<!--******************************************************************-->
<!-- XSLT version 0.1 of CIC inductive objects to MathML content: -->
+<!-- Completely revisited: November 2002, Andrea asperti -->
<!-- First draft: March 2001, Andrea asperti -->
<!--******************************************************************-->
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:param name="section_params" select="0"/>
+ <xsl:variable name="InductiveTypeUrl"><xsl:call-template name="URLofURI4getter"><xsl:with-param name="uri" select="$uri"/></xsl:call-template></xsl:variable>
<!-- expected_args_type contains the types of the arguments expected by
the induction principle -->
- <xsl:variable name="InductiveTypeUrl"><xsl:call-template name="URLofURI4getter"><xsl:with-param name="uri" select="*[1]/@uri"/></xsl:call-template></xsl:variable>
<xsl:variable name="expected_args_types"
- select="document($InductiveTypeUrl)/Definition/type//PROD[not(ancestor::source)]/source/*[1]"/>
+ 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+$section_params)]"/>
+ <xsl:variable name="actual_arguments" select="*[position()>1]"/>
<!-- First check that the induction principle is applied to the
expected number of arguments -->
<xsl:choose>
<xsl:when test="string($argsOK) = 'true'">
<!-- arguments are in the expected form: we create a
"by_induction" content element -->
- <!-- no_params is the number of paramters in square brackets -->
+ <!-- no_params is the number of parameters in square brackets -->
<xsl:variable name="no_params"
select="$inductive_def/@noParams"/>
<!-- the inductive property is the first argument following
is the uri of the inductive definition -->
<m:ci><xsl:value-of select="$inductive_def_uri"/></m:ci>
<!-- next, we have the inductive property, currently not
- used for rendering (it could be omitted??) -->
+ used for rendering (it could be omitted ??) -->
<xsl:apply-templates mode="pure" select="$inductive_property"/>
<!-- each case has its own "inductive_case" element -->
<!-- the inductive case element is composed by:
<m:csymbol>case_lhs</m:csymbol>
<m:ci definitionURL="{$inductive_def_uri}">
<xsl:value-of select="@name"/>
- </m:ci>
+ </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>
+ <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="$inductive_def_uri"/>
+ </xsl:call-template>
</m:apply>
<m:apply>
<m:csymbol>induction_hypothesis</m:csymbol>
<xsl:call-template name="get_induction_hypothesis">
- <xsl:with-param name="no_params"
- select="$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: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="$inductive_def_uri"/>
</xsl:call-template>
</m:apply>
- <xsl:call-template name="get_body">
- <xsl:with-param name="no_params"
- select="$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>
+ <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 -->
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">
- <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="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 >= $no_expected_arg_of_arg"/>
+ select="($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:call-template>
</xsl:otherwise>
</xsl:choose>
-</xsl:template>
+</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.
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'">
+ <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_arg/target/@binder"/></m:ci>
+ <m:ci><xsl:value-of select="$actual_args[1]/@binder"/></m:ci>
<m:type>
- <xsl:apply-templates mode="pure" select="$actual_arg/source/*[1]"/>
+ <xsl:apply-templates mode="pure" select="$actual_args[1]/*"/>
</m:type>
</m:bvar>
<xsl:choose>
- <xsl:when test="$constructor_arity/source//REL[@binder=$inductive_def_name]">
+ <xsl:when test="$constructor_args[1]//MUTIND[@uri=$inductive_def_uri]">
<xsl:call-template name="get_constructor_args">
<xsl:with-param name="constructor_arity"
- select="$constructor_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"/>
+ select="$constructor_args[position()>1]"/>
+ <xsl:with-param name="actual_args"
+ select="$actual_args[position()>2]"/>
+ <xsl:with-param name="inductive_def_uri"
+ select="$inductive_def_uri"/>
</xsl:call-template>
</xsl:when>
<xsl:otherwise>
<xsl:call-template name="get_constructor_args">
- <xsl:with-param name="constructor_arity"
- select="$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: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="$inductive_def_uri"/>
</xsl:call-template>
</xsl:otherwise>
</xsl:choose>
</xsl:if>
- </xsl:when>
- <xsl:otherwise>
- <xsl:call-template name="get_constructor_args">
- <xsl:with-param name="no_params" select="$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="$inductive_def_name"/>
- </xsl:call-template>
- </xsl:otherwise>
- </xsl:choose>
-</xsl:template>
+</xsl:template>
<xsl:template name="get_induction_hypothesis">
- <xsl:param name="no_params" select="0"/>
- <xsl:param name="constructor_arity" select="/.."/>
- <xsl:param name="actual_arg" select="/.."/>
- <xsl:param name="inductive_def_name" select="''"/>
- <xsl:choose>
- <xsl:when test="$no_params = 0">
- <xsl:if test="name($constructor_arity)='PROD'">
+ <xsl:param name="constructor_args" select="/.."/>
+ <xsl:param name="actual_args" select="/.."/>
+ <xsl:param name="inductive_def_uri" select="''"/>
+ <xsl:if test="$constructor_args">
<xsl:choose>
- <xsl:when test="$constructor_arity/source//REL[@binder=$inductive_def_name]">
+ <xsl:when test="$constructor_args[1]//MUTIND[@uri=$inductive_def_uri]">
<m:bvar>
<m:ci>
- <xsl:value-of select="$actual_arg/target/LAMBDA/target/@binder"/>
+ <xsl:value-of select="$actual_args[2]/@binder"/>
</m:ci>
<m:type>
<xsl:apply-templates mode="pure"
- select="$actual_arg/target/LAMBDA/source"/>
+ select="$actual_args[2]/*"/>
</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="$inductive_def_name"/>
+ <xsl:with-param name="constructor_args"
+ select="$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_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="$inductive_def_name"/>
+ <xsl:with-param name="constructor_args"
+ select="$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: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="$no_params = 0">
+ <xsl:param name="constructor_args" select="/.."/>
+ <xsl:param name="actual_args" select="/.."/>
+ <xsl:param name="inductive_def_uri" select="''"/>
+ <xsl:param name="target" select="/.."/>
<xsl:choose>
- <xsl:when test="name($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="$inductive_def_name"/>
- </xsl:call-template>
- </xsl:otherwise>
+ <xsl:when test="$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:template>
</xsl:stylesheet>
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