test/relaxng/spec_0.xml - platform/external/libxml2 - Gitiles

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 <article status="Committee Specification" xmlns:p="http://relaxng.org/ns/proofsystem">

 <articleinfo>
 <releaseinfo>$Id: spec.xml,v 1.159 2001/12/02 12:12:12 jjc Exp $</releaseinfo>
 <title>RELAX NG Specification</title>
 <authorgroup>
 <editor>
   <firstname>James</firstname><surname>Clark</surname>
   <affiliation>
     <address><email>jjc@jclark.com</email></address>
   </affiliation>
 </editor>
 <editor>
   <surname>MURATA</surname><firstname>Makoto</firstname>
   <affiliation>
     <address><email>EB2M-MRT@asahi-net.or.jp</email></address>
   </affiliation>
 </editor>
 </authorgroup>
 <pubdate>3 December 2001</pubdate>
 <releaseinfo role="meta">
 $Id: spec.xml,v 1.159 2001/12/02 12:12:12 jjc Exp $
 </releaseinfo>

 <copyright><year>2001</year><holder>OASIS</holder></copyright>

 <legalnotice>

 <para>Copyright &#169; The Organization for the Advancement of
 Structured Information Standards [OASIS] 2001. All Rights
 Reserved.</para>

 <para>This document and translations of it may be copied and furnished
 to others, and derivative works that comment on or otherwise explain
 it or assist in its implementation may be prepared, copied, published
 and distributed, in whole or in part, without restriction of any kind,
 provided that the above copyright notice and this paragraph are
 included on all such copies and derivative works. However, this
 document itself may not be modified in any way, such as by removing
 the copyright notice or references to OASIS, except as needed for the
 purpose of developing OASIS specifications, in which case the
 procedures for copyrights defined in the OASIS Intellectual Property
 Rights document must be followed, or as required to translate it into
 languages other than English.</para>

 <para>The limited permissions granted above are perpetual and will not
 be revoked by OASIS or its successors or assigns.</para>

 <para>This document and the information contained herein is provided
 on an <quote>AS IS</quote> basis and OASIS DISCLAIMS ALL WARRANTIES,
 EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO ANY WARRANTY THAT THE
 USE OF THE INFORMATION HEREIN WILL NOT INFRINGE ANY RIGHTS OR ANY
 IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR
 PURPOSE.</para>

 </legalnotice>

 <legalnotice role="status"><title>Status of this Document</title>

 <para>This Committee Specification was approved for publication by the
 OASIS RELAX NG technical committee. It is a stable document which
 represents the consensus of the committee. Comments on this document
 may be sent to <ulink
 url="mailto:relax-ng-comment@lists.oasis-open.org"
 >relax-ng-comment@lists.oasis-open.org</ulink>.</para>

 <para>A list of known errors in this document is available at <ulink
 url="http://www.oasis-open.org/committees/relax-ng/spec-20011203-errata.html"
 >http://www.oasis-open.org/committees/relax-ng/spec-20011203-errata.html</ulink
 >.</para>

 </legalnotice>

 <abstract>
 <para>This is the definitive specification of RELAX NG, a simple
 schema language for XML, based on <xref linkend="relax"/> and <xref
 linkend="trex"/>. A RELAX NG schema specifies a pattern for the
 structure and content of an XML document. A RELAX NG schema is itself
 an XML document.</para>
 </abstract>

 <revhistory>
 <revision>
   <revnumber>Committee Specification</revnumber>
   <date>3 December 2001</date>
 </revision>
 <revision>
   <revnumber>Committee Specification</revnumber>
   <date>11 August 2001</date>
 </revision>
 </revhistory>
 </articleinfo>


 <section>
 <title>Introduction</title>

 <para>This document specifies</para>

 <itemizedlist>

 <listitem><para>when an XML document is a correct RELAX NG
 schema</para></listitem>

 <listitem><para>when an XML document is valid with respect to a
 correct RELAX NG schema</para></listitem>

 </itemizedlist>

 <para>An XML document that is being validated with respect to a RELAX NG
 schema is referred to as an instance.</para>

 <para>The structure of this document is as follows.  <xref
 linkend="data-model"/> describes the data model, which is the
 abstraction of an XML document used throughout the rest of the
 document.  <xref linkend="full-syntax"/> describes the syntax of a
 RELAX NG schema; any correct RELAX NG schema must conform to this
 syntax.  <xref linkend="simplification"/> describes a sequence of
 transformations that are applied to simplify a RELAX NG schema;
 applying the transformations also involves checking certain
 restrictions that must be satisfied by a correct RELAX NG
 schema. <xref linkend="simple-syntax"/> describes the syntax that
 results from applying the transformations; this simple syntax is a
 subset of the full syntax.  <xref linkend="semantics"/> describes the
 semantics of a correct RELAX NG schema that uses the simple syntax;
 the semantics specify when an element is valid with respect to a RELAX
 NG schema.  <xref linkend="restriction"/> describes restrictions in
 terms of the simple syntax; a correct RELAX NG schema must be such
 that, after transformation into the simple form, it satisfies these
 restrictions. Finally, <xref linkend="conformance"/> describes
 conformance requirements for RELAX NG validators.</para>

 <para>A tutorial is available separately (see <xref
 linkend="tutorial"/>).</para>

 </section>

 <section id="data-model">
 <title>Data model</title>

 <para>RELAX NG deals with XML documents representing both schemas and
 instances through an abstract data model.  XML documents representing
 schemas and instances must be well-formed in conformance with <xref
 linkend="xml-rec"/> and must conform to the constraints of <xref
 linkend="xml-names"/>.</para>

 <para>An XML document is represented by an element.  An element consists
 of</para>

 <itemizedlist>

 <listitem><para>a name</para></listitem>

 <listitem><para>a context</para></listitem>

 <listitem><para>a set of attributes</para></listitem>

 <listitem><para>an ordered sequence of zero or more children; each
 child is either an element or a non-empty string; the sequence never contains
 two consecutive strings</para></listitem>

 </itemizedlist>

 <para>A name consists of</para>

 <itemizedlist>
 <listitem><para>a string representing the namespace URI; the empty
 string has special significance, representing the absence of any
 namespace</para></listitem>

 <listitem><para>a string representing the local name; this string matches the NCName
 production of <xref linkend="xml-names"/></para></listitem>
 </itemizedlist>

 <para>A context consists of</para>

 <itemizedlist>
 <listitem><para>a base URI</para></listitem>
 <listitem><para>a namespace map; this maps prefixes to namespace URIs,
 and also may specify a default namespace URI (as declared
 by the <literal>xmlns</literal> attribute)</para></listitem>
 </itemizedlist>

 <para>An attribute consists of</para>

 <itemizedlist>
 <listitem><para>a name</para></listitem>
 <listitem><para>a string representing the value</para></listitem>
 </itemizedlist>

 <para>A string consists of a sequence of zero or more characters,
 where a character is as defined in <xref linkend="xml-rec"/>.</para>

 <para>The element for an XML document is constructed from an instance
 of the <xref linkend="infoset"/> as follows.  We use the notation
 [<replaceable>x</replaceable>] to refer to the value of the
 <replaceable>x</replaceable> property of an information item. An
 element is constructed from a document information item by
 constructing an element from the [document element].  An element is
 constructed from an element information item by constructing the name
 from the [namespace name] and [local name], the context from the [base
 URI] and [in-scope namespaces], the attributes from the [attributes],
 and the children from the [children].  The attributes of an element
 are constructed from the unordered set of attribute information items
 by constructing an attribute for each attribute information item.  The
 children of an element are constructed from the list of child
 information items first by removing information items other than
 element information items and character information items, and then by
 constructing an element for each element information item in the list
 and a string for each maximal sequence of character information items.
 An attribute is constructed from an attribute information item by
 constructing the name from the [namespace name] and [local name], and
 the value from the [normalized value].  When constructing the name of
 an element or attribute from the [namespace name] and [local name], if
 the [namespace name] property is not present, then the name is
 constructed from an empty string and the [local name]. A string is
 constructed from a sequence of character information items by
 constructing a character from the [character code] of each character
 information item.</para>

 <para>It is possible for there to be multiple distinct infosets for a
 single XML document.  This is because XML parsers are not required to
 process all DTD declarations or expand all external parsed general
 entities.  Amongst these multiple infosets, there is exactly one
 infoset for which [all declarations processed] is true and which does
 not contain any unexpanded entity reference information items.  This
 is the infoset that is the basis for defining the RELAX NG data
 model.</para>

 <section id="data-model-example">
 <title>Example</title>

 <para>Suppose the document
 <literal>http://www.example.com/doc.xml</literal> is as
 follows:</para>

 <programlisting><![CDATA[<?xml version="1.0"?>
 <foo><pre1:bar1 xmlns:pre1="http://www.example.com/n1"/><pre2:bar2
   xmlns:pre2="http://www.example.com/n2"/></foo>
 ]]></programlisting>

 <para>The element representing this document has</para>

 <itemizedlist>
 <listitem><para>a name which has</para>
 <itemizedlist>

 <listitem><para>the empty string as the namespace URI, representing
 the absence of any namespace</para></listitem>

 <listitem><para><literal>foo</literal> as the local
 name</para></listitem>

 </itemizedlist>

 </listitem>

 <listitem><para>a context which has</para>

 <itemizedlist>
 <listitem><para><literal>http://www.example.com/doc.xml</literal> as the base
 URI</para></listitem>

 <listitem><para>a namespace map which</para>

 <itemizedlist>

 <listitem><para>maps the prefix <literal>xml</literal> to the
 namespace URI
 <literal>http://www.w3.org/XML/1998/namespace</literal>
 (the <literal>xml</literal> prefix is implicitly declared
 by every XML document)</para></listitem>

 <listitem><para>specifies the empty string as the default namespace
 URI</para></listitem>

 </itemizedlist>

 </listitem>

 </itemizedlist>

 </listitem>

 <listitem><para>an empty set of attributes</para></listitem>

 <listitem><para>a sequence of children consisting
 of an element which has</para>

 <itemizedlist>
 <listitem><para>a name which has</para>
 <itemizedlist>

 <listitem><para><literal>http://www.example.com/n1</literal> as the
 namespace URI</para></listitem>

 <listitem><para><literal>bar1</literal> as the local
 name</para></listitem>

 </itemizedlist>

 </listitem>

 <listitem><para>a context which has</para>

 <itemizedlist>
 <listitem><para><literal>http://www.example.com/doc.xml</literal> as the base
 URI</para></listitem>

 <listitem><para>a namespace map which</para>

 <itemizedlist>

 <listitem><para>maps the prefix <literal>pre1</literal> to the
 namespace URI
 <literal>http://www.example.com/n1</literal></para></listitem>

 <listitem><para>maps the prefix <literal>xml</literal> to the
 namespace URI
 <literal>http://www.w3.org/XML/1998/namespace</literal></para></listitem>

 <listitem><para>specifies the empty string as the default namespace
 URI</para></listitem>

 </itemizedlist>

 </listitem>

 </itemizedlist>

 </listitem>

 <listitem><para>an empty set of attributes</para></listitem>

 <listitem><para>an empty sequence of children</para></listitem>

 </itemizedlist>

 <para>followed by an element which has</para>

 <itemizedlist>
 <listitem><para>a name which has</para>
 <itemizedlist>

 <listitem><para><literal>http://www.example.com/n2</literal> as the
 namespace URI</para></listitem>

 <listitem><para><literal>bar2</literal> as the local
 name</para></listitem>

 </itemizedlist>

 </listitem>

 <listitem><para>a context which has</para>

 <itemizedlist>
 <listitem><para><literal>http://www.example.com/doc.xml</literal> as the base
 URI</para></listitem>

 <listitem><para>a namespace map which</para>

 <itemizedlist>

 <listitem><para>maps the prefix <literal>pre2</literal> to the
 namespace URI
 <literal>http://www.example.com/n2</literal></para></listitem>

 <listitem><para>maps the prefix <literal>xml</literal> to the
 namespace URI
 <literal>http://www.w3.org/XML/1998/namespace</literal></para></listitem>

 <listitem><para>specifies the empty string as the default namespace
 URI</para></listitem>

 </itemizedlist>

 </listitem>

 </itemizedlist>

 </listitem>

 <listitem><para>an empty set of attributes</para></listitem>

 <listitem><para>an empty sequence of children</para></listitem>

 </itemizedlist>

 </listitem>
 </itemizedlist>

 </section>

 </section>

 <section id="full-syntax">
 <title>Full syntax</title>

 <para>The following grammar summarizes the syntax of RELAX NG.
 Although we use a notation based on the XML representation of an RELAX
 NG schema as a sequence of characters, the grammar must be understood
 as operating at the data model level.  For example, although the
 syntax uses <literal><![CDATA[<text/>]]></literal>, an instance or
 schema can use <literal><![CDATA[<text></text>]]></literal> instead,
 because they both represent the same element at the data model level.
 All elements shown in the grammar are qualified with the namespace
 URI:</para>

 <programlisting>http://relaxng.org/ns/structure/1.0</programlisting>

 <para>The symbols QName and NCName are defined in <xref
 linkend="xml-names"/>.  The anyURI symbol has the same meaning as the
 anyURI datatype of <xref linkend="xmlschema-2"/>: it indicates a
 string that, after escaping of disallowed values as described in
 Section 5.4 of <xref linkend="xlink"/>, is a URI reference as defined
 in <xref linkend="rfc2396"/> (as modified by <xref
 linkend="rfc2732"/>).  The symbol string matches any string.</para>

 <para>In addition to the attributes shown explicitly, any element can
 have an <literal>ns</literal> attribute and any element can have a
 <literal>datatypeLibrary</literal> attribute. The
 <literal>ns</literal> attribute can have any value.  The value of the
 <literal>datatypeLibrary</literal> attribute must match the anyURI
 symbol as described in the previous paragraph; in addition, it must
 not use the relative form of URI reference and must not have a
 fragment identifier; as an exception to this, the value may be the
 empty string.</para>

 <para>Any element can also have foreign attributes in addition to the
 attributes shown in the grammar. A foreign attribute is an attribute
 with a name whose namespace URI is neither the empty string nor the
 RELAX NG namespace URI.  Any element that cannot have string children
 (that is, any element other than <literal>value</literal>, <literal>param</literal>
 and <literal>name</literal>) may have foreign child elements in addition
 to the child elements shown in the grammar. A foreign element is an
 element with a name whose namespace URI is not the RELAX NG namespace
 URI.  There are no constraints on the relative position of foreign
 child elements with respect to other child elements.</para>

 <para>Any element can also have as children strings that consist
 entirely of whitespace characters, where a whitespace character is one
 of #x20, #x9, #xD or #xA. There are no constraints on the relative
 position of whitespace string children with respect to child
 elements.</para>

 <para>Leading and trailing whitespace is allowed for value of each
 <literal>name</literal>, <literal>type</literal> and
 <literal>combine</literal> attribute and for the content of each
 <literal>name</literal> element.</para>

 <grammarref src="full.rng"/>

 <section id="full-syntax-example">
 <title>Example</title>

 <para>Here is an example of a schema in the full syntax for the
 document in <xref linkend="data-model-example"/>.</para>

 <programlisting><![CDATA[<?xml version="1.0"?>
 <element name="foo"
          xmlns="http://relaxng.org/ns/structure/1.0"
          xmlns:a="http://relaxng.org/ns/annotation/1.0"
          xmlns:ex1="http://www.example.com/n1"
          xmlns:ex2="http://www.example.com/n2">
   <a:documentation>A foo element.</a:document>
   <element name="ex1:bar1">
     <empty/>
   </element>
   <element name="ex2:bar2">
     <empty/>
   </element>
 </element>]]></programlisting>

 </section>

 </section>

 <section id="simplification">
 <title>Simplification</title>

 <para>The full syntax given in the previous section is transformed
 into a simpler syntax by applying the following transformation rules
 in order. The effect must be as if each rule was applied to all
 elements in the schema before the next rule is applied.  A
 transformation rule may also specify constraints that must be
 satisfied by a correct schema. The transformation rules are applied
 at the data model level.  Before the transformations are applied, the
 schema is parsed into an instance of the data model.</para>

 <section>
 <title>Annotations</title>

 <para>Foreign attributes and elements are removed.</para>

 <note><para>It is safe to remove <literal>xml:base</literal>
 attributes at this stage because <literal>xml:base</literal>
 attributes are used in determining the [base URI] of an element
 information item, which is in turn used to construct the base URI of
 the context of an element.  Thus, after a document has been parsed
 into an instance of the data model, <literal>xml:base</literal>
 attributes can be discarded.</para></note>

 </section>

 <section>
 <title>Whitespace</title>

 <para>For each element other than <literal>value</literal> and
 <literal>param</literal>, each child that is a string containing only
 whitespace characters is removed.</para>

 <para>Leading and trailing whitespace characters are removed from the
 value of each <literal>name</literal>, <literal>type</literal> and
 <literal>combine</literal> attribute and from the content of each
 <literal>name</literal> element.</para>

 </section>

 <section>
 <title><literal>datatypeLibrary</literal> attribute</title>

 <para>The value of each <literal>datatypeLibary</literal> attribute is
 transformed by escaping disallowed characters as specified in Section
 5.4 of <xref linkend="xlink"/>.</para>

 <para>For any <literal>data</literal> or <literal>value</literal>
 element that does not have a <literal>datatypeLibrary</literal>
 attribute, a <literal>datatypeLibrary</literal> attribute is
 added. The value of the added <literal>datatypeLibrary</literal>
 attribute is the value of the <literal>datatypeLibrary</literal>
 attribute of the nearest ancestor element that has a
 <literal>datatypeLibrary</literal> attribute, or the empty string if
 there is no such ancestor. Then, any <literal>datatypeLibrary</literal>
 attribute that is on an element other than <literal>data</literal> or
 <literal>value</literal> is removed.</para>

 </section>

 <section>
 <title><literal>type</literal> attribute of <literal>value</literal> element</title>

 <para>For any <literal>value</literal> element that does not have a
 <literal>type</literal> attribute, a <literal>type</literal> attribute
 is added with value <literal>token</literal> and the value of the
 <literal>datatypeLibrary</literal> attribute is changed to the empty
 string.</para>

 </section>

 <section id="href">
 <title><literal>href</literal> attribute</title>

 <para>The value of the <literal>href</literal> attribute on an
 <literal>externalRef</literal> or <literal>include</literal> element
 is first transformed by escaping disallowed characters as specified in
 Section 5.4 of <xref linkend="xlink"/>.  The URI reference is then
 resolved into an absolute form as described in section 5.2 of <xref
 linkend="rfc2396"/> using the base URI from the context of the element
 that bears the <literal>href</literal> attribute.</para>

 <para>The value of the <literal>href</literal> attribute will be used
 to construct an element (as specified in <xref
 linkend="data-model"/>). This must be done as follows.  The URI
 reference consists of the URI itself and an optional fragment
 identifier. The resource identified by the URI is retrieved.  The
 result is a MIME entity: a sequence of bytes labeled with a MIME
 media type.  The media type determines how an element is constructed
 from the MIME entity and optional fragment identifier.  When the media
 type is <literal>application/xml</literal> or
 <literal>text/xml</literal>, the MIME entity must be parsed as an XML
 document in accordance with the applicable RFC (at the term of writing
 <xref linkend="rfc3023"/>) and an element constructed from the result
 of the parse as specified in <xref linkend="data-model"/>.  In
 particular, the <literal>charset</literal> parameter must be handled
 as specified by the RFC. This specification does not define the
 handling of media types other than <literal>application/xml</literal>
 and <literal>text/xml</literal>. The <literal>href</literal> attribute
 must not include a fragment identifier unless the registration of the
 media type of the resource identified by the attribute defines the
 interpretation of fragment identifiers for that media type.</para>

 <note><para><xref linkend="rfc3023"/> does not define the
 interpretation of fragment identifiers for
 <literal>application/xml</literal> or
 <literal>text/xml</literal>.</para></note>

 </section>

 <section>
 <title><literal>externalRef</literal> element</title>

 <para>An <literal>externalRef</literal> element is transformed as
 follows.  An element is constructed using the URI reference that is
 the value of <literal>href</literal> attribute as specified in <xref
 linkend="href"/>. This element must match the syntax for pattern.  The
 element is transformed by recursively applying the rules from this
 subsection and from previous subsections of this section. This must
 not result in a loop. In other words, the transformation of the
 referenced element must not require the dereferencing of an
 <literal>externalRef</literal> attribute with an
 <literal>href</literal> attribute with the same value.</para>

 <para>Any <literal>ns</literal> attribute on the
 <literal>externalRef</literal> element is transferred to the
 referenced element if the referenced element does not already have an
 <literal>ns</literal> attribute.  The <literal>externalRef</literal>
 element is then replaced by the referenced element.</para>

 </section>

 <section>
 <title><literal>include</literal> element</title>

 <para>An <literal>include</literal> element is transformed as follows.
 An element is constructed using the URI reference that is the value of
 <literal>href</literal> attribute as specified in <xref
 linkend="href"/>.  This element must be a <literal>grammar</literal>
 element, matching the syntax for grammar.</para>

 <para>This <literal>grammar</literal> element is transformed by
 recursively applying the rules from this subsection and from previous
 subsections of this section.  This must not result in a loop. In other
 words, the transformation of the <literal>grammar</literal> element
 must not require the dereferencing of an <literal>include</literal>
 attribute with an <literal>href</literal> attribute with the same
 value.</para>

 <para>Define the <firstterm>components</firstterm> of an element to
 be the children of the element together with the components of any
 <literal>div</literal> child elements.  If the
 <literal>include</literal> element has a <literal>start</literal>
 component, then the <literal>grammar</literal> element must have a
 <literal>start</literal> component.  If the <literal>include</literal>
 element has a <literal>start</literal> component, then all
 <literal>start</literal> components are removed from the
 <literal>grammar</literal> element.  If the <literal>include</literal>
 element has a <literal>define</literal> component, then the
 <literal>grammar</literal> element must have a
 <literal>define</literal> component with the same name.  For every
 <literal>define</literal> component of the <literal>include</literal>
 element, all <literal>define</literal> components with the same name
 are removed from the <literal>grammar</literal> element.</para>

 <para>The <literal>include</literal> element is transformed into a
 <literal>div</literal> element.  The attributes of the
 <literal>div</literal> element are the attributes of the
 <literal>include</literal> element other than the
 <literal>href</literal> attribute.  The children of the
 <literal>div</literal> element are the <literal>grammar</literal>
 element (after the removal of the <literal>start</literal> and
 <literal>define</literal> components described by the preceding
 paragraph) followed by the children of the <literal>include</literal>
 element.  The <literal>grammar</literal> element is then renamed to
 <literal>div</literal>.</para>

 </section>

 <section>
 <title><literal>name</literal> attribute of <literal>element</literal>
 and <literal>attribute</literal> elements</title>

 <para>The <literal>name</literal> attribute on an
 <literal>element</literal> or <literal>attribute</literal> element is
 transformed into a <literal>name</literal> child element.</para>

 <para>If an <literal>attribute</literal> element has a
 <literal>name</literal> attribute but no <literal>ns</literal>
 attribute, then an <literal>ns=""</literal> attribute is added to the
 <literal>name</literal> child element.</para>

 </section>

 <section>
 <title><literal>ns</literal> attribute</title>

 <para>For any <literal>name</literal>, <literal>nsName</literal> or
 <literal>value</literal> element that does not have an
 <literal>ns</literal> attribute, an <literal>ns</literal> attribute is
 added. The value of the added <literal>ns</literal> attribute is the
 value of the <literal>ns</literal> attribute of the nearest ancestor
 element that has an <literal>ns</literal> attribute, or the empty
 string if there is no such ancestor. Then, any <literal>ns</literal>
 attribute that is on an element other than <literal>name</literal>,
 <literal>nsName</literal> or <literal>value</literal> is
 removed.</para>

 <note><para>The value of the <literal>ns</literal> attribute is
 <emphasis role="strong">not</emphasis> transformed either by escaping
 disallowed characters, or in any other way, because the value of the
 <literal>ns</literal> attribute is compared against namespace URIs in
 the instance, which are not subject to any
 transformation.</para></note>

 <note><para>Since <literal>include</literal> and
 <literal>externalRef</literal> elements are resolved after
 <literal>datatypeLibrary</literal> attributes are added but before
 <literal>ns</literal> attributes are added, <literal>ns</literal>
 attributes are inherited into external schemas but
 <literal>datatypeLibrary</literal> attributes are not.</para></note>

 </section>

 <section>
 <title>QNames</title>

 <para>For any <literal>name</literal> element containing a prefix, the
 prefix is removed and an <literal>ns</literal> attribute is added
 replacing any existing <literal>ns</literal> attribute. The value of
 the added <literal>ns</literal> attribute is the value to which the
 namespace map of the context of the <literal>name</literal> element
 maps the prefix.  The context must have a mapping for the
 prefix.</para>

 </section>

 <section>
 <title><literal>div</literal> element</title>

 <para>Each <literal>div</literal> element is replaced by its
 children.</para>

 </section>

 <section id="number-child-elements">
 <title>Number of child elements</title>

 <para>A <literal>define</literal>, <literal>oneOrMore</literal>,
 <literal>zeroOrMore</literal>, <literal>optional</literal>, <literal>list</literal> or
 <literal>mixed</literal> element is transformed so that it has exactly
 one child element.  If it has more than one child element, then its
 child elements are wrapped in a <literal>group</literal>
 element. Similarly, an <literal>element</literal> element is transformed so
 that it has exactly two child elements, the first being a name class
 and the second being a pattern. If it has more than two child elements,
 then the child elements other than the first are wrapped in a
 <literal>group</literal> element.</para>

 <para>A <literal>except</literal> element is transformed
 so that it has exactly one child element. If it has more
 than one child element, then its child elements are wrapped
 in a <literal>choice</literal> element.</para>

 <para>If an <literal>attribute</literal> element has only one child
 element (a name class), then a <literal>text</literal> element is
 added.</para>

 <para>A <literal>choice</literal>, <literal>group</literal> or
 <literal>interleave</literal> element is transformed so that it has
 exactly two child elements. If it has one child element, then it is
 replaced by its child element.  If it has more than two child
 elements, then the first two child elements are combined into a new
 element with the same name as the parent element and with the first
 two child elements as its children.  For example,</para>

 <programlisting>&lt;choice&gt; <replaceable>p1</replaceable> <replaceable>p2</replaceable> <replaceable>p3</replaceable> &lt;/choice&gt;</programlisting>

 <para>is transformed to</para>

 <programlisting>&lt;choice&gt; &lt;choice&gt; <replaceable>p1</replaceable> <replaceable>p2</replaceable> &lt;/choice&gt; <replaceable>p3</replaceable> &lt;/choice&gt;</programlisting>

 <para>This reduces the number of child elements by one. The
 transformation is applied repeatedly until there are exactly two child
 elements.</para>

 </section>

 <section>
 <title><literal>mixed</literal> element</title>

 <para>A <literal>mixed</literal> element is transformed into an
 interleaving with a <literal>text</literal> element:</para>

 <programlisting>&lt;mixed> <replaceable>p</replaceable> &lt;/mixed></programlisting>

 <para>is transformed into</para>

 <programlisting>&lt;interleave> <replaceable>p</replaceable> &lt;text/> &lt;/interleave></programlisting>

 </section>

 <section>
 <title><literal>optional</literal> element</title>

 <para>An <literal>optional</literal> element is transformed into
 a choice with <literal>empty</literal>:</para>

 <programlisting>&lt;optional> <replaceable>p</replaceable> &lt;/optional></programlisting>

 <para>is transformed into</para>

 <programlisting>&lt;choice> <replaceable>p</replaceable> &lt;empty/> &lt;/choice></programlisting>

 </section>

 <section>
 <title><literal>zeroOrMore</literal> element</title>

 <para>A <literal>zeroOrMore</literal> element is transformed into a choice
 between <literal>oneOrMore</literal> and
 <literal>empty</literal>:</para>

 <programlisting>&lt;zeroOrMore> <replaceable>p</replaceable> &lt;/zeroOrMore></programlisting>

 <para>is transformed into</para>

 <programlisting>&lt;choice> &lt;oneOrMore> <replaceable>p</replaceable> &lt;/oneOrMore> &lt;empty/> &lt;/choice></programlisting>

 </section>

 <section id="constraints">
 <title>Constraints</title>

 <para>In this rule, no transformation is performed, but various
 constraints are checked.</para>

 <note><para>The constraints in this section, unlike the constraints
 specified in <xref linkend="restriction"/>, can be checked without
 resolving any <literal>ref</literal> elements, and are accordingly
 applied even to patterns that will disappear during later stages of
 simplification because they are not reachable (see <xref
 linkend="define-ref"/>) or because of <literal>notAllowed</literal>
 (see <xref linkend="notAllowed"/>).</para></note>

 <para>An <literal>except</literal> element that is a child of an
 <literal>anyName</literal> element must not have any
 <literal>anyName</literal> descendant elements. An
 <literal>except</literal> element that is a child of an
 <literal>nsName</literal> element must not have any
 <literal>nsName</literal> or <literal>anyName</literal> descendant
 elements.</para>

 <para>A <literal>name</literal> element that occurs as the first child
 of an <literal>attribute</literal> element or as the descendant of the
 first child of an <literal>attribute</literal> element and that has an
 <literal>ns</literal> attribute with value equal to the empty string
 must not have content equal to <literal>xmlns</literal>.</para>

 <para>A <literal>name</literal> or <literal>nsName</literal> element
 that occurs as the first child of an <literal>attribute</literal>
 element or as the descendant of the first child of an
 <literal>attribute</literal> element must not have an
 <literal>ns</literal> attribute with value
 <literal>http://www.w3.org/2000/xmlns</literal>.</para>

 <note><para>The <xref linkend="infoset"/> defines the namespace URI of
 namespace declaration attributes to be
 <literal>http://www.w3.org/2000/xmlns</literal>.</para></note>

 <para>A <literal>data</literal> or <literal>value</literal> element
 must be correct in its use of datatypes. Specifically, the
 <literal>type</literal> attribute must identify a datatype within the
 datatype library identified by the value of the
 <literal>datatypeLibrary</literal> attribute.  For a
 <literal>data</literal> element, the parameter list must be one that
 is allowed by the datatype (see <xref
 linkend="data-pattern"/>).</para>

 </section>

 <section>
 <title><literal>combine</literal> attribute</title>

 <para>For each <literal>grammar</literal> element, all
 <literal>define</literal> elements with the same name are combined
 together.  For any name, there must not be more than one
 <literal>define</literal> element with that name that does not have a
 <literal>combine</literal> attribute.  For any name, if there is a
 <literal>define</literal> element with that name that has a
 <literal>combine</literal> attribute with the value
 <literal>choice</literal>, then there must not also be a
 <literal>define</literal> element with that name that has a
 <literal>combine</literal> attribute with the value
 <literal>interleave</literal>. Thus, for any name, if there is more
 than one <literal>define</literal> element with that name, then there
 is a unique value for the <literal>combine</literal> attribute for
 that name.  After determining this unique value, the
 <literal>combine</literal> attributes are removed.  A pair of
 definitions</para>

 <programlisting>&lt;define name="<replaceable>n</replaceable>"&gt;
   <replaceable>p1</replaceable>
 &lt;/define>
 &lt;define name="<replaceable>n</replaceable>"&gt;
   <replaceable>p2</replaceable>
 &lt;/define></programlisting>

 <para>is combined into</para>

 <programlisting>&lt;define name="<replaceable>n</replaceable>">
   &lt;<replaceable>c</replaceable>&gt;
     <replaceable>p1</replaceable>
     <replaceable>p2</replaceable>
   &lt;/<replaceable>c</replaceable>&gt;
 &lt;/define></programlisting>

 <para>where <replaceable>c</replaceable> is the value of the
 <literal>combine</literal> attribute. Pairs of definitions are
 combined until there is exactly one <literal>define</literal> element
 for each name.</para>

 <para>Similarly, for each <literal>grammar</literal> element all
 <literal>start</literal> elements are combined together.  There must
 not be more than one <literal>start</literal> element that does not
 have a <literal>combine</literal> attribute.  If there is a
 <literal>start</literal> element that has a <literal>combine</literal>
 attribute with the value <literal>choice</literal>, there must not
 also be a <literal>start</literal> element that has a
 <literal>combine</literal> attribute with the value
 <literal>interleave</literal>.</para>

 </section>

 <section>
 <title><literal>grammar</literal> element</title>

 <para>In this rule, the schema is transformed so that its top-level
 element is <literal>grammar</literal> and so that it has no other
 <literal>grammar</literal> elements.</para>

 <para>Define the <firstterm>in-scope grammar</firstterm> for an
 element to be the nearest ancestor <literal>grammar</literal> element.  A
 <literal>ref</literal> element <firstterm>refers to</firstterm> a
 <literal>define</literal> element if the value of their
 <literal>name</literal> attributes is the same and their in-scope
 grammars are the same.  A <literal>parentRef</literal> element
 <firstterm>refers to</firstterm> a <literal>define</literal> element
 if the value of their <literal>name</literal> attributes is the same
 and the in-scope grammar of the in-scope grammar of the
 <literal>parentRef</literal> element is the same as the in-scope
 grammar of the <literal>define</literal> element. Every
 <literal>ref</literal> or <literal>parentRef</literal> element must
 refer to a <literal>define</literal> element.  A
 <literal>grammar</literal> must have a <literal>start</literal> child
 element.</para>

 <para>First, transform the top-level pattern
 <replaceable>p</replaceable> into
 <literal>&lt;grammar>&lt;start><replaceable>p</replaceable>&lt;/start>&lt;/grammar></literal>.
 Next, rename <literal>define</literal> elements so that no two
 <literal>define</literal> elements anywhere in the schema have the
 same name.  To rename a <literal>define</literal> element, change the
 value of its <literal>name</literal> attribute and change the value of
 the <literal>name</literal> attribute of all <literal>ref</literal>
 and <literal>parentRef</literal> elements that refer to that
 <literal>define</literal> element. Next, move all
 <literal>define</literal> elements to be children of the top-level
 <literal>grammar</literal> element, replace each nested
 <literal>grammar</literal> element by the child of its
 <literal>start</literal> element and rename each
 <literal>parentRef</literal> element to <literal>ref</literal>.</para>

 </section>


 <section id="define-ref">
 <title><literal>define</literal> and <literal>ref</literal> elements</title>

 <para>In this rule, the grammar is transformed so that every
 <literal>element</literal> element is the child of a
 <literal>define</literal> element, and the child of every
 <literal>define</literal> element is an <literal>element</literal>
 element.</para>

 <para>First, remove any <literal>define</literal> element that is not
 <firstterm>reachable</firstterm>.  A <literal>define</literal> element
 is reachable if there is reachable <literal>ref</literal> element
 referring to it.  A <literal>ref</literal> element is reachable if it
 is the descendant of the <literal>start</literal> element or of a
 reachable <literal>define</literal> element. Now, for
 each <literal>element</literal> element that is not the child of a
 <literal>define</literal> element, add a <literal>define</literal>
 element to the <literal>grammar</literal> element, and replace the
 <literal>element</literal> element by a <literal>ref</literal> element
 referring to the added <literal>define</literal> element. The value of
 the <literal>name</literal> attribute of the added
 <literal>define</literal> element must be different from value of the
 <literal>name</literal> attribute of all other
 <literal>define</literal> elements. The child of the added
 <literal>define</literal> element is the <literal>element</literal>
 element.</para>

 <para>Define a <literal>ref</literal> element to be
 <firstterm>expandable</firstterm> if it refers to a
 <literal>define</literal> element whose child is not an
 <literal>element</literal> element.  For each <literal>ref</literal>
 element that is expandable and is a descendant of a
 <literal>start</literal> element or an <literal>element</literal>
 element, expand it by replacing the <literal>ref</literal> element by
 the child of the <literal>define</literal> element to which it refers and
 then recursively expanding any expandable <literal>ref</literal>
 elements in this replacement.  This must not result in a loop.
 In other words expanding the replacement of a
 <literal>ref</literal> element having a <literal>name</literal> with
 value <replaceable>n</replaceable> must not require the expansion of
 <literal>ref</literal> element also having a <literal>name</literal>
 with value <replaceable>n</replaceable>.  Finally, remove any
 <literal>define</literal> element whose child is not an
 <literal>element</literal> element.</para>

 </section>

 <section id="notAllowed">
 <title><literal>notAllowed</literal> element</title>

 <para>In this rule, the grammar is transformed so that a
 <literal>notAllowed</literal> element occurs only as the child of
 a <literal>start</literal> or <literal>element</literal> element.  An
 <literal>attribute</literal>, <literal>list</literal>,
 <literal>group</literal>, <literal>interleave</literal>,
 or <literal>oneOrMore</literal> element that has a
 <literal>notAllowed</literal> child element is transformed into a
 <literal>notAllowed</literal> element.  A <literal>choice</literal>
 element that has two <literal>notAllowed</literal> child elements is
 transformed into a <literal>notAllowed</literal> element.  A
 <literal>choice</literal> element that has one
 <literal>notAllowed</literal> child element is transformed into its
 other child element. An <literal>except</literal> element that has a
 <literal>notAllowed</literal> child element is removed.
 The preceding transformations are applied
 repeatedly until none of them is applicable any more.
 Any <literal>define</literal> element that is no longer reachable
 is removed.</para>

 </section>

 <section>
 <title><literal>empty</literal> element</title>

 <para>In this rule, the grammar is transformed so that an
 <literal>empty</literal> element does not occur as a child of a
 <literal>group</literal>, <literal>interleave</literal>, or
 <literal>oneOrMore</literal> element or as the second child of
 a <literal>choice</literal> element. A <literal>group</literal>,
 <literal>interleave</literal> or <literal>choice</literal> element
 that has two <literal>empty</literal> child elements is transformed
 into an <literal>empty</literal> element.  A <literal>group</literal>
 or <literal>interleave</literal> element that has one
 <literal>empty</literal> child element is transformed into its other
 child element.  A <literal>choice</literal> element whose
 second child element is an <literal>empty</literal> element is
 transformed by interchanging its two child elements.  A
 <literal>oneOrMore</literal> element that has an
 <literal>empty</literal> child element is transformed into an
 <literal>empty</literal> element. The preceding transformations are applied
 repeatedly until none of them is applicable any more.</para>

 </section>

 </section>

 <section id="simple-syntax">
 <title>Simple syntax</title>

 <para>After applying all the rules in <xref
 linkend="simplification"/>, the schema will match the following
 grammar:</para>

 <grammarref src="simple.rng"/>

 <para>With this grammar, no elements or attributes are allowed other
 than those explicitly shown.</para>

 <section id="simple-syntax-example">
 <title>Example</title>

 <para>The following is an example of how the schema in <xref
 linkend="full-syntax-example"/> can be transformed into the simple
 syntax:</para>

 <programlisting><![CDATA[<?xml version="1.0"?>
 <grammar xmlns="http://relaxng.org/ns/structure/1.0">
   <start>
     <ref name="foo.element"/>
   </start>

   <define name="foo.element">
     <element>
       <name ns="">foo</name>
       <group>
         <ref name="bar1.element"/>
         <ref name="bar2.element"/>
       </group>
     </element>
   </define>

   <define name="bar1.element">
     <element>
       <name ns="http://www.example.com/n1">bar1</name>
       <empty/>
     </element>
   </define>

   <define name="bar2.element">
     <element>
       <name ns="http://www.example.com/n2">bar2</name>
       <empty/>
     </element>
   </define>
 </grammar>]]></programlisting>

 <note><para>Strictly speaking, the result of simplification is an
 instance of the data model rather than an XML document.  For
 convenience, we use an XML document to represent an instance of the
 data model.</para></note>

 </section>

 </section>

 <section id="semantics">
 <title>Semantics</title>

 <para>In this section, we define the semantics of a correct RELAX NG
 schema that has been transformed into the simple syntax.  The
 semantics of a RELAX NG schema consist of a specification of what XML
 documents are valid with respect to that schema.  The semantics are
 described formally.  The formalism uses axioms and inference rules.
 Axioms are propositions that are provable unconditionally.  An
 inference rule consists of one or more antecedents and exactly one
 consequent.  An antecedent is either positive or negative.  If all the
 positive antecedents of an inference rule are provable and none of the
 negative antecedents are provable, then the consequent of the
 inference rule is provable. An XML document is valid with respect to a
 RELAX NG schema if and only if the proposition that it is valid is
 provable in the formalism specified in this section.</para>

 <note><para>This kind of formalism is similar to a proof system.
 However, a traditional proof system only has positive
 antecedents.</para></note>

 <para>The notation for inference rules separates the antecedents from
 the consequent by a horizontal line: the antecedents are above the
 line; the consequent is below the line.  If an antecedent is of the
 form not(<replaceable>p</replaceable>), then it is a negative
 antecedent; otherwise, it is a positive antecedent.  Both axioms and
 inferences
 rules may use variables.  A variable has a name and optionally a
 subscript.  The name of a variable is italicized.  Each variable has a
 range that is determined by its name.  Axioms and inference rules are
 implicitly universally quantified over the variables they contain.  We
 explain this further below.</para>

 <para>The possibility that an inference rule or axiom may contain more
 than one occurrence of a particular variable requires that an identity
 relation be defined on each kind of object over which a variable can
 range.  The identity relation for all kinds of object is value-based.
 Two objects of a particular kind are identical if the constituents of
 the objects are identical.  For example, two attributes are considered
 the same if they have the same name and the same value. Two characters
 are identical if their Unicode character codes are the same.</para>

 <section id="name-classes">
 <title>Name classes</title>

 <para>The main semantic concept for name classes is that of a name
 belonging to a name class. A name class is an element that matches the
 production nameClass. A name is as defined in <xref
 linkend="data-model"/>: it consists of a namespace URI and a local
 name.</para>

 <para>We use the following notation:</para>

 <variablelist>

 <varlistentry><term><p:var range="name"/></term><listitem><para>is a variable
 that ranges over names</para></listitem></varlistentry>

 <varlistentry><term><p:var range="nameClass"/></term><listitem><para>ranges over name classes</para></listitem></varlistentry>

 <varlistentry><term><p:judgement name="belongs">
       <p:var range="name"/>
       <p:var range="nameClass"/>
     </p:judgement></term><listitem><para>

 asserts that name <p:var range="name"/> is a member of name class <p:var range="nameClass"/>

 </para></listitem></varlistentry>

 </variablelist>

 <para>We are now ready for our first axiom, which is called "anyName
 1":</para>

 <p:proofSystem>
   <p:rule name="anyName 1">
     <p:judgement name="belongs">
       <p:var range="name"/>
       <p:element name="anyName"/>
     </p:judgement>
   </p:rule>
 </p:proofSystem>

 <para>This says for any name <p:var range="name"/>, <p:var
 range="name"/> belongs to the name class <p:element name="anyName"/>,
 in other words <p:element name="anyName"/> matches any name. Note the
 effect of the implicit universal quantification over the variables in
 the axiom: this is what makes the axiom apply for any name <p:var
 range="name"/>.</para>

 <para>Our first inference rule is almost as simple:</para>

 <p:proofSystem>
   <p:rule name="anyName 2">
     <p:not>
       <p:judgement name="belongs">
 	<p:var range="name"/>
 	<p:var range="nameClass"/>
       </p:judgement>
     </p:not>
     <p:judgement name="belongs">
       <p:var range="name"/>
       <p:element name="anyName">
         <p:element name="except">
   	  <p:var range="nameClass"/>
         </p:element>
       </p:element>
     </p:judgement>
   </p:rule>

 </p:proofSystem>

 <para>This says that for any name <p:var range="name"/>
 and for any name class 	<p:var range="nameClass"/>,
 if <p:var range="name"/> does not belong to <p:var range="nameClass"/>,
 then <p:var range="name"/> belongs to
       <p:element name="anyName">
         <p:element name="except">
   	  <p:var range="nameClass"/>
         </p:element>
       </p:element>. In other words,       <p:element name="anyName">
         <p:element name="except">
   	  <p:var range="nameClass"/>
         </p:element>
       </p:element> matches any name that does not match <p:var range="nameClass"/>.</para>

 <para>We now need the following additional notation:</para>

 <variablelist>

 <varlistentry><term><p:var range="ncname"/></term>

 <listitem><para>ranges over local names; a local name is a string that
 matches the NCName production of <xref linkend="xml-names"/>, that is,
 a name with no colons</para></listitem>
 </varlistentry>

 <varlistentry><term><p:var range="uri"/></term><listitem><para>ranges over URIs</para></listitem></varlistentry>

 <varlistentry>
 <term>
   <p:function name="name">
     <p:var range="uri"/>
     <p:var range="ncname"/>
   </p:function>
 </term>
 <listitem><para>constructs a name with URI <p:var range="uri"/> and local
 name <p:var range="ncname"/></para></listitem>
 </varlistentry>

 </variablelist>

 <para>The remaining axioms and inference rules for name classes are as
 follows:</para>

 <p:proofSystem>

   <p:rule name="nsName 1">
     <p:judgement name="belongs">
       <p:function name="name">
         <p:var range="uri"/>
         <p:var range="ncname"/>
       </p:function>
       <p:element name="nsName">
         <p:attribute name="ns">
           <p:var range="uri"/>
         </p:attribute>
       </p:element>
     </p:judgement>
   </p:rule>

   <p:rule name="nsName 2">
     <p:not>
       <p:judgement name="belongs">
 	<p:function name="name">
 	  <p:var range="uri"/>
 	  <p:var range="ncname"/>
 	</p:function>
 	<p:var range="nameClass"/>
       </p:judgement>
     </p:not>
     <p:judgement name="belongs">
       <p:function name="name">
         <p:var range="uri"/>
         <p:var range="ncname"/>
       </p:function>
       <p:element name="nsName">
         <p:attribute name="ns">
           <p:var range="uri"/>
         </p:attribute>
         <p:element name="except">
           <p:var range="nameClass"/>
         </p:element>
       </p:element>
     </p:judgement>
   </p:rule>

   <p:rule name="name">
     <p:judgement name="belongs">
       <p:function name="name">
         <p:var range="uri"/>
         <p:var range="ncname"/>
       </p:function>
       <p:element name="name">
         <p:attribute name="ns">
           <p:var range="uri"/>
         </p:attribute>
         <p:var range="ncname"/>
       </p:element>
     </p:judgement>
   </p:rule>

   <p:rule name="name choice 1">
     <p:judgement name="belongs">
       <p:var range="name"/>
       <p:var range="nameClass" sub="1"/>
     </p:judgement>
     <p:judgement name="belongs">
       <p:var range="name"/>
       <p:element name="choice">
         <p:var range="nameClass" sub="1"/>
         <p:var range="nameClass" sub="2"/>
       </p:element>
     </p:judgement>
   </p:rule>

   <p:rule name="name choice 2">
     <p:judgement name="belongs">
       <p:var range="name"/>
       <p:var range="nameClass" sub="2"/>
     </p:judgement>
     <p:judgement name="belongs">
       <p:var range="name"/>
       <p:element name="choice">
         <p:var range="nameClass" sub="1"/>
         <p:var range="nameClass" sub="2"/>
       </p:element>
     </p:judgement>
   </p:rule>

 </p:proofSystem>

 </section>


 <section>
 <title>Patterns</title>

 <para>The axioms and inference rules for patterns use the following
 notation:</para>

 <variablelist>

 <varlistentry><term><p:var range="context"/></term><listitem><para>ranges
 over contexts (as defined in <xref
 linkend="data-model"/>)</para></listitem></varlistentry>

 <varlistentry><term><p:var range="att"/></term><listitem><para>ranges over
 sets of attributes; a set with a single member
 is considered the same as that member</para></listitem></varlistentry>

 <varlistentry><term><p:var
 range="mixed"/></term><listitem><para>ranges over sequences of
 elements and strings; a sequence with a single member is considered
 the same as that member; the sequences ranged over by <p:var
 range="mixed"/> may contain consecutive strings and may contain strings
 that are empty; thus, there are sequences ranged over by <p:var
 range="mixed"/> that cannot occur as the children of an
 element</para></listitem></varlistentry>

 <varlistentry><term><p:var range="pattern"/></term><listitem><para>ranges
 over patterns (elements matching the pattern
 production)</para></listitem></varlistentry>

 <varlistentry><term><p:judgement name="match">
       <p:var range="context"/>
       <p:var range="att"/>
       <p:var range="mixed"/>
       <p:var range="pattern"/>
     </p:judgement></term><listitem><para>

 asserts that with respect to context <p:var range="context"/>, the
 attributes <p:var range="att"/> and the sequence of elements and
 strings <p:var range="mixed"/> matches the pattern <p:var
 range="pattern"/></para></listitem></varlistentry>

 </variablelist>

 <section id="choice-pattern">
 <title><literal>choice</literal> pattern</title>

 <para>The semantics of the <literal>choice</literal> pattern are as follows:</para>

 <p:proofSystem>
   <p:rule name="choice 1">

     <p:judgement name="match">
       <p:var range="context"/>
       <p:var range="att"/>
       <p:var range="mixed"/>
       <p:var range="pattern" sub="1"/>
     </p:judgement>

     <p:judgement name="match">
       <p:var range="context"/>
       <p:var range="att"/>
       <p:var range="mixed"/>
       <p:element name="choice">
 	<p:var range="pattern" sub="1"/>
 	<p:var range="pattern" sub="2"/>
       </p:element>
     </p:judgement>

   </p:rule>

   <p:rule name="choice 2">

     <p:judgement name="match">
       <p:var range="context"/>
       <p:var range="att"/>
       <p:var range="mixed"/>
       <p:var range="pattern" sub="2"/>
     </p:judgement>

     <p:judgement name="match">
       <p:var range="context"/>
       <p:var range="att"/>
       <p:var range="mixed"/>
       <p:element name="choice">
 	<p:var range="pattern" sub="1"/>
 	<p:var range="pattern" sub="2"/>
       </p:element>
     </p:judgement>

   </p:rule>


 </p:proofSystem>

 </section>

 <section>
 <title><literal>group</literal> pattern</title>

 <para>We use the following additional notation:</para>

 <variablelist>

 <varlistentry><term><p:function name="append">
 	<p:var range="mixed" sub="1"/>
 	<p:var range="mixed" sub="2"/>
       </p:function></term><listitem>
 <para>represents the concatenation of the sequences <p:var range="mixed" sub="1"/> and <p:var range="mixed" sub="2"/>

 </para></listitem></varlistentry>

 <varlistentry><term><p:function name="union">
 	<p:var range="att" sub="1"/>
 	<p:var range="att" sub="2"/>
       </p:function></term><listitem>
 <para>represents the union of <p:var range="att" sub="1"/>
 and <p:var range="att" sub="2"/></para>
 </listitem>
 </varlistentry>

 </variablelist>

 <para>The semantics of the <literal>group</literal> pattern are as follows:</para>

 <p:proofSystem>
   <p:rule name="group">

     <p:judgement name="match">
       <p:var range="context"/>
       <p:var range="att" sub="1"/>
       <p:var range="mixed" sub="1"/>
       <p:var range="pattern" sub="1"/>
     </p:judgement>

     <p:judgement name="match">
       <p:var range="context"/>
       <p:var range="att" sub="2"/>
       <p:var range="mixed" sub="2"/>
       <p:var range="pattern" sub="2"/>
     </p:judgement>

     <p:judgement name="match">
       <p:var range="context"/>
       <p:function name="union">
 	<p:var range="att" sub="1"/>
 	<p:var range="att" sub="2"/>
       </p:function>
       <p:function name="append">
 	<p:var range="mixed" sub="1"/>
 	<p:var range="mixed" sub="2"/>
       </p:function>
       <p:element name="group">
 	<p:var range="pattern" sub="1"/>
 	<p:var range="pattern" sub="2"/>
       </p:element>
     </p:judgement>

   </p:rule>

 </p:proofSystem>

 <note><para>The restriction in <xref linkend="attribute-restrictions"/>
 ensures that the set of attributes constructed in the consequent will
 not have multiple attributes with the same name.</para></note>

 </section>


 <section id="empty-pattern">
 <title><literal>empty</literal> pattern</title>

 <para>We use the following additional notation:</para>

 <variablelist>
 <varlistentry><term><p:function name="emptySequence"/></term><listitem><para>represents an empty sequence</para></listitem></varlistentry>

 <varlistentry><term><p:function name="emptySet"/></term><listitem><para>represents an empty set</para></listitem></varlistentry>

 </variablelist>

 <para>The semantics of the <literal>empty</literal> pattern are as follows:</para>

 <p:proofSystem>
   <p:rule name="empty">
     <p:judgement name="match">
       <p:var range="context"/>
       <p:function name="emptySet"/>
       <p:function name="emptySequence"/>
       <p:element name="empty"></p:element>
       <p:function name="emptySet"/>
       <p:function name="emptySet"/>
     </p:judgement>
   </p:rule>
 </p:proofSystem>

 </section>


 <section id="text-pattern">
 <title><literal>text</literal> pattern</title>

 <para>We use the following additional notation:</para>

 <variablelist>
 <varlistentry><term><p:var range="string"/></term><listitem><para>ranges
 over strings</para></listitem></varlistentry>
 </variablelist>

 <para>The semantics of the <literal>text</literal> pattern are as follows:</para>

 <p:proofSystem>
   <p:rule name="text 1">
     <p:judgement name="match">
       <p:var range="context"/>
       <p:function name="emptySet"/>
       <p:function name="emptySequence"/>
       <p:element name="text"></p:element>
       <p:function name="emptySet"/>
       <p:function name="emptySet"/>
     </p:judgement>
   </p:rule>

   <p:rule name="text 2">
     <p:judgement name="match">
       <p:var range="context"/>
       <p:function name="emptySet"/>
       <p:var range="mixed"/>
       <p:element name="text"></p:element>
       <p:function name="emptySet"/>
       <p:function name="emptySet"/>
     </p:judgement>
     <p:judgement name="match">
       <p:var range="context"/>
       <p:function name="emptySet"/>
       <p:function name="append">
         <p:var range="mixed"/>
         <p:var range="string"/>
       </p:function>
       <p:element name="text"></p:element>
       <p:function name="emptySet"/>
       <p:function name="emptySet"/>
     </p:judgement>
   </p:rule>

 </p:proofSystem>

 <para>The effect of the above rule is that a <literal>text</literal>
 element matches zero or more strings.</para>

 </section>


 <section>
 <title><literal>oneOrMore</literal> pattern</title>

 <para>We use the following additional notation:</para>

 <variablelist>
 <varlistentry><term><p:judgement name="disjoint">
       <p:var range="att" sub="1"/>
       <p:var range="att" sub="2"/>
     </p:judgement></term><listitem><para>
 asserts that there is no name that is
 the name of both an attribute in <p:var range="att" sub="1"/>
 and of an attribute in <p:var range="att" sub="2"/>
 </para></listitem></varlistentry>
 </variablelist>

 <para>The semantics of the <literal>oneOrMore</literal> pattern are as follows:</para>

 <p:proofSystem>
   <p:rule name="oneOrMore 1">
     <p:judgement name="match">
       <p:var range="context"/>
       <p:var range="att"/>
       <p:var range="mixed"/>
       <p:var range="pattern"/>
     </p:judgement>

     <p:judgement name="match">
       <p:var range="context"/>
       <p:var range="att"/>
       <p:var range="mixed"/>
       <p:element name="oneOrMore">
         <p:var range="pattern"/>
       </p:element>
     </p:judgement>
   </p:rule>

   <p:rule name="oneOrMore 2">
     <p:judgement name="match">
       <p:var range="context"/>
       <p:var range="att" sub="1"/>
       <p:var range="mixed" sub="1"/>
       <p:var range="pattern"/>
     </p:judgement>

     <p:judgement name="match">
       <p:var range="context"/>
       <p:var range="att" sub="2"/>
       <p:var range="mixed" sub="2"/>
       <p:element name="oneOrMore">
         <p:var range="pattern"/>
       </p:element>
     </p:judgement>

     <p:judgement name="disjoint">
       <p:var range="att" sub="1"/>
       <p:var range="att" sub="2"/>
     </p:judgement>

     <p:judgement name="match">
       <p:var range="context"/>
       <p:function name="union">
 	<p:var range="att" sub="1"/>
 	<p:var range="att" sub="2"/>
       </p:function>
       <p:function name="append">
 	<p:var range="mixed" sub="1"/>
 	<p:var range="mixed" sub="2"/>
       </p:function>
       <p:element name="oneOrMore">
         <p:var range="pattern"/>
       </p:element>
     </p:judgement>
   </p:rule>

 </p:proofSystem>

 </section>


 <section>
 <title><literal>interleave</literal> pattern</title>

 <para>We use the following additional notation:</para>

 <variablelist>
 <varlistentry><term><p:judgement name="interleave">
       <p:var range="mixed" sub="1"/>
       <p:var range="mixed" sub="2"/>
       <p:var range="mixed" sub="3"/>
     </p:judgement></term><listitem><para>

 asserts that <p:var range="mixed" sub="1"/>
 is an interleaving of <p:var range="mixed" sub="2"/>
 and <p:var range="mixed" sub="3"/>
 </para></listitem></varlistentry>

 </variablelist>

 <para>The semantics of interleaving are defined by the following rules.</para>


 <p:proofSystem>
   <p:rule name="interleaves 1">

     <p:judgement name="interleave">
       <p:function name="emptySequence"/>
       <p:function name="emptySequence"/>
       <p:function name="emptySequence"/>
     </p:judgement>

   </p:rule>

   <p:rule name="interleaves 2">

     <p:judgement name="interleave">
       <p:var range="mixed" sub="1"/>
       <p:var range="mixed" sub="2"/>
       <p:var range="mixed" sub="3"/>
     </p:judgement>

     <p:judgement name="interleave">
       <p:function name="append">
         <p:var range="mixed" sub="4"/>
         <p:var range="mixed" sub="1"/>
       </p:function>
       <p:function name="append">
         <p:var range="mixed" sub="4"/>
         <p:var range="mixed" sub="2"/>
       </p:function>
       <p:var range="mixed" sub="3"/>
     </p:judgement>

   </p:rule>

   <p:rule name="interleaves 3">

     <p:judgement name="interleave">
       <p:var range="mixed" sub="1"/>
       <p:var range="mixed" sub="2"/>
       <p:var range="mixed" sub="3"/>
     </p:judgement>

     <p:judgement name="interleave">
       <p:function name="append">
         <p:var range="mixed" sub="4"/>
         <p:var range="mixed" sub="1"/>
       </p:function>
       <p:var range="mixed" sub="2"/>
       <p:function name="append">
         <p:var range="mixed" sub="4"/>
         <p:var range="mixed" sub="3"/>
       </p:function>
     </p:judgement>

   </p:rule>

 </p:proofSystem>

 <para>For example, the interleavings of
 <literal><![CDATA[<a/><a/>]]></literal> and
 <literal><![CDATA[<b/>]]></literal> are
 <literal><![CDATA[<a/><a/><b/>]]></literal>,
 <literal><![CDATA[<a/><b/><a/>]]></literal>, and
 <literal><![CDATA[<b/><a/><a/>]]></literal>.</para>

 <para>The semantics of the <literal>interleave</literal> pattern are
 as follows:</para>

 <p:proofSystem>
   <p:rule name="interleave">

     <p:judgement name="match">
       <p:var range="context"/>
       <p:var range="att" sub="1"/>
       <p:var range="mixed" sub="1"/>
       <p:var range="pattern" sub="1"/>
     </p:judgement>

     <p:judgement name="match">
       <p:var range="context"/>
       <p:var range="att" sub="2"/>
       <p:var range="mixed" sub="2"/>
       <p:var range="pattern" sub="2"/>
     </p:judgement>

     <p:judgement name="interleave">
       <p:var range="mixed" sub="3"/>
       <p:var range="mixed" sub="1"/>
       <p:var range="mixed" sub="2"/>
     </p:judgement>


     <p:judgement name="match">
       <p:var range="context"/>
       <p:function name="union">
 	<p:var range="att" sub="1"/>
 	<p:var range="att" sub="2"/>
       </p:function>
       <p:var range="mixed" sub="3"/>
       <p:element name="interleave">
 	<p:var range="pattern" sub="1"/>
 	<p:var range="pattern" sub="2"/>
       </p:element>
     </p:judgement>

   </p:rule>

 </p:proofSystem>

 <note><para>The restriction in <xref linkend="attribute-restrictions"/>
 ensures that the set of attributes constructed in the consequent will
 not have multiple attributes with the same name.</para></note>

 </section>

 <section id="element-pattern">
 <title><literal>element</literal> and <literal>attribute</literal> pattern</title>

 <para>The value of an attribute is always a single string, which may
 be empty.  Thus, the empty sequence is not a possible attribute value.
 On the hand, the children of an element can be an empty sequence and
 cannot consist of an empty string.  In order to ensure that validation
 handles attributes and elements consistently, we introduce a variant
 of matching called <firstterm>weak matching</firstterm>.  Weak
 matching is used when matching the pattern for the value of an
 attribute or for the attributes and children of an element.  We use
 the following notation to define weak matching.</para>

 <variablelist>

 <varlistentry><term><p:function
 name="emptyString"/></term><listitem><para>represents an empty
 string</para></listitem></varlistentry>

 <varlistentry><term><p:var
 range="whiteSpace"/></term><listitem><para>ranges over the empty
 sequence and strings that consist entirely of
 whitespace</para></listitem></varlistentry>

 <varlistentry><term><p:judgement name="weakMatch">
       <p:var range="context"/>
       <p:var range="att"/>
       <p:var range="mixed"/>
       <p:var range="pattern"/>
     </p:judgement></term><listitem><para>

 asserts that with respect to context <p:var range="context"/>, the
 attributes <p:var range="att"/> and the sequence of elements and
 strings <p:var range="mixed"/> weakly matches the pattern <p:var
 range="pattern"/></para></listitem></varlistentry>

 </variablelist>

 <para>The semantics of weak matching are as follows:</para>

 <p:proofSystem>
   <p:rule name="weak match 1">
     <p:judgement name="match">
       <p:var range="context"/>
       <p:var range="att"/>
       <p:var range="mixed"/>
       <p:var range="pattern"/>
     </p:judgement>
     <p:judgement name="weakMatch">
       <p:var range="context"/>
       <p:var range="att"/>
       <p:var range="mixed"/>
       <p:var range="pattern"/>
     </p:judgement>
   </p:rule>
   <p:rule name="weak match 2">
     <p:judgement name="match">
       <p:var range="context"/>
       <p:var range="att"/>
       <p:function name="emptySequence"/>
       <p:var range="pattern"/>
     </p:judgement>
     <p:judgement name="weakMatch">
       <p:var range="context"/>
       <p:var range="att"/>
       <p:var range="whiteSpace"/>
       <p:var range="pattern"/>
     </p:judgement>
   </p:rule>
   <p:rule name="weak match 3">
     <p:judgement name="match">
       <p:var range="context"/>
       <p:var range="att"/>
       <p:function name="emptyString"/>
       <p:var range="pattern"/>
     </p:judgement>
     <p:judgement name="weakMatch">
       <p:var range="context"/>
       <p:var range="att"/>
       <p:function name="emptySequence"/>
       <p:var range="pattern"/>
     </p:judgement>
   </p:rule>
 </p:proofSystem>

 <para>We use the following additional notation:</para>

 <variablelist>

 <varlistentry><term><p:function name="attribute">
         <p:var range="name"/>
         <p:var range="string"/>
       </p:function></term><listitem><para>

 constructs an attribute with name <p:var range="name"/>
 and value <p:var range="string"/>
 </para></listitem></varlistentry>

 <varlistentry><term><p:function name="element">
 	<p:var range="name"/>
         <p:var range="context"/>
 	<p:var range="att"/>
 	<p:var range="mixed"/>
       </p:function></term><listitem><para>

 constructs an element with name <p:var range="name"/>,
 context <p:var range="context"/>,
 attributes <p:var range="att"/>
 and mixed sequence <p:var range="mixed"/> as children
 </para></listitem></varlistentry>

 <varlistentry><term><p:judgement name="okAsChildren">
       <p:var range="mixed"/>
     </p:judgement></term><listitem><para>

 asserts that the mixed sequence <p:var range="mixed"/> can occur as
 the children of an element: it does not contain any member that is an
 empty string, nor does it contain two consecutive members that are
 both strings</para></listitem></varlistentry>

 <varlistentry><term><p:judgement name="bind">
       <p:var range="ncname"/>
       <p:var range="nameClass"/>
       <p:var range="pattern"/>
     </p:judgement></term><listitem><para>

 asserts that the grammar contains
 <p:element name="define">
   <p:attribute name="name">
     <p:var range="ncname"/>
   </p:attribute>
   <p:element name="element">
      <p:var range="nameClass"/>
      <p:var range="pattern"/>
   </p:element>
 </p:element>
 </para></listitem></varlistentry>

 </variablelist>

 <para>The semantics of the <literal>attribute</literal> pattern are as follows:</para>

 <p:proofSystem>
   <p:rule name="attribute">

     <p:judgement name="weakMatch">
       <p:var range="context"/>
       <p:function name="emptySet"/>
       <p:var range="string"/>
       <p:var range="pattern"/>
     </p:judgement>

     <p:judgement name="belongs">
       <p:var range="name"/>
       <p:var range="nameClass"/>
     </p:judgement>

     <p:judgement name="match">
       <p:var range="context"/>
       <p:function name="attribute">
         <p:var range="name"/>
         <p:var range="string"/>
       </p:function>
       <p:function name="emptySequence"/>
       <p:element name="attribute">
         <p:var range="nameClass"/>
 	<p:var range="pattern"/>
       </p:element>
     </p:judgement>

   </p:rule>

 </p:proofSystem>

 <para>The semantics of the <literal>element</literal> pattern are as follows:</para>

 <p:proofSystem>
   <p:rule name="element">

     <p:judgement name="weakMatch">
       <p:var range="context" sub="1"/>
       <p:var range="att"/>
       <p:var range="mixed"/>
       <p:var range="pattern"/>
     </p:judgement>

     <p:judgement name="belongs">
       <p:var range="name"/>
       <p:var range="nameClass"/>
     </p:judgement>

     <p:judgement name="okAsChildren">
       <p:var range="mixed"/>
     </p:judgement>

     <p:judgement name="bind">
       <p:var range="ncname"/>
       <p:var range="nameClass"/>
       <p:var range="pattern"/>
     </p:judgement>

     <p:judgement name="match">
       <p:var range="context" sub="2"/>
       <p:function name="emptySet"/>
       <p:function name="append">
         <p:var range="whiteSpace" sub="1"/>
 	<p:function name="element">
 	  <p:var range="name"/>
 	  <p:var range="context" sub="1"/>
 	  <p:var range="att"/>
 	  <p:var range="mixed"/>
 	</p:function>
         <p:var range="whiteSpace" sub="2"/>
       </p:function>
       <p:element name="ref">
         <p:attribute name="name">
           <p:var range="ncname"/>
         </p:attribute>
       </p:element>
     </p:judgement>

   </p:rule>

 </p:proofSystem>


 </section>

 <section id="data-pattern">
 <title><literal>data</literal> and <literal>value</literal> pattern</title>

 <para>RELAX NG relies on datatype libraries to perform datatyping.
 A datatype library is identified by a URI.  A datatype within a
 datatype library is identified by an NCName.  A datatype library
 provides two services.</para>

 <itemizedlist>

 <listitem><para>It can determine whether a string is a legal
 representation of a datatype. This service accepts a list of zero or
 more parameters. For example, a string datatype might have a parameter
 specifying the length of a string.  The datatype library determines
 what parameters are applicable for each datatype.</para></listitem>

 <listitem><para>It can determine whether two strings represent the
 same value of a datatype.  This service does not have any
 parameters.</para></listitem>

 </itemizedlist>

 <para>Both services may make use of the context of a string.  For
 example, a datatype representing a QName would use the namespace
 map.</para>

 <para>We use the following additional notation:</para>

 <variablelist>
 <varlistentry><term><p:judgement name="datatypeAllows">
       <p:var range="uri"/>
       <p:var range="ncname"/>
       <p:var range="params"/>
       <p:var range="string"/>
       <p:var range="context"/>
     </p:judgement></term><listitem><para>

 asserts that in the datatype library identified by URI <p:var range="uri"/>, the string <p:var range="string"/> interpreted with
 context <p:var range="context"/> is a legal
 value of datatype <p:var range="ncname"/> with parameters <p:var range="params"/></para></listitem></varlistentry>

 <varlistentry><term><p:judgement name="datatypeEqual">
       <p:var range="uri"/>
       <p:var range="ncname"/>
       <p:var range="string" sub="1"/>
       <p:var range="context" sub="1"/>
       <p:var range="string" sub="2"/>
       <p:var range="context" sub="2"/>
     </p:judgement></term><listitem><para>

 asserts that in the datatype library identified by URI <p:var range="uri"/>, string <p:var range="string" sub="1"/> interpreted with
 context <p:var range="context" sub="1"/> represents the same value of
 the datatype <p:var range="ncname"/> as the string <p:var range="string" sub="2"/> interpreted in the context of <p:var range="context" sub="2"/>
 </para></listitem></varlistentry>

 <varlistentry><term><p:var range="params"/></term><listitem><para>ranges over sequences of parameters</para></listitem></varlistentry>

 <varlistentry><term><p:context>
      <p:var range="context"/>
    </p:context></term><listitem><para>

 within the start-tag of a pattern refers to the context
 of the pattern element
 </para></listitem></varlistentry>

 <varlistentry>
 <term>
   <p:function name="context">
      <p:var range="uri"/>
      <p:var range="context"/>
   </p:function>
 </term>
 <listitem><para>constructs a context which is the same as <p:var range="context"/>
 except that the default namespace is <p:var range="uri"/>; if <p:var
 range="uri"/> is the empty string, then there is no default namespace
 in the constructed context</para></listitem></varlistentry>

 </variablelist>

 <para>The datatypeEqual function must be reflexive, transitive
 and symmetric, that is, the following inference rules must hold:</para>

 <p:proofSystem>
   <p:rule name="datatypeEqual reflexive">
     <p:judgement name="datatypeAllows">
       <p:var range="uri"/>
       <p:var range="ncname"/>
       <p:var range="params"/>
       <p:var range="string"/>
       <p:var range="context"/>
     </p:judgement>
     <p:judgement name="datatypeEqual">
       <p:var range="uri"/>
       <p:var range="ncname"/>
       <p:var range="string"/>
       <p:var range="context"/>
       <p:var range="string"/>
       <p:var range="context"/>
     </p:judgement>
   </p:rule>
   <p:rule name="datatypeEqual transitive">
     <p:judgement name="datatypeEqual">
       <p:var range="uri"/>
       <p:var range="ncname"/>
       <p:var range="string" sub="1"/>
       <p:var range="context" sub="1"/>
       <p:var range="string" sub="2"/>
       <p:var range="context" sub="2"/>
     </p:judgement>
     <p:judgement name="datatypeEqual">
       <p:var range="uri"/>
       <p:var range="ncname"/>
       <p:var range="string" sub="2"/>
       <p:var range="context" sub="3"/>
       <p:var range="string" sub="3"/>
       <p:var range="context" sub="3"/>
     </p:judgement>
     <p:judgement name="datatypeEqual">
       <p:var range="uri"/>
       <p:var range="ncname"/>
       <p:var range="string" sub="1"/>
       <p:var range="context" sub="1"/>
       <p:var range="string" sub="3"/>
       <p:var range="context" sub="3"/>
     </p:judgement>
   </p:rule>
   <p:rule name="datatypeEqual symmetric">
     <p:judgement name="datatypeEqual">
       <p:var range="uri"/>
       <p:var range="ncname"/>
       <p:var range="string" sub="1"/>
       <p:var range="context" sub="1"/>
       <p:var range="string" sub="2"/>
       <p:var range="context" sub="2"/>
     </p:judgement>
     <p:judgement name="datatypeEqual">
       <p:var range="uri"/>
       <p:var range="ncname"/>
       <p:var range="string" sub="2"/>
       <p:var range="context" sub="2"/>
       <p:var range="string" sub="1"/>
       <p:var range="context" sub="1"/>
     </p:judgement>
   </p:rule>
 </p:proofSystem>

 <para>The semantics of the <literal>data</literal> and
 <literal>value</literal> patterns are as follows:</para>

 <p:proofSystem>
   <p:rule name="value">
     <p:judgement name="datatypeEqual">
       <p:var range="uri" sub="1"/>
       <p:var range="ncname"/>
       <p:var range="string" sub="1"/>
       <p:var range="context" sub="1"/>
       <p:var range="string" sub="2"/>
       <p:function name="context">
         <p:var range="uri" sub="2"/>
         <p:var range="context" sub="2"/>
       </p:function>
     </p:judgement>
     <p:judgement name="match">
       <p:var range="context" sub="1"/>
       <p:function name="emptySet"/>
       <p:var range="string" sub="1"/>
       <p:element name="value">
         <p:attribute name="datatypeLibrary">
           <p:var range="uri" sub="1"/>
         </p:attribute>
         <p:attribute name="type">
           <p:var range="ncname"/>
         </p:attribute>
         <p:attribute name="ns">
           <p:var range="uri" sub="2"/>
         </p:attribute>
         <p:context>
           <p:var range="context" sub="2"/>
         </p:context>
         <p:var range="string" sub="2"/>
       </p:element>
       <p:function name="emptySet"/>
       <p:function name="emptySet"/>
     </p:judgement>
   </p:rule>

   <p:rule name="data 1">
     <p:judgement name="datatypeAllows">
       <p:var range="uri"/>
       <p:var range="ncname"/>
       <p:var range="params"/>
       <p:var range="string"/>
       <p:var range="context"/>
     </p:judgement>
     <p:judgement name="match">
       <p:var range="context"/>
       <p:function name="emptySet"/>
       <p:var range="string"/>
       <p:element name="data">
         <p:attribute name="datatypeLibrary">
           <p:var range="uri"/>
         </p:attribute>
         <p:attribute name="type">
           <p:var range="ncname"/>
         </p:attribute>
         <p:var range="params"/>
       </p:element>
       <p:function name="emptySet"/>
       <p:function name="emptySet"/>
     </p:judgement>
   </p:rule>

   <p:rule name="data 2">
     <p:judgement name="datatypeAllows">
       <p:var range="uri"/>
       <p:var range="ncname"/>
       <p:var range="params"/>
       <p:var range="string"/>
       <p:var range="context"/>
     </p:judgement>
     <p:not>
       <p:judgement name="match">
 	<p:var range="context"/>
 	<p:var range="att"/>
 	<p:var range="string"/>
         <p:var range="pattern"/>
       </p:judgement>
     </p:not>
     <p:judgement name="match">
       <p:var range="context"/>
       <p:function name="emptySet"/>
       <p:var range="string"/>
       <p:element name="data">
         <p:attribute name="datatypeLibrary">
           <p:var range="uri"/>
         </p:attribute>
         <p:attribute name="type">
           <p:var range="ncname"/>
         </p:attribute>
         <p:var range="params"/>
         <p:element name="except">
           <p:var range="pattern"/>
         </p:element>
       </p:element>
       <p:function name="emptySet"/>
       <p:function name="emptySet"/>
     </p:judgement>
   </p:rule>

 </p:proofSystem>

 </section>

 <section id="built-in-datatype">
 <title>Built-in datatype library</title>

 <para>The empty URI identifies a special built-in datatype library.
 This provides two datatypes, <literal>string</literal> and
 <literal>token</literal>.  No parameters are allowed for either of
 these datatypes.</para>

 <variablelist>
 <varlistentry><term>
     <p:judgement name="equal">
       <p:var range="string" sub="1"/>
       <p:var range="string" sub="2"/>
     </p:judgement></term>
 <listitem><para>asserts that <p:var range="string" sub="1"/>
 and <p:var range="string" sub="2"/> are identical</para></listitem>
 </varlistentry>

 <varlistentry><term>
       <p:function name="normalizeWhiteSpace">
         <p:var range="string"/>
       </p:function>
 </term>
 <listitem><para>returns the string <p:var range="string"/>,
 with leading and trailing whitespace characters removed,
 and with each other maximal sequence of whitespace characters
 replaced by a single space character </para></listitem>
 </varlistentry>
 </variablelist>

 <para>The semantics of the two built-in datatypes are as
 follows:</para>

 <p:proofSystem>

   <p:rule name="string allows">
     <p:judgement name="datatypeAllows">
       <p:function name="emptyString"/>
       <p:string>string</p:string>
       <p:function name="emptySequence"/>
       <p:var range="string"/>
       <p:var range="context"/>
     </p:judgement>
   </p:rule>

   <p:rule name="string equal">
     <p:judgement name="datatypeEqual">
       <p:function name="emptyString"/>
       <p:string>string</p:string>
       <p:var range="string"/>
       <p:var range="context" sub="1"/>
       <p:var range="string"/>
       <p:var range="context" sub="2"/>
     </p:judgement>
   </p:rule>

   <p:rule name="token allows">
     <p:judgement name="datatypeAllows">
       <p:function name="emptyString"/>
       <p:string>token</p:string>
       <p:function name="emptySequence"/>
       <p:var range="string"/>
       <p:var range="context"/>
     </p:judgement>
   </p:rule>

   <p:rule name="token equal">
     <p:judgement name="equal">
       <p:function name="normalizeWhiteSpace">
         <p:var range="string" sub="1"/>
       </p:function>
       <p:function name="normalizeWhiteSpace">
         <p:var range="string" sub="2"/>
       </p:function>
     </p:judgement>
     <p:judgement name="datatypeEqual">
       <p:function name="emptyString"/>
       <p:string>token</p:string>
       <p:var range="string" sub="1"/>
       <p:var range="context" sub="1"/>
       <p:var range="string" sub="2"/>
       <p:var range="context" sub="2"/>
     </p:judgement>
   </p:rule>

 </p:proofSystem>

 </section>

 <section>
 <title><literal>list</literal> pattern</title>

 <para>We use the following additional notation:</para>

 <variablelist>
 <varlistentry><term><p:function name="split">
         <p:var range="string"/>
       </p:function></term><listitem><para>

 returns a sequence of strings one for each whitespace delimited token
 of <p:var range="string"/>; each string in the returned sequence will
 be non-empty and will not contain any
 whitespace</para></listitem></varlistentry>

 </variablelist>

 <para>The semantics of the <literal>list</literal> pattern are as follows:</para>

 <p:proofSystem>
   <p:rule name="list">

     <p:judgement name="match">
       <p:var range="context"/>
       <p:function name="emptySet"/>
       <p:function name="split">
         <p:var range="string"/>
       </p:function>
       <p:var range="pattern"/>
     </p:judgement>

     <p:judgement name="match">
       <p:var range="context"/>
       <p:function name="emptySet"/>
       <p:var range="string"/>
       <p:element name="list">
 	<p:var range="pattern"/>
       </p:element>
     </p:judgement>

   </p:rule>
 </p:proofSystem>

 <note><para>It is crucial in the above inference rule that the
 sequence that is matched against a pattern can contain consecutive
 strings.</para></note>

 </section>

 </section>

 <section id="validity">
 <title>Validity</title>

 <para>Now we can define when an element is valid with respect to a
 schema.  We use the following additional notation:</para>

 <variablelist>

 <varlistentry><term><p:var range="element"/></term><listitem><para>ranges over elements</para></listitem></varlistentry>

 <varlistentry><term><p:judgement name="valid">
       <p:var range="element"/>
     </p:judgement></term><listitem><para>

 asserts that the element <p:var range="element"/> is valid with
 respect to the grammar</para></listitem></varlistentry>

 <varlistentry><term><p:judgement name="start">
       <p:var range="pattern"/>
     </p:judgement></term><listitem><para>
 asserts that the grammar contains
 <p:element name="start"><p:var range="pattern"/> </p:element></para></listitem></varlistentry>

 </variablelist>

 <para>An element is valid if together with an empty set of attributes
 it matches the <literal>start</literal> pattern of the grammar.</para>

 <p:proofSystem>
   <p:rule name="valid">
     <p:judgement name="start">
       <p:var range="pattern"/>
     </p:judgement>
     <p:judgement name="match">
       <p:var range="context"/>
       <p:function name="emptySet"/>
       <p:var range="element"/>
       <p:var range="pattern"/>
     </p:judgement>
     <p:judgement name="valid">
       <p:var range="element"/>
     </p:judgement>
   </p:rule>


 </p:proofSystem>

 </section>

 <section>
 <title>Example</title>

 <para>Let <p:var range="element" sub="0"/> be</para>

 <p:formula>

 <p:function name="element">
   <p:function name="name">
     <p:function name="emptyString"/>
     <p:string>foo</p:string>
   </p:function>
   <p:var range="context" sub="0"/>
   <p:function name="emptySet"/>
   <p:var range="mixed"/>
 </p:function>

 </p:formula>

 <para>where <p:var range="mixed"/> is</para>

 <p:formula>
   <p:function name="append">
     <p:var range="element" sub="1"/>
     <p:var range="element" sub="2"/>
   </p:function>
 </p:formula>

 <para>and <p:var range="element" sub="1"/> is</para>

 <p:formula>
   <p:function name="element">
     <p:function name="name">
       <p:string>http://www.example.com/n1</p:string>
       <p:string>bar1</p:string>
     </p:function>
     <p:var range="context" sub="1"/>
     <p:function name="emptySet"/>
     <p:function name="emptySequence"/>
   </p:function>
 </p:formula>

 <para>and <p:var range="element" sub="2"/> is</para>

 <p:formula>
   <p:function name="element">
     <p:function name="name">
       <p:string>http://www.example.com/n2</p:string>
       <p:string>bar2</p:string>
     </p:function>
     <p:var range="context" sub="2"/>
     <p:function name="emptySet"/>
     <p:function name="emptySequence"/>
   </p:function>
 </p:formula>

 <para>Assuming appropriate definitions of <p:var range="context"
 sub="0"/>, <p:var range="context" sub="1"/> and <p:var range="context"
 sub="2"/>, this represents the document in <xref
 linkend="data-model-example"/>.</para>

 <para>We now show how <p:var range="element" sub="0"/> can be shown to
 be valid with respect to the schema in <xref
 linkend="simple-syntax-example"/>.  The schema is equivalent to the
 following propositions:</para>

 <p:formula>
   <p:judgement name="start">
     <p:element name="ref">
       <p:attribute name="name"><p:string>foo</p:string></p:attribute>
     </p:element>
   </p:judgement>
 </p:formula>

 <p:formula>
   <p:judgement name="bind">
     <p:string>foo.element</p:string>
     <p:element name="name">
       <p:attribute name="ns"><p:function name="emptyString"/></p:attribute>
       <p:string>foo</p:string>
     </p:element>
     <p:element name="group">
       <p:element name="ref">
 	<p:attribute name="name">
 	  <p:string>bar1</p:string>
 	</p:attribute>
       </p:element>
       <p:element name="ref">
 	<p:attribute name="name">
 	  <p:string>bar2</p:string>
 	</p:attribute>
       </p:element>
     </p:element>
   </p:judgement>
 </p:formula>

 <p:formula>
   <p:judgement name="bind">
     <p:string>bar1.element</p:string>
     <p:element name="name">
       <p:attribute name="ns">
 	<p:string>http://www.example.com/n1</p:string>
       </p:attribute>
       <p:string>bar1</p:string>
     </p:element>
     <p:element name="empty"/>
   </p:judgement>
 </p:formula>

 <p:formula>
   <p:judgement name="bind">
     <p:string>bar2.element</p:string>
     <p:element name="name">
       <p:attribute name="ns">
 	<p:string>http://www.example.com/n2</p:string>
       </p:attribute>
       <p:string>bar2</p:string>
     </p:element>
     <p:element name="empty"/>
   </p:judgement>
 </p:formula>


 <para>Let name class <p:var range="nameClass" sub="1"/> be</para>

 <p:formula>
   <p:element name="name">
     <p:attribute name="ns">
       <p:string>http://www.example.com/n1</p:string>
     </p:attribute>
     <p:string>bar1</p:string>
   </p:element>
 </p:formula>

 <para>and let <p:var range="nameClass" sub="2"/> be</para>

 <p:formula>
   <p:element name="name">
     <p:attribute name="ns">
       <p:string>http://www.example.com/n2</p:string>
     </p:attribute>
     <p:string>bar2</p:string>
   </p:element>
 </p:formula>

 <para>Then, by the inference rule (name) in <xref
 linkend="name-classes"/>, we have</para>

 <p:formula>
   <p:judgement name="belongs">
     <p:function name="name">
       <p:string>http://www.example.com/n1</p:string>
       <p:string>bar1</p:string>
     </p:function>
     <p:var range="nameClass" sub="1"/>
   </p:judgement>
 </p:formula>

 <para>and</para>

 <p:formula>
   <p:judgement name="belongs">
     <p:function name="name">
       <p:string>http://www.example.com/n2</p:string>
       <p:string>bar2</p:string>
     </p:function>
     <p:var range="nameClass" sub="2"/>
   </p:judgement>
 </p:formula>


 <para>By the inference rule (empty) in <xref linkend="empty-pattern"/>,
 we have</para>

 <p:formula>
   <p:judgement name="match">
     <p:var range="context" sub="1"/>
     <p:function name="emptySet"/>
     <p:function name="emptySequence"/>
     <p:element name="empty"></p:element>
   </p:judgement>
 </p:formula>

 <para>and</para>

 <p:formula>
   <p:judgement name="match">
     <p:var range="context" sub="2"/>
     <p:function name="emptySet"/>
     <p:function name="emptySequence"/>
     <p:element name="empty"></p:element>
   </p:judgement>
 </p:formula>

 <para>Thus by the inference rule (element) in <xref
 linkend="element-pattern"/>, we have</para>

 <p:formula>
   <p:judgement name="match">
     <p:var range="context" sub="0"/>
     <p:function name="emptySet"/>
     <p:var range="element" sub="1"/>
     <p:element name="ref">
       <p:attribute name="name">
         <p:string>bar1</p:string>
       </p:attribute>
     </p:element>
   </p:judgement>
 </p:formula>

 <para>Note that we have chosen <p:var
 range="context" sub="0"/>, since any context is allowed.</para>

 <para>Likewise, we have</para>

 <p:formula>
   <p:judgement name="match">
     <p:var range="context" sub="0"/>
     <p:function name="emptySet"/>
     <p:var range="element" sub="2"/>
     <p:element name="ref">
       <p:attribute name="name">
         <p:string>bar2</p:string>
       </p:attribute>
     </p:element>
   </p:judgement>
 </p:formula>

 <para>By the inference rule (group) in <xref
 linkend="choice-pattern"/>, we have</para>

 <p:formula>
   <p:judgement name="match">
     <p:var range="context" sub="0"/>
     <p:function name="emptySet"/>
     <p:function name="append">
       <p:var range="element" sub="1"/>
       <p:var range="element" sub="2"/>
     </p:function>
     <p:element name="group">
       <p:element name="ref">
         <p:attribute name="name">
           <p:string>bar1</p:string>
         </p:attribute>
       </p:element>
       <p:element name="ref">
         <p:attribute name="name">
           <p:string>bar2</p:string>
         </p:attribute>
       </p:element>
     </p:element>
   </p:judgement>
 </p:formula>

 <para>By the inference rule (element) in <xref
 linkend="element-pattern"/>, we have</para>

 <p:formula>
   <p:judgement name="match">
     <p:var range="context" sub="3"/>
     <p:function name="emptySet"/>
     <p:function name="element">
       <p:function name="name">
         <p:function name="emptyString"/>
         <p:string>foo</p:string>
       </p:function>
       <p:var range="context" sub="0"/>
       <p:function name="emptySet"/>
       <p:var range="mixed"/>
     </p:function>
     <p:element name="ref">
       <p:attribute name="name">
         <p:string>foo</p:string>
       </p:attribute>
     </p:element>
   </p:judgement>
 </p:formula>

 <para>Here <p:var range="context" sub="3"/> is an arbitrary
 context.</para>

 <para>Thus we can apply the inference rule (valid) in <xref
 linkend="validity"/> and obtain</para>

 <p:formula>
   <p:judgement name="valid">
     <p:var range="element" sub="0"/>
   </p:judgement>
 </p:formula>

 </section>

 </section>

 <section id="restriction">
 <title>Restrictions</title>

 <para>The following constraints are all checked after the grammar has
 been transformed to the simple form described in <xref
 linkend="simple-syntax"/>. The purpose of these restrictions is to
 catch user errors and to facilitate implementation.</para>

 <section id="contextual-restriction">
 <title>Contextual restrictions</title>

 <para>In this section we describe restrictions on where elements are
 allowed in the schema based on the names of the ancestor elements. We
 use the concept of a <firstterm>prohibited path</firstterm> to
 describe these restrictions. A path is a sequence of NCNames separated
 by <literal>/</literal> or <literal>//</literal>.</para>

 <itemizedlist>

 <listitem><para>An element matches a path
 <replaceable>x</replaceable>, where <replaceable>x</replaceable> is an
 NCName, if and only if the local name of the element is
 <replaceable>x</replaceable></para></listitem>

 <listitem><para>An element matches a path
 <replaceable>x</replaceable><literal>/</literal><replaceable>p</replaceable>,
 where <replaceable>x</replaceable> is an NCName and
 <replaceable>p</replaceable> is a path, if and only if the local name
 of the element is <replaceable>x</replaceable> and the element has a
 child that matches <replaceable>p</replaceable></para></listitem>

 <listitem><para>An element matches a path
 <replaceable>x</replaceable><literal>//</literal><replaceable>p</replaceable>,
 where <replaceable>x</replaceable> is an NCName and
 <replaceable>p</replaceable> is a path, if and only if the local name
 of the element is <replaceable>x</replaceable> and the element has a
 descendant that matches <replaceable>p</replaceable></para></listitem>

 </itemizedlist>

 <para>For example, the element</para>

 <programlisting><![CDATA[<foo>
   <bar>
     <baz/>
   </bar>
 </foo>]]></programlisting>

 <para>matches the paths <literal>foo</literal>,
 <literal>foo/bar</literal>, <literal>foo//bar</literal>,
 <literal>foo//baz</literal>, <literal>foo/bar/baz</literal>,
 <literal>foo/bar//baz</literal> and <literal>foo//bar/baz</literal>,
 but not <literal>foo/baz</literal> or
 <literal>foobar</literal>.</para>

 <para>A correct RELAX NG schema must be such that, after
 transformation to the simple form, it does not contain any element
 that matches a prohibited path.</para>

 <section>
 <title><literal>attribute</literal> pattern</title>

 <para>The following paths are prohibited:</para>

 <itemizedlist>
 <listitem><para><literal>attribute//ref</literal></para></listitem>
 <listitem><para><literal>attribute//attribute</literal></para></listitem>
 </itemizedlist>

 </section>

 <section>
 <title><literal>oneOrMore</literal> pattern</title>

 <para>The following paths are prohibited:</para>

 <itemizedlist>
 <listitem><para><literal>oneOrMore//group//attribute</literal></para></listitem>
 <listitem><para><literal>oneOrMore//interleave//attribute</literal></para></listitem>
 </itemizedlist>

 </section>

 <section id="list-restrictions">
 <title><literal>list</literal> pattern</title>

 <para>The following paths are prohibited:</para>

 <itemizedlist>
 <listitem><para><literal>list//list</literal></para></listitem>
 <listitem><para><literal>list//ref</literal></para></listitem>
 <listitem><para><literal>list//attribute</literal></para></listitem>
 <listitem><para><literal>list//text</literal></para></listitem>
 <listitem><para><literal>list//interleave</literal></para></listitem>
 </itemizedlist>
 </section>

 <section id="context-data-except">
 <title><literal>except</literal> in <literal>data</literal> pattern</title>

 <para>The following paths are prohibited:</para>

 <itemizedlist>
 <listitem><para><literal>data/except//attribute</literal></para></listitem>
 <listitem><para><literal>data/except//ref</literal></para></listitem>
 <listitem><para><literal>data/except//text</literal></para></listitem>
 <listitem><para><literal>data/except//list</literal></para></listitem>
 <listitem><para><literal>data/except//group</literal></para></listitem>
 <listitem><para><literal>data/except//interleave</literal></para></listitem>
 <listitem><para><literal>data/except//oneOrMore</literal></para></listitem>
 <listitem><para><literal>data/except//empty</literal></para></listitem>
 </itemizedlist>

 <note><para>This implies that an <literal>except</literal> element
 with a <literal>data</literal> parent can contain only
 <literal>data</literal>, <literal>value</literal> and
 <literal>choice</literal> elements.</para></note>

 </section>

 <section id="context-start">
 <title><literal>start</literal> element</title>

 <para>The following paths are prohibited:</para>

 <itemizedlist>
 <listitem><para><literal>start//attribute</literal></para></listitem>
 <listitem><para><literal>start//data</literal></para></listitem>
 <listitem><para><literal>start//value</literal></para></listitem>
 <listitem><para><literal>start//text</literal></para></listitem>
 <listitem><para><literal>start//list</literal></para></listitem>
 <listitem><para><literal>start//group</literal></para></listitem>
 <listitem><para><literal>start//interleave</literal></para></listitem>
 <listitem><para><literal>start//oneOrMore</literal></para></listitem>
 <listitem><para><literal>start//empty</literal></para></listitem>
 </itemizedlist>
 </section>

 </section>

 <section id="string-sequences">
 <title>String sequences</title>

 <para>RELAX NG does not allow a pattern such as:</para>

 <programlisting><![CDATA[<element name="foo">
   <group>
     <data type="int"/>
     <element name="bar">
       <empty/>
     </element>
   </group>
 </element>]]></programlisting>

 <para>Nor does it allow a pattern such as:</para>

 <programlisting><![CDATA[<element name="foo">
   <group>
     <data type="int"/>
     <text/>
   </group>
 </element>]]></programlisting>

 <para>More generally, if the pattern for the content of an element or
 attribute contains</para>

 <itemizedlist>

 <listitem><para>a pattern that can match a child
 (that is, an <literal>element</literal>, <literal>data</literal>,
 <literal>value</literal>, <literal>list</literal> or
 <literal>text</literal> pattern), and</para></listitem>

 <listitem><para>a pattern that matches a single string (that is, a
 <literal>data</literal>, <literal>value</literal> or
 <literal>list</literal> pattern),</para></listitem>

 </itemizedlist>

 <para>then the two patterns must be alternatives to each other.</para>

 <para>This rule does not apply to patterns occurring within a
 <literal>list</literal> pattern.</para>

 <para>To formalize this, we use the concept of a content-type.  A
 pattern that is allowable as the content of an element has one of
 three content-types: empty, complex and simple.  We use the following
 notation.</para>

 <variablelist>

 <varlistentry>
 <term><p:function name="empty"/></term>
 <listitem><para>returns the empty content-type</para></listitem>
 </varlistentry>

 <varlistentry>
 <term><p:function name="complex"/></term>
 <listitem><para>returns the complex content-type</para></listitem>
 </varlistentry>

 <varlistentry>
 <term><p:function name="simple"/></term>
 <listitem><para>returns the simple content-type</para></listitem>
 </varlistentry>

 <varlistentry><term><p:var range="contentType"/></term>
 <listitem><para>ranges over content-types</para></listitem>
 </varlistentry>

 <varlistentry><term>
   <p:judgement name="groupable">
     <p:var range="contentType" sub="1"/>
     <p:var range="contentType" sub="2"/>
   </p:judgement>
 </term>
 <listitem><para>asserts that the content-types <p:var
 range="contentType" sub="1"/> and <p:var range="contentType" sub="2"/>
 are groupable</para></listitem>
 </varlistentry>

 </variablelist>

 <para>The empty content-type is groupable with anything.  In addition,
 the complex content-type is groupable with the complex content-type. The
 following rules formalize this.</para>

 <p:proofSystem>
 <p:rule name="group empty 1">
   <p:judgement name="groupable">
     <p:function name="empty"/>
     <p:var range="contentType"/>
   </p:judgement>
 </p:rule>
 <p:rule name="group empty 2">
   <p:judgement name="groupable">
     <p:var range="contentType"/>
     <p:function name="empty"/>
   </p:judgement>
 </p:rule>
 <p:rule name="group complex">
   <p:judgement name="groupable">
     <p:function name="complex"/>
     <p:function name="complex"/>
   </p:judgement>
 </p:rule>
 </p:proofSystem>

 <para>Some patterns have a content-type. We use the following
 additional notation.</para>

 <variablelist>

 <varlistentry><term>
   <p:judgement name="contentType">
     <p:var range="pattern"/>
     <p:var range="contentType"/>
   </p:judgement>
 </term>
 <listitem><para>asserts that pattern <p:var range="pattern"/> has
 content-type <p:var range="contentType"/></para></listitem>
 </varlistentry>

 <varlistentry><term>
   <p:function name="max">
     <p:var range="contentType" sub="1"/>
     <p:var range="contentType" sub="2"/>
   </p:function>
 </term>
 <listitem><para>returns the maximum of <p:var range="contentType"
 sub="1"/> and <p:var range="contentType" sub="2"/> where the
 content-types in increasing order are <p:function name="empty"/>,
 <p:function name="complex"/>, <p:function
 name="simple"/></para></listitem>
 </varlistentry>

 </variablelist>

 <para>The following rules define when a pattern has a content-type and,
 if so, what it is.</para>

 <p:proofSystem>
 <p:rule name="value">
   <p:judgement name="contentType">
     <p:element name="value">
       <p:attribute name="datatypeLibrary">
 	<p:var range="uri" sub="1"/>
       </p:attribute>
       <p:attribute name="type">
 	<p:var range="ncname"/>
       </p:attribute>
       <p:attribute name="ns">
 	<p:var range="uri" sub="2"/>
       </p:attribute>
       <p:var range="string"/>
     </p:element>
     <p:function name="simple"/>
   </p:judgement>
 </p:rule>

 <p:rule name="data 1">
   <p:judgement name="contentType">
     <p:element name="data">
       <p:attribute name="datatypeLibrary">
 	<p:var range="uri"/>
       </p:attribute>
       <p:attribute name="type">
 	<p:var range="ncname"/>
       </p:attribute>
       <p:var range="params"/>
     </p:element>
     <p:function name="simple"/>
   </p:judgement>
 </p:rule>

 <p:rule name="data 2">
   <p:judgement name="contentType">
     <p:var range="pattern"/>
     <p:var range="contentType"/>
   </p:judgement>
   <p:judgement name="contentType">
     <p:element name="data">
       <p:attribute name="datatypeLibrary">
 	<p:var range="uri"/>
       </p:attribute>
       <p:attribute name="type">
 	<p:var range="ncname"/>
       </p:attribute>
       <p:var range="params"/>
       <p:element name="except">
         <p:var range="pattern"/>
       </p:element>
     </p:element>
     <p:function name="simple"/>
   </p:judgement>
 </p:rule>

 <p:rule name="list">
   <p:judgement name="contentType">
     <p:element name="list">
       <p:var range="pattern"/>
     </p:element>
     <p:function name="simple"/>
   </p:judgement>
 </p:rule>

 <p:rule name="text">
   <p:judgement name="contentType">
     <p:element name="text"/>
     <p:function name="complex"/>
   </p:judgement>
 </p:rule>

 <p:rule name="ref">
   <p:judgement name="contentType">
     <p:element name="ref">
       <p:attribute name="name">
 	<p:var range="ncname"/>
       </p:attribute>
     </p:element>
     <p:function name="complex"/>
   </p:judgement>
 </p:rule>

 <p:rule name="empty">
   <p:judgement name="contentType">
     <p:element name="empty"/>
     <p:function name="empty"/>
   </p:judgement>
 </p:rule>

 <p:rule name="attribute">
   <p:judgement name="contentType">
     <p:var range="pattern"/>
     <p:var range="contentType"/>
   </p:judgement>
   <p:judgement name="contentType">
     <p:element name="attribute">
       <p:var range="nameClass"/>
       <p:var range="pattern"/>
     </p:element>
     <p:function name="empty"/>
   </p:judgement>
 </p:rule>

 <p:rule name="group">
   <p:judgement name="contentType">
     <p:var range="pattern" sub="1"/>
     <p:var range="contentType" sub="1"/>
   </p:judgement>
   <p:judgement name="contentType">
     <p:var range="pattern" sub="2"/>
     <p:var range="contentType" sub="2"/>
   </p:judgement>
   <p:judgement name="groupable">
     <p:var range="contentType" sub="1"/>
     <p:var range="contentType" sub="2"/>
   </p:judgement>
   <p:judgement name="contentType">
     <p:element name="group">
       <p:var range="pattern" sub="1"/>
       <p:var range="pattern" sub="2"/>
     </p:element>
     <p:function name="max">
       <p:var range="contentType" sub="1"/>
       <p:var range="contentType" sub="2"/>
     </p:function>
   </p:judgement>
 </p:rule>

 <p:rule name="interleave">
   <p:judgement name="contentType">
     <p:var range="pattern" sub="1"/>
     <p:var range="contentType" sub="1"/>
   </p:judgement>
   <p:judgement name="contentType">
     <p:var range="pattern" sub="2"/>
     <p:var range="contentType" sub="2"/>
   </p:judgement>
   <p:judgement name="groupable">
     <p:var range="contentType" sub="1"/>
     <p:var range="contentType" sub="2"/>
   </p:judgement>
   <p:judgement name="contentType">
     <p:element name="interleave">
       <p:var range="pattern" sub="1"/>
       <p:var range="pattern" sub="2"/>
     </p:element>
     <p:function name="max">
       <p:var range="contentType" sub="1"/>
       <p:var range="contentType" sub="2"/>
     </p:function>
   </p:judgement>
 </p:rule>

 <p:rule name="oneOrMore">
   <p:judgement name="contentType">
     <p:var range="pattern"/>
     <p:var range="contentType"/>
   </p:judgement>
   <p:judgement name="groupable">
     <p:var range="contentType"/>
     <p:var range="contentType"/>
   </p:judgement>
   <p:judgement name="contentType">
     <p:element name="oneOrMore">
       <p:var range="pattern"/>
     </p:element>
     <p:var range="contentType"/>
   </p:judgement>
 </p:rule>

 <p:rule name="choice">
   <p:judgement name="contentType">
     <p:var range="pattern" sub="1"/>
     <p:var range="contentType" sub="1"/>
   </p:judgement>
   <p:judgement name="contentType">
     <p:var range="pattern" sub="2"/>
     <p:var range="contentType" sub="2"/>
   </p:judgement>
   <p:judgement name="contentType">
     <p:element name="choice">
       <p:var range="pattern" sub="1"/>
       <p:var range="pattern" sub="2"/>
     </p:element>
     <p:function name="max">
       <p:var range="contentType" sub="1"/>
       <p:var range="contentType" sub="2"/>
     </p:function>
   </p:judgement>
 </p:rule>

 </p:proofSystem>

 <note><para>The antecedent in the (data 2) rule above is in fact
 redundant because of the prohibited paths in <xref
 linkend="context-data-except"/>.</para></note>

 <para>Now we can describe the restriction. We use the following
 notation.</para>

 <variablelist>

 <varlistentry><term>
   <p:judgement name="incorrectSchema"/>
 </term>
 <listitem><para>asserts that the schema is incorrect</para></listitem>
 </varlistentry>

 </variablelist>

 <para>All patterns occurring as the content of an element pattern must
 have a content-type.</para>

 <p:proofSystem>

 <p:rule name="element">
   <p:judgement name="bind">
     <p:var range="ncname"/>
     <p:var range="nameClass"/>
     <p:var range="pattern"/>
   </p:judgement>
   <p:not>
     <p:judgement name="contentType">
       <p:var range="pattern"/>
       <p:var range="contentType"/>
     </p:judgement>
   </p:not>
   <p:judgement name="incorrectSchema"/>
 </p:rule>

 </p:proofSystem>

 </section>

 <section id="attribute-restrictions">
 <title>Restrictions on attributes</title>

 <para>Duplicate attributes are not allowed.  More precisely, for a
 pattern <literal>&lt;group> <replaceable>p1</replaceable>
 <replaceable>p2</replaceable> &lt;/group></literal> or
 <literal>&lt;interleave> <replaceable>p1</replaceable>
 <replaceable>p2</replaceable> &lt;/interleave></literal>, there must
 not be a name that belongs to both the name class of an
 <literal>attribute</literal> pattern occurring in
 <replaceable>p1</replaceable> and the name class of an
 <literal>attribute</literal> pattern occurring in
 <replaceable>p2</replaceable>. A pattern <replaceable>p1</replaceable>
 is defined to <firstterm>occur in</firstterm> a pattern
 <replaceable>p2</replaceable> if</para>

 <itemizedlist>

 <listitem><para><replaceable>p1</replaceable> is
 <replaceable>p2</replaceable>, or</para></listitem>

 <listitem><para><replaceable>p2</replaceable> is a
 <literal>choice</literal>, <literal>interleave</literal>,
 <literal>group</literal> or <literal>oneOrMore</literal> element and
 <replaceable>p1</replaceable> occurs in one or more children of
 <replaceable>p2</replaceable>.</para></listitem>

 </itemizedlist>

 <para>Attributes using infinite name classes must be repeated.  More
 precisely, an <literal>attribute</literal> element that has an
 <literal>anyName</literal> or <literal>nsName</literal> descendant
 element must have a <literal>oneOrMore</literal> ancestor
 element.</para>

 <note><para>This restriction is necessary for closure under
 negation.</para></note>

 </section>

 <section id="interleave-restrictions">
 <title>Restrictions on <literal>interleave</literal></title>

 <para>For a pattern <literal>&lt;interleave>
 <replaceable>p1</replaceable> <replaceable>p2</replaceable>
 &lt;/interleave></literal>,</para>

 <itemizedlist>

 <listitem><para>there must not be a name that belongs to both the name
 class of an <literal>element</literal> pattern referenced by a
 <literal>ref</literal> pattern occurring in
 <replaceable>p1</replaceable> and the name class of an
 <literal>element</literal> pattern referenced by a
 <literal>ref</literal> pattern occurring in
 <replaceable>p2</replaceable>, and</para></listitem>

 <listitem><para>a <literal>text</literal> pattern must not occur in
 both <replaceable>p1</replaceable> and
 <replaceable>p2</replaceable>.</para></listitem>

 </itemizedlist>

 <para><xref linkend="attribute-restrictions"/> defines when one
 pattern is considered to occur in another pattern.</para>

 </section>

 </section>

 <section id="conformance">
 <title>Conformance</title>

 <para>A conforming RELAX NG validator must be able to determine for
 any XML document whether it is a correct RELAX NG schema.  A
 conforming RELAX NG validator must be able to determine for any XML
 document and for any correct RELAX NG schema whether the document is
 valid with respect to the schema.</para>

 <para>However, the requirements in the preceding paragraph do not
 apply if the schema uses a datatype library that the validator does
 not support.  A conforming RELAX NG validator is only required to
 support the built-in datatype library described in <xref
 linkend="built-in-datatype"/>.  A validator that claims conformance to
 RELAX NG should document which datatype libraries it supports.  The
 requirements in the preceding paragraph also do not apply if the
 schema includes <literal>externalRef</literal> or
 <literal>include</literal> elements and the validator is unable to
 retrieve the resource identified by the URI or is unable to construct
 an element from the retrieved resource.  A validator that claims
 conformance to RELAX NG should document its capabilities for handling
 URI references.</para>

 </section>

 <appendix>
 <title>RELAX NG schema for RELAX NG</title>

 <rngref src="relaxng.rng"/>

 </appendix>

 <appendix>
 <title>Changes since version 0.9</title>

 <para>The changes in this version relative to version 0.9
 are as follows:</para>

 <itemizedlist>

 <listitem><para>in the namespace URI, <literal>0.9</literal> has been
 changed to <literal>1.0</literal></para></listitem>

 <listitem><para><literal>data/except//empty</literal> has been added
 as a prohibited path (see <xref
 linkend="context-data-except"/>)</para></listitem>

 <listitem><para><literal>start//empty</literal> has been added
 as a prohibited path (see <xref
 linkend="context-start"/>)</para></listitem>

 <listitem><para><xref linkend="number-child-elements"/> now specifies how a
 <literal>list</literal> element with more than one child element is
 transformed</para></listitem>

 <listitem><para><xref linkend="notAllowed"/> now specifies how a
 <literal>notAllowed</literal> element occurring in an
 <literal>except</literal> element is transformed</para></listitem>

 <listitem><para>although a relative URI is not allowed as the value of
 the <literal>ns</literal> and <literal>datatypeLibrary</literal>
 attributes, an empty string is allowed (see <xref
 linkend="full-syntax"/>)</para></listitem>

 <listitem><para>the removal of unreachable definitions in <xref
 linkend="define-ref"/> is now correctly specified</para></listitem>

 <listitem><para><xref linkend="notAllowed"/> now specifies that
 <literal>define</literal> elements that are no longer reachable are
 removed</para></listitem>

 <listitem><para><xref linkend="constraints"/> has been added; the
 restrictions on the contents of <literal>except</literal> in name
 classes that are now specified in the newly added section were
 previously specified in a subsection of <xref
 linkend="contextual-restriction"/>, which has been
 removed</para></listitem>

 <listitem><para>the treatment of element and attribute values that
 consist only of whitespace has been refined (see <xref
 linkend="element-pattern"/> and <xref
 linkend="data-pattern"/>)</para></listitem>

 <listitem><para>attributes with infinite name classes are now required
 to be repeated (see <xref
 linkend="attribute-restrictions"/>)</para></listitem>

 <listitem><para>restrictions have been imposed on
 <literal>interleave</literal> (see <xref
 linkend="interleave-restrictions"/>); <literal>list//interleave</literal>
 has been added as a prohibited path (see <xref
 linkend="list-restrictions"/>)</para></listitem>

 <listitem><para>some of the prohibited paths in <xref
 linkend="contextual-restriction"/> have been corrected to use
 <literal>ref</literal> rather than
 <literal>element</literal></para></listitem>

 <listitem><para>an error in the inference rule (text 1) in <xref
 linkend="text-pattern"/> has been corrected</para></listitem>

 <listitem><para>the value of the <literal>ns</literal> attribute is
 now unconstrained (see <xref
 linkend="full-syntax"/>)</para></listitem>

 </itemizedlist>

 </appendix>

 <appendix>
 <title>RELAX NG TC (Non-Normative)</title>

 <para>This specification was prepared and approved for publication by
 the RELAX NG TC. The current members of the TC are:</para>

 <itemizedlist>
 <listitem><para>Fabio Arciniegas</para></listitem>
 <listitem><para>James Clark</para></listitem>
 <listitem><para>Mike Fitzgerald</para></listitem>
 <listitem><para>KAWAGUCHI Kohsuke</para></listitem>
 <listitem><para>Josh Lubell</para></listitem>
 <listitem><para>MURATA Makoto</para></listitem>
 <listitem><para>Norman Walsh</para></listitem>
 <listitem><para>David Webber</para></listitem>
 </itemizedlist>

 </appendix>

 <bibliography><title>References</title>

 <bibliodiv><title>Normative</title>

 <bibliomixed id="xml-rec"><abbrev>XML 1.0</abbrev>Tim Bray,
 Jean Paoli, and
 C. M. Sperberg-McQueen, Eve Maler, editors.
 <citetitle><ulink url="http://www.w3.org/TR/REC-xml">Extensible Markup
 Language (XML) 1.0 Second Edition</ulink></citetitle>.
 W3C (World Wide Web Consortium), 2000.</bibliomixed>

 <bibliomixed id="xml-names"><abbrev>XML Namespaces</abbrev>Tim Bray,
 Dave Hollander,
 and Andrew Layman, editors.
 <citetitle><ulink url="http://www.w3.org/TR/REC-xml-names/">Namespaces in
 XML</ulink></citetitle>.
 W3C (World Wide Web Consortium), 1999.</bibliomixed>

 <bibliomixed id="xlink"><abbrev>XLink</abbrev>Steve DeRose, Eve Maler
 and David Orchard, editors.
 <citetitle><ulink url="http://www.w3.org/TR/xlink/">XML Linking
 Language (XLink) Version 1.0</ulink></citetitle>.
 W3C (World Wide Web Consortium), 2001.</bibliomixed>

 <bibliomixed id="infoset"><abbrev>XML Infoset</abbrev>John Cowan, Richard Tobin,
 editors.
 <citetitle><ulink url="http://www.w3.org/TR/xml-infoset/">XML
 Information Set</ulink></citetitle>.
 W3C (World Wide Web Consortium), 2001.</bibliomixed>

 <bibliomixed id="rfc2396"><abbrev>RFC 2396</abbrev>T. Berners-Lee, R. Fielding, L. Masinter.
 <citetitle><ulink url="http://www.ietf.org/rfc/rfc2396.txt" >RFC 2396:
 Uniform Resource Identifiers (URI): Generic
 Syntax</ulink></citetitle>.
 IETF (Internet Engineering Task Force). 1998.</bibliomixed>

 <bibliomixed id="rfc2732"><abbrev>RFC 2732</abbrev>R. Hinden, B. Carpenter, L. Masinter.
 <citetitle><ulink url="http://www.ietf.org/rfc/rfc2732.txt">RFC 2732: Format for Literal IPv6 Addresses in URL's</ulink></citetitle>.
 IETF (Internet Engineering Task Force), 1999.</bibliomixed>

 <bibliomixed id="rfc3023"><abbrev>RFC 3023</abbrev> M. Murata,
 S. St.Laurent, D. Kohn.  <citetitle><ulink
 url="http://www.ietf.org/rfc/rfc3023.txt">RFC 3023: XML Media
 Types</ulink></citetitle>. IETF (Internet Engineering Task Force),
 2001.</bibliomixed>

 </bibliodiv>

 <bibliodiv><title>Non-Normative</title>

 <bibliomixed id="xmlschema-2"><abbrev>W3C XML Schema Datatypes</abbrev>Paul V. Biron, Ashok Malhotra, editors.
 <citetitle><ulink url="http://www.w3.org/TR/xmlschema-2/">XML Schema Part 2: Datatypes</ulink></citetitle>.
 W3C (World Wide Web Consortium), 2001.</bibliomixed>

 <bibliomixed id="trex"><abbrev>TREX</abbrev>James Clark.
 <citetitle><ulink url="http://www.thaiopensource.com/trex/">TREX - Tree Regular Expressions for XML</ulink></citetitle>.
 Thai Open Source Software Center, 2001.</bibliomixed>

 <bibliomixed id="relax"><abbrev>RELAX</abbrev>MURATA Makoto.
 <citetitle><ulink url="http://www.xml.gr.jp/relax/">RELAX (Regular
 Language description for XML)</ulink></citetitle>.  INSTAC
 (Information Technology Research and Standardization Center), 2001.</bibliomixed>

 <bibliomixed id="xsfd"><abbrev>XML Schema Formal</abbrev>Allen Brown,
 Matthew Fuchs, Jonathan Robie, Philip Wadler, editors.
 <citetitle><ulink url="http://www.w3.org/TR/xmlschema-formal/">XML Schema: Formal Description</ulink></citetitle>.
 W3C (World Wide Web Consortium), 2001.</bibliomixed>

 <bibliomixed id="tutorial"><abbrev>Tutorial</abbrev>James Clark,
 Makoto MURATA, editors.  <citetitle><ulink
 url="http://www.oasis-open.org/committees/relax-ng/tutorial.html">RELAX
 NG Tutorial</ulink></citetitle>.  OASIS, 2001.</bibliomixed>

 </bibliodiv>

 </bibliography>

 </article>