xsl:call-template name="get_constructor_args">
+ <xsl:with-param name="no_params" select="$no_params - 1"/>
+ <xsl:with-param name="constructor_arity"
+ select="$constructor_arity/target/*[1]"/>
+ <xsl:with-param name="actual_arg"
+ select="$actual_arg"/>
+ <xsl:with-param name="inductive_def_name"
+ select="$inductive_def_name"/>
+ </xsl:call-template>
+ </xsl:otherwise>
+ </xsl:choose>
+</xsl:template>
+
+<xsl:template name="get_induction_hypothesis">
+ <xsl:param name="no_params" select="0"/>
+ <xsl:param name="constructor_arity" select="/.."/>
+ <xsl:param name="actual_arg" select="/.."/>
+ <xsl:param name="inductive_def_name" select="''"/>
+ <xsl:choose>
+ <xsl:when test="$no_params = 0">
+ <xsl:if test="name($constructor_arity)='PROD'">
+ <xsl:choose>
+ <xsl:when test="$constructor_arity/source//REL[@binder=$inductive_def_name]">
+ <m:bvar>
+ <m:ci>
+ <xsl:value-of select="$actual_arg/target/LAMBDA/target/@binder"/>
+ </m:ci>
+ <m:type>
+ <xsl:apply-templates mode="pure"
+ select="$actual_arg/target/LAMBDA/source"/>
+ </m:type>
+ </m:bvar>
+ <xsl:call-template name="get_induction_hypothesis">
+ <xsl:with-param name="constructor_arity"
+ select="$constructor_arity/target/*[1]"/>
+ <xsl:with-param name="actual_arg"
+ select="$actual_arg/target/LAMBDA/target/*[1]"/>
+ <xsl:with-param name="inductive_def_name"
+ select="$inductive_def_name"/>
+ </xsl:call-template>
+ </xsl:when>
+ <xsl:otherwise>
+ <xsl:call-template name="get_induction_hypothesis">
+ <xsl:with-param name="constructor_arity"
+ select="$constructor_arity/target/*[1]"/>
+ <xsl:with-param name="actual_arg"
+ select="$actual_arg/target/*[1]"/>
+ <xsl:with-param name="inductive_def_name"
+ select="$inductive_def_name"/>
+ </xsl:call-template>
+ </xsl:otherwise>
+ </xsl:choose>
+ </xsl:if>
+ </xsl:when>
+ <xsl:otherwise>
+ <xsl:call-template name="get_induction_hypothesis">
+ <xsl:with-param name="no_params" select="$no_params - 1"/>
+ <xsl:with-param name="constructor_arity"
+ select="$constructor_arity/target/*[1]"/>
+ <xsl:with-param name="actual_arg"
+ select="$actual_arg"/>
+ <xsl:with-param name="inductive_def_name"
+ select="$inductive_def_name"/>
+ </xsl:call-template>
+ </xsl:otherwise>
+ </xsl:choose>
+</xsl:template>
+
+<xsl:template name="get_body">
+ <xsl:param name="no_params" select="0"/>
+ <xsl:param name="constructor_arity" select="/.."/>
+ <xsl:param name="actual_arg" select="/.."/>
+ <xsl:param name="inductive_def_name" select="''"/>
+ <xsl:choose>
+ <xsl:when test="$no_params = 0">
+ <xsl:choose>
+ <xsl:when test="name($constructor_arity)='PROD'">
+ <xsl:choose>
+ <xsl:when test="$constructor_arity/source//REL[@binder=$inductive_def_name]">
+ <xsl:call-template name="get_body">
+ <xsl:with-param name="constructor_arity"
+ select="$constructor_arity/target/*[1]"/>
+ <xsl:with-param name="actual_arg"
+ select="$actual_arg/target/LAMBDA/target/*[1]"/>
+ <xsl:with-param name="inductive_def_name"
+ select="$inductive_def_name"/>
+ </xsl:call-template>
+ </xsl:when>
+ <xsl:otherwise>
+ <xsl:call-template name="get_body">
+ <xsl:with-param name="constructor_arity"
+ select="$constructor_arity/target/*[1]"/>
+ <xsl:with-param name="actual_arg"
+ select="$actual_arg/target/*[1]"/>
+ <xsl:with-param name="inductive_def_name"
+ select="$inductive_def_name"/>
+ </xsl:call-template>
+ </xsl:otherwise>
+ </xsl:choose>
+ </xsl:when>
+ <xsl:otherwise>
+ <xsl:apply-templates mode="noannot" select="$actual_arg"/>
+ </xsl:otherwise>
+ </xsl:choose>
+ </xsl:when>
+ <xsl:otherwise>
+ <xsl:call-template name="get_body">
+ <xsl:with-param name="no_params" select="$no_params - 1"/>
+ <xsl:with-param name="constructor_arity"
+ select="$constructor_arity/target/*[1]"/>
+ <xsl:with-param name="actual_arg"
+ select="$actual_arg"/>
+ <xsl:with-param name="inductive_def_name"
+ select="$inductive_def_name"/>
+ </xsl:call-template>
+ </xsl:otherwise>
+ </xsl:choose>
+</xsl:template>
+
+
+</xsl:stylesheet>
+
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