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SXPath: SXML Query Language

SXPath is a query language for SXML, an instance of XML Information set (Infoset) in the form of s-expressions. See (sxml ssax) for the definition of SXML and more details. SXPath is also a translation into Scheme of an XML Path Language, XPath. XPath and SXPath describe means of selecting a set of Infoset’s items or their properties.

To facilitate queries, XPath maps the XML Infoset into an explicit tree, and introduces important notions of a location path and a current, context node. A location path denotes a selection of a set of nodes relative to a context node. Any XPath tree has a distinguished, root node – which serves as the context node for absolute location paths. Location path is recursively defined as a location step joined with a location path. A location step is a simple query of the database relative to a context node. A step may include expressions that further filter the selected set. Each node in the resulting set is used as a context node for the adjoining location path. The result of the step is a union of the sets returned by the latter location paths.

The SXML representation of the XML Infoset (see SSAX.scm) is rather suitable for querying as it is. Bowing to the XPath specification, we will refer to SXML information items as ’Nodes’:

 	<Node> ::= <Element> | <attributes-coll> | <attrib>
 		   | "text string" | <PI>

This production can also be described as

	<Node> ::= (name . <Nodeset>) | "text string"

An (ordered) set of nodes is just a list of the constituent nodes:

 	<Nodeset> ::= (<Node> ...)

Nodesets, and Nodes other than text strings are both lists. A <Nodeset> however is either an empty list, or a list whose head is not a symbol. A symbol at the head of a node is either an XML name (in which case it’s a tag of an XML element), or an administrative name such as ’@’. This uniform list representation makes processing rather simple and elegant, while avoiding confusion. The multi-branch tree structure formed by the mutually-recursive datatypes <Node> and <Nodeset> lends itself well to processing by functional languages.

A location path is in fact a composite query over an XPath tree or its branch. A singe step is a combination of a projection, selection or a transitive closure. Multiple steps are combined via join and union operations. This insight allows us to elegantly implement XPath as a sequence of projection and filtering primitives – converters – joined by combinators. Each converter takes a node and returns a nodeset which is the result of the corresponding query relative to that node. A converter can also be called on a set of nodes. In that case it returns a union of the corresponding queries over each node in the set. The union is easily implemented as a list append operation as all nodes in a SXML tree are considered distinct, by XPath conventions. We also preserve the order of the members in the union. Query combinators are high-order functions: they take converter(s) (which is a Node|Nodeset -> Nodeset function) and compose or otherwise combine them. We will be concerned with only relative location paths [XPath]: an absolute location path is a relative path applied to the root node.

Similarly to XPath, SXPath defines full and abbreviated notations for location paths. In both cases, the abbreviated notation can be mechanically expanded into the full form by simple rewriting rules. In case of SXPath the corresponding rules are given as comments to a sxpath function, below. The regression test suite at the end of this file shows a representative sample of SXPaths in both notations, juxtaposed with the corresponding XPath expressions. Most of the samples are borrowed literally from the XPath specification, while the others are adjusted for our running example, tree1.

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