Xpath to detect whether children are interleaved - xslt

Question

I need an XSLT 1.0 test expression that will indicate whether the elements of the current node t are perfectly interleaved, like this
<t>
<cat />
<dog />
<horse />
<cat />
<dog />
<horse />
</t>
or has some other order, such as
<t>
<cat />
<cat />
<dog />
<dog />
<horse />
<horse />
</t>
or
<t>
<cat />
<dog />
<cat/>
<horse/>
<cat/>
<horse />
</t>
If the first, there can be any number of such tuples. If the second, there can be any number (including zero) of each kind of child and in any order.
The special case of one cat, one dog, one horse can test true or false, whichever makes the algorithm easier.
I do know beforehand the names of the three elements.
EDIT. At Dimitre's request, let me try saying it another, maybe simpler, way.
The context node has any number of children, but each child has one of only three names. Before processing these children, I need to test whether they appear in a repeating pattern, such as A B C A B C A B C, or C A B C A B, or any other combination of repeated triplets, triplets in which each of the three appears once (A B C A B C tests true, A B B A B B tests false).

Answer 1

Provided that the order of the tuple is fixed, this template will return true for all cases where there are 1 or more tuples and false otherwise:
<xsl:template match="t">
<xsl:sequence
select="
count(*) gt 2 and
count(*) = count(*[
self::cat and position() mod 3 = 1 or
self::dog and position() mod 3 = 2 or
self::horse and position() mod 3 = 0])"/>
</xsl:template>
If the order of the tuple can vary, this template will return true for all cases where there are 1 or more tuples that are ordered the same as the first instance of the tuple and false otherwise
<xsl:template match="t">
<xsl:variable name="cat.pos" select="(count(cat[1]/preceding-sibling::*) + 1) mod 3"/>
<xsl:variable name="dog.pos" select="(count(dog[1]/preceding-sibling::*) + 1) mod 3"/>
<xsl:variable name="horse.pos" select="(count(horse[1]/preceding-sibling::*) + 1) mod 3"/>
<xsl:sequence
select="
count(*) gt 2 and
count(*) = count(*[
self::cat and position() mod 3 = $cat.pos or
self::dog and position() mod 3 = $dog.pos or
self::horse and position() mod 3 = $horse.pos])"/>
</xsl:template>

Answer 2

test="name(*[last()])=name(*[3])
and name(*[1])!=name(*[2])
and name(*[2])!=name(*[3])
and name(*[1])!=name(*[3])
and not(*[position() > 3][name()!=name(preceding-sibling::*[3])])"
returns true if the interleave is perfect (or if there are only three items).
Edits: Added the first condition to ensure the final tuple is complete and the three middle conditions to ensure the repeated tuple includes each of the three items (i.e., does not include duplicates).