## Re: [xsl] XPath expression to express: There must be an empty sequence

 Subject: Re: [xsl] XPath expression to express: There must be an empty sequence From: "Christoph Naber pentium120mhz@xxxxxxxxx" Date: Sun, 19 Nov 2017 19:47:59 -0000
Hello Roger,

I understand - taking your last question into account where you wanted to generate the sequences - that you want the XSLT rules to verify, if some set of sequences is a solution for the combinatorical problem:

```For the set S with m elements list the n-tuples for n := [0, m]
(https://en.wikipedia.org/wiki/Permutation#Permutations_with_repetition)```

The total number of "permutations with repetition" according to this requirement will be
sum(m^k) for k := 0 to m and m := count(element)

Hopefully the mathematical background helps you tackling the problem...

One straight solution based on this mathematical fact would be to check whether the are
"sum(m^k) for k := 0 to m and m := count(element)" different sequences.

```Best regards
Christoph Naber```

Am 19.11.2017 um 19:38 schrieb Costello, Roger L. costello@xxxxxxxxx:
Hi Folks,

I have a set:

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

Here are some sequences derived from the set:

```<sequences>
<sequence/>
<sequence>
<item>A</item>
</sequence>
<sequence>
<item>B</item>
</sequence>
<sequence>
<item>A</item>
<item>A</item>
</sequence>
<sequence>
<item>A</item>
<item>B</item>
</sequence>
<sequence>
<item>B</item>
<item>A</item>
</sequence>
<sequence>
<item>B</item>
<item>B</item>
</sequence>
</sequences>```

```Notice that:
- there is an empty sequence
- there is a sequence corresponding to each element of the set
- and there are other sequences (that I'm not concerned with for now)```

I want to create XPath expressions which express the rules that sequences must satisfy to be valid.

First rule: There must be an empty sequence. I expressed that rule with this XPath expression:

sequence[not(item)]

Assume that the root element, <sequences>, is the context node.

Is that the right way to express the rule? Is there a better XPath expression? By "better" I mean simpler, plainer, more transparent. I seek simplicity and clarity over efficiency and cleverness.

Second rule: There must be a singleton sequence corresponding to every element in the set. A "singleton sequence" is a <sequence> containing one <item>.

I expressed that rule with this XPath expression:

every \$element in \$set//element satisfies exists(sequence[(item = \$element) and not(item)])

Assume that \$set is a variable whose value is the set.

Is that the right way to express the rule? Is there a better XPath expression?

/Roger