This document defines the W3C XML Query Data Model, which is the
foundation of the W3C XML Query Algebra; the XML Query Algebra
will be specified in a future document.
Together, these two documents [will] provide
a precise semantics of the XML Query Language.
This section describes the status of this document at the time of its
publication. Other documents may supersede this document. The latest status
of this document series is maintained at the W3C.
This is a First Public Working Draft for review by W3C Members and other interested
parties. It is a draft document and may be updated, replaced or made
obsolete by other documents at any time. It is inappropriate to use W3C
Working Drafts as reference material or to cite them as other than "work in
progress". This is work in progress and does not imply endorsement by the
W3C membership.
This document has been produced as part of the W3C XML Activity, following
the procedures set out for the W3C Process. The document has been written by
the XML Query Working Group.
The XML Query Working Group feels that the contents of this Working Draft
are reasonably stable, and therefore encourages feedback.
Comments on this document should be sent to the W3C mailing list
www-xml-query-comments@w3.org (archived at
http://lists.w3.org/Archives/Public/www-xml-query-comments/).
A list of current W3C Recommendations and other technical documents can be
found at http://www.w3.org/TR/.
1 Introduction
2 Concepts
2.1 Types and Signatures
2.1.1 Reference Type
2.1.2 Schema Types
2.2 Post Schema-Validated Infoset
3 Nodes
3.1 Data Model Instance
3.2 Document
3.3 Elements
3.4 Attributes
3.5 Namespaces
3.6 Processing Instructions
3.7 Comments
3.8 Values
3.9 Information Items
4 Example
5 Constraints on the Data Model
6 References
Appendices
A XML Information Set Mapping
A.1 Notation and Pseudo-code Syntax
A.2 Information Items
A.3 Document Item
A.4 Element Items
A.5 Attribute Items
A.6 Namespace Items
A.7 Processing Instruction Items
A.8 Comment Items
A.9 Other Information Items
B Candidate Operators for XML Query Algebra
B.1 Equality Operators
B.2 Serialization Operators
B.3 Order Operators
B.4 Accessors for Reference Values
C Internal Open Issues
1 Introduction
This document defines the W3C XML Query Data Model, which is the
foundation of the W3C XML Query Algebra; the XML Query Algebra
will be specified in a future document. Together, these two documents
[will] provide a precise semantics of the XML Query Language.
Several XML data models have been developed in the W3C Activities.
The XML Information Set (
http://www.w3.org/TR/xml-infoset)
provides a description of the information available in a well-formed XML
document. The XPath Recommendation (
http://www.w3.org/TR/xpath), which
is used by both XSLT (
http://www.w3.org/TR/xslt)
and XPointer (
http://www.w3.org/TR/xptr),
contains a data model and a mapping that relates the XPath data
model to the XML Information Set (hence ``Infoset''). The Document Object Model (
http://www.w3.org/TR/DOM-Level-2/)
is an API for HTML and XML documents, but it does imply an underlying
abstract data model. The XML Schema Working Group is defining features, such as
structures
(http://www.w3.org/TR/xmlschema-1)
and datatypes
(http://www.w3.org/TR/xmlschema-2), that extend an instance of the XML Information Set
with more precise type information.
The XML Query Data Model defines formally the information contained in the
input to an XML Query processor;
in other words, an XML Query processor evaluates a
query on an instance of the XML Query Data Model.
Our model is based on the XML Information Set,
but it requires the following new features to meet
the XML Query Working Group's requirements:
In this document, we provide a precise and formal definition of
how values in the XML Query Data Model are constructed and accessed;
these operators are the foundation of the XML Query Algebra, and
therefore, require a more formal treatment than is provided in
the definitions of the XPath and Infoset data models.
For comparison, we note wherever the XML Query Data Model differs from that of
XPath, and we provide a formal definition of the
mapping from the Infoset to the XML Query Data Model in
Appendix A.
An instance of the XML
Query data model represents one or more complete XML documents or document
parts. As with the Infoset, the XML Query Data Model specifies what
information in the documents is accessible, but it does not specify
the programming-language interfaces or bindings used to represent or
access the data. We assume that the information contained in an
instance of the XML Query Data Model is static for the duration
query evaluation; in particular, the meaning of a query applied to
input data that changes during query evaluation is undefined.
We define the data model using a functional notation.
We chose this notation because it is simple and permits a
precise and concise definition of the data model.
The notation is presented in the next section.
Although the notation has a functional style,
we emphasize that the data
model can be realized in a variety of programming languages and styles,
for example, as object classes and methods in an object-oriented language.
There is a close correspondence between the data model and the algebraic
operations that are applied to instances of the data model.
In the definition of the data model, we mention several algebraic
operators.
These and other candidate operators are identified
in the Candidate Operators for
XML Query Algebra appendix.
The complete algebra will be defined in a future document.
2 Concepts
Because XML documents are tree-structured, we define the XML Query
data model using conventional terminology
for trees.
Various mathematical representations of trees exist (see [CLR]).
The graph-theoretic representation models a tree as a
tuple (N, E, r),
where N is a set of tree nodes, E is a one-to-many
relation of edges from parent nodes to children nodes, and r is
the distinguished root node of the tree.
The tree-constructor representation
models a tree by recursive application of a tree-creation function
to a list of children trees
[Knuth].
In either representation,
a tree can have data associated with its nodes
(node-labeled), with its edges (edge-labeled), or
with both.
The XPath and Infoset data models
are examples of node-labeled, tree-constructor
representations.
The XML Query Data Model (hence ``data model'') is a node-labeled,
tree-constructor representation,
but also includes a concept of node identity.
The addition of node identity
simplifies the representation of XML reference values, e.g.,
IDREF, XPointer, and URI values.
Unlike the graph model, the data model
does not support both nodes and edges as first-class concepts.
We note, however, whenever a graph model may be more flexible or concise.
2.1 Types and Signatures
The data model defines the structure of various kinds of tree nodes;
functions to construct tree nodes, called constructors;
and functions to access nodes' structure, called
accessors.
This presentation is similar to that in the definition of
the XSLT data model [Wadler].
We use the terms node type to refer to the kind of
a tree node;
schema type to refer to an XML Schema type;
and collection type to refer to tuples, lists, sets, and
disjoint unions.
The term type refers to any node, schema, or collection
type.
The term signature refers to a constructor's or
accessor's function type, i.e., the function's zero or more input
types and
its one output type.
To make the definition of the data model concise, we use the
following notation:
-
N ranges over node types.
-
U ranges over the union of node types, schema types,
and collection types.
-
[ U ] denotes a list of values with type
U; a list is ordered and may contain duplicates.
-
{ U } denotes a set of values with type
U; a set is unordered and does not contain duplicate values.
-
{| U |} denotes a bag of values with
type U; a bag is unordered and may contain duplicate values.
-
(U1, U2, ..., Un) denotes a tuple whose first
component has type U1, second component
has type U2, etc.
-
U1 | U2 | ... | Un denotes
the disjoint union of values with types U1,...,
Un, etc.
-
TN = U denotes
that the string TN is a type name that represents the
type U. A type name may appear wherever its associated
type is expected.
An occurrence of the type symbol
U denotes a value or instance
of that type.
The signatures of constructors and accessors use the following notation:
2.1.1 Reference Type
The data model provides node references as a mechanism to
test and bind the identity of nodes in a given instance of the data
model. The actual mechanism for implementing
node identity is implementation dependent, for example,
node identity might be represented by a key value, an object
identifier, an XPointer value, etc.
The data model provides the function ref to create a reference to a
node and the function deref to produce
the node referent of a reference value.
Their signatures are:
ref : Node -> Ref(Node)
deref : Ref(Node) -> Node
The function ref is surjective, i.e., it is
onto. The function deref is the inverse of ref,
i.e., for all nodes n, node_equal(deref(ref(n)),
n) is true, where node_equal is an implementation-dependent
equality operator over nodes.
Some accessors map values (e.g., IDREF or key values)
into reference values. If a key value does not represent a valid
reference, the ``not a reference'' value, NaR, may be used.
2.1.2 Schema Types
Nodes contain values that are instances of schema types.
The following symbols denote schema types:
A simple type is either primitive (e.g., string,
boolean, float, double, ID, IDREF) or derived
(e.g., language, NMTOKEN, long, etc., or user defined).
A complex type defines the structure and content of an element.
It may be necessary for a query to have access to
a value's type during query execution, i.e., at run time.
Because an instance of an XML Schema is also an XML document
(see
XML Representation of Schemas and Schema Components
in [XMLSchema Part 1]),
a document's schema can be represented as an instance of the
data model.
Because Def_T is an element value in the data model, i.e., an ElemNode,
all of the accessors defined for ElemNode
can be applied to Def_T values.
2.2 Post Schema-Validated Infoset
We assume that an instance of the data model is derived from an instance of
the XML Information Set [XML Infoset] after
XML Schema validation.
Such an instance is called a ``PSV Infoset'',
for post schema-validated Infoset.
Schema information may be associated with a document in two ways. A
document may refer directly to a DTD, and a document may be paired
with an XML Schema, which may be derived from one or more XML Schema
documents. It is also possible for an XML document to have no DTD or
associated schema, i.e., it is ``schemaless''. For a document,
schema pair, the PSV Infoset provides the schema. For a document
that refers directly to a DTD, we assume a mapping from the DTD to
an equivalent schema is provided, and the PSV Infoset provides this
equivalent schema. For a schemaless document, a default schema is
provided by the data model, and we specify in this document that
default schema. In all three cases, a schema can be provided for
the input document and the corresponding data-model instance.
3 Nodes
The basic concept in the data model is a Node. A
Node is one of eight node types:
document, element, value, attribute, namespace
(NS), processing instruction (PI), comment, or information item.
This definition specifies that a Node is the disjoint union of
eight node types:
Node = DocNode | ElemNode | ValueNode | AttrNode
| NSNode | PINode | CommentNode | InfoItemNode
The eight node types are defined in the following subsections.
Note that an implementation of the data model in an object-oriented language
might choose to make Node an interface (or an abstract class) and
to make each node type a concrete class that implements the Node
interface (or a sub-class of the abstract class Node).
A Node has eight accessors, each of which returns true if
the Node value is of the specified type.
isDocNode : Node -> boolean
isElemNode : Node -> boolean
isValueNode : Node -> boolean
isAttrNode : Node -> boolean
isNSNode : Node -> boolean
isPINode : Node -> boolean
isCommentNode : Node -> boolean
isInfoItemNode : Node -> boolean
3.1 Data Model Instance
An XML document is represented by its distinguished
document node, which is a DocNode.
A document part is a sub-tree of a document and is represented by
an ElemNode, ValueNode, PINode, or
CommentNode.
An instance of the data model
represents one or more complete documents or document parts
and may be unordered or ordered.
Therefore, a data-model Instance is
a set, a list, or a bag of one or more nodes:
Instance = { DocNode | ElemNode | ValueNode | PINode | CommentNode }
| [ DocNode | ElemNode | ValueNode | PINode | CommentNode ]
| {| DocNode | ElemNode | ValueNode | PINode | CommentNode |}
3.2 Document
A document is represented by a unique DocNode, which
corresponds to a document information item in the Infoset.
A DocNode has the constructor docNode, which
takes a URI reference value and a non-empty list of its children nodes:
docNode : (URIRefValue, [ Ref(ElemNode) | Ref(PINode) | Ref(CommentNode) ])
-> DocNode
The list of children nodes
may contain zero or more references to PINodes and
CommentNodes and
must contain exactly one reference to an ElemNode.
The accessor uri returns a DocNode's URI
reference value, and
the accessor children returns a
DocNode's list of children:
uri : DocNode -> URIRefValue
children : DocNode -> [ Ref(ElemNode) | Ref(PINode) | Ref(CommentNode) ]
The root accessor returns a reference to the unique
ElemNode in a DocNode's children list:
root : DocNode -> Ref(ElemNode)
3.3 Elements
An ElemNode has the constructor
elemNode, which takes a tag value,
a set of NSNode namespaces, a
set of AttrNode attributes, a list of children nodes, and
a reference to the node's type:
elemNode : (Ref(QNameValue), { Ref(NSNode) }, { Ref(AttrNode) },
[ Ref(ElemNode) | Ref(ValueNode) | Ref(PINode)
| Ref(CommentNode) | Ref(InfoItemNode) ],
Ref(Def_T))
-> ElemNode
An ElemNode's tag is a qualified name value, QNameValue.
An ElemNode's set of namespaces contain one namespace node
for each distinct namespace that is declared explicitly on the element.
The node's children is a list of references to
ElemNode,
ValueNode, PINode,
CommentNode, and InfoItemNode values.
We assume that the element is an instance of
the type represented by Def_T, i.e., the document
``type checks'' or is valid with respect to the given schema.
For a schemaless document, the data model defines a default schema;
in this case, the Def_T value for all ElemNodes
is the ur-type definition [XMLSchema Part 1].
The accessors name, namespaces,
attributes, children, and type
returns an ElemNode's constituent parts:
name : ElemNode -> Ref(QNameValue)
namespaces : ElemNode -> { Ref(NSNode) }
attributes : ElemNode -> { Ref(AttrNode) }
children : ElemNode -> [ Ref(ElemNode) | Ref(ValueNode) | Ref(PINode)
| Ref(CommentNode) | Ref(InfoItemNode) ]
type : ElemNode -> Ref(Def_T)
The accessor parent returns a reference to
the unique parent of an ElemNode.
If an ElemNode is the root node of a
document, parent will
return a reference to the corresponding
DocNode, unless a document node
does not exist, in which case parent returns
NaR, the ``not a reference'' value.
parent : ElemNode -> Ref(ElemNode) | Ref(DocNode) | NaR
NOTE: The XPath data model does not model the complex type of a
node.
This definition adds Def_T
to an element node, and it also adds ValueNode
and InfoItemNode as
permissible children of an element node.
3.4 Attributes
An AttrNode has the constructor
attrNode,
which takes the attribute's name and value:
attrNode : (Ref(QNameValue), Ref(ValueNode)) -> AttrNode
The accessors name and value,
return an attribute's constituent parts:
name : AttrNode -> Ref(QNameValue)
value : AttrNode -> Ref(ValueNode)
For a schemaless document, the data model defines a default schema;
in this case, the type of all AttrNode's values is the
simple type
<simpleType base="string"/>.
The accessor parent returns a reference to
the containing element of an AttrNode.
parent : AttrNode -> Ref(ElemNode)
NOTE:
The XPath data model only permits attribute values to be strings.
This definition permits attribute values to be of any simple type.
3.5 Namespaces
An NSNode has the constructor
nsNode, which
takes an namespace prefix, which may be null, and
the absolute URI of the namespace being declared, which may be null:
nsNode : (Ref(StringValue) | null, Ref(URIRefValue) | null) -> NSNode
The accessors prefix and uri return a
NSNode's constituent parts:
prefix : NSNode -> Ref(StringValue) | null
uri : NSNode -> Ref(URIRefValue) | null
A namespace node may contain:
a non-null prefix and a non-null uri;
a null prefix and a non-null uri;
or a null prefix and a null uri.
A namespace node may not contain a non-null prefix and a null uri.
The accessor parent returns a reference to
the containing element of an NSNode.
parent : NSNode -> Ref(ElemNode)
3.6 Processing Instructions
A PINode has the constructor
piNode, which
takes a local name that is the
processing instruction's target and a string
value:
piNode : (Ref(StringValue), Ref(StringValue)) -> PINode
The local name is a string value that must have type NCNAME, i.e.,
its type value refers to the definition of the derived
type NCName :
<simpleType name="NCName" base="Name"/>
The accessors target, value return
a PINode's constituent parts.
target : PINode -> Ref(StringValue)
value : PINode -> Ref(StringValue)
The accessor parent returns a PINode's
unique parent:
parent : PINode -> Ref(ElemNode) | Ref(DocNode) | NaR
3.7 Comments
A CommentNode has the constructor
commentNode,
which takes a string value:
commentNode : Ref(StringValue) -> CommentNode
The accessor value returns
a CommentNode's value, and
the accessor parent returns a CommentNode's
unique parent:
value : CommentNode -> Ref(StringValue)
parent : CommentNode -> Ref(ElemNode) | Ref(DocNode) | NaR
3.8 Values
A ValueNode is the disjoint union of
fourteen kinds of simple-type values; each value kind has an
associated constructor.
ValueNode = StringValue | BoolValue | FloatValue | DoubleValue
| DecimalValue | TimeDurValue | RecurDurValue | BinaryValue
| URIRefValue | IDValue | IDREFValue | QNameValue
| ENTITYValue | NOTATIONValue
The data model provides constructors for the fourteen primitive
XML Schema datatypes:
stringValue : (string, Ref(Def_string), [Ref(InfoItemNode)]) -> StringValue
boolValue : (boolean, Ref(Def_boolean)) -> BoolValue
floatValue : (float, Ref(Def_float)) -> FloatValue
doubleValue : (double, Ref(Def_double)) -> DoubleValue
decimalValue : (decimal, Ref(Def_decimal)) -> DecimalValue
timeDurValue : (timeDuration, Ref(Def_TimeDuration)) -> TimeDurValue
recurDurValue: (recurringDuration, Ref(Def_recurringDuration))-> RecurDurValue
binaryValue : (binary, Ref(Def_binary)) -> BinaryValue
urirefValue : (uriReference, Ref(Def_uriReference)) -> URIRefValue
idValue : (ID, Ref(Def_ID)) -> IDValue
idrefValue : (IDREF, Ref(Def_IDREF)) -> IDREFValue
qnameValue : (uriReference | null, string, Ref(Def_QName)) -> QNameValue
entityValue : (ENTITY, Ref(Def_ENTITY)) -> ENTITYValue
notationValue: (NOTATION, Ref(Def_NOTATION)) -> NOTATIONValue
Ed. Note:
We note here that the data model does not currently represent
key values and key reference values
as described in XML Schema Part 1 : Structures
[XMLSchema Part 1].
In a future draft of this document, keys and key references will be
represented in the data model.
Derived datatypes are modeled as instances of their primitive base type.
In particular, wherever an instance of Def_ST is
expected,
we assume an instance of ST' is permitted if and only if
ST' is derived from simple type ST.
For example, the derived simple type long has base type
integer, so an instance of long can be
modeled by an IntegerValue whose type is
Ref(Def_long), i.e., it refers to the definition of the
derived type long:
<simpleType name="long" base="integer"/>
The explicit enumeration of each kind of value guarantees
that the type of the value's instance and its type representation
correspond. For example, a StringValue always
contains a string value and a reference to the
representation of a primitive or derived type whose base type is
string.
For example, a product's ``Sku'' number could be represented by the
string value:
StringValue("926-AA", Ref(Def_Sku), [])
where the Sku type is derived from string:
<simpleType name="Sku" base="string">
<pattern value="\d{3}-[A-Z]{2}"/>
</simpleType>
The accessor type returns a ValueNode's type:
type : ValueNode -> Ref(Def_ST)
The accessor string returns a ValueNode's
string representation:
string : ValueNode -> StringValue
The accessor infoItems returns the list of information
items associated with a StringValue; this list may
contain the character information items from which the string value
was created:
infoItems : StringValue -> [ Ref(InfoItemNode) ]
The accessors localPart and uriPart
return a QNameValue's constituent parts:
uriPart : QNameValue -> uriReference | null
localPart : QNameValue -> string
The accessor referent returns a list of element-node references associated
with an IDREFValue or URIRefValue:
referent : (IDREFValue | URIRefValue) -> [ Ref(ElemNode) | NaR ]
If a referent is not in the data-model instance,
referent returns NaR, the ``not a
reference'' value.
In a data-model instance of a PSV infoset,
every IDREF and keyref value is guaranteed to refer to a
ElemNode in the data-model instance.
This may not be the case for a URI value, which could refer to an
element in an arbitrary document that is not contained in the data-model
instance. In this case, referent may return a list
containing NaR.
A ValueNode has fifteen additional
accessors, each of which returns true if
the ValueNode is of the specified type.
isStringValue : ValueNode -> boolean
isBoolValue : ValueNode -> boolean
isFloatValue : ValueNode -> boolean
isDoubleValue : ValueNode -> boolean
isDecimalValue : ValueNode -> boolean
isTimeDurValue : ValueNode -> boolean
isRecurDurValue : ValueNode -> boolean
isBinaryValue : ValueNode -> boolean
isURIRefValue : ValueNode -> boolean
isIDValue : ValueNode -> boolean
isIDREFValue : ValueNode -> boolean
isQNameValue : ValueNode -> boolean
isENTITYValue : ValueNode -> boolean
isNOTATIONValue : ValueNode -> boolean
NOTE: ValueNode replaces the XPath data model's text
node.
3.9 Information Items
An InfoItemNode has the constructor infoItemNode:
infoItemNode : Ref(InfoItem) -> InfoItemNode
An InfoItemNode is an opaque value that preserves those
information items that are not of interest to the data model or query
language, but are required by the underlying Infoset implementation.
It has no accessors.
4 Example
We use the following XML document to illustrate the information contained in
an instance of the data model:
<?xml version=1.0?>
<p:part xmlns:p="http://www.mywebsite.com/PartSchema"
xsi:schemaLocation = "http://www.mywebsite.com/PartSchema
http://www.mywebsite.com/PartSchema"
name="nutbolt">
<mfg>Acme</mfg>
<price>10.50</price>
</p:part>
The XML schema for this document is:
<xsd:schema xmlns:xsd="http://www.w3.org/1999/XMLSchema"
targetNamespace="http://www.mywebsite.com/PartSchema">
<xsd:element name="part" type="part_type">
<xsd:complexType name="part_type">
<xsd:element name = "mfg" type="xsd:string"/>
<xsd:element name = "price" type="xsd:decimal"/>
<xsd:attribute name = "name" type="xsd:string"/>
</xsd:complexType>
</xsd:element>
</xsd:schema>
For this example, we chose a XML document that includes an
XML Schema to illustrate the relationship between
document content and its associated schema type information.
In general, an XML Schema is not required,
that is, the data model can represent a schemaless, well-formed XML
document with the default typing described in this document.
The XML document is represented by the data-model accessors below.
The value D1 represents a DocNode;
the values E1, E2, etc. represent ElemNodes;
the values A1, etc. represent AttrNodes;
the values N1, etc. represent NSNodes.
children(D1) = [ Ref(E1) ]
root(D1) = Ref(E1)
name(E1) = QNameValue("http://www.mywebsite.com/PartSchema",
"part", Ref(Def_QName))
children(E1) = [ Ref(E2), Ref(E3) ]
attributes(E1) = { Ref(A1) }
namespaces(E1) = { Ref(N1) }
type(E1) = Ref(Def_part_type)
parent(E1) = Ref(D1)
name(A1) = QNameValue(null, "name", Ref(Def_QName))
value(A1) = Ref(StringValue("nutbolt", Ref(Def_string)))
parent(A1) = Ref(E1)
prefix(N1) = Ref(StringValue("p", Ref(Def_string)))
uri(N1) = URIRefValue("http://www.mywebsite.com/PartSchema",
Ref(Def_uriReference))
parent(N1) = Ref(E1)
name(E2) = QNameValue(null, "mfg", Ref(Def_QName))
children(E2) = [ Ref(StringValue("Acme", Ref(Def_string))) ]
attributes(E2) = {}
namespaces(E2) = {}
type(E2) = Ref(Def_string)
parent(E2) = Ref(E1)
name(E3) = QNameValue(null, "price", Ref(Def_QName))
children(E3) = [ Ref(DecimalValue(10.50, Ref(Def_decimal))) ]
attributes(E3) = {}
namespaces(E3) = {}
type(E3) = Ref(Def_decimal)
parent(E3) = Ref(E1)
A graphical depiction of the
data-model instance, containing the information described in
the text above, is also included.
Recall that an XML schema is also an XML document, which can be
represented in the data model. The complex and
simple types in the example schema are represented below:
name(Def_part_type) = QNameValue("http://www.w3.org/1999/XMLSchema",
"complexType", Ref(Def_QName))
children(Def_part_type) = [ Ref(E4), Ref(E5), Ref(E6) ]
attributes(Def_part_type) = { Ref(A2) }
namespaces(Def_part_type) = {}
type(Def_part_type) = Ref(Def_complexType)
name(A2) = QNameValue(null, "name", Ref(Def_QName))
value(A2) = Ref(StringValue("part_type", Ref(Def_NCName), []))
name(E4) = QNameValue("http://www.w3.org/1999/XMLSchema",
"element", Ref(Def_QName))
children(E4) = []
attributes(E4) = { Ref(A3), Ref(A6) }
namespaces(E4) = {}
type(E4) = Ref(Def_element)
name(A3) = QNameValue(null, "name", Ref(Def_QName))
value(A3) = Ref(StringValue("mfg", Ref(Def_NCName), []))
name(A6) = QNameValue(null, "type", Ref(Def_QName))
value(A6) = Ref(QNameValue("http://www.w3.org/1999/XMLSchema",
"string", Ref(Def_QName), []))
name(E5) = QNameValue("http://www.w3.org/1999/XMLSchema",
"element", Ref(Def_QName))
children(E5) = []
attributes(E5) = { Ref(A4), Ref(A7) }
namespaces(E5) = {}
type(E5) = Ref(Def_element)
name(A4) = QNameValue(null, "name", Ref(Def_QName))
value(A4) = Ref(StringValue("price", Ref(Def_NCName)))
name(A7) = QNameValue(null, "type", Ref(Def_QName))
value(A7) = Ref(QNameValue("http://www.w3.org/1999/XMLSchema",
"decimal", Ref(Def_QName), []))
name(E6) = QNameValue("http://www.w3.org/1999/XMLSchema",
"attribute", Ref(Def_QName))
children(E6) = []
attributes(E6) = { Ref(A5), Ref(A8) }
namespaces(E6) = {}
type(E6) = Ref(Def_attribute)
name(A5) = QNameValue(null, "name", Ref(Def_QName))
value(A5) = Ref(StringValue("name", Ref(Def_NCName), []))
name(A8) = QNameValue(null, "type", Ref(Def_QName))
value(A8) = Ref(QNameValue("http://www.w3.org/1999/XMLSchema",
"string", Ref(Def_QName), []))
For conciseness, we eliminate the definitions of
builtin schema components, e.g., complexType,
and of primitive simple types, e.g., string.
5 Constraints on the Data Model
A data-model instance must satisfy the following constraints:
-
Node references:
We assume that the representation of a node reference is defined by the
query system that implements the data model, not by the query language
itself.
Node references are not serialized, i.e., they exist only for use by
the query system, and
they are not guaranteed to be globally unique or persistent, although
some implementation of the data model may choose to support
persistent node references.
Multiple techniques may exist for implementing references,
and there may be multiple techniques for implementing identity.
-
Node identity: the function ref is one-to-one and onto, i.e.,
ref_equal(ref(n1), ref(n2)) holds if and only if
n1
and n2 are the same node.
We assume that the operator
ref_equal is an implementation-dependent
equality operator over node references.
-
Unique parent: the parent accessor is a many-to-one
function, i.e., a node has exactly one parent.
-
Parent-child relationships:
Given two ElemNode references ref(p)
and ref(n),
ref_equal(parent(n), ref(p))
holds if and only if ref(n) is in children(p).
Similarly, given a DocNode reference ref(d)
and a node reference ref(n),
ref_equal(parent(n), ref(d))
if and only if ref(n) is in children(d).
Finally, given a AttrNode (or NSNode) reference ref(a)
and a node reference ref(n),
ref_equal(parent(a), ref(n))
if and only if ref(a) is in attributes(n)
(namespaces(n)).
-
Duplicate-free list of children:
Given a node n
and any two node references r1 and r2 at distinct
positions in children(n), not ref_equal(r1,
r2) must hold
i.e., the ordered list of children nodes is duplicate free.
6 References
-
CLR
-
T. Cormen, C. Leiserson, R. Rivest,
Introduction to Algorithms,
MIT Press, 1991.
-
Knuth
- D. Knuth, The Art of Computer Programming,
Vol. 1, Addison-Wesley, 1973.
-
Wadler
- P. Wadler, A formal
semantics of patterns in XSLT. Available at:
http://www.cs.bell-labs.com/who/wadler/papers/xsl-semantics/xsl-semantics.pdf
-
XML Infoset
-
World Wide Web Consortium,
XML Information Set (Infoset). Available at: http://www.w3.org/TR/xml-infoset
-
XPath
-
World Wide Web Consortium,
XML Path Language (XPath). Available at: http://www.w3.org/TR/xpath.html
-
XMLSchema Part 1
-
World Wide Web Consortium,
XML Schema Part 1 : Structures.
Available at: http://www.w3.org/TR/xmlschema-1
-
XMLSchema Part 2
-
World Wide Web Consortium,
XML Schema Part 2 : Datatypes.
Available at: http://www.w3.org/TR/xmlschema-2
A XML Information Set Mapping
The XML Information Set (http://www.w3.org/TR/xml-infoset)
provides a description of the information available in a well-formed XML
document.
In this appendix,
we define the Infoset in the same
notation as the data model, and
we define functions that map
from an instance of the Infoset to an instance of the data model
in a pseudo-code notation.
Ed. Note:
In a future draft of this document, a mapping from the XML Query
data model into the Infoset will be provided.
A.1 Notation and Pseudo-code Syntax
We name accessors of the PSV Infoset
using the convention psv_<item-name>_<property>
.
For example, psv_elem_attributes is the accessor
that returns an element item's attributes property.
The comments in the accessor definitions specify
whether a property is core or
peripheral.
The following operations are defined on lists and are used in the
function definitions:
-
[] constructs the empty list.
-
[n] constructs a list with one element n.
-
h :: t constructs a list with head element h and
tail list t.
It is often necessary to deconstruct a list value, for example, into
its head element and tail list.
We use the same notation to match and deconstruct list values.
For example, this function maps all "a" values in a
list
to "b" values by deconstructing and matching the argument
list L:
fun a2b(L) {
case L of [] => []
| [ "a" ] :: t => [ "b" ] :: (a2b t)
| h :: t => h :: (a2b t)
}
a2b [ "a", "c", "a" ] = [ "b", "c", "b" ]
The case expression matches its list argument
L against each list pattern and evaluates the
right-hand-side of the first pattern that matches L.
The function concat_list concatenates two lists, and
concat_string concatenates two strings:
concat_list : ([ U ], [ U ]) -> [ U ]
concat_string : (string, string) -> string
For example,
concat_list [ 1, 2 ] [ 3, 4 ] = [ 1, 2, 3, 4 ]
concat_string "First" "Last" = "FirstLast"
The function flat_list takes a list of
lists and returns the flattened list:
flat_list : [ [ U ] ] -> [ U ]
For example,
flat_list([ [1], [2, 3] ]) = [ 1, 2, 3 ]
The function
map_set applies a function to every
member of a set and returns the transformed set;
map_list is analogous for lists:
map_set : ((U1 -> U2), { U1 }) -> { U2 }
map_list : ((U1 -> U2), [ U1 ]) -> [ U2 ]
For example, given the function addOne:
fun add_one(x) { return x + 1 }
map_set add_one { 1, 2 } = { 2, 3 }
map_list add_one [ 1, 2 ] = [ 2, 3 ]
A.2 Information Items
The basic concept in the Infoset is an InfoItem. An
InfoItem is one of ten item types:
InfoItem = DocItem | ElemItem | CDATAItem | AttrItem
| NSItem | PIItem | CommentItem | SkipEntityItem
| EntityMarker | CDATAMarker
No constructors are defined for Item values, because they
are constructed by an Infoset processor, not the data model.
A.3 Document Item
The following accessors are defined on a document information item:
/* core */
psv_doc_children : DocItem -> [ /* core */
Ref(PIItem) | Ref(ElemItem)
/* peripheral */
| Ref(CommentItem) | Ref(DocTypeItem) ]
psv_doc_notations : DocItem-> { Ref(NotationItem) }
psv_doc_base_uri : DocItem -> uriReference
/* core : unparsed entities; peripheral : parsed entities */
psv_doc_entities : DocItem -> { Ref(EntityItem) }
Exactly one ElemItem is required in the psv_doc_children
list and it is the root element of the document tree.
The following pseudo-code documents the mapping from an
instance of the PSV infoset to an instance of the data model.
The function dm_docNode
maps a document information item (DocItem) to a document
node (DocNode):
dm_docNode : DocItem -> DocNode
fun dm_docNode(d) {
kids = map_list dm_node (psv_doc_children d)
return docNode(uriValue(psv_doc_base_uri d, ref(Def_uriReference)), kids)
}
In the definition of kids,
map_list applies the function dm_node to each child
of the DocItem value d; this constructs a
new list of children nodes, each of which has type Node.
The application of the constructor docNode constructs the
document node in the data model.
A.4 Element Items
The following accessors are defined on element information items:
/* core */
psv_elem_uri : ElemItem -> uriReference
psv_elem_local_name: ElemItem -> string
psv_elem_children : ElemItem -> [ /* core */
Ref(PIItem)
| Ref(ElemItem)
| Ref(SkipEntityItem)
| Ref(CDATAItem)
/* peripheral */
| Ref(CommentItem)
/* start, end marker pairs : */
| (Ref(EntityMarker), Ref(EntityMarker))
| (Ref(CDATAMarker), Ref(CDATAMarker))
]
/* core */
psv_elem_attrs : ElemItem -> { AttrItem }
psv_elem_decl_ns : ElemItem -> { NSItem } /* declared namespaces */
psv_elem_base_uri : ElemItem -> uriReference
psv_elem_parent : ElemItem -> (Ref(ElemItem) | Ref(DocItem))
/* Infoset item for schema type */
psv_elem_schema_type : ElemItem -> Ref(ElemItem)
/* peripheral */
psv_elem_inscope_ns : ElemItem -> { NSItem } /* in-scope namespaces */
The function dm_elemNode
maps an ElemItem to an ElemNode:
dm_elemNode : ElemItem -> ElemNode
fun dm_elemNode(e) {
name = qnameValue(psv_elem_uri e, psv_elem_local_name e, Ref(Def_QName))
nsnodes = map_set dm_nsNode (psv_elem_decl_ns e)
attrnodes = map_set dm_attrNode (psv_elem_attrs e)
kids = dm_collapse_strings(map_list dm_node (psv_elem_children e))
type = dm_schema_type(psv_elem_schema_type e)
newkids = if (isSimpleType(type)) (map_list (dm_coerce_string type) kids)
else kids
return elemNode(name, nsnodes, attrnodes, newkids, type)
}
This function extracts components from the ElemItem,
transforms them into instances of data-model values, and then
constructs an ElemNode value.
The function dm_schema_type
returns a reference to the Def_T value that corresponds to the
schema type represented by its information-item argument.
dm_schema_type : Ref(ElemItem) -> Ref(Def_T)
We assume above that if an element's type is a simple type,
its list of children must contain one string value.
The function dm_coerce_string
coerces its string-valued second argument into an instance of the
simple type referenced by its first argument.
dm_coerce_string : (Ref(Def_ST), StringValue) -> ST
Ed. Note:
This mapping does not capture an element item's keyref values,
which are maintained in the element item's identity constraints table.
The identity constraints table is created for ``bookkeeping purposes''
by an XML Schema processor (see [XMLSchema Part 1]).
The mapping of an element item's identity constraints table into
keyref values will be specified in a future draft of this document.
The function dm_node maps an information item to a
reference to a data-model node.
All information items are preserved in the data model, but the
document type, skipped entity reference, entity markers, and character
data markers are represented by the opaque data type InfoItemNode.
dm_node : InfoItem -> Ref(Node)
fun dm_node(i) {
case i of
Ref(PIItem e) => ref(dm_piNode e)
| Ref(ElemItem e) => ref(dm_elemNode e)
| Ref(CommentItem) => ref(dm_commNode e)
| Ref(CharDataItem e) => ref(dm_char2string e)
| r as Ref(DocTypeItem) => ref(infoItemNode r)
| r as Ref(SkipEntityItem) => ref(infoItemNode r)
| p as (Ref(EntityMarker), Ref(EntityMarker)) => ref(infoItemNode p)
| p as (Ref(CDATAMarker), Ref(CDATAMarker)) => ref(infoItemNode p)
}
The function dm_char2string takes one CDATA item and maps
it to a StringValue with a string value of length one.
Note that the StringValue constructor preserves the
original CDATA item in a InfoItemNode.
dm_char2string : CDATAItem -> StringValue
fun dm_char2string(c) {
/* convert (psv_cdata_code c) to string of length 1 */
stringValue(code2string(psv_cdata_code c), Ref(Def_string),
[infoItemNode (ref c)])
}
The function dm_collapse_strings
synthesizes a single string value from multiple CDATA items.
It does this by
collapsing one or more consecutive StringValues in its
argument list,
each of which must have the simple schema type string,
into one StringValue whose content is the concatenation
of the values of the consecutive StringValues.
All other node values are returned unchanged.
dm_collapse_strings : [ Ref(Node) ] -> [ Ref(Node) ]
fun dm_collapse_strings(nodelist) {
case nodelist of :
[] => return []
| [ n ] => return [ n ]
| h1 as Ref(StringValue(s1, Ref(Def_string), i1)) :: t1 =>
{ case t1 of :
[] => return [ h1 ]
/* Collapse two consecutive strings and
apply dm_collapse_strings recursively */
| Ref(StringValue(s2, Ref(Def_string), i2)) :: t2 =>
return dm_collapse_strings(
ref(stringValue(concat_string(s1, s2),
Ref(Def_string),
concat_list(i1, i2))) :: t2)
| h :: t => return (h :: (dm_collapse_strings t))
}
}
A.5 Attribute Items
The following accessors are defined for attribute information items:
/* core */
psv_attr_children : AttrItem -> [ Ref(CDATAItem) ]
psv_attr_uri : AttrItem -> uriReference
psv_attr_local_name : AttrItem -> string
psv_attr_owner_elem : AttrItem -> Ref(ElemItem)
/* Infoset item for schema type */
psv_attr_schema_type : AttrItem -> Ref(ElemItem)
/* peripheral */
psv_attr_type : AttrItem -> string
psv_attr_spec_flag : AttrItem -> SpecifiedFlag
psv_attr_default : AttrItem -> [ Ref(CDATAItem) ]
psv_attr_start_entity : AttrItem -> Ref(EntityMarker)
psv_attr_end_entity : AttrItem -> Ref(EntityMarker)
The function dm_attrNode
maps an AttrItem to an AttrNode:
dm_attrNode : AttrItem -> AttrNode
fun dm_attrNode(a) {
name = qnameValue(psv_attr_uri a, psv_attr_local_name a, ref(Def_QName))
/* An attribute value should be one string */
value = head(dm_collapse_strings(map_list dm_node (psv_attr_children a)))
type = dm_schema_type(psv_attr_schema_type a)
/* convert value to appropriate type */
return attrNode(name, (dm_coerce_string type value))
}
A.6 Namespace Items
The following accessors are defined for namespaces:
/* core */
psv_ns_prefix : NSItem -> string
psv_ns_uri : NSItem -> uriReference
psv_ns_value : NSItem -> [ Ref(CDATAItem) | Ref(EntityMarker) ]
psv_ns_owner_elem : NSItem -> Ref(ElemItem)
The function dm_nsNode
maps an NSItem to an NSNode:
dm_nsNode : NSItem -> NSNode
fun dm_nsNode(i) {
/* what happens to NS node's CDATA children? */
return nsNode(stringValue(psv_ns_prefix i, ref(Def_string), []),
urirefValue(psv_ns_uri i, ref(Def_uriReference))
}
A.7 Processing Instruction Items
The following accessors are defined on processing-instruction information items:
/* core */
psv_pi_target : PIItem -> string
psv_pi_value : PIItem -> string
psv_pi_base_uri : PIItem -> uriReference
psv_pi_parent : PIItem
-> (Ref(ElemItem) | Ref(DocItem) | Ref(DocTypeItem))
The function dm_piNode
maps an PIItem to an PINode:
dm_piNode : PIItem -> PINode
fun dm_piNode(i) {
return piNode(stringValue(psv_pi_target i, ref(Def_NCName), []),
stringValue(psv_pi_value i, ref(Def_string), []))
}
A.8 Comment Items
The following accessor is defined on comment information items:
/* core */
psv_comm_value : CommentItem -> string
psv_comm_parent : CommentItem
-> (Ref(ElemItem) | Ref(DocItem) | Ref(DocTypeItem))
The function dm_commNode
maps an CommentItem to an CommentNode:
dm_commNode : CommentItem -> CommentNode
fun dm_commNode(i) {
return commNode(stringValue(psv_comm_value i, ref(Def_string), []))
}
A.9 Other Information Items
The data model represents
document type, skipped entity reference, entity markers, and character
data markers as instances of the opaque data type InfoItemNode.
For completeness,
the following accessors are defined for these information items.
/* Skip Entity Item : core */
psv_skip_entity_item : SkipEntityItem -> string
psv_skip_entity_ref : SkipEntityItem -> Ref(EntityItem)
psv_skip_entity_parent : SkipEntityItem -> Ref(ElemItem)
/* CDATA Item : core */
psv_cdata_code : CDATAItem -> Code
psv_cdata_parent : CDATAItem -> Ref(ElemItem)
/* CDATA Item : peripheral */
psv_cdata_whitespace : CDATAItem -> boolean
psv_cdata_predefined : CDATAItem -> boolean
/* Document Type Item : peripheral */
psv_doctype_entity : DocTypeItem -> Ref(EntityItem)
psv_doctype_children : DocTypeItem -> [ Ref(CommentItem) | Ref(PIItem) ]
psv_doctype_parent : DocTypeItem -> Ref(DocItem)
/* Entity Item : core */
psv_entity_name : EntityItem -> string
psv_entity_sysid : EntityItem -> string
psv_entity_pubid : EntityItem -> string
psv_entity_notat : EntityItem -> Ref(NotationItem)
psv_entity_base_uri : EntityItem -> uriReference
/* Entity Item : peripheral */
psv_entity_type : EntityItem -> string
psv_entity_content : EntityItem -> string
psv_entity_encoding : EntityItem -> string
psv_entity_standalone: EntityItem -> string /* "yes", "no", "notpresent" */
/* Entity Marker : core */
psv_entity_marker_entity : EntityMarker -> Ref(EntityItem)
psv_entity_marker_parent : DocTypeItem
-> (Ref(ElemItem) | Ref(AttrItem) | Ref(NSItem))
/* Notation Item : core */
psv_notation_name : NotationItem -> string
psv_notation_sysid : NotationItem -> string
psv_notation_pubid : NotationItem -> string
psv_notation_base_uri: NotationItem -> uriReference
/* CDATA Marker : core */
psv_cdata_marker_parent : CDataMarker
-> (Ref(ElemItem) | Ref(AttrItem) | Ref(NSItem))
B Candidate Operators for XML Query Algebra
There is a close correspondence between the data model and the algebraic
operations that are applied to instances of the data model.
In this appendix, we identify those algebraic operators that
are candidate operators for the algebra.
B.1 Equality Operators
An algebra typically defines at least one equality operator for all
types in the data model.
We assume the algebra includes two equality operators:
node_equal and ref_equal, which
define equality on node values and on node references.
We assume that these operators are provided by the data-model
implementation and conform to the constraints specified in Constraints on the Data Model.
The algebra may define other equality operators, for example,
that perform coercions between values of different types.
B.2 Serialization Operators
In the XPath data model, every kind of node has an associated
string value,
i.e., a string serialization
of the node's value.
The data model already provides an operator for serializing a
ValueNode as a string.
The algebra also may include one or more operators to serialize a
Node as a string:
serialize : Node -> StringValue
One serialization operator may emit a node value
in Canonical XML.
Other operators may choose other serializations.
B.3 Order Operators
Given an instance of the data model, an ordering relation
on its nodes can be defined.
For example, document order, i.e., the absolute order of nodes in an
input document, is a property that a user
of the XML Query Language may want to query.
Given a single input document, a global,
total order can be defined on nodes.
In general, however, it may not be possible to define a global order,
for example when a data model instance contains nodes from multiple
input documents.
Therefore, it may be useful and necessary to have
multiple ordering relations, e.g., one that is global and one that is
partial:
globalOrder : (Instance, Node) -> IntegerValue
partialOrder : (Instance, Node) -> IntegerValue
Order operators must be defined over a particular instance of the data
model.
The functions return an integer order value given an instance of the
data model and a node contained in that instance.
B.4 Accessors for Reference Values
Although reference values are often contained in attribute nodes,
they typically represent element-to-element relationships.
For convenience, the algebra may define additional accessor functions that produce
the references associated with a particular element.
For example, the idrefs function takes an
ElemNode and returns a list of references to element
nodes that are referenced by IDREF values in the element's
attribute and children components; this accessor is defined in terms
of existing accessors:
idrefs : ElemNode -> [ Ref(ElemNode) ]
fun idrefs(n) {
concat_list(
flat_list [ referent(v) | a <- list(attributes(n)), v = value(a),
isIDREFValue(v) ],
flat_list [ referent(c) | c <- children(n), isIDREFValue(c) ])
)
}
The function is defined using a list comprehension, which is based
on a familiar notation for sets. The second expression above:
[ referent(c) | c <- children(n), isIDREFValue(c) ]
is read as follows: return the list of the referent values
of each node c
such that c is a
child of n and c is a IDREFValue.
Since referent produces a list, the result of this
expression is a list of lists: flat_list takes a list of
lists and returns the flattened list, and
concat_list concatenates
the two lists into one.
The attributes accessor returns a set, not a list, so the
list function converts (non-deterministically) a set to a list.
The links accessor is analogous to
idrefs, but returns non-null URI values
that occur in the element's attributes and children components;
it is defined as:
links : ElemNode -> [ Ref(ElemNode) ]
fun links(n) {
concat_list(
flat_list [ referent(v) | a <- list(attributes(n)), v = value(a),
isURIRefValue(v), not(referent(v) = NaR) ],
flat_list [ referent(v) | c <- children(n), isURIRefValue(c),
not(referent(c) = NaR)])
}
C Internal Open Issues