[xsl] Generate sequences of the permutations of a set

["Costello, Roger L. costello@xxxxxxxxx" <xsl-list-service@xxxxxxxxxxxxxxxxxxxxxx>]

Hi Folks,

I want an XSLT program that generates sequences of the permutations of a set.

For example, here is a set containing 2 elements:

<set>
    <element>A</element>
    <element>B</element>
</set>

I want the XSLT to generate these sequences:

<sequences>
    <sequence/>
    <sequence>A</sequence>
    <sequence>B</sequence>
    <sequence>AA</sequence>
    <sequence>AB</sequence>
    <sequence>BA</sequence>
    <sequence>BB</sequence>
</sequences>

Let's take another example. Here is a set containing 3 elements:

<set>
    <element>A</element>
    <element>B</element>
    <element>C</element>
</set>

I want the XSLT to generate these sequences:

<sequences>
    <sequence/>
    <sequence>A</sequence>
    <sequence>B</sequence>
    <sequence>C</sequence>
    <sequence>AA</sequence>
    <sequence>AB</sequence>
    <sequence>AC</sequence>
    <sequence>BA</sequence>
    <sequence>BB</sequence>
    <sequence>BC</sequence>
    <sequence>CA</sequence>
    <sequence>CB</sequence>
    <sequence>CC</sequence>
    <sequence>AAA</sequence>
    <sequence>AAB</sequence>
    <sequence>AAC</sequence>
    <sequence>ABA</sequence>
    <sequence>ABB</sequence>
    <sequence>ABC</sequence>
    <sequence>ACA</sequence>
    <sequence>ACB</sequence>
    <sequence>ACC</sequence>
    <sequence>BAA</sequence>
    <sequence>BAB</sequence>
    <sequence>BAC</sequence>
    <sequence>BBA</sequence>
    <sequence>BBB</sequence>
    <sequence>BBC</sequence>
    <sequence>BCA</sequence>
    <sequence>BCB</sequence>
    <sequence>BCC</sequence>
    <sequence>CAA</sequence>
    <sequence>CAB</sequence>
    <sequence>CAC</sequence>
    <sequence>CBA</sequence>
    <sequence>CBB</sequence>
    <sequence>CBC</sequence>
    <sequence>CCA</sequence>
    <sequence>CCB</sequence>
    <sequence>CCC</sequence>
</sequences>

I desire all the sequences -- including the empty sequence -- of all the
permutations, up to the length of the set.

I have written (below) an XSLT program to do this. But, I have two questions:

1. Is it correct? Do you see any errors in my XSLT implementation?

2. I seek plainness and transparency over efficiency and cleverness. I want
the XSLT to be super-super-easy to understand. It must use meaningful names.
Can you suggest ways to make the XSLT more plain, more transparent, more
easily understandable?  /Roger

<xsl:stylesheet xmlns:xsl="http://www.w3.org/1999/XSL/Transform";
    xmlns:xs="http://www.w3.org/2001/XMLSchema";
    exclude-result-prefixes="xs generate"
    xmlns:generate="function"
    version="2.0">

    <xsl:output method="xml" />

    <xsl:variable name="empty" select="''" as="xs:string"/>
    <xsl:variable name="one" select="1" as="xs:integer"/>
    <xsl:variable name="set_elements" select="/set/element" as="xs:string+"/>

    <xsl:template match="/">
        <sequences>
            <sequence/>
            <xsl:sequence select="generate:sequences_of_length_n($empty,
$one)" />
        </sequences>
    </xsl:template>

    <xsl:function name="generate:sequences_of_length_n"
as="element(sequence)*">
        <xsl:param name="sequences_of_length_n_minus_1" as="xs:string*" />
        <xsl:param name="n" as="xs:integer" />

        <xsl:if test="$n le count($set_elements)">
            <xsl:variable name="sequences_of_length_n" as="xs:string+">
                <xsl:for-each select="$sequences_of_length_n_minus_1">
                    <xsl:variable name="a_sequence_of_length_n_minus_1"
select="." as="xs:string"/>
                    <xsl:for-each select="$set_elements">
                        <xsl:variable name="a_set_element" select="."
as="xs:string"/>
                        <xsl:sequence
select="concat($a_sequence_of_length_n_minus_1, $a_set_element)" />
                    </xsl:for-each>
                </xsl:for-each>
            </xsl:variable>
            <xsl:for-each select="$sequences_of_length_n">
                <sequence><xsl:value-of select="."/></sequence>
            </xsl:for-each>
            <xsl:sequence
select="generate:sequences_of_length_n($sequences_of_length_n, $n+1)" />
        </xsl:if>
    </xsl:function>
</xsl:stylesheet>