XML processing in Scheme SXPath -- SXML Query Language $Id: sxpathlib.scm,v 3.918 2004/02/05 22:52:33 kl Exp kl $ This code is in Public Domain It's based on SXPath by Oleg Kiselyov, and multiple improvements implemented by Dmitry Lizorkin. The list of differences from original SXPath.scm my be found in changelog.txt Kirill Lisovsky lisovsky@acm.org * * * SXPath is a query language for SXML, an instance of XML Information set (Infoset) in the form of s-expressions. See SSAX.scm for the definition of SXML and more details. SXPath is also a translation into Scheme of an XML Path Language, XPath: http://www.w3.org/TR/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 . <Nodelist>) | "text string" An (ordered) set of nodes is just a list of the constituent nodes: <Nodelist> ::= (<Node> ...) Nodelists, and Nodes other than text strings are both lists. A <Nodelist> 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 <Nodelist> 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 nodelist 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|Nodelist -> Nodelist 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.

**Basic converters and applicators**-
f: nodeset?

f: as-nodeset

**Node test**-
f: sxml:element?

f: ntype-names??

f: ntype??

f: ntype-namespace-id??

f: node-eq?

f: node-equal?

f: node-pos

f: sxml:filter

f: take-until

f: take-after

f: map-union

f: node-reverse

f: node-trace

**Converter combinators**-
f: select-kids

f: node-self

f: node-join

f: node-reduce

f: node-or

f: node-closure

**Unified with sxpath-ext and sxml-tools**-
f: sxml:node?

f: sxml:attr-list

f: sxml:attribute

f: sxml:child

f: sxml:parent

**Popular short cuts**-
f: node-parent

f: sxml:child-nodes

f: sxml:child-elements

A converter is a function type Converter = Node|Nodelist -> Nodelist A converter can also play a role of a predicate: in that case, if a converter, applied to a node or a nodelist, yields a non-empty nodelist, the converter-predicate is deemed satisfied. Throughout this file a nil nodelist is equivalent to #f in denoting a failure.

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Returns #t if given object is a nodelist

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If x is a nodelist - returns it as is, otherwise wrap it in a list.

The following functions implement 'Node test's as defined in Sec. 2.3 of XPath document. A node test is one of the components of a location step. It is also a converter-predicate in SXPath.

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Predicate which returns #t if <obj> is SXML element, otherwise returns #f.

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The function ntype-names?? takes a list of acceptable node names as a criterion and returns a function, which, when applied to a node, will return #t if the node name is present in criterion list and #f othervise. ntype-names?? :: ListOfNames -> Node -> Boolean

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The function ntype?? takes a type criterion and returns a function, which, when applied to a node, will tell if the node satisfies the test. ntype?? :: Crit -> Node -> Boolean The criterion 'crit' is one of the following symbols: id - tests if the Node has the right name (id) @ - tests if the Node is an <attributes-list> * - tests if the Node is an <Element> *text* - tests if the Node is a text node *data* - tests if the Node is a data node (text, number, boolean, etc., but not pair) *PI* - tests if the Node is a PI node *COMMENT* - tests if the Node is a COMMENT node *ENTITY* - tests if the Node is a ENTITY node *any* - #t for any type of Node

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This function takes a namespace-id, and returns a predicate Node -> Boolean, which is #t for nodes with this very namespace-id. ns-id is a string (ntype-namespace-id?? #f) will be #t for nodes with non-qualified names.

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This function takes a predicate and returns it complemented That is if the given predicate yelds #f or '() the complemented one yields the given node (#t) and vice versa.

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Curried equivalence converter-predicates

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node-pos:: N -> Nodelist -> Nodelist, or node-pos:: N -> Converter Select the N'th element of a Nodelist and return as a singular Nodelist; Return an empty nodelist if the Nth element does not exist. ((node-pos 1) Nodelist) selects the node at the head of the Nodelist, if exists; ((node-pos 2) Nodelist) selects the Node after that, if exists. N can also be a negative number: in that case the node is picked from the tail of the list. ((node-pos -1) Nodelist) selects the last node of a non-empty nodelist; ((node-pos -2) Nodelist) selects the last but one node, if exists.

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filter:: Converter -> Converter A filter applicator, which introduces a filtering context. The argument converter is considered a predicate, with either #f or nil result meaning failure.

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take-until:: Converter -> Converter, or take-until:: Pred -> Node|Nodelist -> Nodelist Given a converter-predicate and a nodelist, apply the predicate to each element of the nodelist, until the predicate yields anything but #f or nil. Return the elements of the input nodelist that have been processed till 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 till (but not including) the first element that satisfies the predicate. The nodelist returned by ((take-until (not pred)) nset) is a subset -- to be more precise, a prefix -- of the nodelist returned by ((filter pred) nset)

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take-after:: Converter -> Converter, or take-after:: Pred -> Node|Nodelist -> Nodelist Given a converter-predicate and a nodelist, apply the predicate to each element of the nodelist, until the predicate yields anything but #f or nil. Return the elements of the input nodelist that have not been processed: that is, return the elements of the input nodelist that follow the first element that satisfied the predicate. take-after along with take-until partition an input nodelist into three parts: the first element that satisfies a predicate, all preceding elements and all following elements.

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Apply proc to each element of lst and return the list of results. if proc returns a nodelist, 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.

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node-reverse :: Converter, or node-reverse:: Node|Nodelist -> Nodelist Reverses the order of nodes in the nodelist This basic converter is needed to implement a reverse document order (see the XPath Recommendation).

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node-trace:: String -> Converter (node-trace title) is an identity converter. In addition it prints out a node or nodelist it is applied to, prefixed with the 'title'. This converter is very useful for debugging.

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 nodelist union.

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select-kids:: Pred -> Node -> Nodelist Given a Node, return an (ordered) subset its children that satisfy the Pred (a converter, actually) select-kids:: Pred -> Nodelist -> Nodelist The same as above, but select among children of all the nodes in the Nodelist More succinctly, the signature of this function is select-kids:: Converter -> Converter

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node-self:: Pred -> Node -> Nodelist, or node-self:: Converter -> Converter Similar to select-kids but apply to the Node itself rather than to its children. The resulting Nodelist will contain either one component, or will be empty (if the Node failed the Pred).

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node-join:: [LocPath] -> Node|Nodelist -> Nodelist, or node-join:: [Converter] -> Converter join the sequence of location steps or paths as described in the title comments above.

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node-reduce:: [LocPath] -> Node|Nodelist -> Nodelist, or node-reduce:: [Converter] -> Converter A regular functional composition of converters. From a different point of view, ((apply node-reduce converters) nodelist) is equivalent to (foldl apply nodelist converters) i.e., folding, or reducing, a list of converters with the nodelist as a seed.

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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.

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node-closure:: Converter -> Converter Select all _descendants_ of a node that satisfy a converter-predicate. 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) (node-or (select-kids f) (node-reduce (select-kids (ntype?? '*)) (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 (ntype?? '*)) will return an empty nodelist. At this point further iterations will no longer affect the result and can be stopped.

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According to XPath specification 2.3, this test is true for any XPath node. For SXML auxiliary lists and lists of attributes has to be excluded.

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Returns the list of attributes for a given SXML node Empty list is returned if the given node os not an element, or if it has no list of attributes

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Attribute axis

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Child axis This function is similar to 'select-kids', but it returns an empty child-list for PI, Comment and Entity nodes

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Parent axis Given a predicate, it returns a function RootNode -> Converter which which yields a node -> parent converter then applied to a rootnode. Thus, such a converter may be constructed using ((sxml:parent test-pred) rootnode) and returns a parent of a node it is applied to. If applied to a nodelist, it returns the list of parents of nodes in the nodelist. 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. The parent:: axis can be used with any SXML node.

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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 nodelist, it returns the list of parents of nodes in the nodelist. 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. Please note: this function is provided for backward compatibility with SXPath/SXPathlib ver. 3.5.x.x and earlier. Now it's a particular case of 'sxml:parent' application:

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Returns #t if given object is a nodelist

(define (nodeset? x) (or (and (pair? x) (not (symbol? (car x)))) (null? x)))

If x is a nodelist - returns it as is, otherwise wrap it in a list.

(define (as-nodeset x) (if (nodeset? x) x (list x)))

This function takes a predicate and returns it complemented That is if the given predicate yelds #f or '() the complemented one yields the given node (#t) and vice versa.

(define (sxml:complement pred) (lambda(node) (case (pred node) ((#f '()) node) (else #f))))

Curried equivalence converter-predicates

(define (node-eq? other) (lambda (node) (eq? other node)))

(define (node-equal? other) (lambda (node) (equal? other node)))

node-pos:: N -> Nodelist -> Nodelist, or node-pos:: N -> Converter Select the N'th element of a Nodelist and return as a singular Nodelist; Return an empty nodelist if the Nth element does not exist. ((node-pos 1) Nodelist) selects the node at the head of the Nodelist, if exists; ((node-pos 2) Nodelist) selects the Node after that, if exists. N can also be a negative number: in that case the node is picked from the tail of the list. ((node-pos -1) Nodelist) selects the last node of a non-empty nodelist; ((node-pos -2) Nodelist) selects the last but one node, if exists.

(define (node-pos n) (lambda (nodelist) (cond ((not (nodeset? nodelist)) '()) ((null? nodelist) nodelist) ((eqv? n 1) (list (car nodelist))) ((negative? n) ((node-pos (+ n 1 (length nodelist))) nodelist)) (else (assert (positive? n)) ((node-pos (-- n)) (cdr nodelist))))))

filter:: Converter -> Converter A filter applicator, which introduces a filtering context. The argument converter is considered a predicate, with either #f or nil result meaning failure.

(define (sxml:filter pred?) (lambda (lst) ; a nodelist or a node (will be converted to a singleton nset) (let loop ((lst (as-nodeset lst)) (res '())) (if (null? lst) (reverse res) (let ((pred-result (pred? (car lst)))) (loop (cdr lst) (if (and pred-result (not (null? pred-result))) (cons (car lst) res) res)))))))

take-until:: Converter -> Converter, or take-until:: Pred -> Node|Nodelist -> Nodelist Given a converter-predicate and a nodelist, apply the predicate to each element of the nodelist, until the predicate yields anything but #f or nil. Return the elements of the input nodelist that have been processed till 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 till (but not including) the first element that satisfies the predicate. The nodelist returned by ((take-until (not pred)) nset) is a subset -- to be more precise, a prefix -- of the nodelist returned by ((filter pred) nset)

(define (take-until pred?) (lambda (lst) ; a nodelist or a node (will be converted to a singleton nset) (let loop ((lst (as-nodeset lst))) (if (null? lst) lst (let ((pred-result (pred? (car lst)))) (if (and pred-result (not (null? pred-result))) '() (cons (car lst) (loop (cdr lst))))) ))))

take-after:: Converter -> Converter, or take-after:: Pred -> Node|Nodelist -> Nodelist Given a converter-predicate and a nodelist, apply the predicate to each element of the nodelist, until the predicate yields anything but #f or nil. Return the elements of the input nodelist that have not been processed: that is, return the elements of the input nodelist that follow the first element that satisfied the predicate. take-after along with take-until partition an input nodelist into three parts: the first element that satisfies a predicate, all preceding elements and all following elements.

(define (take-after pred?) (lambda (lst) ; a nodelist or a node (will be converted to a singleton nset) (let loop ((lst (as-nodeset lst))) (if (null? lst) lst (let ((pred-result (pred? (car lst)))) (if (and pred-result (not (null? pred-result))) (cdr lst) (loop (cdr lst)))) ))))

Apply proc to each element of lst and return the list of results. if proc returns a nodelist, 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.

(define (map-union proc lst) (if (null? lst) lst (let ((proc-res (proc (car lst)))) ((if (nodeset? proc-res) append cons) proc-res (map-union proc (cdr lst))))))

node-reverse :: Converter, or node-reverse:: Node|Nodelist -> Nodelist Reverses the order of nodes in the nodelist This basic converter is needed to implement a reverse document order (see the XPath Recommendation).

(define node-reverse (lambda (node-or-nodelist) (if (not (nodeset? node-or-nodelist)) (list node-or-nodelist) (reverse node-or-nodelist))))

node-trace:: String -> Converter (node-trace title) is an identity converter. In addition it prints out a node or nodelist it is applied to, prefixed with the 'title'. This converter is very useful for debugging.

(define (node-trace title) (lambda (node-or-nodelist) (cout nl "-->" title " :") (pp node-or-nodelist) node-or-nodelist))

According to XPath specification 2.3, this test is true for any XPath node. For SXML auxiliary lists and lists of attributes has to be excluded.

(define (sxml:node? node) (not (and (pair? node) (memq (car node) '(@ @@)))))

Returns the list of attributes for a given SXML node Empty list is returned if the given node os not an element, or if it has no list of attributes

(define (sxml:attr-list obj) (if (and (sxml:element? obj) (not (null? (cdr obj))) (pair? (cadr obj)) (eq? '@ (caadr obj))) (cdadr obj) '()))

Attribute axis

(define (sxml:attribute test-pred?) (let ((fltr (sxml:filter test-pred?))) (lambda (node) (fltr (apply append (map sxml:attr-list (as-nodeset node)))))))

Child axis This function is similar to 'select-kids', but it returns an empty child-list for PI, Comment and Entity nodes

(define (sxml:child test-pred?) (lambda (node) ; node or node-set (cond ((null? node) node) ((not (pair? node)) '()) ; No children ((memq (car node) '(*PI* *COMMENT* *ENTITY*)) ; PI, Comment or Entity '()) ; No children ((symbol? (car node)) ; it's a single node ((sxml:filter test-pred?) (cdr node))) (else (map-union (sxml:child test-pred?) node)))))

Parent axis Given a predicate, it returns a function RootNode -> Converter which which yields a node -> parent converter then applied to a rootnode. Thus, such a converter may be constructed using ((sxml:parent test-pred) rootnode) and returns a parent of a node it is applied to. If applied to a nodelist, it returns the list of parents of nodes in the nodelist. 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. The parent:: axis can be used with any SXML node.

(define (sxml:parent test-pred?) (lambda (root-node) ; node or nodelist (lambda (node) ; node or nodelist (if (nodeset? node) (map-union ((sxml:parent test-pred?) root-node) node) (let rpt ((pairs (apply append (map (lambda (root-n) (map (lambda (arg) (cons arg root-n)) (append (sxml:attr-list root-n) (sxml:child-nodes root-n)))) (as-nodeset root-node))) )) (if (null? pairs) '() (let ((pair (car pairs))) (if (eq? (car pair) node) ((sxml:filter test-pred?) (list (cdr pair))) (rpt (append (map (lambda (arg) (cons arg (car pair))) (append (sxml:attr-list (car pair)) (sxml:child-nodes (car pair)))) (cdr pairs) ))))))))))

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 nodelist, it returns the list of parents of nodes in the nodelist. 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. Please note: this function is provided for backward compatibility with SXPath/SXPathlib ver. 3.5.x.x and earlier. Now it's a particular case of 'sxml:parent' application:

(define node-parent (sxml:parent (ntype?? '*any*)))

(define sxml:child-nodes (sxml:child sxml:node?))

(define sxml:child-elements (select-kids sxml:element?))

Predicate which returns #t if <obj> is SXML element, otherwise returns #f.

(define (sxml:element? obj) (and (pair? obj) (symbol? (car obj)) (not (memq (car obj) ; '(@ @@ *PI* *COMMENT* *ENTITY* *NAMESPACES*) ; the line above is a workaround for old SXML '(@ @@ *PI* *COMMENT* *ENTITY*)))))

The function ntype-names?? takes a list of acceptable node names as a criterion and returns a function, which, when applied to a node, will return #t if the node name is present in criterion list and #f othervise. ntype-names?? :: ListOfNames -> Node -> Boolean

(define (ntype-names?? crit) (lambda(node) (and (pair? node) (memq (car node) crit))))

The function ntype?? takes a type criterion and returns a function, which, when applied to a node, will tell if the node satisfies the test. ntype?? :: Crit -> Node -> Boolean The criterion 'crit' is one of the following symbols: id - tests if the Node has the right name (id) @ - tests if the Node is an <attributes-list> * - tests if the Node is an <Element> *text* - tests if the Node is a text node *data* - tests if the Node is a data node (text, number, boolean, etc., but not pair) *PI* - tests if the Node is a PI node *COMMENT* - tests if the Node is a COMMENT node *ENTITY* - tests if the Node is a ENTITY node *any* - #t for any type of Node

(define (ntype?? crit) (case crit ((*) sxml:element?) ((*any*) (lambda (node) #t)) ((*text*) (lambda (node) (string? node))) ((*data*) (lambda (node) (not (pair? node)))) (else (lambda (node) (and (pair? node) (eq? crit (car node))))) ))

This function takes a namespace-id, and returns a predicate Node -> Boolean, which is #t for nodes with this very namespace-id. ns-id is a string (ntype-namespace-id?? #f) will be #t for nodes with non-qualified names.

(define (ntype-namespace-id?? ns-id) (lambda (node) (and (pair? node) (not (memq (car node) '(@ @@ *PI* *COMMENT* *ENTITY*))) (let ((nm (symbol->string (car node)))) (cond ((string-rindex nm #\:) => (lambda (pos) (and (= pos (string-length ns-id)) (string-prefix? ns-id nm)))) (else (not ns-id)))))))

select-kids:: Pred -> Node -> Nodelist Given a Node, return an (ordered) subset its children that satisfy the Pred (a converter, actually) select-kids:: Pred -> Nodelist -> Nodelist The same as above, but select among children of all the nodes in the Nodelist More succinctly, the signature of this function is select-kids:: Converter -> Converter

(define (select-kids test-pred?) (lambda (node) ; node or node-set (cond ((null? node) node) ((not (pair? node)) '()) ; No children ((symbol? (car node)) ((sxml:filter test-pred?) (cdr node))) ; it's a single node (else (map-union (select-kids test-pred?) node)))))

node-self:: Pred -> Node -> Nodelist, or node-self:: Converter -> Converter Similar to select-kids but apply to the Node itself rather than to its children. The resulting Nodelist will contain either one component, or will be empty (if the Node failed the Pred).

(define node-self sxml:filter)

node-join:: [LocPath] -> Node|Nodelist -> Nodelist, or node-join:: [Converter] -> Converter join the sequence of location steps or paths as described in the title comments above.

(define (node-join . selectors) (lambda (nodelist) ; Nodelist or node (let loop ((nodelist nodelist) (selectors selectors)) (if (null? selectors) nodelist (loop (if (nodeset? nodelist) (map-union (car selectors) nodelist) ((car selectors) nodelist)) (cdr selectors))))))

node-reduce:: [LocPath] -> Node|Nodelist -> Nodelist, or node-reduce:: [Converter] -> Converter A regular functional composition of converters. From a different point of view, ((apply node-reduce converters) nodelist) is equivalent to (foldl apply nodelist converters) i.e., folding, or reducing, a list of converters with the nodelist as a seed.

(define (node-reduce . converters) (lambda (nodelist) ; Nodelist or node (let loop ((nodelist nodelist) (converters converters)) (if (null? converters) nodelist (loop ((car converters) nodelist) (cdr 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.

(define (node-or . converters) (lambda (node-or-nodelist) (let loop ((result '()) (converters converters)) (if (null? converters) result (loop (append result (or ((car converters) node-or-nodelist) '())) (cdr converters))))))

node-closure:: Converter -> Converter Select all _descendants_ of a node that satisfy a converter-predicate. 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) (node-or (select-kids f) (node-reduce (select-kids (ntype?? '*)) (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 (ntype?? '*)) will return an empty nodelist. At this point further iterations will no longer affect the result and can be stopped.

(define (node-closure test-pred?) (let ((kid-selector (select-kids test-pred?))) (lambda (node) ; Nodelist or node (let loop ((parent node) (result '())) (if (null? parent) result (loop (sxml:child-elements parent) (append result (kid-selector parent))) )))))