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;; XML processing in Scheme
; SXPath -- SXML Query Language
; $Id: sxpathlib.scm,v 1.1 2003-07-22 11:22:11 shirok Exp $
; 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
; * * *
; 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:
; 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.
;; Read-only decrement
(define-macro (mm x) `(- ,x 1))
; Basic converters and applicators
; A converter is a function
; type Converter = Node|Nodeset -> Nodeset
; A converter can also play a 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. Throughout
; this file a nil nodeset is equivalent to #f in denoting a failure.
; Returns #t if given object is a nodeset
(define (nodeset? x)
(or (and (pair? x) (not (symbol? (car x)))) (null? x)))
; If x is a nodeset - returns it as is, otherwise wrap it in a list.
(define (as-nodeset x)
(if (nodeset? x) x (list x)))
; Node test
; 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.
; 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)
; 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)
(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))))
((string-rindex nm #\:)
=> (lambda (pos)
(= pos (string-length ns-id))
(string-prefix? ns-id nm))))
(else (not ns-id)))))))
; This function takes a predicate and returns it inverted
; That is if the given predicate yelds #f or '() the inverted one
; yields the given node (#t) and vice versa.
(define (sxml:invert pred)
(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 -> Nodeset -> Nodeset, or
; node-pos:: N -> Converter
; Select the N'th element of a Nodeset and return as a singular Nodeset;
; Return an empty nodeset if the Nth element does not exist.
; ((node-pos 1) Nodeset) selects the node at the head of the Nodeset,
; if exists; ((node-pos 2) Nodeset) 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) Nodeset) selects the last node of a non-empty nodeset;
; ((node-pos -2) Nodeset) selects the last but one node, if exists.
(define (node-pos n)
(lambda (nodeset)
((not (nodeset? nodeset)) '())
((null? nodeset) nodeset)
((eqv? n 1) (list (car nodeset)))
((negative? n) ((node-pos (+ n 1 (length nodeset))) nodeset))
(assert (positive? n))
((node-pos (mm n)) (cdr nodeset))))))
; 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 nodeset 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)
; take-until:: Converter -> Converter, or
; take-until:: Pred -> Node|Nodeset -> Nodeset
; Given a converter-predicate 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
; 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 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)
(define (take-until pred?)
(lambda (lst) ; a nodeset 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|Nodeset -> Nodeset
; Given a converter-predicate 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.
(define (take-after pred?)
(lambda (lst) ; a nodeset 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 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.
(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|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).
(define node-reverse
(lambda (node-or-nodeset)
(if (not (nodeset? node-or-nodeset)) (list node-or-nodeset)
(reverse node-or-nodeset))))
; node-trace:: String -> Converter
; (node-trace title) is an identity converter. In addition it prints out
; a node or nodeset it is applied to, prefixed with the 'title'.
; This converter is very useful for debugging.
(define (node-trace title)
(lambda (node-or-nodeset)
(cout nl "-->" title " :")
(pp node-or-nodeset)
; 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.
; select-kids:: Pred -> Node -> Nodeset
; Given a Node, return an (ordered) subset its children that satisfy
; the Pred (a converter, actually)
; select-kids:: Pred -> Nodeset -> Nodeset
; The same as above, but select among children of all the nodes in
; the Nodeset
; More succinctly, the signature of this function is
; select-kids:: Converter -> Converter
(define (select-kids test-pred?)
(lambda (node) ; node or node-set
((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 -> Nodeset, or
; node-self:: Converter -> Converter
; Similar to select-kids but apply 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 Pred).
(define node-self sxml:filter)
; node-join:: [LocPath] -> Node|Nodeset -> Nodeset, 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 (nodeset) ; Nodeset or node
(let loop ((nodeset nodeset) (selectors selectors))
(if (null? selectors) nodeset
(if (nodeset? nodeset)
(map-union (car selectors) nodeset)
((car selectors) nodeset))
(cdr selectors))))))
; 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.
(define (node-reduce . converters)
(lambda (nodeset) ; Nodeset or node
(let loop ((nodeset nodeset) (converters converters))
(if (null? converters) nodeset
(loop ((car converters) nodeset) (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-nodeset)
; (if (null? converters) node-or-nodeset
; (append
; ((car converters) node-or-nodeset)
; ((apply node-or (cdr converters)) node-or-nodeset)))))
; More optimal implementation follows
(define (node-or . converters)
(lambda (node-or-nodeset)
(let loop ((result '()) (converters converters))
(if (null? converters) result
(loop (append result (or ((car converters) node-or-nodeset) '()))
(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 nodeset. At
; this point further iterations will no longer affect the result and
; can be stopped.
(define (node-closure test-pred?)
(lambda (node) ; Nodeset or node
(let loop ((parent node) (result '()))
(if (null? parent) result
(loop (sxml:child-elements parent)
(append result
((select-kids test-pred?) parent)))
; Unified with sxpath-ext and sxml-tools
; 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)
(apply append
(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
((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 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.
; The parent:: axis can be used with any SXML node.
(define (sxml:parent test-pred?)
(lambda (root-node) ; node or nodeset
(lambda (node) ; node or nodeset
(if (nodeset? node)
(map-union ((sxml:parent test-pred?) root-node) node)
(let rpt ((pairs
(apply append
(lambda (root-n)
(lambda (arg) (cons arg root-n))
(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
(lambda (arg) (cons arg (car pair)))
(sxml:attr-list (car pair))
(sxml:child-nodes (car pair))))
(cdr pairs)
; Popular short cuts
; 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.
; 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?))
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