The pipeline
<p:declare-step xmlns:html="http://www.w3.org/1999/xhtml" xmlns:p="http://www.w3.org/ns/xproc" version="3.0">
<p:output port="result"/>
<p:add-attribute match="//html:*" attribute-value="html" attribute-name="class">
<p:with-input>
<html xmlns="http://www.w3.org/1999/xhtml">
<body>
<h1>Header</h1>
<p>Some text with
<em>emphazised</em> phrase.</p>
<ul>
<li>item</li>
<li>
<p>item</p>
</li>
<li>
<p>
<b>bold</b>
</p>
</li>
</ul>
</body>
</html>
</p:with-input>
</p:add-attribute>
</p:declare-step>
Schematron validation
<s:schema xmlns:s="http://purl.oclc.org/dsdl/schematron" queryBinding="xslt2">
<s:ns prefix="html" uri="http://www.w3.org/1999/xhtml"/>
<s:pattern>
<s:rule context="/">
<s:assert test="html:html">The document root is not "html:html".</s:assert>
<s:assert test="html:html/@class='html'">Element "html:html" does not have @class='html'.</s:assert>
<s:assert test="html:html/html:body/@class='html'">Element "html/body" does not have @class='html'.</s:assert>
<s:assert test="html:html/html:body/html:h1/@class='html'">Element "html/body/h1" does not have @class='html'.</s:assert>
<s:assert test="html:html/html:body/html:p/@class='html'">Element "html/body/p" does not have @class='html'.</s:assert>
<s:assert test="html:html/html:body/html:p/html:em/@class='html'">Element "html/body/p/em" does not have @class='html'.</s:assert>
<s:assert test="html:html/html:body/html:ul/@class='html'">Element "html/body/ul" does not have @class='html'.</s:assert>
<s:assert test="html:html/html:body/html:ul/html:li/@class='html'">Element "html/body/ul/li" does not have @class='html'.</s:assert>
<s:assert test="html:html/html:body/html:ul/html:li[2]/html:p/@class='html'">Element "html/body/ul/li[2]/p" does not have @class='html'.</s:assert>
<s:assert test="html:html/html:body/html:ul/html:li[3]/html:p/@class='html'">Element "html/body/ul/li[3]/p" does not have @class='html'.</s:assert>
<s:assert test="html:html/html:body/html:ul/html:li[3]/html:p//html:b/@class='html'">Element "html/body/ul/li[3]/p/b" does not have @class='html'.</s:assert>
</s:rule>
</s:pattern>
</s:schema>
