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

["Christoph Naber pentium120mhz@xxxxxxxxx" <xsl-list-service@xxxxxxxxxxxxxxxxxxxxxx>]

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[2])])
>
> 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