Okay so for those that are interested, here is the solution that I ended up with:
1) I wrote my own XPath 2 parser as I wanted a simplified AST to start operating from. The project I am working on needs to be under GPL2 and I could not find a decent Java library that was compatible with that license - https://github.com/exquery/xpath2-parser/ 2) I then wrote some utility functions for descending through the Path expressions and making subset comparisons - https://github.com/adamretter/TEI-Completer/blob/master/src/main/java/org/humanistika/oxygen/tei/completer/XPathUtil.java#L79 Yes, this has many limitations and is most likely not complete yet, but it serves me well for the small subset of XPath path expressions that I want to support. 3) You can see in my test-cases how I consider one path expression as a subset of another path expression: https://github.com/adamretter/TEI-Completer/blob/master/src/test/java/org/humanistika/oxygen/tei/completer/XPathUtilTest.java#L40 Maybe that is of interest to some of you... Cheers On 28 January 2016 at 12:18, Adam Retter <[email protected]> wrote: > Okay thanks to everyone for the replies. > > I think the scope of what I was looking for got thrown out in all the > discussion, or perhaps I wasn't clear enough early in my initial post. > > I am not interested in XQuery, and I am only interested in a small > subset of XPath. I am concerned with comparing two path expressions, > these path expressions may have predicates, what I didn't make clear > is that those predicates may not contain functions, only the > comparison operators eq, ne, gt, ge, lt, le, and =, !=, >, >=, <, <=. > > > As Christian observed, [1] is not the same as [@a eq 'b']. In my > original post, I posed these two path expressions: > > 1. //w > > 2. /x/y/z/w[@a = 'v'] > > In this instance I can actually ignore the predicate, as I can see > that /x/y/z/w would already produce the subset of //w and the > predicate only serves to restrict that further. > > I am not looking for a formal proof in any sense. I am looking for > something practical that I can use in code. > > > On 28 January 2016 at 09:55, Pavel Velikhov <[email protected]> wrote: >> >> Finally, can it be proved that /w[@a=b] is a subset of /w, taking into >> account that the filter can only contain standard operators (eq, gt, lt, etc >> as defined in the op namespace)? >> >> >> Okay, now we are close! However now formal do you want the proof to be? I >> can give this informal proof: >> >> The first path expression selects some subset of the children of the node >> that it applies, where the label is 'w'. The second one selects all >> descendants with label 'w', hence it's result contains all nodes of the >> first path expression. >> >> But if you want to go formal, you need to use the semantics of XQuery path >> expressions, as well as the formal specification of the data model. There >> used to be a formal document on XQuery data model. >> >> >> >> 2016-01-27 17:46 GMT+01:00 Christian Grün <[email protected]>: >>> >>> > Well, so, to continue, let's assume that there are no user-defined >>> > functions, and in fact the only thing we want to proof is select+filter, >>> > where a filter is limited to the default operators. From that is it >>> > follows >>> > that >>> > >>> > -path1: >>> > select-child-nodes-by-name(select-child-nodes-by-name($context,'x'),'w') >>> > -path2: select-descendant-nodes-by-name($context,'w') >>> >>> Just to complete this: The predicate must not be numeric (//w[1] is >>> not equivalent to /descendant::w[1]). >>> >>> >>> >>> > Op woensdag 27 januari 2016 heeft daniela florescu <[email protected]> >>> > het >>> > volgende geschreven: >>> >> >>> >> > >>> >> > It seems to be a long-standing tradition that computer scientists, >>> >> > when >>> >> > asked to prove a difficult conjecture C, respond by giving a proof >>> >> > for a >>> >> > simplified conjecture C'. While this might lead to progress in the >>> >> > long run, >>> >> > and enables them to get papers published in the academic literature, >>> >> > it is >>> >> > totally useless to practical engineeers who want to know whether they >>> >> > can >>> >> > safely rely on C. >>> >> >>> >> Michael, >>> >> >>> >> >>> >> what you say is nice and true. >>> >> >>> >> However given that: >>> >> 1. path expressions point (syntactically hence esemantically) into >>> >> XQuery’s expressions >>> >> 2. XQuery expression language is Turing complete >>> >> 3. Subsumption for a Turing complete language is undecidable. >>> >> >>> >> Well, I can hardly see a way to decide this problem other then by >>> >> introducing SOME restrictions >>> >> of some sort… but of course some restrictions that would not nullify >>> >> the >>> >> original problem all together >>> >> and make the solution useless. >>> >> >>> >> Best, >>> >> Dana >>> > >>> > >>> > >>> > -- >>> > >>> > W.S. Hager >>> > Lagua Web Solutions >>> > http://lagua.nl >>> > >>> > >>> > >>> > _______________________________________________ >>> > [email protected] >>> > http://x-query.com/mailman/listinfo/talk >> >> >> >> >> -- >> >> W.S. Hager >> Lagua Web Solutions >> http://lagua.nl > > > > -- > Adam Retter > > skype: adam.retter > tweet: adamretter > http://www.adamretter.org.uk -- Adam Retter skype: adam.retter tweet: adamretter http://www.adamretter.org.uk _______________________________________________ [email protected] http://x-query.com/mailman/listinfo/talk
