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<hr>
<h4 class="subsection" id="SXPath-1"><span>7.21.6 SXPath<a class="copiable-link" href="#SXPath-1"> &para;</a></span></h4>
<ul class="mini-toc">
<li><a href="#Overview-2" accesskey="1">Overview</a></li>
<li><a href="#Basic-Converters-and-Applicators" accesskey="2">Basic Converters and Applicators</a></li>
<li><a href="#Converter-Combinators" accesskey="3">Converter Combinators</a></li>
</ul>
<div class="subsubsection-level-extent" id="Overview-2">
<h4 class="subsubsection"><span>7.21.6.1 Overview<a class="copiable-link" href="#Overview-2"> &para;</a></span></h4>
<h3 class="heading" id="SXPath_003a-SXML-Query-Language"><span>SXPath: SXML Query Language<a class="copiable-link" href="#SXPath_003a-SXML-Query-Language"> &para;</a></span></h3>
<p>SXPath is a query language for SXML, an instance of XML Information set
(Infoset) in the form of s-expressions. See <code class="code">(sxml ssax)</code> for the
definition of SXML and more details. SXPath is also a translation into
Scheme of an XML Path Language, <a class="uref" href="http://www.w3.org/TR/xpath">XPath</a>.
XPath and SXPath describe means of selecting a set of Infoset&rsquo;s items or
their properties.
</p>
<p>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 &ndash; 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.
</p>
<p>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 &rsquo;Nodes&rsquo;:
</p>
<div class="example">
<pre class="example-preformatted"> &lt;Node&gt; ::= &lt;Element&gt; | &lt;attributes-coll&gt; | &lt;attrib&gt;
| &quot;text string&quot; | &lt;PI&gt;
</pre></div>
<p>This production can also be described as
</p>
<div class="example">
<pre class="example-preformatted"> &lt;Node&gt; ::= (name . &lt;Nodeset&gt;) | &quot;text string&quot;
</pre></div>
<p>An (ordered) set of nodes is just a list of the constituent nodes:
</p>
<div class="example">
<pre class="example-preformatted"> &lt;Nodeset&gt; ::= (&lt;Node&gt; ...)
</pre></div>
<p>Nodesets, and Nodes other than text strings are both lists. A &lt;Nodeset&gt;
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&rsquo;s a
tag of an XML element), or an administrative name such as &rsquo;@&rsquo;. This
uniform list representation makes processing rather simple and elegant,
while avoiding confusion. The multi-branch tree structure formed by the
mutually-recursive datatypes &lt;Node&gt; and &lt;Nodeset&gt; lends itself well to
processing by functional languages.
</p>
<p>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 <em class="emph">elegantly</em> implement XPath
as a sequence of projection and filtering primitives &ndash; converters &ndash;
joined by <em class="dfn">combinators</em>. 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 -&gt;
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.
</p>
<p>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 <code class="code">sxpath</code> procedure.
See <a class="xref" href="#sxpath_002dprocedure_002ddocs">SXPath procedure documentation</a>.
</p>
<p>The regression test suite at the end of the file <samp class="file">SXPATH-old.scm</samp>
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.
</p>
<p>Much of the following material is taken from the SXPath sources by Oleg
Kiselyov et al.
</p>
</div>
<div class="subsubsection-level-extent" id="Basic-Converters-and-Applicators">
<h4 class="subsubsection"><span>7.21.6.2 Basic Converters and Applicators<a class="copiable-link" href="#Basic-Converters-and-Applicators"> &para;</a></span></h4>
<p>A converter is a function mapping a nodeset (or a single node) to another
nodeset. Its type can be represented like this:
</p>
<div class="example">
<pre class="example-preformatted">type Converter = Node|Nodeset -&gt; Nodeset
</pre></div>
<p>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 <code class="code">#f</code> in denoting failure.
</p>
<dl class="first-deffn">
<dt class="deffn" id="index-nodeset_003f"><span class="category-def">Scheme Procedure: </span><span><strong class="def-name">nodeset?</strong> <var class="def-var-arguments">x</var><a class="copiable-link" href="#index-nodeset_003f"> &para;</a></span></dt>
<dd><p>Return <code class="code">#t</code> if <var class="var">x</var> is a nodeset.
</p></dd></dl>
<dl class="first-deffn">
<dt class="deffn" id="index-node_002dtypeof_003f"><span class="category-def">Scheme Procedure: </span><span><strong class="def-name">node-typeof?</strong> <var class="def-var-arguments">crit</var><a class="copiable-link" href="#index-node_002dtypeof_003f"> &para;</a></span></dt>
<dd><p>This function implements a &rsquo;Node test&rsquo; 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.
</p>
<p>The function <code class="code">node-typeof?</code> takes a type criterion and returns a
function, which, when applied to a node, will tell if the node satisfies
the test.
</p>
<p>The criterion <var class="var">crit</var> is a symbol, one of the following:
</p>
<dl class="table">
<dt><code class="code">id</code></dt>
<dd><p>tests if the node has the right name (id)
</p>
</dd>
<dt><code class="code">@</code></dt>
<dd><p>tests if the node is an &lt;attributes-coll&gt;
</p>
</dd>
<dt><code class="code">*</code></dt>
<dd><p>tests if the node is an &lt;Element&gt;
</p>
</dd>
<dt><code class="code">*text*</code></dt>
<dd><p>tests if the node is a text node
</p>
</dd>
<dt><code class="code">*PI*</code></dt>
<dd><p>tests if the node is a PI (processing instruction) node
</p>
</dd>
<dt><code class="code">*any*</code></dt>
<dd><p><code class="code">#t</code> for any type of node
</p></dd>
</dl>
</dd></dl>
<dl class="first-deffn">
<dt class="deffn" id="index-node_002deq_003f"><span class="category-def">Scheme Procedure: </span><span><strong class="def-name">node-eq?</strong> <var class="def-var-arguments">other</var><a class="copiable-link" href="#index-node_002deq_003f"> &para;</a></span></dt>
<dd><p>A curried equivalence converter predicate that takes a node <var class="var">other</var>
and returns a function that takes another node. The two nodes are
compared using <code class="code">eq?</code>.
</p></dd></dl>
<dl class="first-deffn">
<dt class="deffn" id="index-node_002dequal_003f"><span class="category-def">Scheme Procedure: </span><span><strong class="def-name">node-equal?</strong> <var class="def-var-arguments">other</var><a class="copiable-link" href="#index-node_002dequal_003f"> &para;</a></span></dt>
<dd><p>A curried equivalence converter predicate that takes a node <var class="var">other</var>
and returns a function that takes another node. The two nodes are
compared using <code class="code">equal?</code>.
</p></dd></dl>
<dl class="first-deffn">
<dt class="deffn" id="index-node_002dpos"><span class="category-def">Scheme Procedure: </span><span><strong class="def-name">node-pos</strong> <var class="def-var-arguments">n</var><a class="copiable-link" href="#index-node_002dpos"> &para;</a></span></dt>
<dd><p>Select the <var class="var">n</var>&rsquo;th element of a nodeset and return as a singular
nodeset. If the <var class="var">n</var>&rsquo;th element does not exist, return an empty
nodeset. If <var class="var">n</var> is a negative number the node is picked from the
tail of the list.
</p>
<div class="example">
<pre class="example-preformatted">((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.
</pre></div>
</dd></dl>
<dl class="first-deffn">
<dt class="deffn" id="index-filter-2"><span class="category-def">Scheme Procedure: </span><span><strong class="def-name">filter</strong> <var class="def-var-arguments">pred?</var><a class="copiable-link" href="#index-filter-2"> &para;</a></span></dt>
<dd><p>A filter applicator, which introduces a filtering context. The argument
converter <var class="var">pred?</var> is considered a predicate, with either <code class="code">#f</code>
or <code class="code">nil</code> meaning failure.
</p></dd></dl>
<dl class="first-deffn">
<dt class="deffn" id="index-take_002duntil"><span class="category-def">Scheme Procedure: </span><span><strong class="def-name">take-until</strong> <var class="def-var-arguments">pred?</var><a class="copiable-link" href="#index-take_002duntil"> &para;</a></span></dt>
<dd><div class="example">
<pre class="example-preformatted">take-until:: Converter -&gt; Converter, or
take-until:: Pred -&gt; Node|Nodeset -&gt; Nodeset
</pre></div>
<p>Given a converter-predicate <var class="var">pred?</var> and a nodeset, apply the
predicate to each element of the nodeset, until the predicate yields
anything but <code class="code">#f</code> or <code class="code">nil</code>. Return the elements of the input
nodeset that have been processed until that moment (that is, which fail
the predicate).
</p>
<p><code class="code">take-until</code> is a variation of the <code class="code">filter</code> above:
<code class="code">take-until</code> passes elements of an ordered input set up to (but not
including) the first element that satisfies the predicate. The nodeset
returned by <code class="code">((take-until (not pred)) nset)</code> is a subset &ndash; to be
more precise, a prefix &ndash; of the nodeset returned by <code class="code">((filter
pred) nset)</code>.
</p></dd></dl>
<dl class="first-deffn">
<dt class="deffn" id="index-take_002dafter"><span class="category-def">Scheme Procedure: </span><span><strong class="def-name">take-after</strong> <var class="def-var-arguments">pred?</var><a class="copiable-link" href="#index-take_002dafter"> &para;</a></span></dt>
<dd><div class="example">
<pre class="example-preformatted">take-after:: Converter -&gt; Converter, or
take-after:: Pred -&gt; Node|Nodeset -&gt; Nodeset
</pre></div>
<p>Given a converter-predicate <var class="var">pred?</var> and a nodeset, apply the
predicate to each element of the nodeset, until the predicate yields
anything but <code class="code">#f</code> or <code class="code">nil</code>. 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.
</p>
<p><code class="code">take-after</code> along with <code class="code">take-until</code> partition an input
nodeset into three parts: the first element that satisfies a predicate,
all preceding elements and all following elements.
</p></dd></dl>
<dl class="first-deffn">
<dt class="deffn" id="index-map_002dunion"><span class="category-def">Scheme Procedure: </span><span><strong class="def-name">map-union</strong> <var class="def-var-arguments">proc lst</var><a class="copiable-link" href="#index-map_002dunion"> &para;</a></span></dt>
<dd><p>Apply <var class="var">proc</var> to each element of <var class="var">lst</var> and return the list of results.
If <var class="var">proc</var> returns a nodeset, splice it into the result
</p>
<p>From another point of view, <code class="code">map-union</code> is a function
<code class="code">Converter-&gt;Converter</code>, which places an argument-converter in a joining
context.
</p></dd></dl>
<dl class="first-deffn">
<dt class="deffn" id="index-node_002dreverse"><span class="category-def">Scheme Procedure: </span><span><strong class="def-name">node-reverse</strong> <var class="def-var-arguments">node-or-nodeset</var><a class="copiable-link" href="#index-node_002dreverse"> &para;</a></span></dt>
<dd><div class="example">
<pre class="example-preformatted">node-reverse :: Converter, or
node-reverse:: Node|Nodeset -&gt; Nodeset
</pre></div>
<p>Reverses the order of nodes in the nodeset. This basic converter is
needed to implement a reverse document order (see the XPath
Recommendation).
</p></dd></dl>
<dl class="first-deffn">
<dt class="deffn" id="index-node_002dtrace"><span class="category-def">Scheme Procedure: </span><span><strong class="def-name">node-trace</strong> <var class="def-var-arguments">title</var><a class="copiable-link" href="#index-node_002dtrace"> &para;</a></span></dt>
<dd><div class="example">
<pre class="example-preformatted">node-trace:: String -&gt; Converter
</pre></div>
<p><code class="code">(node-trace title)</code> is an identity converter. In addition it
prints out the node or nodeset it is applied to, prefixed with the
<var class="var">title</var>. This converter is very useful for debugging.
</p></dd></dl>
</div>
<div class="subsubsection-level-extent" id="Converter-Combinators">
<h4 class="subsubsection"><span>7.21.6.3 Converter Combinators<a class="copiable-link" href="#Converter-Combinators"> &para;</a></span></h4>
<p>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.
</p>
<p>From a different point of view, a combinator is a fixed, named
<em class="dfn">pattern</em> 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, <code class="code">map-union</code> and
<code class="code">filter</code> applicators, and the nodeset union.
</p>
<dl class="first-deffn">
<dt class="deffn" id="index-select_002dkids"><span class="category-def">Scheme Procedure: </span><span><strong class="def-name">select-kids</strong> <var class="def-var-arguments">test-pred?</var><a class="copiable-link" href="#index-select_002dkids"> &para;</a></span></dt>
<dd><p><code class="code">select-kids</code> 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
<var class="var">test-pred?</var>.
</p></dd></dl>
<dl class="first-deffn">
<dt class="deffn" id="index-node_002dself"><span class="category-def">Scheme Procedure: </span><span><strong class="def-name">node-self</strong> <var class="def-var-arguments">pred?</var><a class="copiable-link" href="#index-node_002dself"> &para;</a></span></dt>
<dd><p>Similar to <code class="code">select-kids</code> except that the predicate <var class="var">pred?</var> 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.
</p></dd></dl>
<dl class="first-deffn">
<dt class="deffn" id="index-node_002djoin"><span class="category-def">Scheme Procedure: </span><span><strong class="def-name">node-join</strong> <var class="def-var-arguments">. selectors</var><a class="copiable-link" href="#index-node_002djoin"> &para;</a></span></dt>
<dd><div class="example">
<pre class="example-preformatted">node-join:: [LocPath] -&gt; Node|Nodeset -&gt; Nodeset, or
node-join:: [Converter] -&gt; Converter
</pre></div>
<p>Join the sequence of location steps or paths as described above.
</p></dd></dl>
<dl class="first-deffn">
<dt class="deffn" id="index-node_002dreduce"><span class="category-def">Scheme Procedure: </span><span><strong class="def-name">node-reduce</strong> <var class="def-var-arguments">. converters</var><a class="copiable-link" href="#index-node_002dreduce"> &para;</a></span></dt>
<dd><div class="example">
<pre class="example-preformatted">node-reduce:: [LocPath] -&gt; Node|Nodeset -&gt; Nodeset, or
node-reduce:: [Converter] -&gt; Converter
</pre></div>
<p>A regular functional composition of converters. From a different point
of view, <code class="code">((apply node-reduce converters) nodeset)</code> is equivalent
to <code class="code">(foldl apply nodeset converters)</code>, i.e., folding, or reducing,
a list of converters with the nodeset as a seed.
</p></dd></dl>
<dl class="first-deffn">
<dt class="deffn" id="index-node_002dor"><span class="category-def">Scheme Procedure: </span><span><strong class="def-name">node-or</strong> <var class="def-var-arguments">. converters</var><a class="copiable-link" href="#index-node_002dor"> &para;</a></span></dt>
<dd><div class="example">
<pre class="example-preformatted">node-or:: [Converter] -&gt; Converter
</pre></div>
<p>This combinator applies all converters to a given node and produces the
union of their results. This combinator corresponds to a union
(<code class="code">|</code> operation) for XPath location paths.
</p></dd></dl>
<dl class="first-deffn">
<dt class="deffn" id="index-node_002dclosure"><span class="category-def">Scheme Procedure: </span><span><strong class="def-name">node-closure</strong> <var class="def-var-arguments">test-pred?</var><a class="copiable-link" href="#index-node_002dclosure"> &para;</a></span></dt>
<dd><div class="example">
<pre class="example-preformatted">node-closure:: Converter -&gt; Converter
</pre></div>
<p>Select all <em class="emph">descendants</em> of a node that satisfy a
converter-predicate <var class="var">test-pred?</var>. This combinator is similar to
<code class="code">select-kids</code> but applies to grand... children as well. This
combinator implements the <code class="code">descendant::</code> XPath axis. Conceptually,
this combinator can be expressed as
</p>
<div class="example">
<pre class="example-preformatted">(define (node-closure f)
(node-or
(select-kids f)
(node-reduce (select-kids (node-typeof? '*)) (node-closure f))))
</pre></div>
<p>This definition, as written, looks somewhat like a fixpoint, and it will
run forever. It is obvious however that sooner or later
<code class="code">(select-kids (node-typeof? '*))</code> will return an empty nodeset. At
this point further iterations will no longer affect the result and can
be stopped.
</p></dd></dl>
<dl class="first-deffn">
<dt class="deffn" id="index-node_002dparent"><span class="category-def">Scheme Procedure: </span><span><strong class="def-name">node-parent</strong> <var class="def-var-arguments">rootnode</var><a class="copiable-link" href="#index-node_002dparent"> &para;</a></span></dt>
<dd><div class="example">
<pre class="example-preformatted">node-parent:: RootNode -&gt; Converter
</pre></div>
<p><code class="code">(node-parent rootnode)</code> 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 <var class="var">rootnode</var> does not
have to be the root node of the whole SXML tree &ndash; it may be a root node
of a branch of interest.
</p>
<p>Given the notation of Philip Wadler&rsquo;s paper on semantics of XSLT,
</p>
<pre class="verbatim"> parent(x) = { y | y=subnode*(root), x=subnode(y) }
</pre>
<p>Therefore, <code class="code">node-parent</code> is not the fundamental converter: it can
be expressed through the existing ones. Yet <code class="code">node-parent</code> is a
rather convenient converter. It corresponds to a <code class="code">parent::</code> axis
of SXPath. Note that the <code class="code">parent::</code> axis can be used with an
attribute node as well.
</p></dd></dl>
<a class="anchor" id="sxpath_002dprocedure_002ddocs"></a><dl class="first-deffn">
<dt class="deffn" id="index-sxpath"><span class="category-def">Scheme Procedure: </span><span><strong class="def-name">sxpath</strong> <var class="def-var-arguments">path</var><a class="copiable-link" href="#index-sxpath"> &para;</a></span></dt>
<dd><p>Evaluate an abbreviated SXPath.
</p>
<div class="example">
<pre class="example-preformatted">sxpath:: AbbrPath -&gt; Converter, or
sxpath:: AbbrPath -&gt; Node|Nodeset -&gt; Nodeset
</pre></div>
<p><var class="var">path</var> is a list. It is translated to the full SXPath according to
the following rewriting rules:
</p>
<div class="example">
<pre class="example-preformatted">(sxpath '())
&rArr; (node-join)
(sxpath '(path-component ...))
&rArr; (node-join (sxpath1 path-component) (sxpath '(...)))
(sxpath1 '//)
&rArr; (node-or
(node-self (node-typeof? '*any*))
(node-closure (node-typeof? '*any*)))
(sxpath1 '(equal? x))
&rArr; (select-kids (node-equal? x))
(sxpath1 '(eq? x))
&rArr; (select-kids (node-eq? x))
(sxpath1 ?symbol)
&rArr; (select-kids (node-typeof? ?symbol)
(sxpath1 procedure)
&rArr; procedure
(sxpath1 '(?symbol ...))
&rArr; (sxpath1 '((?symbol) ...))
(sxpath1 '(path reducer ...))
&rArr; (node-reduce (sxpath path) (sxpathr reducer) ...)
(sxpathr number)
&rArr; (node-pos number)
(sxpathr path-filter)
&rArr; (filter (sxpath path-filter))
</pre></div>
</dd></dl>
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