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7.22.6 SXPath Overview

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 the case of SXPath the corresponding rules are given in the documentation of the sxpath procedure. See SXPath procedure documentation.

The regression test suite at the end of the file SXPATH-old.scm 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.

Much of the following material is taken from the SXPath sources by Oleg Kiselyov et al. Basic Converters and Applicators

A converter is a function mapping a nodeset (or a single node) to another nodeset. Its type can be represented like this:

type Converter = Node|Nodeset -> Nodeset

A converter can also play the role of a predicate: in that case, if a converter, applied to a node or a nodeset, yields a non-empty nodeset, the converter-predicate is deemed satisfied. Likewise, an empty nodeset is equivalent to #f in denoting failure.

Scheme Procedure: nodeset? x

Return #t if x is a nodeset.

Scheme Procedure: node-typeof? crit

This function implements a ’Node test’ as defined in Sec. 2.3 of the XPath document. A node test is one of the components of a location step. It is also a converter-predicate in SXPath.

The function node-typeof? takes a type criterion and returns a function, which, when applied to a node, will tell if the node satisfies the test.

The criterion crit is a symbol, one of the following:


tests if the node has the right name (id)


tests if the node is an <attributes-coll>


tests if the node is an <Element>


tests if the node is a text node


tests if the node is a PI (processing instruction) node


#t for any type of node

Scheme Procedure: node-eq? other

A curried equivalence converter predicate that takes a node other and returns a function that takes another node. The two nodes are compared using eq?.

Scheme Procedure: node-equal? other

A curried equivalence converter predicate that takes a node other and returns a function that takes another node. The two nodes are compared using equal?.

Scheme Procedure: node-pos n

Select the n’th element of a nodeset and return as a singular nodeset. If the n’th element does not exist, return an empty nodeset. If n is a negative number the node is picked from the tail of the list.

((node-pos 1) nodeset)  ; return the the head of the nodeset (if exists)
((node-pos 2) nodeset)  ; return the node after that (if exists)
((node-pos -1) nodeset) ; selects the last node of a non-empty nodeset
((node-pos -2) nodeset) ; selects the last but one node, if exists.
Scheme Procedure: filter pred?

A filter applicator, which introduces a filtering context. The argument converter pred? is considered a predicate, with either #f or nil meaning failure.

Scheme Procedure: take-until pred?
take-until:: Converter -> Converter, or
take-until:: Pred -> Node|Nodeset -> Nodeset

Given a converter-predicate pred? and a nodeset, apply the predicate to each element of the nodeset, until the predicate yields anything but #f or nil. Return the elements of the input nodeset that have been processed until that moment (that is, which fail the predicate).

take-until is a variation of the filter above: take-until passes elements of an ordered input set up to (but not including) the first element that satisfies the predicate. The nodeset returned by ((take-until (not pred)) nset) is a subset – to be more precise, a prefix – of the nodeset returned by ((filter pred) nset).

Scheme Procedure: take-after pred?
take-after:: Converter -> Converter, or
take-after:: Pred -> Node|Nodeset -> Nodeset

Given a converter-predicate pred? and a nodeset, apply the predicate to each element of the nodeset, until the predicate yields anything but #f or nil. Return the elements of the input nodeset that have not been processed: that is, return the elements of the input nodeset that follow the first element that satisfied the predicate.

take-after along with take-until partition an input nodeset into three parts: the first element that satisfies a predicate, all preceding elements and all following elements.

Scheme Procedure: map-union proc lst

Apply proc to each element of lst and return the list of results. If proc returns a nodeset, splice it into the result

From another point of view, map-union is a function Converter->Converter, which places an argument-converter in a joining context.

Scheme Procedure: node-reverse node-or-nodeset
node-reverse :: Converter, or
node-reverse:: Node|Nodeset -> Nodeset

Reverses the order of nodes in the nodeset. This basic converter is needed to implement a reverse document order (see the XPath Recommendation).

Scheme Procedure: node-trace title
node-trace:: String -> Converter

(node-trace title) is an identity converter. In addition it prints out the node or nodeset it is applied to, prefixed with the title. This converter is very useful for debugging. Converter Combinators

Combinators are higher-order functions that transmogrify a converter or glue a sequence of converters into a single, non-trivial converter. The goal is to arrive at converters that correspond to XPath location paths.

From a different point of view, a combinator is a fixed, named pattern of applying converters. Given below is a complete set of such patterns that together implement XPath location path specification. As it turns out, all these combinators can be built from a small number of basic blocks: regular functional composition, map-union and filter applicators, and the nodeset union.

Scheme Procedure: select-kids test-pred?

select-kids takes a converter (or a predicate) as an argument and returns another converter. The resulting converter applied to a nodeset returns an ordered subset of its children that satisfy the predicate test-pred?.

Scheme Procedure: node-self pred?

Similar to select-kids except that the predicate pred? is applied to the node itself rather than to its children. The resulting nodeset will contain either one component, or will be empty if the node failed the predicate.

Scheme Procedure: node-join . selectors
node-join:: [LocPath] -> Node|Nodeset -> Nodeset, or
node-join:: [Converter] -> Converter

Join the sequence of location steps or paths as described above.

Scheme Procedure: node-reduce . converters
node-reduce:: [LocPath] -> Node|Nodeset -> Nodeset, or
node-reduce:: [Converter] -> Converter

A regular functional composition of converters. From a different point of view, ((apply node-reduce converters) nodeset) is equivalent to (foldl apply nodeset converters), i.e., folding, or reducing, a list of converters with the nodeset as a seed.

Scheme Procedure: node-or . converters
node-or:: [Converter] -> Converter

This combinator applies all converters to a given node and produces the union of their results. This combinator corresponds to a union (| operation) for XPath location paths.

Scheme Procedure: node-closure test-pred?
node-closure:: Converter -> Converter

Select all descendants of a node that satisfy a converter-predicate test-pred?. This combinator is similar to select-kids but applies to grand... children as well. This combinator implements the descendant:: XPath axis. Conceptually, this combinator can be expressed as

(define (node-closure f)
    (select-kids f)
    (node-reduce (select-kids (node-typeof? '*)) (node-closure f))))

This definition, as written, looks somewhat like a fixpoint, and it will run forever. It is obvious however that sooner or later (select-kids (node-typeof? '*)) will return an empty nodeset. At this point further iterations will no longer affect the result and can be stopped.

Scheme Procedure: node-parent rootnode
node-parent:: RootNode -> Converter

(node-parent rootnode) yields a converter that returns a parent of a node it is applied to. If applied to a nodeset, it returns the list of parents of nodes in the nodeset. The rootnode does not have to be the root node of the whole SXML tree – it may be a root node of a branch of interest.

Given the notation of Philip Wadler’s paper on semantics of XSLT,

  parent(x) = { y | y=subnode*(root), x=subnode(y) }

Therefore, node-parent is not the fundamental converter: it can be expressed through the existing ones. Yet node-parent is a rather convenient converter. It corresponds to a parent:: axis of SXPath. Note that the parent:: axis can be used with an attribute node as well.

Scheme Procedure: sxpath path

Evaluate an abbreviated SXPath.

sxpath:: AbbrPath -> Converter, or
sxpath:: AbbrPath -> Node|Nodeset -> Nodeset

path is a list. It is translated to the full SXPath according to the following rewriting rules:

(sxpath '())
⇒ (node-join)

(sxpath '(path-component ...))
⇒ (node-join (sxpath1 path-component) (sxpath '(...)))

(sxpath1 '//)
⇒ (node-or
   (node-self (node-typeof? '*any*))
   (node-closure (node-typeof? '*any*)))

(sxpath1 '(equal? x))
⇒ (select-kids (node-equal? x))

(sxpath1 '(eq? x))
⇒ (select-kids (node-eq? x))

(sxpath1 ?symbol)
⇒ (select-kids (node-typeof? ?symbol)

(sxpath1 procedure)
⇒ procedure

(sxpath1 '(?symbol ...))
⇒ (sxpath1 '((?symbol) ...))

(sxpath1 '(path reducer ...))
⇒ (node-reduce (sxpath path) (sxpathr reducer) ...)

(sxpathr number)
⇒ (node-pos number)

(sxpathr path-filter)
⇒ (filter (sxpath path-filter))

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