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W3C

XML Path Language (XPath) 4.0 WG Review Draft

W3C Editor's Draft 12 April 2021

This version:
https://qt3cg.org/
Most recent version of XPath 4:
https://www.w3.org/TR/xpath-4/
Most recent version of XPath:
https://www.w3.org/TR/xpath/
Most recent Recommendation of XPath:
https://www.w3.org/TR/2014/REC-xpath-30-20140408/
Editor:
Michael Kay, Saxonica <mike@saxonica.com>

Please check the errata for any errors or issues reported since publication.

See also translations.


Abstract

XPath 4.0 is an expression language that allows the processing of values conforming to the data model defined in [XQuery and XPath Data Model (XDM) 3.1]. The name of the language derives from its most distinctive feature, the path expression, which provides a means of hierarchic addressing of the nodes in an XML tree. As well as modeling the tree structure of XML, the data model also includes atomic values, function items, and sequences. This version of XPath supports JSON as well as XML, adding maps and arrays to the data model and supporting them with new expressions in the language and new functions in [XQuery and XPath Functions and Operators 3.1]. These are the most important new features in XPath 4.0:

  1. 4.14.1 Maps.

  2. 4.14.2 Arrays.

XPath 4.0 is a superset of [XML Path Language (XPath) Version 3.0]. A detailed list of changes made since XPath 3.0 can be found in I Change Log.

Status of this Document

This is a first proposal by the editor, with no official standing whatsoever. Comments are invited.


1 Introduction

The primary purpose of XPath is to address the nodes of XML trees and JSON trees. XPath gets its name from its use of a path notation for navigating through the hierarchical structure of an XML document. XPath uses a compact, non-XML syntax to facilitate use of XPath within URIs and XML attribute values. XPath 4.0 adds a similar syntax for navigating JSON trees.

[Definition: XPath 4.0 operates on the abstract, logical structure of an XML document or JSON object, rather than its surface syntax. This logical structure, known as the data model, is defined in [XQuery and XPath Data Model (XDM) 3.1].]

XPath is designed to be embedded in a host language such as [XSL Transformations (XSLT) Version 3.0] or [XQuery 3.1: An XML Query Language]. [Definition: A host language for XPath is a language or specification that incorporates XPath as a sublanguage and that defines how the static and dynamic context for evaluation of XPath expressions are to be established.]

XPath 4.0 is a subset of XQuery 4.0. In general, any expression that is syntactically valid and executes successfully in both XPath 4.0 and XQuery 4.0 will return the same result in both languages. There are a few exceptions to this rule:

Because these languages are so closely related, their grammars and language descriptions are generated from a common source to ensure consistency, and the editors of these specifications work together closely.

XPath 4.0 also depends on and is closely related to the following specifications:

This document specifies a grammar for XPath 4.0, using the same basic EBNF notation used in [XML 1.0]. Unless otherwise noted (see A.2 Lexical structure), whitespace is not significant in expressions. Grammar productions are introduced together with the features that they describe, and a complete grammar is also presented in the appendix [A XPath 4.0 Grammar]. The appendix is the normative version.

In the grammar productions in this document, named symbols are underlined and literal text is enclosed in double quotes. For example, the following productions describe the syntax of a static function call:

[76]    FunctionCall    ::=    EQName ArgumentList
[58]    ArgumentList    ::=    "(" ((PositionalArguments ("," KeywordArguments)?) | KeywordArguments)? ")"

The productions should be read as follows: A function call consists of an EQName followed by an ArgumentList. The argument list consists of an opening parenthesis, an optional list of one or more arguments (separated by commas), and a closing parenthesis.

This document normatively defines the static and dynamic semantics of XPath 4.0. In this document, examples and material labeled as "Note" are provided for explanatory purposes and are not normative.

Certain aspects of language processing are described in this specification as implementation-defined or implementation-dependent.

A language aspect described in this specification as implementation-defined or implementation dependent may be further constrained by the specifications of a host language in which XPath is embedded.

2 Basics

The basic building block of XPath 4.0 is the expression, which is a string of [Unicode] characters; the version of Unicode to be used is implementation-defined. The language provides several kinds of expressions which may be constructed from keywords, symbols, and operands. In general, the operands of an expression are other expressions. XPath 4.0 allows expressions to be nested with full generality.

Note:

This specification contains no assumptions or requirements regarding the character set encoding of strings of [Unicode] characters.

Like XML, XPath 4.0 is a case-sensitive language. Keywords in XPath 4.0 use lower-case characters and are not reserved—that is, names in XPath 4.0 expressions are allowed to be the same as language keywords, except for certain unprefixed function-names listed in A.3 Reserved Function Names.

[Definition: In the data model, a value is always a sequence.] [Definition: A sequence is an ordered collection of zero or more items.] [Definition: An item is either an atomic value, a node, or a functionDM31.] [Definition: An atomic value is a value in the value space of an atomic type, as defined in [XML Schema 1.0] or [XML Schema 1.1].] [Definition: A node is an instance of one of the node kinds defined in Section 6 Nodes DM31.] Each node has a unique node identity, a typed value, and a string value. In addition, some nodes have a name. The typed value of a node is a sequence of zero or more atomic values. The string value of a node is a value of type xs:string. The name of a node is a value of type xs:QName.

[Definition: A sequence containing exactly one item is called a singleton.] An item is identical to a singleton sequence containing that item. Sequences are never nested—for example, combining the values 1, (2, 3), and ( ) into a single sequence results in the sequence (1, 2, 3). [Definition: A sequence containing zero items is called an empty sequence.]

[Definition: The term XDM instance is used, synonymously with the term value, to denote an unconstrained sequence of items.]

Element nodes have a property called in-scope namespaces. [Definition: The in-scope namespaces property of an element node is a set of namespace bindings, each of which associates a namespace prefix with a URI.] For a given element, one namespace binding may have an empty prefix; the URI of this namespace binding is the default namespace within the scope of the element.

In [XML Path Language (XPath) Version 1.0], the in-scope namespaces of an element node are represented by a collection of namespace nodes arranged on a namespace axis. As of XPath 2.0, the namespace axis is deprecated and need not be supported by a host language. A host language that does not support the namespace axis need not represent namespace bindings in the form of nodes.

[Definition: An expanded QName is a triple: its components are a prefix, a local name, and a namespace URI. In the case of a name in no namespace, the namespace URI and prefix are both absent. In the case of a name in the default namespace, the prefix is absent.] When comparing two expanded QNames, the prefixes are ignored: the local name parts must be equal under the Unicode Codepoint Collation, and the namespace URI parts must either both be absent, or must be equal under the Unicode Codepoint Collation.

In the XPath 4.0 grammar, QNames representing the names of elements, attributes, functions, variables, types, or other such constructs are written as instances of the grammatical production EQName.

[134]    EQName    ::=    QName | URIQualifiedName
[144]    QName    ::=    [http://www.w3.org/TR/REC-xml-names/#NT-QName]Names
[145]    NCName    ::=    [http://www.w3.org/TR/REC-xml-names/#NT-NCName]Names
[139]    URIQualifiedName    ::=    BracedURILiteral NCName
[140]    BracedURILiteral    ::=    "Q" "{" [^{}]* "}"

The EQName production allows a QName to be written in one of three ways:

[Definition: A lexical QName is a name that conforms to the syntax of the QName production].

The namespace URI value in a URIQualifiedName is whitespace normalized according to the rules for the xs:anyURI type in Section 3.2.17 anyURI XS1-2 or Section 3.3.17 anyURI XS11-2. It is a static error [err:XQST0070] if the namespace URI for an EQName is http://www.w3.org/2000/xmlns/.

Here are some examples of EQNames:

This document uses the following namespace prefixes to represent the namespace URIs with which they are listed. Although these prefixes are used within this specification to refer to the corresponding namespaces, not all of these bindings will necessarily be present in the static context of every expression, and authors are free to use different prefixes for these namespaces, or to bind these prefixes to different namespaces.

[Definition: Within this specification, the term URI refers to a Universal Resource Identifier as defined in [RFC3986] and extended in [RFC3987] with the new name IRI.] The term URI has been retained in preference to IRI to avoid introducing new names for concepts such as "Base URI" that are defined or referenced across the whole family of XML specifications.

Note:

In most contexts, processors are not required to raise errors if a URI is not lexically valid according to [RFC3986] and [RFC3987]. See 2.4.5 URI Literals for details.

2.1 Expression Context

[Definition: The expression context for a given expression consists of all the information that can affect the result of the expression.]

This information is organized into two categories called the static context and the dynamic context.

2.1.1 Static Context

[Definition: The static context of an expression is the information that is available during static analysis of the expression, prior to its evaluation.] This information can be used to decide whether the expression contains a static error.

The individual components of the static context are described below. A default initial value for each component must be specified by the host language. The scope of each component is specified in C.1 Static Context Components.

  • [Definition: XPath 1.0 compatibility mode. This value is true if rules for backward compatibility with XPath Version 1.0 are in effect; otherwise it is false. ]

  • [Definition: Statically known namespaces. This is a mapping from prefix to namespace URI that defines all the namespaces that are known during static processing of a given expression.]

    The URI value is whitespace normalized according to the rules for the xs:anyURI type in Section 3.2.17 anyURI XS1-2 or Section 3.3.17 anyURI XS11-2.

    The statically known namespaces may include a binding for the zero-length prefix; however, this is only used in limited circumstances because the rules for resolving unprefixed QNames depend on the how such a name is used.

    Note the difference between in-scope namespaces, which is a dynamic property of an element node, and statically known namespaces, which is a static property of an expression.

  • [Definition: Default element namespace. This is a namespace URI or absentDM31. The namespace URI, if present, is used for any unprefixed QName appearing in a position where an element name is expected.] The URI value is whitespace normalized according to the rules for the xs:anyURI type in Section 3.2.17 anyURI XS1-2 or Section 3.3.17 anyURI XS11-2.

  • [Definition: Default type namespace. This is a namespace URI or absentDM31. The namespace URI, if present, is used for any unprefixed QName appearing in a position where a type name is expected.] The URI value is whitespace normalized according to the rules for the xs:anyURI type in Section 3.2.17 anyURI XS1-2 or Section 3.3.17 anyURI XS11-2.

  • [Definition: Function name resolver. This is an algorithm that takes as input a lexical QName and arity, and delivers as its result an expanded QName.] The expanded QName and arity must uniquely identify a function signature in the statically known function signatures, or a static error is reported. This algorithm is used when function names are resolved statically, specifically when they appear in static function calls or function references. The

    Note:

    Different host languages or APIs may adopt different strategies for resolving unprefixed function names. Possible approaches include (but are not limited to):

    1. Treating all unprefixed names as references to functions in the namespace http://www.w3.org/2005/xpath-functions.

    2. Treating all unprefixed names as references to functions in a default namespace established in some way determined by the host language or API.

    3. Searching multiple namespaces, with some strategy for resolving conflicts.

    4. Giving different precedence to functions declared in different ways, for example giving locally-declared functions precedence over globally-declared functions.

    5. Resolving particular magic names (such as xsl:original) using host-language defined rules.

  • [Definition: In-scope schema definitions. This is a generic term for all the element declarations, attribute declarations, and schema type definitions that are in scope during static analysis of an expression.] It includes the following three parts:

  • [Definition: In-scope variables. This is a mapping from expanded QName to type. It defines the set of variables that are available for reference within an expression. The expanded QName is the name of the variable, and the type is the static type of the variable.]

    An expression that binds a variable extends the in-scope variables, within the scope of the variable, with the variable and its type. Within the body of an inline function expression , the in-scope variables are extended by the names and types of the function parameters.

  • [Definition: Context item static type. This component defines the static type of the context item within the scope of a given expression.]

  • [Definition: Item type aliases. This is a mapping from expanded QName to ItemTypes.]

    [Definition: A type alias is an expanded QName that is mapped to an ItemType in the item type aliases of the static context.]

    Item type aliases allow frequently-used item types, especially complex item types such as record types, to be given simple names, so that the definition of the type is not repeated every time it is used.

    Note:

    Item type aliases can be defined in XQuery 4.0 and in XSLT 4.0, but not in XPath 4.0 itself.

  • [Definition: Statically known function signatures. This is a mapping from (expanded QName, arity) to function signatureDM31. ] The entries in this mapping define the set of functions that are available to be called from a static function call, or referenced from a named function reference. Each such function is uniquely identified by its expanded QName and arity (number of parameters). Given a statically known function's expanded QName and arity, this component supplies the function's signatureDM31, which specifies various static properties of the function, including types.

    The statically known function signatures include the signatures of functions from a variety of sources, including the built-in functions. Implementations must ensure that no two functions have the same expanded QName and the same arity (even if the signatures are consistent).

  • [Definition: Statically known collations. This is an implementation-defined mapping from URI to collation. It defines the names of the collations that are available for use in processing expressions.] [Definition: A collation is a specification of the manner in which strings and URIs are compared and, by extension, ordered. For a more complete definition of collation, see Section 5.3 Comparison of strings FO31.]

  • [Definition: Default collation. This identifies one of the collations in statically known collations as the collation to be used by functions and operators for comparing and ordering values of type xs:string and xs:anyURI (and types derived from them) when no explicit collation is specified.]

  • [Definition: Static Base URI. This is an absolute URI, used to resolve relative URI references. ] If E is a subexpression of F then the Static Base URI of E is the same as the Static Base URI of F. There are no constructs in XPath that require resolution of relative URI references during static analysis. The Static Base URI is available during dynamic evaluation by use of the fn:static-base-uri function, and is used implicitly during dynamic evaluation by functions such as fn:doc. Relative URI references are resolved as described in 2.4.6 Resolving a Relative URI Reference.

  • [Definition: Statically known documents. This is a mapping from strings to types. The string represents the absolute URI of a resource that is potentially available using the fn:doc function. The type is the static type of a call to fn:doc with the given URI as its literal argument. ] If the argument to fn:doc is a string literal that is not present in statically known documents, then the static type of fn:doc is document-node()?.

    Note:

    The purpose of the statically known documents is to provide static type information, not to determine which documents are available. A URI need not be found in the statically known documents to be accessed using fn:doc.

  • [Definition: Statically known collections. This is a mapping from strings to types. The string represents the absolute URI of a resource that is potentially available using the fn:collection function. The type is the type of the sequence of items that would result from calling the fn:collection function with this URI as its argument.] If the argument to fn:collection is a string literal that is not present in statically known collections, then the static type of fn:collection is item()*.

    Note:

    The purpose of the statically known collections is to provide static type information, not to determine which collections are available. A URI need not be found in the statically known collections to be accessed using fn:collection.

  • [Definition: Statically known default collection type. This is the type of the sequence of items that would result from calling the fn:collection function with no arguments.] Unless initialized to some other value by an implementation, the value of statically known default collection type is item()*.

  • [Definition: Statically known decimal formats. This is a mapping from QNames to decimal formats, with one default format that has no visible name, referred to as the unnamed decimal format. Each format is available for use when formatting numbers using the fn:format-number function.]

    Each decimal format defines a set of properties, which control the interpretation of characters in the picture string supplied to the fn:format-number function, and also specify characters to be used in the result of formatting the number.

    The following properties specify characters used both in the picture string, and in the formatted number. In each case the value is a single character:

    • [Definition: decimal-separator is the character used to separate the integer part of the number from the fractional part, both in the picture string and in the formatted number; the default value is the period character (.)]

    • [Definition: exponent-separator is the character used to separate the mantissa from the exponent in scientific notation both in the picture string and in the formatted number; the default value is the character (e).]

    • [Definition: grouping-separator is the character typically used as a thousands separator, both in the picture string and in the formatted number; the default value is the comma character (,)]

    • [Definition: percent is the character used both in the picture string and in the formatted number to indicate that the number is written as a per-hundred fraction; the default value is the percent character (%)]

    • [Definition: per-mille is the character used both in the picture string and in the formatted number to indicate that the number is written as a per-thousand fraction; the default value is the Unicode per-mille character (#x2030)]

    • [Definition: zero-digit is the character used to represent the digit zero; the default value is the Western digit zero (#x30). This character must be a digit (category Nd in the Unicode property database), and it must have the numeric value zero. This property implicitly defines the ten Unicode characters that are used to represent the values 0 to 9: Unicode is organized so that each set of decimal digits forms a contiguous block of characters in numerical sequence. Within the picture string any of these ten character can be used (interchangeably) as a place-holder for a mandatory digit. Within the final result string, these ten characters are used to represent the digits zero to nine.]

    The following properties specify characters to be used in the picture string supplied to the fn:format-number function, but not in the formatted number. In each case the value must be a single character.

    • [Definition: digit is a character used in the picture string to represent an optional digit; the default value is the number sign character (#)]

    • [Definition: pattern-separator is a character used to separate positive and negative sub-pictures in a picture string; the default value is the semi-colon character (;)]

    The following properties specify characters or strings that may appear in the result of formatting the number, but not in the picture string:

    • [Definition: infinity is the string used to represent the double value infinity (INF); the default value is the string "Infinity"]

    • [Definition: NaN is the string used to represent the double value NaN (not-a-number); the default value is the string "NaN"]

    • [Definition: minus-sign is the single character used to mark negative numbers; the default value is the hyphen-minus character (#x2D). ]

2.1.2 Dynamic Context

[Definition: The dynamic context of an expression is defined as information that is needed for the dynamic evaluation of an expression.] If evaluation of an expression relies on some part of the dynamic context that is absentDM31, a dynamic error is raised [err:XPDY0002].

The individual components of the dynamic context are described below. Further rules governing the semantics of these components can be found in C.2 Dynamic Context Components.

The dynamic context consists of all the components of the static context, and the additional components listed below.

[Definition: The first three components of the dynamic context (context item, context position, and context size) are called the focus of the expression. ] The focus enables the processor to keep track of which items are being processed by the expression. If any component in the focus is defined, both the context item and context position are known.

Note:

If any component in the focus is defined, context size is usually defined as well. However, when streaming, the context size cannot be determined without lookahead, so it may be undefined. If so, expressions like last() will raise a dynamic error because the context size is undefined.

[Definition: A singleton focus is a focus that refers to a single item; in a singleton focus, context item is set to the item, context position = 1 and context size = 1.]

Certain language constructs, notably the path operator E1/E2, the simple map operator E1!E2, and the predicate E1[E2], create a new focus for the evaluation of a sub-expression. In these constructs, E2 is evaluated once for each item in the sequence that results from evaluating E1. Each time E2 is evaluated, it is evaluated with a different focus. The focus for evaluating E2 is referred to below as the inner focus, while the focus for evaluating E1 is referred to as the outer focus. The inner focus is used only for the evaluation of E2. Evaluation of E1 continues with its original focus unchanged.

  • [Definition: The context item is the item currently being processed.] [Definition: When the context item is a node, it can also be referred to as the context node.] The context item is returned by an expression consisting of a single dot (.). When an expression E1/E2 or E1[E2] is evaluated, each item in the sequence obtained by evaluating E1 becomes the context item in the inner focus for an evaluation of E2.

  • [Definition: The context position is the position of the context item within the sequence of items currently being processed.] It changes whenever the context item changes. When the focus is defined, the value of the context position is an integer greater than zero. The context position is returned by the expression fn:position(). When an expression E1/E2 or E1[E2] is evaluated, the context position in the inner focus for an evaluation of E2 is the position of the context item in the sequence obtained by evaluating E1. The position of the first item in a sequence is always 1 (one). The context position is always less than or equal to the context size.

  • [Definition: The context size is the number of items in the sequence of items currently being processed.] Its value is always an integer greater than zero. The context size is returned by the expression fn:last(). When an expression E1/E2 or E1[E2] is evaluated, the context size in the inner focus for an evaluation of E2 is the number of items in the sequence obtained by evaluating E1.

  • [Definition: Variable values. This is a mapping from expanded QName to value. It contains the same expanded QNames as the in-scope variables in the static context for the expression. The expanded QName is the name of the variable and the value is the dynamic value of the variable, which includes its dynamic type.]

  • [Definition: Named functions. This is a mapping from (expanded QName, arity) to functionDM31. ] It supplies a function for each signature in statically known function signatures and may supply other functions (see 2.2.4 Consistency Constraints). Named functions can include external functions. [Definition: External functions are functions that are implemented outside the query environment.] For example, an implementation might provide a set of implementation-defined external functions in addition to the core function library described in [XQuery and XPath Functions and Operators 3.1]. [Definition: An implementation-defined function is an external function that is implementation-defined ]. [Definition: A host language function is an external function defined by the host language.]

  • [Definition: Current dateTime. This information represents an implementation-dependent point in time during the processing of an expression, and includes an explicit timezone. It can be retrieved by the fn:current-dateTime function. If invoked multiple times during the execution of an expression, this function always returns the same result.]

  • [Definition: Implicit timezone. This is the timezone to be used when a date, time, or dateTime value that does not have a timezone is used in a comparison or arithmetic operation. The implicit timezone is an implementation-defined value of type xs:dayTimeDuration. See Section 3.2.7.3 Timezones XS1-2 or Section 3.3.7 dateTime XS11-2 for the range of valid values of a timezone.]

  • [Definition: Default language. This is the natural language used when creating human-readable output (for example, by the functions fn:format-date and fn:format-integer) if no other language is requested. The value is a language code as defined by the type xs:language.]

  • [Definition: Default calendar. This is the calendar used when formatting dates in human-readable output (for example, by the functions fn:format-date and fn:format-dateTime) if no other calendar is requested. The value is a string.]

  • [Definition: Default place. This is a geographical location used to identify the place where events happened (or will happen) when formatting dates and times using functions such as fn:format-date and fn:format-dateTime, if no other place is specified. It is used when translating timezone offsets to civil timezone names, and when using calendars where the translation from ISO dates/times to a local representation is dependent on geographical location. Possible representations of this information are an ISO country code or an Olson timezone name, but implementations are free to use other representations from which the above information can be derived.]

  • [Definition: Available documents. This is a mapping of strings to document nodes. Each string represents the absolute URI of a resource. The document node is the root of a tree that represents that resource using the data model. The document node is returned by the fn:doc function when applied to that URI.] The set of available documents is not limited to the set of statically known documents, and it may be empty.

    If there are one or more URIs in available documents that map to a document node D, then the document-uri property of D must either be absent, or must be one of these URIs.

    Note:

    This means that given a document node $N, the result of fn:doc(fn:document-uri($N)) is $N will always be true, unless fn:document-uri($N) is an empty sequence.

  • [Definition: Available text resources. This is a mapping of strings to text resources. Each string represents the absolute URI of a resource. The resource is returned by the fn:unparsed-text function when applied to that URI.] The set of available text resources is not limited to the set of statically known documents, and it may be empty.

  • [Definition: Available collections. This is a mapping of strings to sequences of items. Each string represents the absolute URI of a resource. The sequence of items represents the result of the fn:collection function when that URI is supplied as the argument. ] The set of available collections is not limited to the set of statically known collections, and it may be empty.

    For every document node D that is in the target of a mapping in available collections, or that is the root of a tree containing such a node, the document-uri property of D must either be absent, or must be a URI U such that available documents contains a mapping from U to D.

    Note:

    This means that for any document node $N retrieved using the fn:collection function, either directly or by navigating to the root of a node that was returned, the result of fn:doc(fn:document-uri($N)) is $N will always be true, unless fn:document-uri($N) is an empty sequence. This implies a requirement for the fn:doc and fn:collection functions to be consistent in their effect. If the implementation uses catalogs or user-supplied URI resolvers to dereference URIs supplied to the fn:doc function, the implementation of the fn:collection function must take these mechanisms into account. For example, an implementation might achieve this by mapping the collection URI to a set of document URIs, which are then resolved using the same catalog or URI resolver that is used by the fn:doc function.

  • [Definition: Default collection. This is the sequence of items that would result from calling the fn:collection function with no arguments.] The value of default collection may be initialized by the implementation.

  • [Definition: Available URI collections. This is a mapping of strings to sequences of URIs. The string represents the absolute URI of a resource which can be interpreted as an aggregation of a number of individual resources each of which has its own URI. The sequence of URIs represents the result of the fn:uri-collection function when that URI is supplied as the argument. ] There is no implication that the URIs in this sequence can be successfully dereferenced, or that the resources they refer to have any particular media type.

    Note:

    An implementation may maintain some consistent relationship between the available collections and the available URI collections, for example by ensuring that the result of fn:uri-collection(X)!fn:doc(.) is the same as the result of fn:collection(X). However, this is not required. The fn:uri-collection function is more general than fn:collection in that it allows access to resources other than XML documents; at the same time, fn:collection allows access to nodes that might lack individual URIs, for example nodes corresponding to XML fragments stored in the rows of a relational database.

  • [Definition: Default URI collection. This is the sequence of URIs that would result from calling the fn:uri-collection function with no arguments.] The value of default URI collection may be initialized by the implementation.

  • [Definition: Environment variables. This is a mapping from names to values. Both the names and the values are strings. The names are compared using an implementation-defined collation, and are unique under this collation. The set of environment variables is implementation-defined and may be empty.]

    Note:

    A possible implementation is to provide the set of POSIX environment variables (or their equivalent on other operating systems) appropriate to the process in which the expression is evaluated.

2.2 Processing Model

XPath 4.0 is defined in terms of the data model and the expression context.

Processing                          Model Overview

Figure 1: Processing Model Overview

Figure 1 provides a schematic overview of the processing steps that are discussed in detail below. Some of these steps are completely outside the domain of XPath 4.0; in Figure 1, these are depicted outside the line that represents the boundaries of the language, an area labeled external processing. The external processing domain includes generation of XDM instances that represent the data to be queried (see 2.2.1 Data Model Generation), schema import processing (see 2.2.2 Schema Import Processing) and serialization. The area inside the boundaries of the language is known as the XPath processing domain , which includes the static analysis and dynamic evaluation phases (see 2.2.3 Expression Processing). Consistency constraints on the XPath processing domain are defined in 2.2.4 Consistency Constraints.

2.2.1 Data Model Generation

The input data for an expression must be represented as one or more XDM instances. This process occurs outside the domain of XPath 4.0, which is why Figure 1 represents it in the external processing domain. Here are some steps by which an XML document might be converted to an XDM instance:

  1. A document may be parsed using an XML parser that generates an XML Information Set (see [XML Infoset]). The parsed document may then be validated against one or more schemas. This process, which is described in [XML Schema 1.0 Part 1] or [XML Schema 1.1 Part 1], results in an abstract information structure called the Post-Schema Validation Infoset (PSVI). If a document has no associated schema, its Information Set is preserved. (See DM1 in Fig. 1.)

  2. The Information Set or PSVI may be transformed into an XDM instance by a process described in [XQuery and XPath Data Model (XDM) 3.1]. (See DM2 in Fig. 1.)

The above steps provide an example of how an XDM instance might be constructed. An XDM instance might also be synthesized directly from a relational database, or constructed in some other way (see DM3 in Fig. 1.) XPath 4.0 is defined in terms of the data model, but it does not place any constraints on how XDM instances are constructed.

[Definition: Each element node and attribute node in an XDM instance has a type annotation (described in Section 2.7 Schema Information DM31). The type annotation of a node is a reference to an XML Schema type. ] The type-name of a node is the name of the type referenced by its type annotation. If the XDM instance was derived from a validated XML document as described in Section 3.3 Construction from a PSVI DM31, the type annotations of the element and attribute nodes are derived from schema validation. XPath 4.0 does not provide a way to directly access the type annotation of an element or attribute node.

The value of an attribute is represented directly within the attribute node. An attribute node whose type is unknown (such as might occur in a schemaless document) is given the type annotation xs:untypedAtomic.

The value of an element is represented by the children of the element node, which may include text nodes and other element nodes. The type annotation of an element node indicates how the values in its child text nodes are to be interpreted. An element that has not been validated (such as might occur in a schemaless document) is annotated with the schema type xs:untyped. An element that has been validated and found to be partially valid is annotated with the schema type xs:anyType. If an element node is annotated as xs:untyped, all its descendant element nodes are also annotated as xs:untyped. However, if an element node is annotated as xs:anyType, some of its descendant element nodes may have a more specific type annotation.

2.2.2 Schema Import Processing

The in-scope schema definitions in the static context are provided by the host language (see step SI1 in Figure 1) and must satisfy the consistency constraints defined in 2.2.4 Consistency Constraints.

2.2.3 Expression Processing

XPath 4.0 defines two phases of processing called the static analysis phase and the dynamic evaluation phase (see Fig. 1). During the static analysis phase, static errors, dynamic errors, or type errors may be raised. During the dynamic evaluation phase, only dynamic errors or type errors may be raised. These kinds of errors are defined in 2.3.1 Kinds of Errors.

Within each phase, an implementation is free to use any strategy or algorithm whose result conforms to the specifications in this document.

2.2.3.1 Static Analysis Phase

[Definition: The static analysis phase depends on the expression itself and on the static context. The static analysis phase does not depend on input data (other than schemas).]

During the static analysis phase, the XPath expression is parsed into an internal representation called the operation tree (step SQ1 in Figure 1). A parse error is raised as a static error [err:XPST0003]. The static context is initialized by the implementation (step SQ2). The static context is used to resolve schema type names, function names, namespace prefixes, and variable names (step SQ4). If a name of one of these kinds in the operation tree is not found in the static context, a static error ([err:XPST0008] or [err:XPST0017]) is raised (however, see exceptions to this rule in 3.6.3.2 Element Test and 3.6.3.4 Attribute Test.)

The operation tree is then normalized by making explicit the implicit operations such as atomization and extraction of Effective Boolean Values (step SQ5).

During the static analysis phase, a processor may perform type analysis. The effect of type analysis is to assign a static type to each expression in the operation tree. [Definition: The static type of an expression is the best inference that the processor is able to make statically about the type of the result of the expression.] This specification does not define the rules for type analysis nor the static types that are assigned to particular expressions: the only constraint is that the inferred type must match all possible values that the expression is capable of returning.

Examples of inferred static types might be:

  • For the expression concat(a,b) the inferred static type is xs:string

  • For the expression $a = $v the inferred static type is xs:boolean

  • For the expression $s[exp] the inferred static type has the same item type as the static type of $s, but a cardinality that allows the empty sequence even if the static type of $s does not allow an empty sequence.

  • The inferred static type of the expression data($x) (whether written explicitly or inserted into the operation tree in places where atomization is implicit) depends on the inferred static type of $x: for example, if $x has type element(*, xs:integer) then data($x) has static type xs:integer.

In XQuery 1.0 and XPath 2.0, rules for static type inferencing were published normatively in [XQuery 1.0 and XPath 2.0 Formal Semantics], but implementations were allowed to refine these rules to infer a more precise type where possible. In XQuery 3.1 and XPath 3.1, the rules for static type inferencing are entirely implementation-dependent.

Every kind of expression also imposes requirements on the type of its operands. For example, with the expression substring($a, $b, $c), $a must be of type xs:string (or something that can be converted to xs:string by the function calling rules), while $b and $c must be of type xs:double.

If the Static Typing Feature is in effect, a processor must raise a type error during static analysis if the inferred static type of an expression is not subsumed by the required type of the context where the expression is used. For example, the call of substring above would cause a type error if the inferred static type of $a is xs:integer; equally, a type error would be reported during static analysis if the inferred static type is xs:anyAtomicType.

If the Static Typing Feature is not in effect, a processor may raise a type error during static analysis only when one of the following conditions is met:

  1. When the inferred static type of an expression has no overlap (intersection) with the required type, and cannot be converted to the required type using the coercion rules. For example, given the call fn:upper-case($s), the processor may raise an error if the declared or inferred type of $s is xs:integer, but not if it is xs:anyAtomicType.

  2. When the only possible value of an expression that is consistent with the required type is the empty sequence. Consider for example the expression fn:codepoints-to-string(fn:tokenize($in)). Since fn:codepoints-to-string requires xs:integer* while fn:tokenize($in) delivers xs:string*, this expression can succeed only in the special case where the value is empty, so processors may report this as an error. An error must not be raised under this rule unless both the inferred static type and the required type permit values other than the empty sequence.

  3. When an ForwardStep or ReverseStep is used, and it is known during static analysis that the step will select no nodes.

    One example of this is an expression such as @price/text(): attribute nodes never have children, so this expression will never select anything.

    Another example arises when schema information is available: if it is known that the variable $emp holds a value of type schema-element(employee), and that no element of this type can have an attribute named @sallary (sic), then a type error may be reported if the expression $emp/@sallary is encountered.

    Note:

    A static error must not be reported simply because a predicate will always return false: the expression a[name()='b'] will always return an empty sequence, but it is not an error.

  4. When the KeySpecifier in a Lookup expression is such that the result of the lookup will inevitably be empty. For example if the context item is known to be of type record(longitude, latitude) then a static type error may be raised against the expression ?altitude.

For backwards compatibility, processors should provide an option to avoid reporting type errors in respect of constructs such as @a/@b that were executed without error in previous versions. Note in particular that the construct /.. was sometimes recommended in XPath 1.0 as the preferred way to denote an empty node-set.

Alternatively, if the Static Typing Feature is not in effect, the processor may defer all type checking until the dynamic evaluation phase.

2.2.3.2 Dynamic Evaluation Phase

[Definition: The dynamic evaluation phase is the phase during which the value of an expression is computed.] It is dependent on successful completion of the static analysis phase.

The dynamic evaluation phase can occur only if no errors were detected during the static analysis phase. If the Static Typing Feature is in effect, all type errors are detected during static analysis and serve to inhibit the dynamic evaluation phase.

The dynamic evaluation phase depends on the operation tree of the expression being evaluated (step DQ1), on the input data (step DQ4), and on the dynamic context (step DQ5), which in turn draws information from the external environment (step DQ3) and the static context (step DQ2). The dynamic evaluation phase may create new data-model values (step DQ4) and it may extend the dynamic context (step DQ5)—for example, by binding values to variables.

[Definition: A dynamic type is associated with each value as it is computed. The dynamic type of a value may be more specific than the static type of the expression that computed it (for example, the static type of an expression might be xs:integer*, denoting a sequence of zero or more integers, but at evaluation time its value may have the dynamic type xs:integer, denoting exactly one integer.)]

If an operand of an expression is found to have a dynamic type that is not appropriate for that operand, a type error is raised [err:XPTY0004].

Even though static typing can catch many type errors before an expression is executed, it is possible for an expression to raise an error during evaluation that was not detected by static analysis. For example, an expression may contain a cast of a string into an integer, which is statically valid. However, if the actual value of the string at run time cannot be cast into an integer, a dynamic error will result. Similarly, an expression may apply an arithmetic operator to a value whose static type is xs:untypedAtomic. This is not a static error, but at run time, if the value cannot be successfully cast to a numeric type, a dynamic error will be raised.

When the Static Typing Feature is in effect, it is also possible for static analysis of an expression to raise a type error, even though execution of the expression on certain inputs would be successful. For example, an expression might contain a function that requires an element as its parameter, and the static analysis phase might infer the static type of the function parameter to be an optional element. This case is treated as a type error and inhibits evaluation, even though the function call would have been successful for input data in which the optional element is present.

2.2.4 Consistency Constraints

In order for XPath 4.0 to be well defined, the input XDM instances, the static context, and the dynamic context must be mutually consistent. The consistency constraints listed below are prerequisites for correct functioning of an XPath 4.0 implementation. Enforcement of these consistency constraints is beyond the scope of this specification. This specification does not define the result of an expression under any condition in which one or more of these constraints is not satisfied.

2.3 Error Handling

2.3.1 Kinds of Errors

As described in 2.2.3 Expression Processing, XPath 4.0 defines a static analysis phase, which does not depend on input data, and a dynamic evaluation phase, which does depend on input data. Errors may be raised during each phase.

[Definition: An error that can be detected during the static analysis phase, and is not a type error, is a static error.] A syntax error is an example of a static error.

[Definition: A dynamic error is an error that must be detected during the dynamic evaluation phase and may be detected during the static analysis phase. Numeric overflow is an example of a dynamic error.]

[Definition: A type error may be raised during the static analysis phase or the dynamic evaluation phase. During the static analysis phase, a type error occurs when the static type of an expression does not match the expected type of the context in which the expression occurs. During the dynamic evaluation phase, a type error occurs when the dynamic type of a value does not match the expected type of the context in which the value occurs.]

The outcome of the static analysis phase is either success or one or more type errors, static errors, or statically-detected dynamic errors. The result of the dynamic evaluation phase is either a result value, a type error, or a dynamic error.

If more than one error is present, or if an error condition comes within the scope of more than one error defined in this specification, then any non-empty subset of these errors may be reported.

During the static analysis phase, if the Static Typing Feature is in effect and the static type assigned to an expression other than () or data(()) is empty-sequence(), a static error is raised [err:XPST0005]. This catches cases in which a query refers to an element or attribute that is not present in the in-scope schema definitions, possibly because of a spelling error.

Independently of whether the Static Typing Feature is in effect, if an implementation can determine during the static analysis phase that an XPath expression, if evaluated, would necessarily raise a dynamic error or that an expression, if evaluated, would necessarily raise a type error, the implementation may (but is not required to) report that error during the static analysis phase.

An implementation can raise a dynamic error for an XPath expression statically only if the expression can never execute without raising that error, as in the following example:

error()

The following example contains a type error, which can be reported statically even if the implementation can not prove that the expression will actually be evaluated.

if (empty($arg))
then
  "cat" * 2
else
  0

[Definition: In addition to static errors, dynamic errors, and type errors, an XPath 4.0 implementation may raise warnings, either during the static analysis phase or the dynamic evaluation phase. The circumstances in which warnings are raised, and the ways in which warnings are handled, are implementation-defined.]

In addition to the errors defined in this specification, an implementation may raise a dynamic error for a reason beyond the scope of this specification. For example, limitations may exist on the maximum numbers or sizes of various objects. An error must be raised if such a limitation is exceeded [err:XPDY0130].

2.3.2 Identifying and Reporting Errors

The errors defined in this specification are identified by QNames that have the form err:XPYYnnnn , where:

  • err denotes the namespace for XPath and XQuery errors, http://www.w3.org/2005/xqt-errors. This binding of the namespace prefix err is used for convenience in this document, and is not normative.

  • XP identifies the error as an XPath error (some errors, originally defined by XQuery and later added to XPath, use the code XQ instead).

  • YY denotes the error category, using the following encoding:

    • ST denotes a static error.

    • DY denotes a dynamic error.

    • TY denotes a type error.

  • nnnn is a unique numeric code.

Note:

The namespace URI for XPath and XQuery errors is not expected to change from one version of XPath to another. However, the contents of this namespace may be extended to include additional error definitions.

The method by which an XPath 4.0 processor reports error information to the external environment is implementation-defined.

An error can be represented by a URI reference that is derived from the error QName as follows: an error with namespace URI NS and local part LP can be represented as the URI reference NS # LP . For example, an error whose QName is err:XPST0017 could be represented as http://www.w3.org/2005/xqt-errors#XPST0017.

Note:

Along with a code identifying an error, implementations may wish to return additional information, such as the location of the error or the processing phase in which it was detected. If an implementation chooses to do so, then the mechanism that it uses to return this information is implementation-defined.

2.3.3 Handling Dynamic Errors

Except as noted in this document, if any operand of an expression raises a dynamic error, the expression also raises a dynamic error. If an expression can validly return a value or raise a dynamic error, the implementation may choose to return the value or raise the dynamic error (see 2.3.4 Errors and Optimization). For example, the logical expression expr1 and expr2 may return the value false if either operand returns false, or may raise a dynamic error if either operand raises a dynamic error.

If more than one operand of an expression raises an error, the implementation may choose which error is raised by the expression. For example, in this expression:

($x div $y) + xs:decimal($z)

both the sub-expressions ($x div $y) and xs:decimal($z) may raise an error. The implementation may choose which error is raised by the "+" expression. Once one operand raises an error, the implementation is not required, but is permitted, to evaluate any other operands.

[Definition: In addition to its identifying QName, a dynamic error may also carry a descriptive string and one or more additional values called error values.] An implementation may provide a mechanism whereby an application-defined error handler can process error values and produce diagnostic messages. The host language may also provide error handling mechanisms.

A dynamic error may be raised by a built-in function or operator. For example, the div operator raises an error if its operands are xs:decimal values and its second operand is equal to zero. Errors raised by built-in functions and operators are defined in [XQuery and XPath Functions and Operators 3.1].

A dynamic error can also be raised explicitly by calling the fn:error function, which always raises a dynamic error and never returns a value. This function is defined in Section 3.1.1 fn:error FO31. For example, the following function call raises a dynamic error, providing a QName that identifies the error, a descriptive string, and a diagnostic value (assuming that the prefix app is bound to a namespace containing application-defined error codes):

fn:error(xs:QName("app:err057"), "Unexpected value", fn:string($v))

2.3.4 Errors and Optimization

Because different implementations may choose to evaluate or optimize an expression in different ways, certain aspects of raising dynamic errors are implementation-dependent, as described in this section.

An implementation is always free to evaluate the operands of an operator in any order.

In some cases, a processor can determine the result of an expression without accessing all the data that would be implied by the formal expression semantics. For example, the formal description of filter expressions suggests that $s[1] should be evaluated by examining all the items in sequence $s, and selecting all those that satisfy the predicate position()=1. In practice, many implementations will recognize that they can evaluate this expression by taking the first item in the sequence and then exiting. If $s is defined by an expression such as //book[author eq 'Berners-Lee'], then this strategy may avoid a complete scan of a large document and may therefore greatly improve performance. However, a consequence of this strategy is that a dynamic error or type error that would be detected if the expression semantics were followed literally might not be detected at all if the evaluation exits early. In this example, such an error might occur if there is a book element in the input data with more than one author subelement.

The extent to which a processor may optimize its access to data, at the cost of not raising errors, is defined by the following rules.

Consider an expression Q that has an operand (sub-expression) E. In general the value of E is a sequence. At an intermediate stage during evaluation of the sequence, some of its items will be known and others will be unknown. If, at such an intermediate stage of evaluation, a processor is able to establish that there are only two possible outcomes of evaluating Q, namely the value V or an error, then the processor may deliver the result V without evaluating further items in the operand E. For this purpose, two values are considered to represent the same outcome if their items are pairwise the same, where nodes are the same if they have the same identity, and values are the same if they are equal and have exactly the same type.

There is an exception to this rule: If a processor evaluates an operand E (wholly or in part), then it is required to establish that the actual value of the operand E does not violate any constraints on its cardinality. For example, the expression $e eq 0 results in a type error if the value of $e contains two or more items. A processor is not allowed to decide, after evaluating the first item in the value of $e and finding it equal to zero, that the only possible outcomes are the value true or a type error caused by the cardinality violation. It must establish that the value of $e contains no more than one item.

These rules apply to all the operands of an expression considered in combination: thus if an expression has two operands E1 and E2, it may be evaluated using any samples of the respective sequences that satisfy the above rules.

The rules cascade: if A is an operand of B and B is an operand of C, then the processor needs to evaluate only a sufficient sample of B to determine the value of C, and needs to evaluate only a sufficient sample of A to determine this sample of B.

The effect of these rules is that the processor is free to stop examining further items in a sequence as soon as it can establish that further items would not affect the result except possibly by causing an error. For example, the processor may return true as the result of the expression S1 = S2 as soon as it finds a pair of equal values from the two sequences.

Another consequence of these rules is that where none of the items in a sequence contributes to the result of an expression, the processor is not obliged to evaluate any part of the sequence. Again, however, the processor cannot dispense with a required cardinality check: if an empty sequence is not permitted in the relevant context, then the processor must ensure that the operand is not an empty sequence.

Examples:

  • If an implementation can find (for example, by using an index) that at least one item returned by $expr1 in the following example has the value 47, it is allowed to return true as the result of the some expression, without searching for another item returned by $expr1 that would raise an error if it were evaluated.

    some $x in $expr1 satisfies $x = 47
  • In the following example, if an implementation can find (for example, by using an index) the product element-nodes that have an id child with the value 47, it is allowed to return these nodes as the result of the path expression, without searching for another product node that would raise an error because it has an id child whose value is not an integer.

    //product[id = 47]

For a variety of reasons, including optimization, implementations may rewrite expressions into a different form. There are a number of rules that limit the extent of this freedom:

  • Other than the raising or not raising of errors, the result of evaluating a rewritten expression must conform to the semantics defined in this specification for the original expression.

    Note:

    This allows an implementation to return a result in cases where the original expression would have raised an error, or to raise an error in cases where the original expression would have returned a result. The main cases where this is likely to arise in practice are (a) where a rewrite changes the order of evaluation, such that a subexpression causing an error is evaluated when the expression is written one way and is not evaluated when the expression is written a different way, and (b) where intermediate results of the evaluation cause overflow or other out-of-range conditions.

    Note:

    This rule does not mean that the result of the expression will always be the same in non-error cases as if it had not been rewritten, because there are many cases where the result of an expression is to some degree implementation-dependent or implementation-defined.

  • Conditional expressions must not raise a dynamic error in respect of subexpressions occurring in a branch that is not selected, and must not return the value delivered by a branch unless that branch is selected. Thus, the following example must not raise a dynamic error if the document abc.xml does not exist:

    if (doc-available('abc.xml')) then doc('abc.xml') else ()

    Of course, the condition must be evaluated in order to determine which branch is selected, and the query must not be rewritten in a way that would bypass evaluating the condition.

  • As stated earlier, an expression must not be rewritten to dispense with a required cardinality check: for example, string-length(//title) must raise an error if the document contains more than one title element.

  • Expressions must not be rewritten in such a way as to create or remove static errors. The static errors in this specification are defined for the original expression, and must be preserved if the expression is rewritten.

Expression rewrite is illustrated by the following examples.

  • Consider the expression //part[color eq "Red"]. An implementation might choose to rewrite this expression as //part[color = "Red"][color eq "Red"]. The implementation might then process the expression as follows: First process the "=" predicate by probing an index on parts by color to quickly find all the parts that have a Red color; then process the "eq" predicate by checking each of these parts to make sure it has only a single color. The result would be as follows:

    • Parts that have exactly one color that is Red are returned.

    • If some part has color Red together with some other color, an error is raised.

    • The existence of some part that has no color Red but has multiple non-Red colors does not trigger an error.

  • The expression in the following example cannot raise a casting error if it is evaluated exactly as written (i.e., left to right). Since neither predicate depends on the context position, an implementation might choose to reorder the predicates to achieve better performance (for example, by taking advantage of an index). This reordering could cause the expression to raise an error.

    $N[@x castable as xs:date][xs:date(@x) gt xs:date("2000-01-01")]

    To avoid unexpected errors caused by expression rewrite, tests that are designed to prevent dynamic errors should be expressed using conditional expressions. For example, the above expression can be written as follows:

    $N[if (@x castable as xs:date)
       then xs:date(@x) gt xs:date("2000-01-01")
       else false()]

2.4 Concepts

This section explains some concepts that are important to the processing of XPath 4.0 expressions.

2.4.1 Document Order

An ordering called document order is defined among all the nodes accessible during processing of a given expression, which may consist of one or more trees (documents or fragments). Document order is defined in Section 2.4 Document Order DM31, and its definition is repeated here for convenience. Document order is a total ordering, although the relative order of some nodes is implementation-dependent. [Definition: Informally, document order is the order in which nodes appear in the XML serialization of a document.] [Definition: Document order is stable, which means that the relative order of two nodes will not change during the processing of a given expression, even if this order is implementation-dependent.] [Definition: The node ordering that is the reverse of document order is called reverse document order.]

Within a tree, document order satisfies the following constraints:

  1. The root node is the first node.

  2. Every node occurs before all of its children and descendants.

  3. Namespace nodes immediately follow the element node with which they are associated. The relative order of namespace nodes is stable but implementation-dependent.

  4. Attribute nodes immediately follow the namespace nodes of the element node with which they are associated. The relative order of attribute nodes is stable but implementation-dependent.

  5. The relative order of siblings is the order in which they occur in the children property of their parent node.

  6. Children and descendants occur before following siblings.

The relative order of nodes in distinct trees is stable but implementation-dependent, subject to the following constraint: If any node in a given tree T1 is before any node in a different tree T2, then all nodes in tree T1 are before all nodes in tree T2.

2.4.2 Atomization

The semantics of some XPath 4.0 operators depend on a process called atomization. Atomization is applied to a value when the value is used in a context in which a sequence of atomic values is required. The result of atomization is either a sequence of atomic values or a type error [err:FOTY0012]FO31. [Definition: Atomization of a sequence is defined as the result of invoking the fn:data function, as defined in Section 2.4 fn:data FO31.]

The semantics of fn:data are repeated here for convenience. The result of fn:data is the sequence of atomic values produced by applying the following rules to each item in the input sequence:

  • If the item is an atomic value, it is returned.

  • If the item is a node, its typed value is returned (a type error [err:FOTY0012]FO31 is raised if the node has no typed value.)

  • If the item is a functionDM31 (other than an array) or map a type error [err:FOTY0013]FO31 is raised.

  • If the item is an array $a, atomization is defined as $a?* ! fn:data(.), which is equivalent to atomizing the members of the array.

    Note:

    This definition recursively atomizes members that are arrays. Hence, the result of atomizing the array [ [1, 2, 3], [4, 5, 6] ] is the sequence (1, 2, 3, 4, 5, 6).

Atomization is used in processing the following types of expressions:

  • Arithmetic expressions

  • Comparison expressions

  • Function calls and returns

  • Cast expressions

2.4.3 Effective Boolean Value

Under certain circumstances (listed below), it is necessary to find the effective boolean value of a value. [Definition: The effective boolean value of a value is defined as the result of applying the fn:boolean function to the value, as defined in Section 7.3.1 fn:boolean FO31.]

The dynamic semantics of fn:boolean are repeated here for convenience:

  1. If its operand is an empty sequence, fn:boolean returns false.

  2. If its operand is a sequence whose first item is a node, fn:boolean returns true.

  3. If its operand is a singleton value of type xs:boolean or derived from xs:boolean, fn:boolean returns the value of its operand unchanged.

  4. If its operand is a singleton value of type xs:string, xs:anyURI, xs:untypedAtomic, or a type derived from one of these, fn:boolean returns false if the operand value has zero length; otherwise it returns true.

  5. If its operand is a singleton value of any numeric type or derived from a numeric type, fn:boolean returns false if the operand value is NaN or is numerically equal to zero; otherwise it returns true.

  6. In all other cases, fn:boolean raises a type error [err:FORG0006]FO31.

    Note:

    For instance, fn:boolean raises a type error if the operand is a function, a map, or an array.

The effective boolean value of a sequence is computed implicitly during processing of the following types of expressions:

  • Logical expressions (and, or)

  • The fn:not function

  • Certain types of predicates, such as a[b]

  • Conditional expressions (if)

  • Quantified expressions (some, every)

  • General comparisons, in XPath 1.0 compatibility mode.

Note:

The definition of effective boolean value is not used when casting a value to the type xs:boolean, for example in a cast expression or when passing a value to a function whose expected parameter is of type xs:boolean.

2.4.4 Input Sources

XPath 4.0 has a set of functions that provide access to XML documents (fn:doc, fn:doc-available), collections (fn:collection, fn:uri-collection), text files (fn:unparsed-text, fn:unparsed-text-lines, fn:unparsed-text-available), and environment variables (fn:environment-variable, fn:available-environment-variables). These functions are defined in Section 14.6 Functions giving access to external information FO31.

An expression can access input data either by calling one of these input functions or by referencing some part of the dynamic context that is initialized by the external environment, such as a variable or context item.

2.4.5 URI Literals

XPath 4.0 requires a statically known, valid URI in a BracedURILiteral. An implementation may raise a static error [err:XQST0046] if the value of a Braced URI Literal is of nonzero length and is neither an absolute URI nor a relative URI.

Note:

The xs:anyURI type is designed to anticipate the introduction of Internationalized Resource Identifiers (IRI's) as defined in [RFC3987].

Whitespace is normalized using the whitespace normalization rules of fn:normalize-space. If the result of whitespace normalization contains only whitespace, the corresponding URI consists of the empty string.

A Braced URI Literal or URI Literal is not subjected to percent-encoding or decoding as defined in [RFC3986].

2.4.6 Resolving a Relative URI Reference

[Definition: To resolve a relative URI $rel against a base URI $base is to expand it to an absolute URI, as if by calling the function fn:resolve-uri($rel, $base).] During static analysis, the base URI is the Static Base URI. During dynamic evaluation, the base URI used to resolve a relative URI reference depends on the semantics of the expression.

Any process that attempts to resolve URI against a base URI, or to dereference the URI, may apply percent-encoding or decoding as defined in the relevant RFCs.

3 Types

The type system of XPath 4.0 is based on [XML Schema 1.0] or [XML Schema 1.1].

[Definition: A sequence type is a type that can be expressed using the SequenceType syntax. Sequence types are used whenever it is necessary to refer to a type in an XPath 4.0 expression. The term sequence type suggests that this syntax is used to describe the type of an XPath 4.0 value, which is always a sequence.]

[Definition: A schema type is a type that is (or could be) defined using the facilities of [XML Schema 1.0] or [XML Schema 1.1] (including the built-in types).] A schema type can be used as a type annotation on an element or attribute node (unless it is a non-instantiable type such as xs:NOTATION or xs:anyAtomicType, in which case its derived types can be so used). Every schema type is either a complex type or a simple type; simple types are further subdivided into list types, union types, and atomic types (see [XML Schema 1.0] or [XML Schema 1.1] for definitions and explanations of these terms.)

[Definition: A generalized atomic type is a schema-defined type which is either (a) an atomic type or (b) a pure union type ].

[Definition: A pure union type is an XML Schema union type that satisfies the following constraints: (1) {variety} is union, (2) the {facets} property is empty, (3) no type in the transitive membership of the union type has {variety} list, and (4) no type in the transitive membership of the union type is a type with {variety} union having a non-empty {facets} property].

Note:

The definition of pure union type excludes union types derived by non-trivial restriction from other union types, as well as union types that include list types in their membership. Pure union types have the property that every instance of an atomic type defined as one of the member types of the union is also a valid instance of the union type.

Note:

The current (second) edition of XML Schema 1.0 contains an error in respect of the substitutability of a union type by one of its members: it fails to recognize that this is unsafe if the union is derived by restriction from another union.

This problem is fixed in XSD 1.1, but the effect of the resolution is that an atomic value labeled with an atomic type cannot be treated as being substitutable for a union type without explicit validation. This specification therefore allows union types to be used as item types only if they are defined directly as the union of a number of atomic types.

Generalized atomic types represent the intersection between the categories of sequence type and schema type. A generalized atomic type, such as xs:integer or my:hatsize, is both a sequence type and a schema type.

3.1 Predefined Schema Types

The in-scope schema types in the static context are initialized with a set of predefined schema types that is determined by the host language. This set may include some or all of the schema types in the namespace http://www.w3.org/2001/XMLSchema, represented in this document by the namespace prefix xs. The schema types in this namespace are defined in [XML Schema 1.0] or [XML Schema 1.1] and augmented by additional types defined in [XQuery and XPath Data Model (XDM) 3.1]. An implementation that has based its type system on [XML Schema 1.0] is not required to support the xs:dateTimeStamp or xs:error types.

The schema types defined in Section 2.7.2 Predefined Types DM31 are summarized below.

  1. [Definition: xs:untyped is used as the type annotation of an element node that has not been validated, or has been validated in skip mode.] No predefined schema types are derived from xs:untyped.

  2. [Definition: xs:untypedAtomic is an atomic type that is used to denote untyped atomic data, such as text that has not been assigned a more specific type.] An attribute that has been validated in skip mode is represented in the data model by an attribute node with the type annotation xs:untypedAtomic. No predefined schema types are derived from xs:untypedAtomic.

  3. [Definition: xs:dayTimeDuration is derived by restriction from xs:duration. The lexical representation of xs:dayTimeDuration is restricted to contain only day, hour, minute, and second components.]

  4. [Definition: xs:yearMonthDuration is derived by restriction from xs:duration. The lexical representation of xs:yearMonthDuration is restricted to contain only year and month components.]

  5. [Definition: xs:anyAtomicType is an atomic type that includes all atomic values (and no values that are not atomic). Its base type is xs:anySimpleType from which all simple types, including atomic, list, and union types, are derived. All primitive atomic types, such as xs:decimal and xs:string, have xs:anyAtomicType as their base type.]

    Note:

    xs:anyAtomicType will not appear as the type of an actual value in an XDM instance.

  6. [Definition: xs:error is a simple type with no value space. It is defined in Section 3.16.7.3 xs:error XS11-1 and can be used in the 3.4 Sequence Types to raise errors.]

The relationships among the schema types in the xs namespace are illustrated in Figure 2. A more complete description of the XPath 4.0 type hierarchy can be found in Section 1.6 Type System FO31.

Type Hierarchy Diagram

Figure 2: Hierarchy of Schema Types used in XPath 4.0.

3.2 Namespace-sensitive Types

[Definition: The namespace-sensitive types are xs:QName, xs:NOTATION, types derived by restriction from xs:QName or xs:NOTATION, list types that have a namespace-sensitive item type, and union types with a namespace-sensitive type in their transitive membership.]

It is not possible to preserve the type of a namespace-sensitive value without also preserving the namespace binding that defines the meaning of each namespace prefix used in the value. Therefore, XPath 4.0 defines some error conditions that occur only with namespace-sensitive values. For instance, casting to a namespace-sensitive type raises a type error [err:FONS0004]FO31 if the namespace bindings for the result cannot be determined.

3.3 Typed Value and String Value

Every node has a typed value and a string value, except for nodes whose value is absentDM31. [Definition: The typed value of a node is a sequence of atomic values and can be extracted by applying the Section 2.4 fn:data FO31 function to the node.] [Definition: The string value of a node is a string and can be extracted by applying the Section 2.3 fn:string FO31 function to the node.]

An implementation may store both the typed value and the string value of a node, or it may store only one of these and derive the other as needed. The string value of a node must be a valid lexical representation of the typed value of the node, but the node is not required to preserve the string representation from the original source document. For example, if the typed value of a node is the xs:integer value 30, its string value might be "30" or "0030".

The typed value, string value, and type annotation of a node are closely related. If the node was created by mapping from an Infoset or PSVI, the relationships among these properties are defined by rules in Section 2.7 Schema Information DM31.

As a convenience to the reader, the relationship between typed value and string value for various kinds of nodes is summarized and illustrated by examples below.

  1. For text and document nodes, the typed value of the node is the same as its string value, as an instance of the type xs:untypedAtomic. The string value of a document node is formed by concatenating the string values of all its descendant text nodes, in document order.

  2. The typed value of a comment, namespace, or processing instruction node is the same as its string value. It is an instance of the type xs:string.

  3. The typed value of an attribute node with the type annotation xs:anySimpleType or xs:untypedAtomic is the same as its string value, as an instance of xs:untypedAtomic. The typed value of an attribute node with any other type annotation is derived from its string value and type annotation using the lexical-to-value-space mapping defined in [XML Schema 1.0] or [XML Schema 1.1] Part 2 for the relevant type.

    Example: A1 is an attribute having string value "3.14E-2" and type annotation xs:double. The typed value of A1 is the xs:double value whose lexical representation is 3.14E-2.

    Example: A2 is an attribute with type annotation xs:IDREFS, which is a list datatype whose item type is the atomic datatype xs:IDREF. Its string value is "bar baz faz". The typed value of A2 is a sequence of three atomic values ("bar", "baz", "faz"), each of type xs:IDREF. The typed value of a node is never treated as an instance of a named list type. Instead, if the type annotation of a node is a list type (such as xs:IDREFS), its typed value is treated as a sequence of the generalized atomic type from which it is derived (such as xs:IDREF).

  4. For an element node, the relationship between typed value and string value depends on the node's type annotation, as follows:

    1. If the type annotation is xs:untyped or xs:anySimpleType or denotes a complex type with mixed content (including xs:anyType), then the typed value of the node is equal to its string value, as an instance of xs:untypedAtomic. However, if the nilled property of the node is true, then its typed value is the empty sequence.

      Example: E1 is an element node having type annotation xs:untyped and string value "1999-05-31". The typed value of E1 is "1999-05-31", as an instance of xs:untypedAtomic.

      Example: E2 is an element node with the type annotation formula, which is a complex type with mixed content. The content of E2 consists of the character "H", a child element named subscript with string value "2", and the character "O". The typed value of E2 is "H2O" as an instance of xs:untypedAtomic.

    2. If the type annotation denotes a simple type or a complex type with simple content, then the typed value of the node is derived from its string value and its type annotation in a way that is consistent with schema validation. However, if the nilled property of the node is true, then its typed value is the empty sequence.

      Example: E3 is an element node with the type annotation cost, which is a complex type that has several attributes and a simple content type of xs:decimal. The string value of E3 is "74.95". The typed value of E3 is 74.95, as an instance of xs:decimal.

      Example: E4 is an element node with the type annotation hatsizelist, which is a simple type derived from the atomic type hatsize, which in turn is derived from xs:integer. The string value of E4 is "7 8 9". The typed value of E4 is a sequence of three values (7, 8, 9), each of type hatsize.

      Example: E5 is an element node with the type annotation my:integer-or-string which is a union type with member types xs:integer and xs:string. The string value of E5 is "47". The typed value of E5 is 47 as an xs:integer, since xs:integer is the member type that validated the content of E5. In general, when the type annotation of a node is a union type, the typed value of the node will be an instance of one of the member types of the union.

      Note:

      If an implementation stores only the string value of a node, and the type annotation of the node is a union type, the implementation must be able to deliver the typed value of the node as an instance of the appropriate member type.

    3. If the type annotation denotes a complex type with empty content, then the typed value of the node is the empty sequence and its string value is the zero-length string.

    4. If the type annotation denotes a complex type with element-only content, then the typed value of the node is absentDM31. The fn:data function raises a type error [err:FOTY0012]FO31 when applied to such a node. The string value of such a node is equal to the concatenated string values of all its text node descendants, in document order.

      Example: E6 is an element node with the type annotation weather, which is a complex type whose content type specifies element-only. E6 has two child elements named temperature and precipitation. The typed value of E6 is absentDM31, and the fn:data function applied to E6 raises an error.

3.4 Sequence Types

Whenever it is necessary to refer to a type in an XPath 4.0 expression, the SequenceType syntax is used.

[94]    SequenceType    ::=    ("empty-sequence" "(" ")")
| (ItemType OccurrenceIndicator?)
[96]    ItemType    ::=    AnyItemTest | TypeName | KindTest | FunctionTest | MapTest | ArrayTest | AtomicOrUnionType | RecordTest | LocalUnionType | EnumerationType | ParenthesizedItemType
[95]    OccurrenceIndicator    ::=    "?" | "*" | "+"

With the exception of the special type empty-sequence(), a sequence type consists of an item type that constrains the type of each item in the sequence, and a cardinality that constrains the number of items in the sequence. Apart from the item type item(), which permits any kind of item, item types divide into node types (such as element()), generalized atomic types (such as xs:integer) and function types (such as function() as item()*).

Lexical QNames appearing in a sequence type have their prefixes expanded to namespace URIs by means of the statically known namespaces and (where applicable) the default element namespace or default type namespace . Equality of QNames is defined by the eq operator.

Item types representing element and attribute nodes may specify the required type annotations of those nodes, in the form of a schema type. Thus the item type element(*, us:address) denotes any element node whose type annotation is (or is derived from) the schema type named us:address.

The occurrence indicators '+', '*', and '?' bind to the last ItemType in the SequenceType, as described in occurrence-indicators constraint.

Here are some examples of sequence types that might be used in XPath 4.0:

  • xs:date refers to the built-in atomic schema type named xs:date

  • attribute()? refers to an optional attribute node

  • element() refers to any element node

  • element(po:shipto, po:address) refers to an element node that has the name po:shipto and has the type annotation po:address (or a schema type derived from po:address)

  • element(*, po:address) refers to an element node of any name that has the type annotation po:address (or a type derived from po:address)

  • element(customer) refers to an element node named customer with any type annotation

  • schema-element(customer) refers to an element node whose name is customer (or is in the substitution group headed by customer) and whose type annotation matches the schema type declared for a customer element in the in-scope element declarations

  • node()* refers to a sequence of zero or more nodes of any kind

  • item()+ refers to a sequence of one or more items

  • function(*) refers to any functionDM31, regardless of arity or type

  • function(node()) as xs:string* refers to a functionDM31 that takes a single argument whose value is a single node, and returns a sequence of zero or more xs:string values

  • (function(node()) as xs:string)* refers to a sequence of zero or more functionsDM31, each of which takes a single argument whose value is a single node, and returns as its result a single xs:string value

3.5 Sequence Type Matching

[Definition: SequenceType matching compares the dynamic type of a value with an expected sequence type. ] For example, an instance of expression returns true if the dynamic type of a given value matches a given sequence type, or false if it does not.

An XPath 4.0 implementation must be able to determine relationships among the types in type annotations in an XDM instance and the types in the in-scope schema definitions (ISSD).

[Definition: The use of a value whose dynamic type is derived from an expected type is known as subtype substitution.] Subtype substitution does not change the actual type of a value. For example, if an xs:integer value is used where an xs:decimal value is expected, the value retains its type as xs:integer.

The definition of SequenceType matching relies on a pseudo-function named derives-from( AT, ET ), which takes an actual simple or complex schema type AT and an expected simple or complex schema type ET, and either returns a boolean value or raises a type error [err:XPTY0004]. This function is defined as follows:

  • derives-from( AT, ET ) raises a type error [err:XPTY0004] if ET is not present in the in-scope schema definitions (ISSD).

  • derives-from( AT, ET ) returns true if any of the following conditions applies:

    • AT is ET

    • ET is the base type of AT

    • ET is a pure union type of which AT is a member type

    • There is a type MT such that derives-from( AT, MT ) and derives-from( MT, ET )

  • Otherwise, derives-from( AT, ET ) returns false

The rules for SequenceType matching are given below, with examples (the examples are for purposes of illustration, and do not cover all possible cases).

An OccurrenceIndicator specifies the number of items in a sequence, as follows:

  • ? matches zero or one items

  • * matches zero or more items

  • + matches one or more items

As a consequence of these rules, any sequence type whose OccurrenceIndicator is * or ? matches a value that is an empty sequence.

3.6 Item Types

[96]    ItemType    ::=    AnyItemTest | TypeName | KindTest | FunctionTest | MapTest | ArrayTest | AtomicOrUnionType | RecordTest | LocalUnionType | EnumerationType | ParenthesizedItemType
[115]    TypeName    ::=    EQName
[127]    LocalUnionType    ::=    "union" "(" ItemType ("," ItemType)* ")"
[99]    KindTest    ::=    DocumentTest
| ElementTest
| AttributeTest
| SchemaElementTest
| SchemaAttributeTest
| PITest
| CommentTest
| TextTest
| NamespaceNodeTest
| AnyKindTest
[101]    DocumentTest    ::=    "document-node" "(" (ElementTest | SchemaElementTest)? ")"
[109]    ElementTest    ::=    "element" "(" (NameTest ("," TypeName "?"?)?)? ")"
[110]    SchemaElementTest    ::=    "schema-element" "(" ElementDeclaration ")"
[111]    ElementDeclaration    ::=    ElementName
[106]    AttributeTest    ::=    "attribute" "(" (NameTest ("," TypeName)?)? ")"
[107]    SchemaAttributeTest    ::=    "schema-attribute" "(" AttributeDeclaration ")"
[108]    AttributeDeclaration    ::=    AttributeName
[113]    ElementName    ::=    EQName
[112]    AttributeName    ::=    EQName
[105]    PITest    ::=    "processing-instruction" "(" (NCName | StringLiteral)? ")"
[103]    CommentTest    ::=    "comment" "(" ")"
[104]    NamespaceNodeTest    ::=    "namespace-node" "(" ")"
[102]    TextTest    ::=    "text" "(" ")"
[100]    AnyKindTest    ::=    "node" "(" ")"
[116]    FunctionTest    ::=    AnyFunctionTest
| TypedFunctionTest
[117]    AnyFunctionTest    ::=    "function" "(" "*" ")"
[118]    TypedFunctionTest    ::=    "function" "(" (SequenceType ("," SequenceType)*)? ")" "as" SequenceType
[132]    ParenthesizedItemType    ::=    "(" ItemType ")"
[119]    MapTest    ::=    AnyMapTest | TypedMapTest
[122]    RecordTest    ::=    "record" "(" FieldDeclaration ("," FieldDeclaration)* ExtensibleFlag? ")"
[129]    ArrayTest    ::=    AnyArrayTest | TypedArrayTest

This section defines the semantics of different ItemTypes in terms of the values that they match.

An item type written simply as an EQName (that is, a NamedType) is interpreted as follows:

  1. If the name is written as a lexical QName, then it is expanded using the in-scope namespaces in the static context. If the name is an unprefixed NCName, then it is taken as being in the default type namespace.

  2. If the name matches an entry in the item type aliases in the static context, then it is taken as a reference to the corresponding item type. The rules that apply are the rules for the expanded item type definition.

  3. Otherwise, it must match the name of a type in the in-scope schema types in the static context: specifically, an atomic type or a plain union type. See 3.6.2 Atomic and Union Types for details.

    Note:

    A name in the xs namespace will always fall into this category, since the namespace is reserved.

  4. If the name cannot be resolved to a type, a static error is raised [err:XPST0051].

3.6.1 General item types

  • item() matches any single item.

    Example: item() matches the atomic value 1, the element <a/>, or the function fn:concat#3.

  • A ParenthesizedItemType matches an item if and only if the item matches the ItemType that is in parentheses.

    Note:

    Parenthesized item types are used primarily when defining nested item types in a function signature: for example a sequence of functions that return booleans might be denoted (function () as xs:boolean)*. In this example the parentheses are needed to indicate where the occurrence indicator belongs.

3.6.2 Atomic and Union Types

A generalized atomic type may be expressed as an in any of the following ways:

Example: The ItemType xs:decimal matches any value of type xs:decimal. It also matches any value of type shoesize, if shoesize is an atomic type derived by restriction from xs:decimal.

Example: Suppose ItemType dress-size is a union type that allows either xs:decimal values for numeric sizes (e.g. 4, 6, 10, 12), or one of an enumerated set of xs:strings (e.g. "small", "medium", "large"). The ItemType dress-size matches any of these values.

Note:

The names of list types such as xs:IDREFS are not accepted in this context, but can often be replaced by a generalized atomic type with an occurrence indicator, such as xs:IDREF+.

3.6.2.1 Local Union Types

A LocalUnionType defines an anonymous union type locally (for example, within a function signature) which may be more convenient than defining the type in an imported schema.

[127]    LocalUnionType    ::=    "union" "(" ItemType ("," ItemType)* ")"

Although the grammar allows any ItemType to appear, each ItemType must identify a generalized atomic type. [TODO: error code]

An item matches a LocalUnionType if it matches any of the generalized atomic types listed within the parentheses.

For example, the type union(xs:date, xs:dateTime, xs:time) matches any value that is an instance of xs:date, xs:dateTime, or xs:time.

Similarly, the type union(xs:NCName, enum("")) matches any value that is either an instance of xs:NCName, or a zero-length string. This might be a suitable type for a variable that holds a namespace prefix.

Note:

Local union types are particularly useful in function signatures, allowing a function to take arguments of a variety of types. The semantics are identical to using a named union type, but a local union type is more convenient because it does not need to be defined in a schema, and does not require a schema-aware processor.

A local union type can also be used in a cast expression: cast @when as union(xs:date, xs:dateTime) allows the attribute @when to be either a date, or a dateTime.

An instance of expression can be used to test whether a value belongs to one of a number of specified types: $x instance of union(xs:string, xs:anyURI, xs:untypedAtomic) returns true if $x is an instance of any of these three atomic types.

3.6.2.2 Enumeration Types

[Definition: An EnumerationType accepts a fixed set of string values.]

[128]    EnumerationType    ::=    "enum" "(" StringLiteral ("," StringLiteral)* ")"

An item matches an EnumerationType if it is an instance of xs:string, and is equal to one of the string literals listed within the parentheses, when compared using the codepoint collation.

For example, the type enum("red", "green", "blue") matches the string "green".

Note:

Unlike a schema-defined type that restricts xs:string with an enumeration facet, matching of an EnumerationType is based purely on value comparison, and not on type annotations. For example, if color is a schema-defined atomic type derived from xs:string with an enumeration facet permitting the values ("red", "green", "blue"), the expression "green" instance of color is false, because the type annotation does not match. By contrast, "green" instance of enum("red", "green", "blue") is true.

An EnumerationType only matches xs:string values, not xs:untypedAtomic or xs:anyURI values, even though these might compare equal. However, the coercion rules allow xs:untypedAtomic or xs:anyURI values to be supplied where the required type is an enumeration type.

3.6.3 Node Types

Some of the constructs described in this section include a TypeName. This appears as T in:

  • element(N, T)

  • attribute(N, T)

  • document-node(element(N, T))

In these constructs, the type name T is expanded using the in-scope namespaces in the static context, using the default type namespace if it is unprefixed. The resulting QName must identify a type in the in-scope schema definitions. This can be any schema type: either a simple type, or (except in the case of attributes) a complex type. If it is a simple type then it can be an atomic, union, or list type. It can be a built-in type (such as xs:integer) or a user-defined type. It must however be the name of a type defined in a schema; it cannot be a type alias.

3.6.3.1 Simple Node Tests
  • node() matches any node.

  • text() matches any text node.

  • processing-instruction() matches any processing-instruction node.

  • processing-instruction( N ) matches any processing-instruction node whose PITarget is equal to fn:normalize-space(N). If fn:normalize-space(N) is not in the lexical space of NCName, a type error is raised [err:XPTY0004]

    Example: processing-instruction(xml-stylesheet) matches any processing instruction whose PITarget is xml-stylesheet.

    For backward compatibility with XPath 1.0, the PITarget of a processing instruction may also be expressed as a string literal, as in this example: processing-instruction("xml-stylesheet").

    If the specified PITarget is not a syntactically valid NCName, a type error is raised [err:XPTY0004].

  • comment() matches any comment node.

  • namespace-node() matches any namespace node.

  • document-node() matches any document node.

  • document-node( E ) matches any document node that contains exactly one element node, optionally accompanied by one or more comment and processing instruction nodes, if E is an ElementTest or SchemaElementTest that matches the element node (see 3.6.3.2 Element Test and 3.6.3.3 Schema Element Test).

    Example: document-node(element(book)) matches a document node containing exactly one element node that is matched by the ElementTest element(book).

  • An ItemType that is an ElementTest, SchemaElementTest, AttributeTest, SchemaAttributeTest, or FunctionTest matches an item as described in the following sections.

3.6.3.2 Element Test
[109]    ElementTest    ::=    "element" "(" (NameTest ("," TypeName "?"?)?)? ")"
[55]    NameTest    ::=    EQName | Wildcard
[113]    ElementName    ::=    EQName
[115]    TypeName    ::=    EQName

An ElementTest is used to match an element node by its name and/or type annotation.

The ElementName and TypeName of an ElementTest have their prefixes expanded to namespace URIs by means of the statically known namespaces, or if unprefixed, the default element namespace or default type namespace respectively. The ElementName need not be present in the in-scope element declarations, but the TypeName must be present in the in-scope schema types [err:XPST0008]. Note that substitution groups do not affect the semantics of ElementTest.

An ElementTest may take any of the following forms:

  1. element() and element(*) match any single element node, regardless of its name or type annotation.

  2. element( ElementName ) matches any element node whose name is ElementName, regardless of its type annotation or nilled property.

    Example: element(person) matches any element node whose name is person.

  3. element(prefix:*) matches any element node whose name is in the namespace bound to the given prefix, regardless of its type annotation or nilled property.

    Example: element(xhtml:*) matches any element node whose name is in the namespace bound to the prefix xhtml.

  4. element(Q{uri}*) matches any element node whose name is in the namespace given as uri, regardless of its type annotation or nilled property.

    Example: element(Q{"http://www.w3.org/2000/svg"}*) matches any element node whose name is in the SVG namespace.

  5. element(*:local) matches any element node whose local name is the name given as local, regardless of its namespace, type annotation or nilled property.

    Example: element(*:html) matches any element node whose local name is "html".

  6. element( ElementName , TypeName ) matches an element node whose name is ElementName if derives-from( AT, TypeName ) is true, where AT is the type annotation of the element node, and the nilled property of the node is false.

    Example: element(person, surgeon) matches a non-nilled element node whose name is person and whose type annotation is surgeon (or is derived from surgeon).

    The ElementName in this example can also be replaced by one of the forms prefix:*, Q{uri}*, or *:local.

  7. element( ElementName, TypeName ?) matches an element node whose name is ElementName if derives-from( AT, TypeName ) is true, where AT is the type annotation of the element node. The nilled property of the node may be either true or false.

    Example: element(person, surgeon?) matches a nilled or non-nilled element node whose name is person and whose type annotation is surgeon (or is derived from surgeon).

    The ElementName in this example can also be replaced by one of the forms prefix:*, Q{uri}*, or *:local.

  8. element(*, TypeName ) matches an element node regardless of its name, if derives-from( AT, TypeName ) is true, where AT is the type annotation of the element node, and the nilled property of the node is false.

    Example: element(*, surgeon) matches any non-nilled element node whose type annotation is surgeon (or is derived from surgeon), regardless of its name.

  9. element(*, TypeName ?) matches an element node regardless of its name, if derives-from( AT, TypeName ) is true, where AT is the type annotation of the element node. The nilled property of the node may be either true or false.

    Example: element(*, surgeon?) matches any nilled or non-nilled element node whose type annotation is surgeon (or is derived from surgeon), regardless of its name.

3.6.3.3 Schema Element Test
[110]    SchemaElementTest    ::=    "schema-element" "(" ElementDeclaration ")"
[111]    ElementDeclaration    ::=    ElementName
[113]    ElementName    ::=    EQName

A SchemaElementTest matches an element node against a corresponding element declaration found in the in-scope element declarations.

The ElementName of a SchemaElementTest has its prefixes expanded to a namespace URI by means of the statically known namespaces, or if unprefixed, the default element namespace . If the ElementName specified in the SchemaElementTest is not found in the in-scope element declarations, a static error is raised [err:XPST0008].

A SchemaElementTest matches a candidate element node if all of the following conditions are satisfied:

  1. Either:

    1. The name N of the candidate node matches the specified ElementName, or

    2. The name N of the candidate node matches the name of an element declaration that is a member of the actual substitution group headed by the declaration of element ElementName.

    Note:

    The term "actual substitution group" is defined in [XML Schema 1.1]. The actual substitution group of an element declaration H includes those element declarations P that are declared to have H as their direct or indirect substitution group head, provided that P is not declared as abstract, and that P is validly substitutable for H, which means that there must be no blocking constraints that prevent substitution.

  2. The schema element declaration named N is not abstract.

  3. derives-from( AT, ET ) is true, where AT is the type annotation of the candidate node and ET is the schema type declared in the schema element declaration named N.

  4. If the schema element declaration named N is not nillable, then the nilled property of the candidate node is false.

Example: The SchemaElementTest schema-element(customer) matches a candidate element node in the following two situations:

  1. customer is a top-level element declaration in the in-scope element declarations; the name of the candidate node is customer; the element declaration of customer is not abstract; the type annotation of the candidate node is the same as or derived from the schema type declared in the customer element declaration; and either the candidate node is not nilled, or customer is declared to be nillable.

  2. customer is a top-level element declaration in the in-scope element declarations; the name of the candidate node is client; client is an actual (non-abstract and non-blocked) member of the substitution group of customer; the type annotation of the candidate node is the same as or derived from the schema type declared for the client element; and either the candidate node is not nilled, or client is declared to be nillable.

3.6.3.4 Attribute Test
[106]    AttributeTest    ::=    "attribute" "(" (NameTest ("," TypeName)?)? ")"
[55]    NameTest    ::=    EQName | Wildcard
[112]    AttributeName    ::=    EQName
[115]    TypeName    ::=    EQName

An AttributeTest is used to match an attribute node by its name and/or type annotation.

The AttributeName and TypeName of an AttributeTest have their prefixes expanded to namespace URIs by means of the statically known namespaces. If unprefixed, the AttributeName is in no namespace, but an unprefixed TypeName is in the default type namespace . The AttributeName need not be present in the in-scope attribute declarations, but the TypeName must be present in the in-scope schema types [err:XPST0008].

An AttributeTest may take any of the following forms:

  1. attribute() and attribute(*) match any single attribute node, regardless of its name or type annotation.

  2. attribute( AttributeName ) matches any attribute node whose name is AttributeName, regardless of its type annotation.

    Example: attribute(price) matches any attribute node whose name is price.

  3. attribute(prefix:*) matches any attribute node whose name is in the namespace bound to the given prefix, regardless of its type annotation.

    Example: attribute(xlink:*) matches any attribute node whose name is in the namespace bound to the prefix xlink.

  4. attribute(Q{uri}*) matches any attribute node whose name is in the namespace given as uri, regardless of its type annotation.

    Example: element(Q{"http://www.w3.org/2000/svg"}*) matches any attribute node whose name is in the SVG namespace.

  5. attribute(*:local) matches any attribute node whose local name is the name given as local, regardless of its namespace or type annotation.

    Example: attribute(*:default-collation) matches any attribute node whose local name is "default-collation".

  6. attribute( AttributeName, TypeName ) matches an attribute node whose name is AttributeName if derives-from( AT, TypeName ) is true, where AT is the type annotation of the attribute node.

    Example: attribute(price, currency) matches an attribute node whose name is price and whose type annotation is currency (or is derived from currency).

    The AttributeName in this example can also be replaced by one of the forms prefix:*, Q{uri}*, or *:local.

  7. attribute(*, TypeName ) matches an attribute node regardless of its name, if derives-from( AT, TypeName ) is true, where AT is the type annotation of the attribute node.

    Example: attribute(*, currency) matches any attribute node whose type annotation is currency (or is derived from currency), regardless of its name.

3.6.3.5 Schema Attribute Test
[107]    SchemaAttributeTest    ::=    "schema-attribute" "(" AttributeDeclaration ")"
[108]    AttributeDeclaration    ::=    AttributeName
[112]    AttributeName    ::=    EQName

A SchemaAttributeTest matches an attribute node against a corresponding attribute declaration found in the in-scope attribute declarations.

The AttributeName of a SchemaAttributeTest has its prefixes expanded to a namespace URI by means of the statically known namespaces. If unprefixed, an AttributeName is in no namespace. If the AttributeName specified in the SchemaAttributeTest is not found in the in-scope attribute declarations, a static error is raised [err:XPST0008].

A SchemaAttributeTest matches a candidate attribute node if both of the following conditions are satisfied:

  1. The name of the candidate node matches the specified AttributeName.

  2. derives-from( AT, ET ) is true, where AT is the type annotation of the candidate node and ET is the schema type declared for attribute AttributeName in the in-scope attribute declarations.

Example: The SchemaAttributeTest schema-attribute(color) matches a candidate attribute node if color is a top-level attribute declaration in the in-scope attribute declarations, the name of the candidate node is color, and the type annotation of the candidate node is the same as or derived from the schema type declared for the color attribute.

3.6.4 Function, Map, and Array Tests

  • The ItemType map(K, V) matches an item M if (a) M is a map, and (b) every entry in M has a key that matches K and an associated value that matches V. For example, map(xs:integer, element(employee)) matches a map if all the keys in the map are integers, and all the associated values are employee elements. Note that a map (like a sequence) carries no intrinsic type information separate from the types of its entries, and the type of existing entries in a map does not constrain the type of new entries that can be added to the map.

    Note:

    In consequence, map(K, V) matches an empty map, whatever the types K and V might be.

  • The ItemType map(*) matches any map regardless of its contents. It is equivalent to map(xs:anyAtomicType, item()*).

  • The ItemType record(K1 as T1, K2 as T2) matches a map having keys K1 and K2, with associated values matching T1 and T2 respectively. Record tests are described in more detail in 3.6.4.3 Record Test.

  • The ItemType array(T) matches any array in which the type of every member is T.

  • The ItemType array(*) matches any array regardless of its contents.

3.6.4.1 Function Test
[116]    FunctionTest    ::=    AnyFunctionTest
| TypedFunctionTest
[117]    AnyFunctionTest    ::=    "function" "(" "*" ")"
[118]    TypedFunctionTest    ::=    "function" "(" (SequenceType ("," SequenceType)*)? ")" "as" SequenceType

A FunctionTest matches a functionDM31, potentially also checking its function signatureDM31 . An AnyFunctionTest matches any item that is a function. A TypedFunctionTest matches an item if it is a functionDM31 and the function's type signature (as defined in Section 2.8.1 Functions DM31) is a subtype of the TypedFunctionTest.

Here are some examples of FunctionTests:

  1. function(*) matches any function, including maps and arrays.

  2. function(int, int) as int matches any functionDM31 with the function signature function(int, int) as int.

  3. function(xs:anyAtomicType) as item()* matches any map, or any function with the required signature.

  4. function(xs:integer) as item()* matches any array, or any function with the required signature.

3.6.4.2 Map Test
[119]    MapTest    ::=    AnyMapTest | TypedMapTest
[120]    AnyMapTest    ::=    "map" "(" "*" ")"
[121]    TypedMapTest    ::=    "map" "(" ItemType "," SequenceType ")"

The MapTest map(*) matches any map. The MapTest map(X, Y) matches any map where the type of every key is an instance of X and the type of every value is an instance of Y.

Although the grammar for TypedMapTest allows the key to be described using the full ItemType syntax, the item type used must be a generalized atomic type. [TODO: error code].

Examples:

Given a map $M whose keys are integers and whose results are strings, such as map{0:"no", 1:"yes"}, consider the results of the following expressions:

  • $M instance of map(*) returns true()

  • $M instance of map(xs:integer, xs:string) returns true()

  • $M instance of map(xs:decimal, xs:anyAtomicType) returns true()

  • not($M instance of map(xs:int, xs:string)) returns true()

  • not($M instance of map(xs:integer, xs:token)) returns true()

Because of the rules for subtyping of function types according to their signature, it follows that the item type function(A) as item()*, where A is an atomic type, also matches any map, regardless of the type of the keys actually found in the map. For example, a map whose keys are all strings can be supplied where the required type is function(xs:integer) as item()*; a call on the map that treats it as a function with an integer argument will always succeed, and will always return an empty sequence.

The function signature of a map matching type map(K, V), treated as a function, is function(xs:anyAtomicType) as V?. It is thus always a subtype of function(xs:anyAtomicType) as item()* regardless of the actual types of the keys and values in the map. The rules for function coercion mean that any map can be supplied as a value in a context where the required type has a more specific return type, such as function(xs:anyAtomicType) as xs:integer, even when the map does not match in the sense required to satisfy the instance of operator. In such cases, a type error will only occur if an actual call on the map (treated as a function) returns a value that is not an instance of the required return type.

Examples:

  • $M instance of function(*) returns true()

  • $M instance of function(xs:anyAtomicType) as item()* returns true()

  • $M instance of function(xs:integer) as item()* returns true()

  • $M instance of function(xs:int) as item()* returns true()

  • $M instance of function(xs:string) as item()* returns true()

  • not($M instance of function(xs:integer) as xs:string) returns true()

Note:

The last case might seem surprising; however, function coercionn ensures that $M can be used successfully anywhere that the required type is function(xs:integer) as xs:string.

3.6.4.3 Record Test
[122]    RecordTest    ::=    "record" "(" FieldDeclaration ("," FieldDeclaration)* ExtensibleFlag? ")"
[123]    FieldDeclaration    ::=    FieldName "?"? ("as" (SequenceType | SelfReference))?
[124]    FieldName    ::=    NCName | StringLiteral
[125]    SelfReference    ::=    ".." OccurrenceIndicator?
[126]    ExtensibleFlag    ::=    "," "*"

A RecordTest matches maps that meet specific criteria.

For example, the RecordTest record(r as xs:double, i as xs:double) matches a map if the map has exactly two entries: an entry with key "r" whose value is a singleton xs:double value, and an entry with key "i" whose value is also a singleton xs:double value.

If the list of fields ends with ",*" then the tuple test is said to be extensible. For example, the RecordTest record(e as element(Employee), *) matches a map if it has an entry with key "e" whose value matches element(Employee), regardless what other entries the map might contain.

A record test can only constrain entries whose keys are strings, but when the record test is marked as extensible, then other entries may be present in the map with non-string keys. Entries whose key is a string can be expressed using an (unquoted) NCName if the key conforms to NCName syntax, or using a (quoted) string literal otherwise.

Note:

Lookup expressions have been extended so that non-NCName keys can be used without parentheses: employee?"middle name"

If the type declaration for a field is omitted, then item()* is assumed: that is, the map entry may have any type.

If the field name is followed by a question mark, then the value must have the specified type if it is present, but it may also be absent. For example, the RecordTest record(first as xs:string, middle? as xs:string, last as xs:string, *) requires the map to have string-valued entries with keys "first" and "last"; it also declares that if the map has an entry with key "middle", the value of that entry must be a single xs:string. Declaring the type as record(first as xs:string, middle? as xs:string?, last as xs:string, *) also allows the entry with key "middle" to be present but empty.

Note:

Within an extensible record test, a FieldDeclaration that is marked optional and has no declared type does not constrain the map in any way, so it serves no practical purpose, but it is permitted because it may have documentary value.

If a field is declared using .. (optionally followed by an occurrence indicator) in place of a SequenceType, this indicates that the record type is recursive: the value of this field, if present, must be an instance of the record type being declared. For example, a record designed to hold error information might be declared as:

record(error-code as xs:QName, message as xs:string, cause? as ..)

A map conforms to this type if it has entries with keys error-code and message of the correct types, and if the cause entry is either absent, or is a map that itself conforms to this type.

A FieldDeclaration that a SelfReference to identify its type must either be optional (marked with a question mark after the name), or must allow the empty sequence as a permitted value (marked by using the occurrence indicator ? or * after the item type). If the field is not optional and does not allow an empty sequence, a static error is raised [err:XPST0140]. This rule ensures that finite instances of the type can be constructed.

A record used to represent a node in a binary tree might be represented as:

record(left? as .., value, right? as ..)

A function to walk this tree and enumerate all the values in depth-first order might be written (using XQuery syntax) as:

declare item-type binary-tree as
    record(left? as .., value, right? as ..);                 
declare function flatten($tree as binary-tree?) as item()* {
    $tree ! (flatten(?left), ?value, flatten(?right))   
}

A record used to represent a node in a tree where each node has an arbitrary number of children might be represented as:

record(value, children as ..*)

A function to walk this tree and enumerate all the values in order might be written (using XQuery syntax) as:

declare item-type tree as
    record(value, children as ..*);                 
declare function flatten($tree as tree) as item()* {
    $tree?value, $tree?children ! flatten(.))   
}

Note:

If a RecordTest contains a SelfReference field that is not optional, and whose type does not permit an empty sequence, then it will not be possible to construct an instance. So a RecordTest such as record(a as ..) serves no practical purpose; but it is not disallowed.

Record tests describe a subset of the value space of maps. They do not define any new kinds of values, or any additional operations. They are useful in many cases to describe more accurately the type of a variable, function parameter, or function result, giving benefits both in the readability of the code, and in the ability of the processor to detect and diagnose type errors and to optimize execution.

In particular, if a variable $rec is known to conform to a particular record type, then when a lookup expression $rec?field is used, (a) the processor can report a type error if $rec cannot contain an entry with name field, and (b) the processor can make static type inferences about the type of value returned by $rec?field.

Note:

A number of functions in the standard function library use maps as function arguments; this is a useful technique where the information to be supplied across the interface is highly variable. However, the type signature for such functions typically declares the argument type as map(*), which gives very little information (and places very few constraints) on the values that are actually passed across. Using record tests offers the possibility of improving this: for example, the options argument of fn:parse-json, previously given as map(*), can now be expressed as record(liberal? as xs:boolean, duplicates? as xs:string, escape? as xs:boolean, fallback as function(xs:string) as xs:string, *). In principle the xs:string type used to describe the duplicates option could also be replaced by a schema-defined subtype of xs:string that enumerates the permitted values ("reject", "use-first", "use-last").

The use of a record test in the signature of such a function causes the coercion rules to be invoked: so, for example, if the function expects an entry in the map to be an xs:double value, it becomes possible to supply a map in which the corresponding entry has type xs:integer.

Greater precision in defining the types of such arguments also enables better type checking, better diagnostics, better optimization, better documentation, and better syntax-directed editing tools.

Note:

One of the motivations for introducing record tests is to enable better pattern matching in XSLT when processing JSON input. With XML input, patterns are often based around XML element names. JSON has no direct equivalent of XML's element names; matching a JSON object such as {longitude: 130.2, latitude: 53.4} relies instead on recognizing the property names appearing in the object. XSLT 4.0, by integrating record tests into pattern matching syntax, allows such an object to be matched with a pattern of the form match="record(longitude, latitude)"

3.6.4.4 Array Test
[129]    ArrayTest    ::=    AnyArrayTest | TypedArrayTest
[130]    AnyArrayTest    ::=    "array" "(" "*" ")"
[131]    TypedArrayTest    ::=    "array" "(" SequenceType ")"

The AnyArrayTest array(*) matches any array. The TypedArrayTest array(X) matches any array in which every array member matches the SequenceType X.

Examples:

  • [ 1, 2 ] instance array(*) returns true()

  • [] instance of array(xs:string) returns true()

  • [ "foo" ] instance of array(xs:string) returns true()

  • [ "foo" ] instance of array(xs:integer) returns false()

  • [(1,2),(3,4)] instance of array(xs:integer) returns false()

  • [(1,2),(3,4)] instance of array(xs:integer+) returns true()

An array also matches certain other ItemTypes, including:

  • item()

  • function(*)

  • function(xs:integer) as item()*

The function signature of an array matching array(X), treated as a function, is function(xs:integer) as X. It is thus always a subtype of function(xs:integer) as item()* regardless of the actual member types in the array. The rules for function coercion mean that any array can be supplied as a value in a context where the required type has a more specific return type, such as function(xs:integer) as xs:integer, even when the array does not match in the sense required to satisfy the instance of operator. In such cases, a type error will only occur if an actual call on the array (treated as a function) returns a value that is not an instance of the required return type.

3.6.5 xs:error

The type xs:error has an empty value space; it never appears as a dynamic type or as the content type of a dynamic element or attribute type. It was defined in XML Schema in the interests of making the type system complete and closed, and it is also available in XPath 4.0 for similar reasons.

Note:

Even though it cannot occur in an instance, xs:error is a valid type name in a sequence type. The practical uses of xs:error as a sequence type are limited, but they do exist. For instance, an error handling function that always raises a dynamic error never returns a value, so xs:error is a good choice for the return type of the function.

The semantics of xs:error are well-defined as a consequence of the fact that xs:error is defined as a union type with no member types. For example:

  • $x instance of xs:error always returns false, regardless of the value of $x.

  • $x cast as xs:error fails dynamically with error [err:FORG0001]FO31, regardless of the value of $x.

  • $x cast as xs:error? raises a dynamic error [err:FORG0001]FO31 if exists($x), evaluates to the empty sequence if empty($x).

  • xs:error($x) has the same semantics as $x cast as xs:error? (see the previous bullet point)

  • $x castable as xs:error evaluates to false, regardless of the value of $x.

  • $x treat as xs:error raises a dynamic error [err:XPDY0050] if evaluated, regardless of the value of $x. It never fails statically.

All of the above examples assume that $x is actually evaluated. If the result of the query does not depend on the value of $x. the rules specified in 2.3.4 Errors and Optimization permit an implementation to avoid evaluating $x and thus to avoid raising an error.

3.7 Subtype Relationships

Given two sequence types, it is possible to determine if one is a subtype of the other. [Definition: A sequence type A is a subtype of a sequence type B if the judgement subtype(A, B) is true.] When the judgement subtype(A, B) is true, it is always the case that for any value V, (V instance of A) implies (V instance of B).

3.7.1 The judgement subtype(A, B)

The judgement subtype(A, B) determines if the sequence type A is a subtype of the sequence type B. A can either be empty-sequence(), xs:error, or an ItemType, Ai, possibly followed by an occurrence indicator. Similarly B can either be empty-sequence(), xs:error, or an ItemType, Bi, possibly followed by an occurrence indicator. The result of the subtype(A, B) judgement can be determined from the table below, which makes use of the auxiliary judgement subtype-itemtype(Ai, Bi) defined in 3.7.2 The judgement subtype-itemtype(A, B) .

Sequence type B
empty-sequence() Bi? Bi* Bi Bi+ xs:error
Sequence type A empty-sequence() true true true false false false
Ai? false subtype-itemtype(Ai, Bi) subtype-itemtype(Ai, Bi) false false false
Ai* false false subtype-itemtype(Ai, Bi) false false false
Ai false subtype-itemtype(Ai, Bi) subtype-itemtype(Ai, Bi) subtype-itemtype(Ai, Bi) subtype-itemtype(Ai, Bi) false
Ai+ false false subtype-itemtype(Ai, Bi) false subtype-itemtype(Ai, Bi) false
xs:error true true true true true true

xs:error+ is treated the same way as xs:error in the above table. xs:error? and xs:error* are treated the same way as empty-sequence().

3.7.2 The judgement subtype-itemtype(A, B)

The judgement subtype-itemtype(A, B) determines whether the ItemType A is a subtype of the ItemType B.

Before applying these rules, any ItemType written as item-type(N) is replaced with the definition of the named item type N, recursively. The rules are written in terms of the lexical form of the two ItemTypes, but it is assumed that trivial variations are first eliminated: comments and unnecessary whitespace are removed, lexical QNames are replaced by URI-qualified names applying appropriate defaults in the case of unprefixed names, equivalent forms such as element() and element(*) are normalized.

A is a subtype of B if and only if at least one of the following conditions applies:

  1. General rules:

    1. A is xs:error.

    2. B is item().

    3. A and B are the same ItemType.

    4. There is an ItemType C such that subtype-itemtype(A, C) and subtype-itemtype(C, B). (This is referred to below as the transitivity rule).

  2. Conditions for atomic and union types:

    1. A and B are generalized atomic types, and derives-from(A, B) returns true.

    2. A is the name of a pure union type, and every type T in the transitive membership of A satisfies subtype-itemType(T, B).

    3. A is a LocalUnionType in the form union(T1, T2, ...) and every type T in (T1, T2, ...) satisfies subtype-itemType(T, B).

    4. A is an EnumerationType, and B matches every string literal in the enumeration of A.

      Note:

      This means, for example, that the type enum("red", "green", "blue") is a subtype of enum("red", "green", "blue", "yellow"), as well as being a subtype of xs:string.

  3. Conditions for node types:

    1. A is a KindTest and B is node().

    2. A is processing-instruction(N) for any name N, and B is processing-instruction().

    3. A is document-node(E) for any ElementTest E, and B is document-node().

    4. All the following are true:

      1. A is document-node(Ae)

      2. B is document-node(Be)

      3. subtype-itemtype(Ae, Be)

    5. A is an ElementTest and B is element() (or element(*)).

    6. All the following are true:

      1. A is either element(An) or element(An, T) or element(An, T?) for some type T

      2. B is either element(Bn) or element(Bn, xs:anyType?)

      3. the expanded QName of An equals the expanded QName of Bn.

    7. All the following are true:

      1. A is element(An, At)

      2. B is element(Bn, Bt)

      3. the expanded QName of An equals the expanded QName of Bn

      4. derives-from(At, Bt).

      TODO: An and Bn as wildcards

    8. All the following are true:

      1. A is either element(An, At) or element(An, At?)

      2. B is element(Bn, Bt?)

      3. the expanded QName of An equals the expanded QName of Bn

      4. derives-from(At, Bt).

      TODO: An and Bn as wildcards

    9. All the following are true:

      1. Ai is either element(*, At) or element(N, At) for any name N

      2. Bi is element(*, Bt)

      3. derives-from(At, Bt).

    10. All the following are true:

      1. A is either element(*, At), element(*, At?), element(N, At), or element(N, At?) for any name N

      2. B is element(*, Bt?)

      3. derives-from(At, Bt).

    11. All the following are true:

      1. A is schema-element(An)

      2. B is schema-element(Bn)

      3. every element declaration that is an actual member of the substitution group of An is also an actual member of the substitution group of Bn

      Note:

      The fact that P is a member of the substitution group of Q does not mean that every element declaration in the substitution group of P is also in the substitution group of Q. For example, Q might block substitution of elements whose type is derived by extension, while P does not.

    12. A is an AttributeTest and B is either attribute() or attribute(*)

    13. All the following are true:

      1. A is either attribute(An) or attribute(An, T) for any type T.

      2. B is either attribute(Bn) or attribute(Bn, xs:anyType)

      3. the expanded QName of An equals the expanded QName of Bn

    14. All the following are true:

      1. A is attribute(An, At)

      2. B is attribute(Bn, Bt)

      3. the expanded QName of An equals the expanded QName of Bn

      4. derives-from(At, Bt).

    15. All the following are true:

      1. A is either attribute(*, At), or attribute(N, At) for any name N

      2. B is attribute(*, Bt)

      3. derives-from(At, Bt).

    16. All the following are true:

      1. A is schema-attribute(An)

      2. B is schema-attribute(Bn)

      3. the expanded QName of An equals the expanded QName of Bn

      4. derives-from(At, Bt).

  4. Conditions for functions, maps and arrays:

    1. All the following are true:

      1. A is a FunctionTest

      2. Bi is function(*)

    2. All the following are true:

      1. A is function(Aa_1, Aa_2, ... Aa_M) as Ar

      2. B is function(Ba_1, Ba_2, ... Ba_N) as Br

      3. N (arity of B) equals M (arity of A)

      4. subtype(Ar, Br)

      5. for all values of I between 1 and N, subtype(Ba_I, Aa_I)

      Note:

      Function return types are covariant because this rule invokes subtype(Ar, Br) for return types. Function arguments are contravariant because this rule invokes subtype(Ba_I, Aa_I) for arguments.

    3. All the following are true:

      1. A is map(K, V), for any K and V

      2. B is map(*)

    4. All the following are true:

      1. A is map(Ka, Va)

      2. B is map(Kb, Vb)

      3. subtype-itemtype(Ka, Kb)

      4. subtype(Va, Vb)

    5. All the following are true:

      1. A is map(*) (or, because of the transitivity rules, any other map type)

      2. B is function(*)

    6. All the following are true:

      1. A is map(*) (or, because of the transitivity rules, any other map type)

      2. B is function(xs:anyAtomicType) as item()*

    7. All the following are true:

      1. A is map(K, V)

      2. B is function(xs:anyAtomicType) as V?

    8. All the following are true:

      1. A is array(X)

      2. B is array(*)

    9. All the following are true:

      1. A is array(X)

      2. B is array(Y)

      3. subtype(X, Y)

    10. All the following are true:

      1. A is array(*) (or, because of the transitivity rules, any other array type)

      2. B is function(*)

    11. All the following are true:

      1. A is array(*) (or, because of the transitivity rules, any other array type)

      2. Bi is function(xs:integer) as item()*

    12. All the following are true:

      1. A is array(X)

      2. B is function(xs:integer) as X

    13. All of the following are true:

      1. A is a record test

      2. B is map(*)

    14. All of the following are true:

      1. A is a record test

      2. A is not extensible

      3. B is map(K, V)

      4. K is either xs:string or xs:anyAtomicType

      5. For every field F in A, where T is the declared type of F (or its default, item()*, subtype(T, V) is true.

    15. All of the following are true:

      1. A is a record test

      2. B is a record test

      3. A is extensible

      4. B is extensible

      5. For every field F that is declared in B, where the declared type of F is U, one of the following is true:

        1. All of the following are true:

          1. F is also declared in A, with required type T

          2. If the field F in B is mandatory, then the field F in Ais also mandatory

          3. subtype(T, U)

        2. TODO: other possibilities?

    16. All of the following are true:

      1. A is a record test

      2. B is a record test

      3. A is not extensible

      4. B is extensible

      5. For every field F that is declared in B, where the declared type of F is U, one of the following is true:

        1. All of the following are true:

          1. F is also declared in A, with required type T

          2. If the field F in B is mandatory, then the field F in Ais also mandatory

          3. subtype(T, U)

        2. TODO: other possibilities?

    17. All of the following are true:

      1. A is a record test

      2. B is a record test

      3. A is not extensible

      4. B is not extensible

      5. For every field F that is declared in B, where the declared type of F is U, one of the following is true:

        1. All of the following are true:

          1. F is also declared in A, with required type T

          2. If the field F in B is mandatory, then the field F in Ais also mandatory

          3. subtype(T, U)

        2. TODO: other possibilities?

4 Expressions

This section discusses each of the basic kinds of expression. Each kind of expression has a name such as PathExpr, which is introduced on the left side of the grammar production that defines the expression. Since XPath 4.0 is a composable language, each kind of expression is defined in terms of other expressions whose operators have a higher precedence. In this way, the precedence of operators is represented explicitly in the grammar.

The order in which expressions are discussed in this document does not reflect the order of operator precedence. In general, this document introduces the simplest kinds of expressions first, followed by more complex expressions. For the complete grammar, see Appendix [A XPath 4.0 Grammar].

The highest-level symbol in the XPath grammar is XPath.

[1]    XPath    ::=    Expr
[7]    Expr    ::=    ExprSingle ("," ExprSingle)*
[8]    ExprSingle    ::=    WithExpr
| ForExpr
| LetExpr
| QuantifiedExpr
| IfExpr
| TernaryConditionalExpr

The XPath 4.0 operator that has lowest precedence is the comma operator, which is used to combine two operands to form a sequence. As shown in the grammar, a general expression (Expr) can consist of multiple ExprSingle operands, separated by commas. The name ExprSingle denotes an expression that does not contain a top-level comma operator (despite its name, an ExprSingle may evaluate to a sequence containing more than one item.)

The symbol ExprSingle is used in various places in the grammar where an expression is not allowed to contain a top-level comma. For example, each of the arguments of a function call must be an ExprSingle, because commas are used to separate the arguments of a function call.

After the comma, the expressions that have next lowest precedence are ForExpr, LetExpr, QuantifiedExpr, IfExpr, and OrExpr. Each of these expressions is described in a separate section of this document.

4.1 Setting Namespace Context

[9]    WithExpr    ::=    "with" NamespaceDeclaration ("," NamespaceDeclaration)* EnclosedExpr
[10]    NamespaceDeclaration    ::=    QName "=" StringLiteral
[6]    EnclosedExpr    ::=    "{" Expr? "}"

The namespace context for an expression can be set using a construct of the form:

with xmlns="http://example.com/,
     xmlns:a="http://example.com/a" {
       /doc/a:element/b
}

The static context for the enclosed expression will be the same as the static context for the WithExpr itself, except for modifications defined below.

The QName used in a NamespaceDeclaration must be either xmlns or xmlns:prefix where prefix is some NCName.

If more than one NamespaceDeclaration specifies the same QName, all but the last of the duplicates are ignored.

If the QName is "xmlns" then:

  • If the StringLiteral is a zero-length string:

  • If the StringLiteral is not zero-length:

    • The default element namespace is set to the supplied namespace URI, meaning that unprefixed element names are treated as being in that namespace.

    • A binding that maps the zero-length prefix to the specified namespace URI is added to the statically known namespaces.

If the QName is in the form xmlns:prefix then the StringLiteral must not be zero-length; the effect is that a binding that maps the given prefix to the specified namespace URI is added to the statically known namespaces.

For example, the expression:

with xmlns="http://www.acme.com/" {a/b[c=3]}

is equivalent to the expression:

Q{http://www.acme.com/}a/Q{http://www.acme.com/}b[Q{http://www.acme.com/}c=3]

4.2 Comments

[143]    Comment    ::=    "(:" (CommentContents | Comment)* ":)"
[148]    CommentContents    ::=    (Char+ - (Char* ('(:' | ':)') Char*))

Comments may be used to provide information relevant to programmers who read an expression. Comments are lexical constructs only, and do not affect expression processing.

Comments are strings, delimited by the symbols (: and :). Comments may be nested.

A comment may be used anywhere ignorable whitespace is allowed (see A.2.4.1 Default Whitespace Handling).

The following is an example of a comment:

(: Houston, we have a problem :)

4.3 Primary Expressions

[Definition: Primary expressions are the basic primitives of the language. They include literals, variable references, context item expressions, and function calls. A primary expression may also be created by enclosing any expression in parentheses, which is sometimes helpful in controlling the precedence of operators.] Map and Array Constructors are described in 4.14 Maps and Arrays.

[69]    PrimaryExpr    ::=    Literal
| VarRef
| ParenthesizedExpr
| ContextItemExpr
| FunctionCall
| FunctionItemExpr
| MapConstructor
| ArrayConstructor
| UnaryLookup
[81]    FunctionItemExpr    ::=    NamedFunctionRef | InlineFunctionExpr

4.3.1 Literals

[Definition: A literal is a direct syntactic representation of an atomic value.] XPath 4.0 supports two kinds of literals: numeric literals and string literals.

[70]    Literal    ::=    NumericLiteral | StringLiteral
[71]    NumericLiteral    ::=    IntegerLiteral | DecimalLiteral | DoubleLiteral
[135]    IntegerLiteral    ::=    Digits
[136]    DecimalLiteral    ::=    ("." Digits) | (Digits "." [0-9]*)
[137]    DoubleLiteral    ::=    (("." Digits) | (Digits ("." [0-9]*)?)) [eE] [+-]? Digits
[138]    StringLiteral    ::=    ('"' (EscapeQuot | [^"])* '"') | ("'" (EscapeApos | [^'])* "'")
[141]    EscapeQuot    ::=    '""'
[142]    EscapeApos    ::=    "''"
[147]    Digits    ::=    [0-9]+

The value of a numeric literal containing no "." and no e or E character is an atomic value of type xs:integer. The value of a numeric literal containing "." but no e or E character is an atomic value of type xs:decimal. The value of a numeric literal containing an e or E character is an atomic value of type xs:double. The value of the numeric literal is determined by casting it to the appropriate type according to the rules for casting from xs:untypedAtomic to a numeric type as specified in Section 19.2 Casting from xs:string and xs:untypedAtomic FO31.

Note:

The effect of the above rule is that in the case of an integer or decimal literal, a dynamic error [err:FOAR0002]FO31 will generally be raised if the literal is outside the range of values supported by the implementation (other options are available: see Section 4.2 Arithmetic operators on numeric values FO31 for details.)

The XML Schema specification allows implementations to impose a limit (which must not be less than 18 digits) on the size of integer and decimal values. The full range of values of built-in subtypes of xs:integer, such as xs:long and xs:unsignedLong, can be supported only if the limit is 20 digits or higher. Negative numbers such as the minimum value of xs:long (-9223372036854775808) are technically unary expressions rather than literals, but implementations may prefer to ensure that they are expressible.

The value of a string literal is an atomic value whose type is xs:string and whose value is the string denoted by the characters between the delimiting apostrophes or quotation marks. If the literal is delimited by apostrophes, two adjacent apostrophes within the literal are interpreted as a single apostrophe. Similarly, if the literal is delimited by quotation marks, two adjacent quotation marks within the literal are interpreted as one quotation mark.

Here are some examples of literal expressions:

  • "12.5" denotes the string containing the characters '1', '2', '.', and '5'.

  • 12 denotes the xs:integer value twelve.

  • 12.5 denotes the xs:decimal value twelve and one half.

  • 125E2 denotes the xs:double value twelve thousand, five hundred.

  • "He said, ""I don't like it.""" denotes a string containing two quotation marks and one apostrophe.

    Note:

    When XPath expressions are embedded in contexts where quotation marks have special significance, such as inside XML attributes, additional escaping may be needed.

The xs:boolean values true and false can be constructed by calls to the built-in functions fn:true() and fn:false(), respectively.

Values of other simple types can be constructed by calling the constructor function for the given type. The constructor functions for XML Schema built-in types are defined in Section 18.1 Constructor functions for XML Schema built-in atomic types FO31. In general, the name of a constructor function for a given type is the same as the name of the type (including its namespace). For example:

  • xs:integer("12") returns the integer value twelve.

  • xs:date("2001-08-25") returns an item whose type is xs:date and whose value represents the date 25th August 2001.

  • xs:dayTimeDuration("PT5H") returns an item whose type is xs:dayTimeDuration and whose value represents a duration of five hours.

Constructor functions can also be used to create special values that have no literal representation, as in the following examples:

  • xs:float("NaN") returns the special floating-point value, "Not a Number."

  • xs:double("INF") returns the special double-precision value, "positive infinity."

Constructor functions are available for all simple types, including union types. For example, if my:dt is a user-defined union type whose member types are xs:date, xs:time, and xs:dateTime, then the expression my:dt("2011-01-10") creates an atomic value of type xs:date. The rules follow XML Schema validation rules for union types: the effect is to choose the first member type that accepts the given string in its lexical space.

It is also possible to construct values of various types by using a cast expression. For example:

  • 9 cast as hatsize returns the atomic value 9 whose type is hatsize.

4.3.2 Variable References

[72]    VarRef    ::=    "$" VarName
[73]    VarName    ::=    EQName

[Definition: A variable reference is an EQName preceded by a $-sign.] An unprefixed variable reference is in no namespace. Two variable references are equivalent if their expanded QNames are equal (as defined by the eq operator). The scope of a variable binding is defined separately for each kind of expression that can bind variables.

Every variable reference must match a name in the in-scope variables.

Every variable binding has a static scope. The scope defines where references to the variable can validly occur. It is a static error [err:XPST0008] to reference a variable that is not in scope. If a variable is bound in the static context for an expression, that variable is in scope for the entire expression except where it is occluded by another binding that uses the same name within that scope.

At evaluation time, the value of a variable reference is the value to which the relevant variable is bound.

4.3.3 Parenthesized Expressions

[74]    ParenthesizedExpr    ::=    "(" Expr? ")"

Parentheses may be used to override the precedence rules. For example, the expression (2 + 4) * 5 evaluates to thirty, since the parenthesized expression (2 + 4) is evaluated first and its result is multiplied by five. Without parentheses, the expression 2 + 4 * 5 evaluates to twenty-two, because the multiplication operator has higher precedence than the addition operator.

Empty parentheses are used to denote an empty sequence, as described in 4.7.1 Sequence Concatenation.

4.3.4 Context Item Expression

[75]    ContextItemExpr    ::=    "."

A context item expression evaluates to the context item, which may be either a node (as in the expression fn:doc("bib.xml")/books/book[fn:count(./author)>1]), or an atomic value or function (as in the expression (1 to 100)[. mod 5 eq 0]).

If the context item is absentDM31, a context item expression raises a dynamic error [err:XPDY0002].

4.3.5 Enclosed Expressions

[6]    EnclosedExpr    ::=    "{" Expr? "}"

[Definition: An enclosed expression is an instance of the EnclosedExpr production, which allows an optional expression within curly braces.] [Definition: In an enclosed expression, the optional expression enclosed in curly braces is called the content expression.] If the content expression is not provided explicitly, the content expression is ().

Note:

Despite the name, an enclosed expression is not actually an expression in its own right; rather it is a construct that is used in the grammar of many other expressions.

4.4 Functions

Functions in XPath 4.0 take two forms:

  • Static functions are named constructs in the 2.1.1 Static Context, typically originating either as built-in functions made available by the implementation, or as user-defined functions declared using the constructs of the host language.

  • Dynamic functions are XDM items: values that can be bound to variables, passed as arguments, returned as function results, and generally manipulated in the same way as other XDM values.

Static and dynamic functions, and the mechanisms for calling them, are described in the following sections.

4.4.1 Static Functions

Note:

TODO: Corresponding changes are needed in 2.1.1 Static Context.

Note:

TODO: define mechanisms in XQuery and XSLT that take advantage of these mechanism for user-defined functions.

The static context for an expression includes a set of named functions. Each function in the static context can be identified given knowledge of its name and arity. Every function in the static context has a name (which is a QName) and a range of permitted arities for calls on that function. Two functions having the same name must not have overlapping arity ranges: the rules are defined more precisely below.

Functions in the static context may include any or all of the following:

  • Built-in functions defined in these specifications or in a host language referencing these specifications.

  • User-defined functions declared using the syntax of a host language such as XQuery or XSLT.

  • External functions made available in some implementation-defined way.

[Definition: The built-in functions are the functions defined in [XQuery and XPath Functions and Operators 3.1]in the http://www.w3.org/2005/xpath-functions, http://www.w3.org/2001/XMLSchema, http://www.w3.org/2005/xpath-functions/math, http://www.w3.org/2005/xpath-functions/map, and http://www.w3.org/2005/xpath-functions/array namespaces. ] The set of built-in functions is specified by the host language. Additional functions may be provided in the static context. XPath per se does not provide a way to declare named functions, but a host language may provide such a mechanism.

Static functions may be variadic. If a function is variadic, the number of arguments appearing in a function call may differ from the number of parameters declared in the function signature. Different kinds of variadic functions are defined, distinguished by the value of the annotation %variadic, which is present on all static functions, and takes one of four values:

  • %variadic("no") indicates that the function is not variadic. In a function call, an argument must be supplied for every parameter in the function signature. It can be supplied either positionally or by keyword, but there must be a one-to-one mapping between arguments and parameter declarations.

  • %variadic("bounded") indicates that the function is bounded-variadic. A bounded-variadic function declares zero or more required parameters and one or more optional parameters. In a function call, an argument must be supplied for every required parameter, and arguments may be supplied for optional parameters: in both cases, the argument may be supplied either positionally or by keyword.

  • %variadic("sequence") indicates that the function is sequence-variadic. A sequence-variadic function declares one or more parameters, of which the last typically has an occurrence indicator of * or + to indicate that a sequence may be supplied. If the declaration includes N parameters, then a call on the function may supply N-1 or more arguments; the values of the Nth and subsequent arguments are concatenated to form a single sequence, which is supplied as the value of the last parameter in the declaration. In a sequence-variadic function, the last parameter is implicitly optional (it defaults to an empty sequence), and all other parameters are required. In a call of a sequence-variadic function, all arguments must be supplied positionally.

  • %variadic("map") indicates that the function is map-variadic. A map-variadic function declares one or more parameters, of which the last must be a type that accepts a map. It may restrict what kind of map is accepted (for example, by using a RecordTest), and it may accept things other than maps, but it must accept a single map as the supplied value. The last parameter is implicitly optional (it defaults to an empty map). All other parameters are required, and must be supplied positionally. All keyword arguments in the function call are assembled into a map, and this map is supplied as the value of the last parameter. Alternatively, the last parameter can be supplied positionally (typically, as an already-assembled map).

    The names and types of the keyword arguments supplied to a map-variadic function may be constrained by declaring the required type in the function signature as a Record Test, which then allows static type checking. However, there is no requirement to use such a type.

A function has a declared arity which is the number of parameters defined in the function declaration. This value, together with the value of the variadic annotation, determine the number of positional arguments and keyword arguments that may appear in a function call. Specifically, for each function there are six properties that can be computed:

  • The minimum number of arguments in total MinA.

  • The maximum number of arguments in total MaxA.

  • The minimum number of positional arguments MinP.

  • The maximum number of positional arguments MaxP.

  • The minimum number of keyword arguments MinK.

  • The maximum number of keyword arguments MaxK.

The values of these properties are given by the following table, where A is the declared arity and R is the number of parameters that do not have a default value. The last parameter in a map-variadic or sequence-variadic value has an implicit default value, so it is not included in this count.

Number of Arguments allowed in a Function Call
%variadic MinA MaxA MinP MaxP MinK MaxK
no A A 0 A 0 A
bounded R A 0 A 0 A
map R unbounded R R 0 unbounded
sequence R unbounded R unbounded 0 0

If two functions F and G in the static context have the same name, then both of the following conditions must be true:

  • MinP(F) > MaxP(G) or MinP(G) > MaxP(F)

  • MinK(F) > MaxK(G) or MinK(G) > MaxK(F)

In consequence, a function call with a known number of positional arguments and a known number of keyword arguments can never match more than one function in the static context.

Similarly, a named function reference such as fn#3 is a reference to a function in the static context with name fn having MinP ≤ 3 and MaxP ≥ 3, and there can be at most one such function.

Taking examples from the standard function library:

  • The function fn:position takes no arguments. It has MinA=0, MaxA=0, MinP=0, MaxP=0, MinK=0, MaxK=0.

  • The function fn:node-name is bounded-variadic. It has one optional argument, which can be supplied either by position or by keyword. It has MinA=0, MaxA=1, MinP=0, MaxP=1, MinK=0, MaxK=1.

  • The function fn:format-date is bounded-variadic. It defines two required parameters (value and picture), followed by three optional parameters (language, calendar, and place). For all three optional parameters, the default value is an empty sequence. The function can be called with any number of positional arguments from 2 to 5. Alternatively the optional parameters can be supplied by keyword: for example format-date(current-date(), "[D1] [MNn] [Y0001]", place: "America/New_York"). It is also possible to supply the required parameters by keyword.

    The function thus has MinA=2, MaxA=5, MinP=0, MaxP=5, MinK=0, MaxK=5.

  • The fn:concat function is sequence-variadic. This means that the function calls fn:concat("a", "b", "c"), fn:concat(("a", "b", "c")), and fn:concat(("a", "b"), "c") all have the same effect (delivering the result "abc"). Keyword arguments cannot be used with this function.

    The function thus has MinA=0, MaxA=unbounded, MinP=0, MaxP=unbounded, MinK=0, MaxK=0.

  • The fn:serialize function is map-variadic. This means that the function call fn:serialize($doc, method: "xml", indent: true()) has the same effect as the function call fn:serialize($doc, map{"method":"xml", "indent":true()})

    The function thus has MinA=1, MaxA=unbounded, MinP=1, MaxP=2, MinK=0, MaxK=unbounded.

A static function call is bound to a function in the static context by matching the name and arity. If the function call has P positional arguments followed by K keyword arguments, then the static context must include a function whose name matches the name in the function call, and that satisfies all the following conditions:

  • MinA ≤ P + K

  • MaxA ≥ P + K

  • MinP ≤ P

  • MaxP ≥ P

  • MinK ≤ K

  • MaxK ≥ K

Similarly, a function reference of the form f#N binds to a function in the static context whose name matches f where MinP ≤ N and MaxP ≥ N. The result of evaluating a function reference is a (dynamic) function which can be invoked using a dynamic function call. Dynamic functions are never variadic and their arguments are always supplied positionally. For example, the function reference fn:concat#3 returns a function with arity 3, which is always invoked by supplying three positional arguments, and whose effect is the same as a static call on fn:concat with three positional arguments. The arity must not exceed the number of arguments that can be supplied positionally. Therefore, in the case of a function reference to a map-variadic functions such as fn:serialize#2, a dynamic call must supply the map-valued argument (the serialization parameters) in the form of a map; the function reference fn:serialize#3 is an error, because MaxP = 2.

The detailed rules for evaluating static function calls and function references are defined in subsequent sections.

4.4.1.1 Static Function Call Syntax
[76]    FunctionCall    ::=    EQName ArgumentList
[58]    ArgumentList    ::=    "(" ((PositionalArguments ("," KeywordArguments)?) | KeywordArguments)? ")"
[60]    PositionalArguments    ::=    Argument ("," Argument)*
[77]    Argument    ::=    ExprSingle | ArgumentPlaceholder
[78]    ArgumentPlaceholder    ::=    "?"
[61]    KeywordArguments    ::=    KeywordArgument ("," KeywordArgument)*
[62]    KeywordArgument    ::=    NCName ":=" ExprSingle

[Definition: A static function call consists of an EQName followed by a parenthesized list of zero or more arguments.]

In general, the argument list consists of zero or more positional arguments, followed by zero or more keyword arguments.

[Definition: A positional argument to a function call is either an argument expression or an ArgumentPlaceholder ("?").]

A keyword argument takes the form name := expr. The effect of positional and keyword arguments is described below.

If the EQName in a static function call is a lexical QName, it is expanded by invoking the function name resolver in the static context.

In other cases, The expanded QName and number of arguments in the static function call must match the name and arity range of a function signature in the static context using the rules defined in the previous section; if there is no match, a static error is raised [err:XPST0017].

[Definition: A static or dynamic function call is a partial function application if one or more arguments is an ArgumentPlaceholder.]

Evaluation of static function calls is described in 4.4.1.2 Evaluating Static Function Calls, while evaluation of dynamic function calls is described in 4.4.2.1 Evaluating Dynamic Function Calls.

Since the arguments of a function call are separated by commas, any argument expression that contains a top-level comma operator must be enclosed in parentheses. Here are some illustrative examples of static function calls:

  • my:three-argument-function(1, 2, 3) denotes a static function call with three positional arguments. The corresponding function declaration must define at least three parameters, and may define more, provided they are optional.

  • my:two-argument-function((1,2), 3) denotes a static function call with two arguments, the first of which is a sequence of two values. The corresponding function declaration must define at least two parameters, and may define more, provided they are optional.

  • my:two-argument-function(1, ()) denotes a static function call with two arguments, the second of which is an empty sequence.

  • my:one-argument-function((1, 2, 3)) denotes a static function call with one argument that is a sequence of three values.

  • my:one-argument-function(( )) denotes a static function call with one argument that is an empty sequence.

  • my:zero-argument-function( ) denotes a static function call with zero arguments.

  • fn:lang(node: $n, language: 'de') is a static function call with two keyword arguments. The corresponding function declaration defines two parameters, a required parameter language and an optional parameter node. This call supplies values for both parameters. It is equivalent to the call fn:lang('de', $n): note that the keyword arguments are in a different order from the parameter declarations.

  • fn:serialize($value, method: 'json', indent: true()) is a static function call with three arguments. This function is declared as map-variadic, so it is effectively called supplying $value for the first parameter, and map{'method':'json', 'indent':true()} for the second.

  • fn:codepoints-to-string(66, 65, 67, 72) is a static function call with four arguments. This function is declared as sequence-variadic, so the four arguments are effectively combined into a sequence (66, 65, 67, 72) which is supplied as the value of the first (and only) parameter. The call is thus equivalent to the single-argument call fn:codepoints-to-string((66, 65, 67, 72)): it returns "BACH". The call could also be written with two arguments: fn:codepoints-to-string((66, 65), (67, 72))).

4.4.1.2 Evaluating Static Function Calls

This section applies to static function calls where none of the arguments is an ArgumentPlaceHolder. For function calls involving placeholders, see 4.4.2.2 Partial Function Application.

When a static function call FC is evaluated with respect to a static context SC and a dynamic context DC, the result is obtained as follows:

  1. The function F to be called is obtained as follows:

    Using the expanded QName corresponding to FC's EQName, and the arity of FC's ArgumentList, the corresponding function is looked up in the named functions component of DC.

    If P is the number of positional arguments in the function call, and K is the number of keyword arguments in the function call, there must be exactly one function in the static context whose name matches the name in the function call, and that has MinP ≤ P and MaxP ≥ P and MinK ≤ K and MaxK ≥ K. Let F denote the function obtained.

  2. [Definition: Argument expressions are evaluated with respect to DC, producing argument values.] The order of argument evaluation is implementation-dependent and it is not required that an argument be evaluated if the function can evaluate its body without evaluating that argument.

  3. Argument values are mapped to parameters in the function declaration as follows:

    1. For non-variadic functions:

      1. A positional argument in position N corresponds to the parameter in position N.

      2. A keyword argument with keyword K corresponds to the parameter with name K.

      There must be exactly one argument corresponding to each parameter in the function declaration.

    2. For bounded-variadic functions:

      1. A positional argument in position N corresponds to the parameter in position N.

      2. A keyword argument with keyword K corresponds to the parameter with name K.

      There must be at most one argument corresponding to each parameter in the function declaration.

      Any parameter for which there is no corresponding argument must be declared as optional, and the default value for that parameter is then used.

      TODO: define how the default value is evaluated, ie. what context is used.

    3. For sequence-variadic functions:

      Let the number of declared parameters be N.

      1. All arguments must be positional.

      2. A positional argument with position M, (M < N) corresponds to the parameter in position M.

      3. The values of arguments in positions greater than or equal to N are concatenated into a sequence, and the resulting sequence is supplied as the value of parameter N. If there are no such arguments (that is, if N-1 arguments are supplied), then the value supplied for parameter N is an empty sequence.

    4. For map-variadic functions:

      Let the number of declared parameters be N.

      1. A positional argument in position M (M < N) corresponds to the parameter in position M.

      2. If there is a positional argument in position N, this corresponds to the parameter in position N, and there must then be no keyword arguments.

      3. The values of keyword arguments are assembled into a map. For each keyword argument, the map has an entry whose name is the keyword (as an instance of xs:string) and whose corresponding value is the argument value. The resulting map is supplied as the value of parameter N.

      4. If there are no keyword arguments, and if there is no positional argument in position N, then the value supplied for parameter N is an empty map.

  4. Each argument value computed by the above rules is converted to the corresponding parameter type in F's signature by applying the coercion rules, resulting in a converted argument value.

  5. The result of the function call is obtained as follows:

    • F's implementation is invoked in an implementation-dependent way. The processor makes the following information available to that invocation:

      • the converted argument values;

      • F's nonlocal variable bindings; and

      • a static context and dynamic context. If F's implementation is associated with a static and a dynamic context, then these are supplied, otherwise SC and DC are supplied.

      How this information is used is implementation-defined. An API used to invoke external functions must state how the static and dynamic contexts are provided to a function that is invoked. The F&O specification states how the static and dynamic contexts are used in each function that it defines. A host language must state how the static and dynamic contexts are used in functions that it provides.

    • The result is either an instance of F's return type or a dynamic error. This result is then the result of evaluating FC.

    • Errors raised by built-in functions are defined in [XQuery and XPath Functions and Operators 3.1].

    • Errors raised by host-language-dependent functions are implementation-defined.

    Example: A Built-in Function

    The following function call uses the function Section 2.5 fn:base-uri FO31. Use of SC and DC and errors raised by this function are all defined in [XQuery and XPath Functions and Operators 3.1].

    fn:base-uri()

4.4.2 Dynamic Functions

A dynamic function (or function, or function item) is an XDM value that can be bound to a variable, or manipulated in various ways by XPath 4.0 expressions. The most significant such expression is a dynamic function call, which supplies values of arguments and evaluates the function to produce a result.

The syntax of dynamic function calls is defined in 4.5.2 Dynamic Function Calls.

A number of constructs can be used to produce a dynamic function, notably:

  • A named function reference (see 4.4.2.3 Named Function References) constructs a function that refers to a static function: for example fn:node-name#1 returns a function whose effect is to call the static fn:node-name function with one argument.

  • An inline function (see 4.4.2.4 Inline Function Expressions) constructs a function whose implementation is defined locally. For example the construct ->($x){$x+1} returns a function whose effect is to increment the value of the supplied argument.

  • A partial function application (see 4.4.2.2 Partial Function Application) derives one function from another by supplying the values of some of its arguments. For example, fn:ends-with(?, ".txt") returns a function with one argument that tests whether the supplied string ends with the substring ".txt".

  • Maps and arrays are also functions. See 4.14.1.1 Map Constructors and 4.14.2.1 Array Constructors.

These constructs are described in detail in the following sections.

4.4.2.1 Evaluating Dynamic Function Calls

This section applies to dynamic function calls whose arguments do not include an ArgumentPlaceHolder. For function calls that include a placeholder, see 4.4.2.2 Partial Function Application.

When a dynamic function call FC is evaluated, the result is obtained as follows:

  1. The function F to be called is obtained by evaluating the base expression of the function call. If this yields a sequence consisting of a single function whose arity matches the number of arguments in the ArgumentList, let F denote that function. Otherwise, a type error is raised [err:XPTY0004].

    Note:

    Keyword arguments are not allowed in a dynamic function call.

  2. Argument expressions are evaluated, producing argument values. The order of argument evaluation is implementation-dependent and an argument need not be evaluated if the function can evaluate its body without evaluating that argument.

  3. Each argument value is converted to the corresponding parameter type in F's signature by applying the coercion rules, resulting in a converted argument value. The correspondence of arguments to parameters is by matching position.

  4. If F is a map, it is evaluated as described in 4.14.1.2 Map Lookup using Function Call Syntax.

  5. If F is an array, it is evaluated as described in 4.14.2.2 Array Lookup using Function Call Syntax.

  6. If F's implementation is an XPath 4.0 expression (e.g., F is an anonymous function, or a partial application of such a function):

    1. F's implementation is evaluated. The static context for this evaluation is the static context of the XPath 4.0 expression. The dynamic context for this evaluation is obtained by taking the dynamic context of the InlineFunctionExpr that contains the FunctionBody, and making the following changes:

      • The focus (context item, context position, and context size) is absentDM31.

      • In the variable values component of the dynamic context, each converted argument value is bound to the corresponding parameter name.

        When this is done, the converted argument value retains its most specific dynamic type, even though this type may be derived from the type of the formal parameter. For example, a function with a parameter $p of type xs:decimal can be invoked with an argument of type xs:integer, which is derived from xs:decimal. During the processing of this function call, the dynamic type of $p inside the body of the function is considered to be xs:integer.

      • F's nonlocal variable bindings are also added to the variable values. (Note that the names of the nonlocal variables are by definition disjoint from the parameter names, so there can be no conflict.)

    2. The value returned by evaluating the function body is then converted to the declared return type of F by applying the coercion rules. The result is then the result of evaluating FC.

      As with argument values, the value returned by a function retains its most specific type, which may be derived from the declared return type of F. For example, a function that has a declared return type of xs:decimal may in fact return a value of dynamic type xs:integer.

    Example: Derived Types and Nonlocal Variable Bindings

    $incr is a nonlocal variable that is available within the function because its variable binding has been added to the variable values of the function.. Even though the parameter and return type of this function are both xs:decimal, the more specific type xs:integer is preserved in both cases.

    let $incr := 1,
        $f := function ($i as xs:decimal) as xs:decimal { $i + $incr }
    return $f(5)                      
    Example: Using the Context Item in an Anonymous Function

    The following example will raise a dynamic error [err:XPDY0002]:

    let $vat := function() { @vat + @price }
    return shop/article/$vat()

    Instead, the context item can be used as an argument to the anonymous function:

    let $vat := function($art) { $art/@vat + $art/@price }
    return shop/article/$vat(.)

    Or, the value can be referenced as a nonlocal variable binding:

    let $ctx := shop/article,
    $vat := function() { for $a in $ctx return $a/@vat + $a/@price }
    return $vat()
    
  7. If F's implementation is not an XPath 4.0 expression (e.g., F is a built-in function or a host language function or a partial application of such a function), the implementation of the function is evaluated, and the result is converted to the declared return type, in the same way as for a static function call (see 4.4.1.1 Static Function Call Syntax).

    Errors may be raised in the same way.

4.4.2.2 Partial Function Application

A partial function application is a static or dynamic function call in which one or more of the arguments is supplied as an ArgumentPlaceHolder.

The result of a partial function application is a (dynamic) function, whose arity is equal to the number of placeholders in the call.

The result is obtained as follows:

  1. The function F to be partially applied is determined in the same way as for a (static or dynamic) function call without placeholders, as described in the preceding sections. For this purpose an ArgumentPlaceHolder contributes to the count of positional arguments.

  2. Arguments other than placeholders are evaluated, mapped to corresponding parameters in the function signature of F, and converted to the required type of the parameter, using the rules for static and dynamic function calls as appropriate.

  3. The result of the partial function application is a new function, which is a partially applied function. [Definition: A partially applied function is a function created by partial function application.] [Definition: In a partial function application, a supplied parameter is a parameter for which the ArgumentList includes a corresponding argument (as distinct from a placeholder).] A partial function application need not have any supplied parameters. A partially applied function has the following properties (which are defined in Section 2.8.1 Functions DM31):

    • name: Absent.

    • parameter names: The parameter names of F, removing the names of supplied parameters. (So the function's arity is the arity of F minus the number of fixed positions.)

    • signature: The signature of F, removing the types of supplied parameters. An implementation which can determine a more specific signature (for example, through use of type analysis) is permitted to do so.

    • implementation: The implementation of F. If this is not an XPath 4.0 expression then the new function's implementation is associated with a static context and a dynamic context in one of two ways: if F's implementation is already associated with contexts, then those are used; otherwise, SC and DC are used.

    • nonlocal variable bindings: The nonlocal variable bindings of F, plus, for each supplied parameter, a binding of the converted argument value to the corresponding parameter name.

    Example: Partial Application of an Anonymous Function

    In the following example, $f is an anonymous function, and $paf is a partially applied function created from $f.

    let $f := function ($seq, $delim) { fn:fold-left($seq, "", fn:concat(?, $delim, ?)) },
        $paf := $f(?, ".")
    return $paf(1 to 5)
    

    $paf is also an anonymous function. It has one parameter, named $delim, which is taken from the corresponding parameter in $f (the other parameter is fixed). The implementation of $paf is the implementation of $f, which is fn:fold-left($seq, "", fn:concat(?, $delim, ?)). This implementation is associated with the SC and DC of the original expression in $f. The nonlocal bindings associate the value "." with the parameter $delim.

    Example: Partial Application of a Built-In Function

    The following partial function application creates a function that computes the sum of squares of a sequence.

    let $sum-of-squares := fn:fold-right(?, 0, function($a, $b) { $a*$a + $b })
    return $sum-of-squares(1 to 3)

    $sum-of-squares is an anonymous function. It has one parameter, named $seq, which is taken from the corresponding parameter in fn:fold-right (the other two parameters are fixed). The implementation is the implementation of fn:fold-right, which is a built-in context-independent function. The nonlocal bindings contain the fixed bindings for the second and third parameters of fn:fold-right.

    Partial function application never returns a map or an array. If $F is a map or an array, then $F(?) is a partial function application that returns a function, but the function it returns is not a map nor an array.

    Example: Partial Application of a Map

    The following partial function application converts a map to an equivalent function that is not a map.

    let $a := map {"A": 1, "B": 2}(?)
    return $a("A")
4.4.2.3 Named Function References
[82]    NamedFunctionRef    ::=    EQName "#" IntegerLiteral
[134]    EQName    ::=    QName | URIQualifiedName

[Definition: A named function reference is an expression which evaluates to a named function.]

The name and arity of the required function are known statically.

If the EQName is a lexical QName, it is expanded using the function name resolver in the static context.

The expanded QName and arity must correspond to a function signature present in the static context. More specifically, for a named function reference F#N, there must be a function in the static context whose name matches F, and that has MinP ≤ N and MaxP ≥ N .

If the function is context dependent, then the returned function is associated with the static context of the named function reference and the dynamic context in which it is evaluated.

[Definition: A named function is a function defined in the static context for the expression. To uniquely identify a particular named function, both its name as an expanded QName and its arity are required.]

If the expanded QName and arity in a named function reference do not match the name and arity of a function signature in the static context, a static error is raised [err:XPST0017].

The value of a NamedFunctionRef is the function obtained by looking up the expanded QName and arity in the named functions component of the dynamic context.

Furthermore, if the function returned by the evaluation of a NamedFunctionRef has an implementation-dependent implementation, then the implementation of this function is associated with the static context of this NamedFunctionRef expression and with the dynamic context in which the NamedFunctionRef is evaluated.

The following are examples of named function references:

  • fn:abs#1 references the fn:abs function which takes a single argument.

  • fn:concat#5 references the fn:concat function which takes 5 arguments.

  • local:myfunc#2 references a function named local:myfunc which takes 2 arguments.

Note:

Function items, as values in the data model, have a fixed arity, and a dynamic function call always supplies the arguments positionally. Although the base function referred to may be variadic, the result of evaluating the function reference is a function that has fixed arity. In effect, the result of evaluating my:func#3 is the same as the result of evaluating the inline function expression function($x, $y, $z){my:func($x, $y, $z)}, except that the returned function has a name (it retains the name my:func).

4.4.2.4 Inline Function Expressions
[83]    InlineFunctionExpr    ::=    (("function" FunctionSignature) | ("->" FunctionSignature?)) FunctionBody
[2]    FunctionSignature    ::=    "(" ParamList? ")" TypeDeclaration?
[3]    ParamList    ::=    Param ("," Param)*
[4]    Param    ::=    "$" EQName TypeDeclaration?
[93]    TypeDeclaration    ::=    "as" SequenceType
[5]    FunctionBody    ::=    EnclosedExpr

[Definition: An inline function expression creates an anonymous function defined directly in the inline function expression.] An inline function expression specifies the names and SequenceTypes of the parameters to the function, the SequenceType of the result, and the body of the function. [Definition: An anonymous function is a function with no name. Anonymous functions may be created, for example, by evaluating an inline function expression or by partial function application.]

Note:

A more concise notation is introduced for simple functions in XPath 4.0 because it can improve the readability of code by reducing visual clutter. For example, a sort operation previously written as sort(//employee, (), function($emp as element(employee)) as xs:string { $emp/@dateOfBirth }) can now be written sort(//employee, (), ->{@dateOfBirth}).

The use of the notation ->{expr} mirrors the use of -> as an arrow operator.

The full inline function syntax allows the names and types of the function argument to be declared, along with the type of the result:

function($x as xs:integer, $y as xs:integer) as xs:integer {$x + $y}

The types can be omitted:

function($x, $y) {$x + $y}

For brevity, the keyword function can be replaced by the symbol ->:

->($x, $y) {$x + $y}

This avoids visual clutter when a function is used as an argument to another function:

fn:for-each-pair($A, $B, ->($a, $b) {$a + $b})

The common case where a function accepts a single argument of type item() can be further abbreviated to ->{EXPR}. This is equivalent to the expanded syntax function($x as item()} as item()* {$x -> {EXPR}}, where x is a system-allocated name that does not conflict with any user-defined variables. That is, it defines an anonymous arity-one function, accepting any single item as its argument value, and returns the result of evaluating the supplied expression with that item as the singleton focus. For example, the following function call returns the sequence (2, 3, 4, 5, 6).

fn:for-each(1 to 5, ->{.+1})

A zero-arity function can be written as, for example, ->(){current-date()}.

If a function parameter is declared using a name but no type, its default type is item()*. If the result type is omitted, its default result type is item()*.

The parameters of an inline function expression are considered to be variables whose scope is the function body. It is a static error [err:XQST0039] for an inline function expression to have more than one parameter with the same name.

The static context for the function body is inherited from the location of the inline function expression, with the exception of the static type of the context item which is initially absentDM31.

The variables in scope for the function body include all variables representing the function parameters, as well as all variables that are in scope for the inline function expression.

Note:

Function parameter names can mask variables that would otherwise be in scope for the function body.

The result of an inline function expression is a single function with the following properties (as defined in Section 2.8.1 Functions DM31):

  • name: An absent name. Absent.

  • parameter names: The parameter names in the InlineFunctionExpr's ParamList.

  • signature: A FunctionTest constructed from the SequenceTypes in the InlineFunctionExpr. An implementation which can determine a more specific signature (for example, through use of type analysis of the function's body) is permitted to do so.

  • implementation: The InlineFunctionExpr's FunctionBody.

  • nonlocal variable bindings: For each nonlocal variable, a binding of it to its value in the variable values component of the dynamic context of the InlineFunctionExpr.

The following are examples of some inline function expressions:

  • This example creates a function that takes no arguments and returns a sequence of the first 6 primes:

    function() as xs:integer+ { 2, 3, 5, 7, 11, 13 }
  • This example creates a function that takes two xs:double arguments and returns their product:

    function($a as xs:double, $b as xs:double) as xs:double { $a * $b }
  • This example creates a function that prepends "$" to a supplied value:

    ->{"$" || .}

    It is equivalent to the function concat("$", ?).

  • This example creates a function that returns the name attribute of a supplied element node:

    ->{@name}

    It is equivalent to the function function($x as item()) as item()* {$x ! @name}.

4.4.3 Coercion Rules

[Definition: The coercion rules are used to convert an argument value to its expected type; that is, to the declared type of the function parameter. ] The expected type is expressed as a sequence type. The coercion rules are applied to a given value as follows:

Note:

In XSLT, the coercion rules are also used to convert the value of a variable to its declared type.

Note:

In previous versions of this specification, the coercion rules were referred to as the function conversion rules. The terminology has changed because the rules are not exclusively associated with functions or function calling.

  • In a static function call, if XPath 1.0 compatibility mode is true and an argument of a static function is not of the expected type, then the following conversions are applied sequentially to the argument value V:

    1. If the expected type calls for a single item or optional single item (examples: xs:string, xs:string?, xs:untypedAtomic, xs:untypedAtomic?, node(), node()?, item(), item()?), then the value V is effectively replaced by V[1].

    2. If the expected type is xs:string or xs:string?, then the value V is effectively replaced by fn:string(V).

    3. If the expected type is xs:double or xs:double?, then the value V is effectively replaced by fn:number(V).

    Note:

    XPath 1.0 compatibility mode has no effect on dynamic function calls, converting the result of an inline function to its required type, partial function application, or implicit function calls that occur when evaluating functions such as fn:for-each and fn:filter.

  • If the expected type is a SequenceType whose ItemType is a generalized atomic type other than a union type or enumeration type, (possibly with an occurrence indicator *, +, or ?), then the following conversions are applied, in order:

    1. Atomization is applied to the given value, resulting in a sequence of atomic values.

    2. Each item in the atomic sequence that is of type xs:untypedAtomic is cast to the expected atomic type. If the expected atomic type is an EnumerationType, the value is cast to xs:string . If the item is of type xs:untypedAtomic and the expected type is namespace-sensitive, a type error [err:XPTY0117] is raised.

    3. For each numeric item in the atomic sequence that can be promoted to the expected atomic type using numeric promotion as described in B.1 Type Promotion, the promotion is done.

    4. For each item of type xs:anyURI in the atomic sequence that can be promoted to the expected atomic type using URI promotion as described in B.1 Type Promotion, the promotion is done.

    5. If the expected type is a sequence type whose item type is an atomic type D, where D is derived from the primitive type P, then any item in the atomic sequence that is an instance of P and that is within the value space of D is relabeled as an instance of D.

      Relabeling an atomic value changes the type annotation but not the value. For example, the xs:integer value 3 can be relabeled as an instance of xs:unsignedByte, because the value is within the value space of xs:unsignedByte.

      Relabeling is not the same as casting. For example, the xs:decimal value 10.1 can be cast to xs:integer, but it cannot be relabeled as xs:integer, because it is not within the value space of xs:integer.

      Note:

      The effect of this rule is that if, for example, a function parameter is declared with an expected type of xs:positiveInteger, then a call that supplies the literal value 3 will succeed, whereas a call that supplies -3 will fail.

      This differs from previous versions of this specification, where both these calls would fail.

      In principle this change allows the arguments of existing functions to be defined with a more precise type. For example, the $position argument of array:get could be defined as xs:positiveInteger rather than xs:integer. In practice, however, it is not always possible to do this, because it would change the error codes thrown when an invalid value is supplied.

      TODO: define the interaction of numeric promotion and relabeling. For example, required type = xs:unsignedByte, supplied value = xs:decimal 255.3.

  • If the expected type is a RecordTest (possibly with an occurrence indicator *, +, or ?), then the supplied value must be a map or sequence of maps, and the values of any entries in these maps whose keys correspond to field declarations in the RecordTest are converted to the required type defined by that field declaration, by applying these rules recursively (but with XPath 1.0 compatibility mode treated as false).

    For example, if the required type is record(longitude as xs:double, latitude as xs:double) and the supplied value is map{"longitude": 0, "latitude":53.2}, then the map is converted to map{"longitude": 0.0e0, "latitude": 53.2e0}.

  • If the expected type is a TypedFunctionTest (possibly with an occurrence indicator *, +, or ?), function coercion is applied to each function in the given value.

    Note:

    Maps and arrays are functions, so function coercion applies to them as well.

  • If, after the above conversions, the resulting value does not match the expected type according to the rules for SequenceType Matching, a type error is raised [err:XPTY0004]. Note that the rules for SequenceType Matching permit a value of a derived type to be substituted for a value of its base type.

4.4.4 Function Coercion

Function coercion is a transformation applied to functionsDM31 during application of the coercion rules. [Definition: Function coercion wraps a functionDM31 in a new function whose signature is the same as the expected type. This effectively delays the checking of the argument and return types until the function is invoked.]

Function coercion is only defined to operate on functionsDM31. Given a function F, and an expected function type, function coercion proceeds as follows:

  1. If F has higher arity than the expected type, a type error is raised [err:XPTY0004]

  2. If F has lower arity than the expected type, then F is wrapped in a new function that declares and ignores the additional argument; the following steps are then applied to this new function.

    For example, if the expected type is function(node(), xs:boolean) as xs:string, and the supplied function is fn:name#1, then the supplied function is effectively replaced by function($n as node(), $b as xs:boolean) as xs:string {fn:name($n)}

    Note:

    This mechanism makes it easier to design versatile and extensible higher-order functions. For example, in previous versions of this specification, the second argument of the fn:filter function expected an argument of type function (item()) as xs:boolean. This has now been extended to function (item(), xs:integer) as xs:boolean, but existing code continues to work, because callback functions that are not interested in the value of the second argument simply ignore it.

    TODO: this change to fn:filter has not yet been made.

  3. Function coercion then returns a new function with the following properties (as defined in Section 2.8.1 Functions DM31):

    • name: The name of F.

    • parameter names: The parameter names of F.

    • signature: Annotations is set to the annotations of F. TypedFunctionTest is set to the expected type.

    • implementation: In effect, a FunctionBody that calls F, passing it the parameters of this new function, in order.

    • nonlocal variable bindings: An empty mapping.

If the result of invoking the new function would necessarily result in a type error, that error may be raised during function coercion. It is implementation dependent whether this happens or not.

These rules have the following consequences:

  • SequenceType matching of the function's arguments and result are delayed until that function is invoked.

  • The coercion rules rules applied to the function's arguments and result are defined by the SequenceType it has most recently been coerced to. Additional coercion rules could apply when the wrapped function is invoked.

  • If an implementation has static type information about a function, that can be used to type check the function's argument and return types during static analysis.

Note:

Although the semantics of function coercion are specified in terms of wrapping the functions, static typing will often be able to reduce the number of places where this is actually necessary.

Since maps and arrays are also functions in XPath 4.0, function coercion applies to them as well. For instance, consider the following expression:

let $m := map {
  "Monday" : true(),
  "Wednesday" : true(),
  "Friday" : true(),
  "Saturday" : false(),
  "Sunday" : false()
},
$days := ("Monday", "Tuesday", "Wednesday", "Thursday", "Friday", "Saturday", "Sunday")
return fn:filter($days,$m)
      

The map $m has a function signature of function(xs:anyAtomicType) as item()*. When the fn:filter() function is called, the following occurs to the map:

  1. The map $m is treated as function ($f), equivalent to map:get($m,?).

  2. The coercion rules result in applying function coercion to $f, wrapping $f in a new function ($p) with the signature function(item()) as xs:boolean.

  3. $p is matched against the SequenceType function(item()) as xs:boolean, and succeeds.

  4. When $p is invoked by fn:filter(), coercion and SequenceType matching rules are applied to the argument, resulting in an item() value ($a) or a type error.

  5. $f is invoked with $a, which returns an xs:boolean or the empty sequence.

  6. $p applies coercion rule and SequenceType matching to the result sequence from $f. When the result is an xs:boolean the SequenceType matching succeeds. When it is an empty sequence (such as when $m does not contain a key for "Tuesday"), SequenceType matching results in a type error [err:XPTY0004], since the expected type is xs:boolean and the actual type is an empty sequence.

Consider the following expression:

let $m := map {
   "Monday" : true(),
   "Tuesday" : false(),
   "Wednesday" : true(),
   "Thursday" : false(),
   "Friday" : true(),
   "Saturday" : false(),
   "Sunday" : false()
}
let $days := ("Monday", "Tuesday", "Wednesday", "Thursday", "Friday", "Saturday", "Sunday")
return fn:filter($days,$m)
      

The result of the expression is the sequence ("Monday", "Wednesday", "Friday")

4.5 Postfix Expressions

[57]    PostfixExpr    ::=    PrimaryExpr (Predicate | PositionalArgumentList | Lookup)*
[64]    Predicate    ::=    "[" Expr "]"
[59]    PositionalArgumentList    ::=    "(" PositionalArguments? ")"
[60]    PositionalArguments    ::=    Argument ("," Argument)*
[77]    Argument    ::=    ExprSingle | ArgumentPlaceholder

[Definition: An expression followed by a predicate (that is, E1[E2]) is referred to as a filter expression: its effect is to return those items from the value of E1 that satisfy the predicate in E2.] Filter expressions are described in 4.5.1 Filter Expressions

An expression (other than a raw EQName) followed by an argument list in parentheses (that is, E1(E2, E3, ...)) is referred to as a dynamic function call. Its effect is to evaluate E1 to obtain a function, and then call that function, with E2, E3, ... as arguments. Dynamic function calls are described in 4.5.2 Dynamic Function Calls.

4.5.1 Filter Expressions

[57]    PostfixExpr    ::=    PrimaryExpr (Predicate | PositionalArgumentList | Lookup)*
[64]    Predicate    ::=    "[" Expr "]"

A filter expression consists of a base expression followed by a predicate, which is an expression written in square brackets. The result of the filter expression consists of the items returned by the base expression, filtered by applying the predicate to each item in turn. The ordering of the items returned by a filter expression is the same as their order in the result of the primary expression.

Note:

Where the expression before the square brackets is a ReverseStep or ForwardStep, the expression is technically not a filter expression but an AxisStep. There are minor differences in the semantics: see 4.6.3 Predicates within Steps

Here are some examples of filter expressions:

  • Given a sequence of products in a variable, return only those products whose price is greater than 100.

    $products[price gt 100]
  • List all the integers from 1 to 100 that are divisible by 5. (See 4.7.1 Sequence Concatenation for an explanation of the to operator.)

    (1 to 100)[. mod 5 eq 0]
  • The result of the following expression is the integer 25:

    (21 to 29)[5]
  • The following example returns the fifth through ninth items in the sequence bound to variable $orders.

    $orders[fn:position() = (5 to 9)]
  • The following example illustrates the use of a filter expression as a step in a path expression. It returns the last chapter or appendix within the book bound to variable $book:

    $book/(chapter | appendix)[fn:last()]

For each item in the input sequence, the predicate expression is evaluated using an inner focus, defined as follows: The context item is the item currently being tested against the predicate. The context size is the number of items in the input sequence. The context position is the position of the context item within the input sequence.

For each item in the input sequence, the result of the predicate expression is coerced to an xs:boolean value, called the predicate truth value, as described below. Those items for which the predicate truth value is true are retained, and those for which the predicate truth value is false are discarded.

The predicate truth value is derived by applying the following rules, in order:

  1. If the value of the predicate expression is a singleton atomic value of a numeric type or derived from a numeric type, the predicate truth value is true if the value of the predicate expression is equal (by the eq operator) to the context position, and is false otherwise.

  2. Otherwise, the predicate truth value is the effective boolean value of the predicate expression.

4.5.2 Dynamic Function Calls

[57]    PostfixExpr    ::=    PrimaryExpr (Predicate | PositionalArgumentList | Lookup)*
[58]    ArgumentList    ::=    "(" ((PositionalArguments ("," KeywordArguments)?) | KeywordArguments)? ")"
[60]    PositionalArguments    ::=    Argument ("," Argument)*
[77]    Argument    ::=    ExprSingle | ArgumentPlaceholder
[78]    ArgumentPlaceholder    ::=    "?"
[61]    KeywordArguments    ::=    KeywordArgument ("," KeywordArgument)*
[62]    KeywordArgument    ::=    NCName ":=" ExprSingle

[Definition: A dynamic function call consists of a base expression that returns the function and a parenthesized list of zero or more arguments (argument expressions or ArgumentPlaceholders).]

A dynamic function call is evaluated as described in 4.4.2.1 Evaluating Dynamic Function Calls.

The following are examples of some dynamic function calls:

  • This example invokes the function contained in $f, passing the arguments 2 and 3:

    $f(2, 3)
  • This example fetches the second item from sequence $f, treats it as a function and invokes it, passing an xs:string argument:

    $f[2]("Hi there")
  • This example invokes the function $f passing no arguments, and filters the result with a positional predicate:

    $f()[2]

Note:

Arguments in a dynamic function call are always supplied positionally.

4.6 Path Expressions

[44]    PathExpr    ::=    ("/" RelativePathExpr?)
| ("//" RelativePathExpr)
| RelativePathExpr
[45]    RelativePathExpr    ::=    StepExpr (("/" | "//") StepExpr)*

[Definition: A path expression can be used to locate nodes within trees. A path expression consists of a series of one or more steps, separated by "/" or "//", and optionally beginning with "/" or "//".] An initial "/" or "//" is an abbreviation for one or more initial steps that are implicitly added to the beginning of the path expression, as described below.

A path expression consisting of a single step is evaluated as described in 4.6.2 Steps.

A "/" at the beginning of a path expression is an abbreviation for the initial step (fn:root(self::node()) treat as document-node())/ (however, if the "/" is the entire path expression, the trailing "/" is omitted from the expansion.) The effect of this initial step is to begin the path at the root node of the tree that contains the context node. If the context item is not a node, a type error is raised [err:XPTY0020]. At evaluation time, if the root node of the context node is not a document node, a dynamic error is raised [err:XPDY0050].

A "//" at the beginning of a path expression is an abbreviation for the initial steps (fn:root(self::node()) treat as document-node())/descendant-or-self::node()/ (however, "//" by itself is not a valid path expression [err:XPST0003].) The effect of these initial steps is to establish an initial node sequence that contains the root of the tree in which the context node is found, plus all nodes descended from this root. This node sequence is used as the input to subsequent steps in the path expression. If the context item is not a node, a type error is raised [err:XPTY0020]. At evaluation time, if the root node of the context node is not a document node, a dynamic error is raised [err:XPDY0050].

Note:

The descendants of a node do not include attribute nodes or namespace nodes.

A path expression that starts with "/" or "//" selects nodes starting from the root of the tree containing the context item; it is often referred to as an absolute path expression.

4.6.1 Relative Path Expressions

[45]    RelativePathExpr    ::=    StepExpr (("/" | "//") StepExpr)*

A relative path expression is a path expression that selects nodes within a tree by following a series of steps starting at the context node (which, unlike an absolute path expression, may be any node in a tree).

Each non-initial occurrence of "//" in a path expression is expanded as described in 4.6.5 Abbreviated Syntax, leaving a sequence of steps separated by "/". This sequence of steps is then evaluated from left to right. So a path such as E1/E2/E3/E4 is evaluated as ((E1/E2)/E3)/E4. The semantics of a path expression are thus defined by the semantics of the binary "/" operator, which is defined in 4.6.1.1 Path operator (/).

Note:

Although the semantics describe the evaluation of a path with more than two steps as proceeding from left to right, the "/" operator is in most cases associative, so evaluation from right to left usually delivers the same result. The cases where "/" is not associative arise when the functions fn:position() and fn:last() are used: A/B/position() delivers a sequence of integers from 1 to the size of (A/B), whereas A/(B/position()) restarts the counting at each B element.

The following example illustrates the use of relative path expressions.

  • child::div1/child::para

    Selects the para element children of the div1 element children of the context node; that is, the para element grandchildren of the context node that have div1 parents.

Note:

Since each step in a path provides context nodes for the following step, in effect, only the last step in a path is allowed to return a sequence of non-nodes.

Note:

The "/" character can be used either as a complete path expression or as the beginning of a longer path expression such as "/*". Also, "*" is both the multiply operator and a wildcard in path expressions. This can cause parsing difficulties when "/" appears on the left-hand side of "*". This is resolved using the leading-lone-slash constraint. For example, "/*" and "/ *" are valid path expressions containing wildcards, but "/*5" and "/ * 5" raise syntax errors. Parentheses must be used when "/" is used on the left-hand side of an operator, as in "(/) * 5". Similarly, "4 + / * 5" raises a syntax error, but "4 + (/) * 5" is a valid expression. The expression "4 + /" is also valid, because / does not occur on the left-hand side of the operator.

Similarly, in the expression / union /*, "union" is interpreted as an element name rather than an operator. For it to be parsed as an operator, the expression should be written (/) union /*.

4.6.1.1 Path operator (/)

The path operator "/" is used to build expressions for locating nodes within trees. Its left-hand side expression must return a sequence of nodes. The operator returns either a sequence of nodes, in which case it additionally performs document ordering and duplicate elimination, or a sequence of non-nodes.

Each operation E1/E2 is evaluated as follows: Expression E1 is evaluated, and if the result is not a (possibly empty) sequence S of nodes, a type error is raised [err:XPTY0019]. Each node in S then serves in turn to provide an inner focus (the node as the context item, its position in S as the context position, the length of S as the context size) for an evaluation of E2, as described in 2.1.2 Dynamic Context. The sequences resulting from all the evaluations of E2 are combined as follows:

  1. If every evaluation of E2 returns a (possibly empty) sequence of nodes, these sequences are combined, and duplicate nodes are eliminated based on node identity. The resulting node sequence is returned in document order.

  2. If every evaluation of E2 returns a (possibly empty) sequence of non-nodes, these sequences are concatenated, in order, and returned. The returned sequence preserves the orderings within and among the subsequences generated by the evaluations of E2 .

  3. If the multiple evaluations of E2 return at least one node and at least one non-node, a type error is raised [err:XPTY0018].

Note:

The semantics of the path operator can also be defined using the simple map operator as follows (forming the union with an empty sequence ($R | ()) has the effect of eliminating duplicates and sorting nodes into document order):

E1/E2 ::= let $R := E1!E2
  return
    if (every $r in $R satisfies $r instance of node())
    then ($R|())
    else if (every $r in $R satisfies not($r instance of node()))
    then $R
    else error()

4.6.2 Steps

[46]    StepExpr    ::=    PostfixExpr | AxisStep
[47]    AxisStep    ::=    (ReverseStep | ForwardStep) PredicateList
[48]    ForwardStep    ::=    (ForwardAxis NodeTest) | AbbrevForwardStep
[51]    ReverseStep    ::=    (ReverseAxis NodeTest) | AbbrevReverseStep
[63]    PredicateList    ::=    Predicate*

[Definition: A step is a part of a path expression that generates a sequence of items and then filters the sequence by zero or more predicates. The value of the step consists of those items that satisfy the predicates, working from left to right. A step may be either an axis step or a postfix expression.] Postfix expressions are described in 4.5 Postfix Expressions.

[Definition: An axis step returns a sequence of nodes that are reachable from the context node via a specified axis. Such a step has two parts: an axis, which defines the "direction of movement" for the step, and a node test, which selects nodes based on their kind, name, and/or type annotation.] If the context item is a node, an axis step returns a sequence of zero or more nodes; otherwise, a type error is raised [err:XPTY0020]. The resulting node sequence is returned in document order. An axis step may be either a forward step or a reverse step, followed by zero or more predicates.

In the abbreviated syntax for a step, the axis can be omitted and other shorthand notations can be used as described in 4.6.5 Abbreviated Syntax.

The unabbreviated syntax for an axis step consists of the axis name and node test separated by a double colon. The result of the step consists of the nodes reachable from the context node via the specified axis that have the node kind, name, and/or type annotation specified by the node test. For example, the step child::para selects the para element children of the context node: child is the name of the axis, and para is the name of the element nodes to be selected on this axis. The available axes are described in 4.6.2.1 Axes. The available node tests are described in 4.6.2.2 Node Tests. Examples of steps are provided in 4.6.4 Unabbreviated Syntax and 4.6.5 Abbreviated Syntax.

4.6.2.1 Axes
[49]    ForwardAxis    ::=    ("child" "::")
| ("descendant" "::")
| ("attribute" "::")
| ("self" "::")
| ("descendant-or-self" "::")
| ("following-sibling" "::")
| ("following" "::")
| ("namespace" "::")
[52]    ReverseAxis    ::=    ("parent" "::")
| ("ancestor" "::")
| ("preceding-sibling" "::")
| ("preceding" "::")
| ("ancestor-or-self" "::")

XPath defines a full set of axes for traversing documents, but a host language may define a subset of these axes. The following axes are defined:

  • The child axis contains the children of the context node, which are the nodes returned by the Section 5.3 children Accessor DM31.

    Note:

    Only document nodes and element nodes have children. If the context node is any other kind of node, or if the context node is an empty document or element node, then the child axis is an empty sequence. The children of a document node or element node may be element, processing instruction, comment, or text nodes. Attribute, namespace, and document nodes can never appear as children.

  • the descendant axis is defined as the transitive closure of the child axis; it contains the descendants of the context node (the children, the children of the children, and so on)

  • the parent axis contains the sequence returned by the Section 5.11 parent Accessor DM31, which returns the parent of the context node, or an empty sequence if the context node has no parent

    Note:

    An attribute node may have an element node as its parent, even though the attribute node is not a child of the element node.

  • the ancestor axis is defined as the transitive closure of the parent axis; it contains the ancestors of the context node (the parent, the parent of the parent, and so on)

    Note:

    The ancestor axis includes the root node of the tree in which the context node is found, unless the context node is the root node.

  • the following-sibling axis contains the context node's following siblings, those children of the context node's parent that occur after the context node in document order; if the context node is an attribute or namespace node, the following-sibling axis is empty

  • the preceding-sibling axis contains the context node's preceding siblings, those children of the context node's parent that occur before the context node in document order; if the context node is an attribute or namespace node, the preceding-sibling axis is empty

  • the following axis contains all nodes that are descendants of the root of the tree in which the context node is found, are not descendants of the context node, and occur after the context node in document order

  • the preceding axis contains all nodes that are descendants of the root of the tree in which the context node is found, are not ancestors of the context node, and occur before the context node in document order

  • the attribute axis contains the attributes of the context node, which are the nodes returned by the Section 5.11 parent Accessor DM31; the axis will be empty unless the context node is an element

  • the self axis contains just the context node itself

  • the descendant-or-self axis contains the context node and the descendants of the context node

  • the ancestor-or-self axis contains the context node and the ancestors of the context node; thus, the ancestor-or-self axis will always include the root node

  • the namespace axis contains the namespace nodes of the context node, which are the nodes returned by the Section 5.7 namespace-nodes Accessor DM31; this axis is empty unless the context node is an element node. The namespace axis is deprecated as of XPath 2.0. If XPath 1.0 compatibility mode is true, the namespace axis must be supported. If XPath 1.0 compatibility mode is false, then support for the namespace axis is implementation-defined. An implementation that does not support the namespace axis when XPath 1.0 compatibility mode is false must raise a static error [err:XPST0010] if it is used. Applications needing information about the in-scope namespaces of an element should use the functions Section 10.2.6 fn:in-scope-prefixes FO31, and Section 10.2.5 fn:namespace-uri-for-prefix FO31.

Axes can be categorized as forward axes and reverse axes. An axis that only ever contains the context node or nodes that are after the context node in document order is a forward axis. An axis that only ever contains the context node or nodes that are before the context node in document order is a reverse axis.

The parent, ancestor, ancestor-or-self, preceding, and preceding-sibling axes are reverse axes; all other axes are forward axes. The ancestor, descendant, following, preceding and self axes partition a document (ignoring attribute and namespace nodes): they do not overlap and together they contain all the nodes in the document.

[Definition: Every axis has a principal node kind. If an axis can contain elements, then the principal node kind is element; otherwise, it is the kind of nodes that the axis can contain.] Thus:

  • For the attribute axis, the principal node kind is attribute.

  • For the namespace axis, the principal node kind is namespace.

  • For all other axes, the principal node kind is element.

4.6.2.2 Node Tests

[Definition: A node test is a condition on the name, kind (element, attribute, text, document, comment, or processing instruction), and/or type annotation of a node. A node test determines which nodes contained by an axis are selected by a step.]

[54]    NodeTest    ::=    KindTest | NameTest
[55]    NameTest    ::=    EQName | Wildcard
[56]    Wildcard    ::=    "*"
| (NCName ":*")
| ("*:" NCName)
| (BracedURILiteral "*")
[134]    EQName    ::=    QName | URIQualifiedName

[Definition: A node test that consists only of an EQName or a Wildcard is called a name test.] A name test that consists of an EQName is true if and only if the kind of the node is the principal node kind for the step axis and the expanded QName of the node is equal (as defined by the eq operator) to the expanded QName specified by the name test. For example, child::para selects the para element children of the context node; if the context node has no para children, it selects an empty set of nodes. attribute::abc:href selects the attribute of the context node with the QName abc:href; if the context node has no such attribute, it selects an empty set of nodes.

If the EQName is a lexical QName, it is resolved into an expanded QName using the statically known namespaces in the expression context. It is a static error [err:XPST0081] if the QName has a prefix that does not correspond to any statically known namespace. An unprefixed QName, when used as a name test on an axis whose principal node kind is element, has the namespace URI of the default element namespace in the expression context; otherwise, it has no namespace URI.

A name test is not satisfied by an element node whose name does not match the expanded QName of the name test, even if it is in a substitution group whose head is the named element.

A node test * is true for any node of the principal node kind of the step axis. For example, child::* will select all element children of the context node, and attribute::* will select all attributes of the context node.

A node test can have the form NCName:*. In this case, the prefix is expanded in the same way as with a lexical QName, using the statically known namespaces in the static context. If the prefix is not found in the statically known namespaces, a static error is raised [err:XPST0081]. The node test is true for any node of the principal node kind of the step axis whose expanded QName has the namespace URI to which the prefix is bound, regardless of the local part of the name.

A node test can contain a BracedURILiteral, e.g. Q{http://example.com/msg}* Such a node test is true for any node of the principal node kind of the step axis whose expanded QName has the namespace URI specified in the BracedURILiteral, regardless of the local part of the name.

A node test can also have the form *:NCName. In this case, the node test is true for any node of the principal node kind of the step axis whose local name matches the given NCName, regardless of its namespace or lack of a namespace.

[Definition: An alternative form of a node test called a kind test can select nodes based on their kind, name, and type annotation.] The syntax and semantics of a kind test are described in 3.4 Sequence Types and 3.5 Sequence Type Matching. When a kind test is used in a node test, only those nodes on the designated axis that match the kind test are selected. Shown below are several examples of kind tests that might be used in path expressions:

  • node() matches any node.

  • text() matches any text node.

  • comment() matches any comment node.

  • namespace-node() matches any namespace node.

  • element() matches any element node.

  • schema-element(person) matches any element node whose name is person (or is in the substitution group headed by person), and whose type annotation is the same as (or is derived from) the declared type of the person element in the in-scope element declarations.

  • element(person) matches any element node whose name is person, regardless of its type annotation.

  • element(person, surgeon) matches any non-nilled element node whose name is person, and whose type annotation is surgeon or is derived from surgeon.

  • element(*, surgeon) matches any non-nilled element node whose type annotation is surgeon (or is derived from surgeon), regardless of its name.

  • attribute() matches any attribute node.

  • attribute(price) matches any attribute whose name is price, regardless of its type annotation.

  • attribute(*, xs:decimal) matches any attribute whose type annotation is xs:decimal (or is derived from xs:decimal), regardless of its name.

  • document-node() matches any document node.

  • document-node(element(book)) matches any document node whose content consists of a single element node that satisfies the kind test element(book), interleaved with zero or more comments and processing instructions.

4.6.3 Predicates within Steps

[47]    AxisStep    ::=    (ReverseStep | ForwardStep) PredicateList
[63]    PredicateList    ::=    Predicate*
[64]    Predicate    ::=    "[" Expr "]"

A predicate within a Step has similar syntax and semantics to a predicate within a filter expression. The only difference is in the way the context position is set for evaluation of the predicate.

For the purpose of evaluating the context position within a predicate, the input sequence is considered to be sorted as follows: into document order if the predicate is in a forward-axis step, into reverse document order if the predicate is in a reverse-axis step, or in its original order if the predicate is not in a step.

Here are some examples of axis steps that contain predicates:

  • This example selects the second chapter element that is a child of the context node:

    child::chapter[2]
  • This example selects all the descendants of the context node that are elements named "toy" and whose color attribute has the value "red":

    descendant::toy[attribute::color = "red"]
  • This example selects all the employee children of the context node that have both a secretary child element and an assistant child element:

    child::employee[secretary][assistant]

Note:

When using predicates with a sequence of nodes selected using a reverse axis, it is important to remember that the context positions for such a sequence are assigned in reverse document order. For example, preceding::foo[1] returns the first qualifying foo element in reverse document order, because the predicate is part of an axis step using a reverse axis. By contrast, (preceding::foo)[1] returns the first qualifying foo element in document order, because the parentheses cause (preceding::foo) to be parsed as a primary expression in which context positions are assigned in document order. Similarly, ancestor::*[1] returns the nearest ancestor element, because the ancestor axis is a reverse axis, whereas (ancestor::*)[1] returns the root element (first ancestor in document order).

The fact that a reverse-axis step assigns context positions in reverse document order for the purpose of evaluating predicates does not alter the fact that the final result of the step is always in document order.

4.6.4 Unabbreviated Syntax

This section provides a number of examples of path expressions in which the axis is explicitly specified in each step. The syntax used in these examples is called the unabbreviated syntax. In many common cases, it is possible to write path expressions more concisely using an abbreviated syntax, as explained in 4.6.5 Abbreviated Syntax.

  • child::para selects the para element children of the context node

  • child::* selects all element children of the context node

  • child::text() selects all text node children of the context node

  • child::node() selects all the children of the context node. Note that no attribute nodes are returned, because attributes are not children.

  • attribute::name selects the name attribute of the context node

  • attribute::* selects all the attributes of the context node

  • parent::node() selects the parent of the context node. If the context node is an attribute node, this expression returns the element node (if any) to which the attribute node is attached.

  • descendant::para selects the para element descendants of the context node

  • ancestor::div selects all div ancestors of the context node

  • ancestor-or-self::div selects the div ancestors of the context node and, if the context node is a div element, the context node as well

  • descendant-or-self::para selects the para element descendants of the context node and, if the context node is a para element, the context node as well

  • self::para selects the context node if it is a para element, and otherwise returns an empty sequence

  • child::chapter/descendant::para selects the para element descendants of the chapter element children of the context node

  • child::*/child::para selects all para grandchildren of the context node

  • / selects the root of the tree that contains the context node, but raises a dynamic error if this root is not a document node

  • /descendant::para selects all the para elements in the same document as the context node

  • /descendant::list/child::member selects all the member elements that have a list parent and that are in the same document as the context node

  • child::para[fn:position() = 1] selects the first para child of the context node

  • child::para[fn:position() = fn:last()] selects the last para child of the context node

  • child::para[fn:position() = fn:last()-1] selects the last but one para child of the context node

  • child::para[fn:position() > 1] selects all the para children of the context node other than the first para child of the context node

  • following-sibling::chapter[fn:position() = 1] selects the next chapter sibling of the context node

  • preceding-sibling::chapter[fn:position() = 1] selects the previous chapter sibling of the context node

  • /descendant::figure[fn:position() = 42] selects the forty-second figure element in the document containing the context node

  • /child::book/child::chapter[fn:position() = 5]/child::section[fn:position() = 2] selects the second section of the fifth chapter of the book whose parent is the document node that contains the context node

  • child::para[attribute::type eq "warning"] selects all para children of the context node that have a type attribute with value warning

  • child::para[attribute::type eq 'warning'][fn:position() = 5] selects the fifth para child of the context node that has a type attribute with value warning

  • child::para[fn:position() = 5][attribute::type eq "warning"] selects the fifth para child of the context node if that child has a type attribute with value warning

  • child::chapter[child::title = 'Introduction'] selects the chapter children of the context node that have one or more title children whose typed value is equal to the string Introduction

  • child::chapter[child::title] selects the chapter children of the context node that have one or more title children

  • child::*[self::chapter or self::appendix] selects the chapter and appendix children of the context node

  • child::*[self::chapter or self::appendix][fn:position() = fn:last()] selects the last chapter or appendix child of the context node

4.6.5 Abbreviated Syntax

[50]    AbbrevForwardStep    ::=    "@"? NodeTest
[53]    AbbrevReverseStep    ::=    ".."

The abbreviated syntax permits the following abbreviations:

  1. The attribute axis attribute:: can be abbreviated by @. For example, a path expression para[@type="warning"] is short for child::para[attribute::type="warning"] and so selects para children with a type attribute with value equal to warning.

  2. If the axis name is omitted from an axis step, the default axis is child, with two exceptions: (1) if the NodeTest in an axis step contains an AttributeTest or SchemaAttributeTest then the default axis is attribute; (2) if the NodeTest in an axis step is a NamespaceNodeTest then the default axis is namespace - in an implementation that does not support the namespace axis, an error is raised [err:XQST0134].

    Note:

    The namespace axis is deprecated as of XPath 2.0, but required in some languages that use XPath, including XSLT.

    For example, the path expression section/para is an abbreviation for child::section/child::para, and the path expression section/@id is an abbreviation for child::section/attribute::id. Similarly, section/attribute(id) is an abbreviation for child::section/attribute::attribute(id). Note that the latter expression contains both an axis specification and a node test.

  3. Each non-initial occurrence of // is effectively replaced by /descendant-or-self::node()/ during processing of a path expression. For example, div1//para is short for child::div1/descendant-or-self::node()/child::para and so will select all para descendants of div1 children.

    Note:

    The path expression //para[1] does not mean the same as the path expression /descendant::para[1]. The latter selects the first descendant para element; the former selects all descendant para elements that are the first para children of their respective parents.

  4. A step consisting of .. is short for parent::node(). For example, ../title is short for parent::node()/child::title and so will select the title children of the parent of the context node.

    Note:

    The expression ., known as a context item expression, is a primary expression, and is described in 4.3.4 Context Item Expression.

Here are some examples of path expressions that use the abbreviated syntax:

  • para selects the para element children of the context node

  • * selects all element children of the context node

  • text() selects all text node children of the context node

  • @name selects the name attribute of the context node

  • @* selects all the attributes of the context node

  • para[1] selects the first para child of the context node

  • para[fn:last()] selects the last para child of the context node

  • */para selects all para grandchildren of the context node

  • /book/chapter[5]/section[2] selects the second section of the fifth chapter of the book whose parent is the document node that contains the context node

  • chapter//para selects the para element descendants of the chapter element children of the context node

  • //para selects all the para descendants of the root document node and thus selects all para elements in the same document as the context node

  • //@version selects all the version attribute nodes that are in the same document as the context node

  • //list/member selects all the member elements in the same document as the context node that have a list parent

  • .//para selects the para element descendants of the context node

  • .. selects the parent of the context node

  • ../@lang selects the lang attribute of the parent of the context node

  • para[@type="warning"] selects all para children of the context node that have a type attribute with value warning

  • para[@type="warning"][5] selects the fifth para child of the context node that has a type attribute with value warning

  • para[5][@type="warning"] selects the fifth para child of the context node if that child has a type attribute with value warning

  • chapter[title="Introduction"] selects the chapter children of the context node that have one or more title children whose typed value is equal to the string Introduction

  • chapter[title] selects the chapter children of the context node that have one or more title children

  • employee[@secretary and @assistant] selects all the employee children of the context node that have both a secretary attribute and an assistant attribute

  • book/(chapter|appendix)/section selects every section element that has a parent that is either a chapter or an appendix element, that in turn is a child of a book element that is a child of the context node.

  • If E is any expression that returns a sequence of nodes, then the expression E/. returns the same nodes in document order, with duplicates eliminated based on node identity.

4.7 Sequence Expressions

XPath 4.0 supports operators to construct, filter, and combine sequences of items. Sequences are never nested—for example, combining the values 1, (2, 3), and ( ) into a single sequence results in the sequence (1, 2, 3).

4.7.1 Sequence Concatenation

[7]    Expr    ::=    ExprSingle ("," ExprSingle)*

[Definition: One way to construct a sequence is by using the comma operator, which evaluates each of its operands and concatenates the resulting sequences, in order, into a single result sequence.] Empty parentheses can be used to denote an empty sequence.

A sequence may contain duplicate items, but a sequence is never an item in another sequence. When a new sequence is created by concatenating two or more input sequences, the new sequence contains all the items of the input sequences and its length is the sum of the lengths of the input sequences.

Note:

In places where the grammar calls for ExprSingle, such as the arguments of a function call, any expression that contains a top-level comma operator must be enclosed in parentheses.

Here are some examples of expressions that construct sequences:

  • The result of this expression is a sequence of five integers:

    (10, 1, 2, 3, 4)
  • This expression combines four sequences of length one, two, zero, and two, respectively, into a single sequence of length five. The result of this expression is the sequence 10, 1, 2, 3, 4.

    (10, (1, 2), (), (3, 4))
  • The result of this expression is a sequence containing all salary children of the context node followed by all bonus children.

    (salary, bonus)
  • Assuming that $price is bound to the value 10.50, the result of this expression is the sequence 10.50, 10.50.

    ($price, $price)

4.7.2 Range Expressions

[25]    RangeExpr    ::=    AdditiveExpr ( "to" AdditiveExpr )?

A RangeExpression can be used to construct a sequence of integers. Each of the operands is converted as though it was an argument of a function with the expected parameter type xs:integer?. If either operand is an empty sequence, or if the integer derived from the first operand is greater than the integer derived from the second operand, the result of the range expression is an empty sequence. If the two operands convert to the same integer, the result of the range expression is that integer. Otherwise, the result is a sequence containing the two integer operands and every integer between the two operands, in increasing order.

The following examples illustrate the semantics:

  • 1 to 4 returns the sequence 1, 2, 3, 4

  • 10 to 10 returns the singleton sequence 10

  • 10 to 1 returns the empty sequence

  • -13 to -10 returns the sequence -13, -12, -11, -10

More formally, a RangeExpression is evaluated as follows:

  1. Each of the operands of the to operator is converted as though it was an argument of a function with the expected parameter type xs:integer?.

  2. If either operand is an empty sequence, or if the integer derived from the first operand is greater than the integer derived from the second operand, the result of the range expression is an empty sequence.

  3. If the two operands convert to the same integer, the result of the range expression is that integer.

  4. Otherwise, the result is a sequence containing the two integer operands and every integer between the two operands, in increasing order.

The following examples illustrate the use of RangeExpressions .

This example uses a range expression as one operand in constructing a sequence. It evaluates to the sequence 10, 1, 2, 3, 4.

(10, 1 to 4)

This example selects the first four items from an input sequence:

$input[position() = 1 to 4]

This example returns the sequence (0, 0.1, 0.2, 0.3, 0.5):

$x = (1 to 5)!.*0.1

This example constructs a sequence of length one containing the single integer 10.

10 to 10

The result of this example is a sequence of length zero.

15 to 10

This example uses the fn:reverse function to construct a sequence of six integers in decreasing order. It evaluates to the sequence 15, 14, 13, 12, 11, 10.

fn:reverse(10 to 15)

4.7.3 Combining Node Sequences

[29]    UnionExpr    ::=    IntersectExceptExpr ( ("union" | "|") IntersectExceptExpr )*
[30]    IntersectExceptExpr    ::=    InstanceofExpr ( ("intersect" | "except") InstanceofExpr )*

XPath 4.0 provides the following operators for combining sequences of nodes:

  • The union and | operators are equivalent. They take two node sequences as operands and return a sequence containing all the nodes that occur in either of the operands.

  • The intersect operator takes two node sequences as operands and returns a sequence containing all the nodes that occur in both operands.

  • The except operator takes two node sequences as operands and returns a sequence containing all the nodes that occur in the first operand but not in the second operand.

All these operators eliminate duplicate nodes from their result sequences based on node identity. The resulting sequence is returned in document order.

If an operand of union, intersect, or except contains an item that is not a node, a type error is raised [err:XPTY0004].

If an IntersectExceptExpr contains more than two InstanceofExprs, they are grouped from left to right. With a UnionExpr, it makes no difference how operands are grouped, the results are the same.

Here are some examples of expressions that combine sequences. Assume the existence of three element nodes that we will refer to by symbolic names A, B, and C. Assume that the variables $seq1, $seq2 and $seq3 are bound to the following sequences of these nodes:

  • $seq1 is bound to (A, B)

  • $seq2 is bound to (A, B)

  • $seq3 is bound to (B, C)

Then:

  • $seq1 union $seq2 evaluates to the sequence (A, B).

  • $seq2 union $seq3 evaluates to the sequence (A, B, C).

  • $seq1 intersect $seq2 evaluates to the sequence (A, B).

  • $seq2 intersect $seq3 evaluates to the sequence containing B only.

  • $seq1 except $seq2 evaluates to the empty sequence.

  • $seq2 except $seq3 evaluates to the sequence containing A only.

In addition to the sequence operators described here, see Section 14 Functions and operators on sequences FO31 for functions defined on sequences.

4.8 Arithmetic Expressions

XPath 4.0 provides arithmetic operators for addition, subtraction, multiplication, division, and modulus, in their usual binary and unary forms.

[26]    AdditiveExpr    ::=    MultiplicativeExpr ( ("+" | "-") MultiplicativeExpr )*
[27]    MultiplicativeExpr    ::=    OtherwiseExpr ( ("*" | "div" | "idiv" | "mod") OtherwiseExpr )*
[36]    UnaryExpr    ::=    ("-" | "+")* ValueExpr
[37]    ValueExpr    ::=    SimpleMapExpr

A subtraction operator must be preceded by whitespace if it could otherwise be interpreted as part of the previous token. For example, a-b will be interpreted as a name, but a - b and a -b will be interpreted as arithmetic expressions. (See A.2.4 Whitespace Rules for further details on whitespace handling.)

If an AdditiveExpr contains more than two MultiplicativeExprs, they are grouped from left to right. So, for instance,

A - B + C - D

is equivalent to

((A - B) + C) - D

Similarly, the operands of a MultiplicativeExpr are grouped from left to right.

The first step in evaluating an arithmetic expression is to evaluate its operands. The order in which the operands are evaluated is implementation-dependent.

If XPath 1.0 compatibility mode is true, each operand is evaluated by applying the following steps, in order:

  1. Atomization is applied to the operand. The result of this operation is called the atomized operand.

  2. If the atomized operand is an empty sequence, the result of the arithmetic expression is the xs:double value NaN, and the implementation need not evaluate the other operand or apply the operator. However, an implementation may choose to evaluate the other operand in order to determine whether it raises an error.

  3. If the atomized operand is a sequence of length greater than one, any items after the first item in the sequence are discarded.

  4. If the atomized operand is now an instance of type xs:boolean, xs:string, xs:decimal (including xs:integer), xs:float, or xs:untypedAtomic, then it is converted to the type xs:double by applying the fn:number function. (Note that fn:number returns the value NaN if its operand cannot be converted to a number.)

If XPath 1.0 compatibility mode is false, each operand is evaluated by applying the following steps, in order:

  1. Atomization is applied to the operand. The result of this operation is called the atomized operand.

  2. If the atomized operand is an empty sequence, the result of the arithmetic expression is an empty sequence, and the implementation need not evaluate the other operand or apply the operator. However, an implementation may choose to evaluate the other operand in order to determine whether it raises an error.

  3. If the atomized operand is a sequence of length greater than one, a type error is raised [err:XPTY0004].

  4. If the atomized operand is of type xs:untypedAtomic, it is cast to xs:double. If the cast fails, a dynamic error is raised. [err:FORG0001]FO31

After evaluation of the operands, if the types of the operands are a valid combination for the given arithmetic operator, the operator is applied to the operands, resulting in an atomic value or a dynamic error (for example, an error might result from dividing by zero.) The combinations of atomic types that are accepted by the various arithmetic operators, and their respective result types, are listed in B.2 Operator Mapping together with the operator functions that define the semantics of the operator for each type combination, including the dynamic errors that can be raised by the operator. The definitions of the operator functions are found in [XQuery and XPath Functions and Operators 3.1].

If the types of the operands, after evaluation, are not a valid combination for the given operator, according to the rules in B.2 Operator Mapping, a type error is raised [err:XPTY0004].

XPath 4.0 supports two division operators named div and idiv. Each of these operators accepts two operands of any numeric type. The semantics of div are defined in Section 4.2.5 op:numeric-integer-divide FO31. The semantics of idiv are defined in Section 4.2.4 op:numeric-divide FO31.

Here are some examples of arithmetic expressions:

  • The first expression below returns the xs:decimal value -1.5, and the second expression returns the xs:integer value -1:

    -3 div 2
    -3 idiv 2
  • Subtraction of two date values results in a value of type xs:dayTimeDuration:

    $emp/hiredate - $emp/birthdate
  • This example illustrates the difference between a subtraction operator and a hyphen:

    $unit-price - $unit-discount
  • Unary operators have higher precedence than binary operators (other than "!", "/", and "[]"), subject of course to the use of parentheses. Therefore, the following two examples have different meanings:

    -$bellcost + $whistlecost
    -($bellcost + $whistlecost)

Note:

Multiple consecutive unary arithmetic operators are permitted.

4.9 String Concatenation Expressions

[24]    StringConcatExpr    ::=    RangeExpr ( "||" RangeExpr )*

String concatenation expressions allow the string representations of values to be concatenated. In XPath 4.0, $a || $b is equivalent to fn:concat($a, $b). The following expression evaluates to the string concatenate:

"con" || "cat" || "enate"

4.10 Comparison Expressions

Comparison expressions allow two values to be compared. XPath 4.0 provides three kinds of comparison expressions, called value comparisons, general comparisons, and node comparisons.

[23]    ComparisonExpr    ::=    StringConcatExpr ( (ValueComp
| GeneralComp
| NodeComp) StringConcatExpr )?
[41]    ValueComp    ::=    "eq" | "ne" | "lt" | "le" | "gt" | "ge"
[40]    GeneralComp    ::=    "=" | "!=" | "<" | "<=" | ">" | ">="
[42]    NodeComp    ::=    "is" | "<<" | ">>"

Note:

When an XPath expression is written within an XML document, the XML escaping rules for special characters must be followed; thus "<" must be written as "&lt;".

4.10.1 Value Comparisons

The value comparison operators are eq, ne, lt, le, gt, and ge. Value comparisons are used for comparing single values.

The first step in evaluating a value comparison is to evaluate its operands. The order in which the operands are evaluated is implementation-dependent. Each operand is evaluated by applying the following steps, in order:

  1. Atomization is applied to each operand. The result of this operation is called the atomized operand.

  2. If an atomized operand is an empty sequence, the result of the value comparison is an empty sequence, and the implementation need not evaluate the other operand or apply the operator. However, an implementation may choose to evaluate the other operand in order to determine whether it raises an error.

  3. If an atomized operand is a sequence of length greater than one, a type error is raised [err:XPTY0004].

  4. If an atomized operand is of type xs:untypedAtomic, it is cast to xs:string.

    Note:

    The purpose of this rule is to make value comparisons transitive. Users should be aware that the general comparison operators have a different rule for casting of xs:untypedAtomic operands. Users should also be aware that transitivity of value comparisons may be compromised by loss of precision during type conversion (for example, two xs:integer values that differ slightly may both be considered equal to the same xs:float value because xs:float has less precision than xs:integer).

  5. If the two operands are instances of different primitive types (meaning the 19 primitive types defined in Section 3.2 Primitive datatypesXS2), then:

    1. If each operand is an instance of one of the types xs:string or xs:anyURI, then both operands are cast to type xs:string.

    2. If each operand is an instance of one of the types xs:decimal or xs:float, then both operands are cast to type xs:float.

    3. If each operand is an instance of one of the types xs:decimal, xs:float, or xs:double, then both operands are cast to type xs:double.

    4. Otherwise, a type error is raised [err:XPTY0004].

      Note:

      The primitive type of an xs:integer value for this purpose is xs:decimal.

  6. Finally, if the types of the operands are a valid combination for the given operator, the operator is applied to the operands.

The combinations of atomic types that are accepted by the various value comparison operators, and their respective result types, are listed in B.2 Operator Mapping together with the operator functions that define the semantics of the operator for each type combination. The definitions of the operator functions are found in [XQuery and XPath Functions and Operators 3.1].

Informally, if both atomized operands consist of exactly one atomic value, then the result of the comparison is true if the value of the first operand is (equal, not equal, less than, less than or equal, greater than, greater than or equal) to the value of the second operand; otherwise the result of the comparison is false.

If the types of the operands, after evaluation, are not a valid combination for the given operator, according to the rules in B.2 Operator Mapping, a type error is raised [err:XPTY0004].

Here are some examples of value comparisons:

  • The following comparison atomizes the node(s) that are returned by the expression $book/author. The comparison is true only if the result of atomization is the value "Kennedy" as an instance of xs:string or xs:untypedAtomic. If the result of atomization is an empty sequence, the result of the comparison is an empty sequence. If the result of atomization is a sequence containing more than one value, a type error is raised [err:XPTY0004].

    $book1/author eq "Kennedy"
  • The following comparison is true because atomization converts an array to its member sequence:

    [ "Kennedy" ] eq "Kennedy"
  • The following path expression contains a predicate that selects products whose weight is greater than 100. For any product that does not have a weight subelement, the value of the predicate is the empty sequence, and the product is not selected. This example assumes that weight is a validated element with a numeric type.

    //product[weight gt 100]
  • The following comparison is true if my:hatsize and my:shoesize are both user-defined types that are derived by restriction from a primitive numeric type:

    my:hatsize(5) eq my:shoesize(5)
  • The following comparison is true. The eq operator compares two QNames by performing codepoint-comparisons of their namespace URIs and their local names, ignoring their namespace prefixes.

    fn:QName("http://example.com/ns1", "this:color") eq fn:QName("http://example.com/ns1", "that:color")

4.10.2 General Comparisons

The general comparison operators are =, !=, <, <=, >, and >=. General comparisons are existentially quantified comparisons that may be applied to operand sequences of any length. The result of a general comparison that does not raise an error is always true or false.

If XPath 1.0 compatibility mode is true, a general comparison is evaluated by applying the following rules, in order:

  1. If either operand is a single atomic value that is an instance of xs:boolean, then the other operand is converted to xs:boolean by taking its effective boolean value.

  2. Atomization is applied to each operand. After atomization, each operand is a sequence of atomic values.

  3. If the comparison operator is <, <=, >, or >=, then each item in both of the operand sequences is converted to the type xs:double by applying the fn:number function. (Note that fn:number returns the value NaN if its operand cannot be converted to a number.)

  4. The result of the comparison is true if and only if there is a pair of atomic values, one in the first operand sequence and the other in the second operand sequence, that have the required magnitude relationship. Otherwise the result of the comparison is false or an error. The magnitude relationship between two atomic values is determined by applying the following rules. If a cast operation called for by these rules is not successful, a dynamic error is raised. [err:FORG0001]FO31

    1. If at least one of the two atomic values is an instance of a numeric type, then both atomic values are converted to the type xs:double by applying the fn:number function.

    2. If at least one of the two atomic values is an instance of xs:string, or if both atomic values are instances of xs:untypedAtomic, then both atomic values are cast to the type xs:string.

    3. If one of the atomic values is an instance of xs:untypedAtomic and the other is not an instance of xs:string, xs:untypedAtomic, or any numeric type, then the xs:untypedAtomic value is cast to the dynamic type of the other value.

    4. After performing the conversions described above, the atomic values are compared using one of the value comparison operators eq, ne, lt, le, gt, or ge, depending on whether the general comparison operator was =, !=, <, <=, >, or >=. The values have the required magnitude relationship if and only if the result of this value comparison is true.

If XPath 1.0 compatibility mode is false, a general comparison is evaluated by applying the following rules, in order:

  1. Atomization is applied to each operand. After atomization, each operand is a sequence of atomic values.

  2. The result of the comparison is true if and only if there is a pair of atomic values, one in the first operand sequence and the other in the second operand sequence, that have the required magnitude relationship. Otherwise the result of the comparison is false or an error. The magnitude relationship between two atomic values is determined by applying the following rules. If a cast operation called for by these rules is not successful, a dynamic error is raised. [err:FORG0001]FO31

    1. If both atomic values are instances of xs:untypedAtomic, then the values are cast to the type xs:string.

    2. If exactly one of the atomic values is an instance of xs:untypedAtomic, it is cast to a type depending on the other value's dynamic type T according to the following rules, in which V denotes the value to be cast:

      1. If T is a numeric type or is derived from a numeric type, then V is cast to xs:double.

      2. If T is xs:dayTimeDuration or is derived from xs:dayTimeDuration, then V is cast to xs:dayTimeDuration.

      3. If T is xs:yearMonthDuration or is derived from xs:yearMonthDuration, then V is cast to xs:yearMonthDuration.

      4. In all other cases, V is cast to the primitive base type of T.

      Note:

      The special treatment of the duration types is required to avoid errors that may arise when comparing the primitive type xs:duration with any duration type.

    3. After performing the conversions described above, the atomic values are compared using one of the value comparison operators eq, ne, lt, le, gt, or ge, depending on whether the general comparison operator was =, !=, <, <=, >, or >=. The values have the required magnitude relationship if and only if the result of this value comparison is true.

When evaluating a general comparison in which either operand is a sequence of items, an implementation may return true as soon as it finds an item in the first operand and an item in the second operand that have the required magnitude relationship. Similarly, a general comparison may raise a dynamic error as soon as it encounters an error in evaluating either operand, or in comparing a pair of items from the two operands. As a result of these rules, the result of a general comparison is not deterministic in the presence of errors.

Here are some examples of general comparisons:

  • The following comparison is true if the typed value of any author subelement of $book1 is "Kennedy" as an instance of xs:string or xs:untypedAtomic:

    $book1/author = "Kennedy"
  • The following comparison is true because atomization converts an array to its member sequence:

    [ "Obama", "Nixon", "Kennedy" ] = "Kennedy"
  • The following example contains three general comparisons. The value of the first two comparisons is true, and the value of the third comparison is false. This example illustrates the fact that general comparisons are not transitive.

    (1, 2) = (2, 3)
    (2, 3) = (3, 4)
    (1, 2) = (3, 4)
  • The following example contains two general comparisons, both of which are true. This example illustrates the fact that the = and != operators are not inverses of each other.

    (1, 2) = (2, 3)
    (1, 2) != (2, 3)
  • Suppose that $a, $b, and $c are bound to element nodes with type annotation xs:untypedAtomic, with string values "1", "2", and "2.0" respectively. Then ($a, $b) = ($c, 3.0) returns false, because $b and $c are compared as strings. However, ($a, $b) = ($c, 2.0) returns true, because $b and 2.0 are compared as numbers.

4.10.3 Node Comparisons

Node comparisons are used to compare two nodes, by their identity or by their document order. The result of a node comparison is defined by the following rules:

  1. The operands of a node comparison are evaluated in implementation-dependent order.

  2. If either operand is an empty sequence, the result of the comparison is an empty sequence, and the implementation need not evaluate the other operand or apply the operator. However, an implementation may choose to evaluate the other operand in order to determine whether it raises an error.

  3. Each operand must be either a single node or an empty sequence; otherwise a type error is raised [err:XPTY0004].

  4. A comparison with the is operator is true if the two operand nodes are the same node; otherwise it is false. See [XQuery and XPath Data Model (XDM) 3.1] for the definition of node identity.

  5. A comparison with the << operator returns true if the left operand node precedes the right operand node in document order; otherwise it returns false.

  6. A comparison with the >> operator returns true if the left operand node follows the right operand node in document order; otherwise it returns false.

Here are some examples of node comparisons:

  • The following comparison is true only if the left and right sides each evaluate to exactly the same single node:

    /books/book[isbn="1558604820"] is /books/book[call="QA76.9 C3845"]
  • The following comparison is true only if the node identified by the left side occurs before the node identified by the right side in document order:

    /transactions/purchase[parcel="28-451"] &lt;&lt; /transactions/sale[parcel="33-870"]

4.11 Logical Expressions

A logical expression is either an and-expression or an or-expression. If a logical expression does not raise an error, its value is always one of the boolean values true or false.

[21]    OrExpr    ::=    AndExpr ( "or" AndExpr )*
[22]    AndExpr    ::=    ComparisonExpr ( "and" ComparisonExpr )*

The first step in evaluating a logical expression is to find the effective boolean value of each of its operands (see 2.4.3 Effective Boolean Value).

The value of an and-expression is determined by the effective boolean values (EBV's) of its operands, as shown in the following table:

AND: EBV2 = true EBV2 = false error in EBV2
EBV1 = true true false error
EBV1 = false false false if XPath 1.0 compatibility mode is true, then false; otherwise either false or error.
error in EBV1 error if XPath 1.0 compatibility mode is true, then error; otherwise either false or error. error

The value of an or-expression is determined by the effective boolean values (EBV's) of its operands, as shown in the following table:

OR: EBV2 = true EBV2 = false error in EBV2
EBV1 = true true true if XPath 1.0 compatibility mode is true, then true; otherwise either true or error.
EBV1 = false true false error
error in EBV1 if XPath 1.0 compatibility mode is true, then error; otherwise either true or error. error error

If XPath 1.0 compatibility mode is true, the order in which the operands of a logical expression are evaluated is effectively prescribed. Specifically, it is defined that when there is no need to evaluate the second operand in order to determine the result, then no error can occur as a result of evaluating the second operand.

If XPath 1.0 compatibility mode is false, the order in which the operands of a logical expression are evaluated is implementation-dependent. In this case, an or-expression can return true if the first expression evaluated is true, and it can raise an error if evaluation of the first expression raises an error. Similarly, an and-expression can return false if the first expression evaluated is false, and it can raise an error if evaluation of the first expression raises an error. As a result of these rules, a logical expression is not deterministic in the presence of errors, as illustrated in the examples below.

Here are some examples of logical expressions:

In addition to and- and or-expressions, XPath 4.0 provides a function named fn:not that takes a general sequence as parameter and returns a boolean value. The fn:not function is defined in [XQuery and XPath Functions and Operators 3.1]. The fn:not function reduces its parameter to an effective boolean value. It then returns true if the effective boolean value of its parameter is false, and false if the effective boolean value of its parameter is true. If an error is encountered in finding the effective boolean value of its operand, fn:not raises the same error.

4.12 For Expressions

XPath provides an iteration facility called a for expression. It can be used to iterate over the items of a sequence, or the members of an array. In this section the term collection is used to mean the sequence or array, and the term component is used to refer to the items of the sequence or the members of the array.

[12]    ForExpr    ::=    SimpleForClause "return" ExprSingle
[13]    SimpleForClause    ::=    "for" "member"? SimpleForBinding ("," SimpleForBinding)*
[14]    SimpleForBinding    ::=    "$" VarName "in" ExprSingle

A for expression is evaluated as follows:

  1. If the for expression uses multiple variables, it is first expanded to a set of nested for expressions, each of which uses only one variable.

    For example, the expression for $x in X, $y in Y return $x + $y is expanded to for $x in X return for $y in Y return $x + $y.

    Similarly, the expression for member $x in X, member $y in Y return $x + $y is expanded to for member $x in X return for member $y in Y return $x + $y.

  2. In a single-variable for expression, the variable is called the range variable, the value of the expression that follows the in keyword is called the binding collection, and the expression that follows the return keyword is called the return expression.

  3. When the member keyword is absent, the result of the single-variable for expression is obtained by evaluating the return expression once for each item in the binding collection, with the range variable bound to that item. The resulting sequences are concatenated (as if by the comma operator) in the order of the items in the binding collection from which they were derived.

  4. When the member keyword is present, the value of the binding collection must be a single array. The result of the single-variable for member expression is obtained by evaluating the return expression once for each member of that array, with the range variable bound to that member. The resulting sequences are concatenated (as if by the comma operator) in the order of the members of the binding collection from which they were derived.

    Note that the result is a sequence, not an array.

The following example illustrates the use of a for expression in restructuring an input document. The example is based on the following input:

<bib>
  <book>
    <title>TCP/IP Illustrated</title>
    <author>Stevens</author>
    <publisher>Addison-Wesley</publisher>
  </book>
  <book>
    <title>Advanced Programming in the Unix Environment</title>
    <author>Stevens</author>
    <publisher>Addison-Wesley</publisher>
  </book>
  <book>
    <title>Data on the Web</title>
    <author>Abiteboul</author>
    <author>Buneman</author>
    <author>Suciu</author>
  </book>
</bib>

The following example transforms the input document into a list in which each author's name appears only once, followed by a list of titles of books written by that author. This example assumes that the context item is the bib element in the input document.

            for $a in fn:distinct-values(book/author)
return ((book/author[. = $a])[1], book[author = $a]/title)
         

The result of the above expression consists of the following sequence of elements. The titles of books written by a given author are listed after the name of the author. The ordering of author elements in the result is implementation-dependent due to the semantics of the fn:distinct-values function.

<author>Stevens</author>
<title>TCP/IP Illustrated</title>
<title>Advanced Programming in the Unix environment</title>
<author>Abiteboul</author>
<title>Data on the Web</title>
<author>Buneman</author>
<title>Data on the Web</title>
<author>Suciu</author>
<title>Data on the Web</title>

The following example illustrates a for expression containing more than one variable:

            for $i in (10, 20),
    $j in (1, 2)
return ($i + $j)
         

The result of the above expression, expressed as a sequence of numbers, is as follows: 11, 12, 21, 22

The scope of a variable bound in a for expression comprises all subexpressions of the for expression that appear after the variable binding. The scope does not include the expression to which the variable is bound. The following example illustrates how a variable binding may reference another variable bound earlier in the same for expression:

            for $x in $z, $y in f($x)
return g($x, $y)
         

The following example illustrates processing of an array.

for member $map in parse-json('[{"x":1, "y":2}, {"x":10, "y":20}]') return $map!(?x+?y)

The result is the sequence (3, 30).

Note:

The focus for evaluation of the return clause of a for expression is the same as the focus for evaluation of the for expression itself. The following example, which attempts to find the total value of a set of order-items, is therefore incorrect:

fn:sum(for $i in order-item return @price * @qty)

Instead, the expression must be written to use the variable bound in the for clause:

fn:sum(for $i in order-item return $i/@price * $i/@qty)

4.13 Let Expressions

XPath allows a variable to be declared and bound to a value using a let expression.

[15]    LetExpr    ::=    SimpleLetClause "return" ExprSingle
[16]    SimpleLetClause    ::=    "let" SimpleLetBinding ("," SimpleLetBinding)*
[17]    SimpleLetBinding    ::=    "$" VarName ":=" ExprSingle

A let expression is evaluated as follows:

  • If the let expression uses multiple variables, it is first expanded to a set of nested let expressions, each of which uses only one variable. For example, the expression let $x := 4, $y := 3 return $x + $y is expanded to let $x := 4 return let $y := 3 return $x + $y.

  • In a single-variable let expression, the variable is called the range variable, the value of the expression that follows the := symbol is called the binding sequence, and the expression that follows the return keyword is called the return expression. The result of the let expression is obtained by evaluating the return expression with the range variable bound to the binding sequence.

The scope of a variable bound in a let expression comprises all subexpressions of the let expression that appear after the variable binding. The scope does not include the expression to which the variable is bound. The following example illustrates how a variable binding may reference another variable bound earlier in the same let expression:

let $x := doc('a.xml')/*, $y := $x//*
return $y[@value gt $x/@min]

4.14 Maps and Arrays

Most modern programming languages have support for collections of key/value pairs, which may be called maps, dictionaries, associative arrays, hash tables, keyed lists, or objects (these are not the same thing as objects in object-oriented systems). In XPath 4.0, we call these maps. Most modern programming languages also support ordered lists of values, which may be called arrays, vectors, or sequences. In XPath 4.0, we have both sequences and arrays. Unlike sequences, an array is an item, and can appear as an item in a sequence.

In previous versions of the language, element structures and sequences were the only complex data structures. We are adding maps and arrays to XPath 4.0 in order to provide lightweight data structures that are easier to optimize and less complex to use for intermediate processing and to allow programs to easily combine XML processing with JSON processing.

Note:

The XPath 4.0 specification focuses on syntax provided for maps and arrays, especially constructors and lookup.

Some of the functionality typically needed for maps and arrays is provided by functions defined in Section 17 Maps and Arrays FO31, including functions used to read JSON to create maps and arrays, serialize maps and arrays to JSON, combine maps to create a new map, remove map entries to create a new map, iterate over the keys of a map, convert an array to create a sequence, combine arrays to form a new array, and iterate over arrays in various ways.

4.14.1 Maps

[Definition: A map is a function that associates a set of keys with values, resulting in a collection of key / value pairs.] [Definition: Each key / value pair in a map is called an entry.] [Definition: The value associated with a given key is called the associated value of the key.]

4.14.1.1 Map Constructors

A Map is created using a MapConstructor.

[84]    MapConstructor    ::=    "map" "{" (MapConstructorEntry ("," MapConstructorEntry)*)? "}"
[85]    MapConstructorEntry    ::=    MapKeyExpr ":" MapValueExpr
[86]    MapKeyExpr    ::=    ExprSingle
[87]    MapValueExpr    ::=    ExprSingle

Note:

In some circumstances, it is necessary to include whitespace before or after the colon of a MapConstructorEntry to ensure that it is parsed as intended.

For instance, consider the expression map{a:b}. Although it matches the EBNF for MapConstructor (with a matching MapKeyExpr and b matching MapValueExpr), the "longest possible match" rule requires that a:b be parsed as a QName, which results in a syntax error. Changing the expression to map{a :b} or map{a: b} will prevent this, resulting in the intended parse.

Similarly, consider these three expressions:

    map{a:b:c}
    map{a:*:c}
    map{*:b:c}

In each case, the expression matches the EBNF in two different ways, but the "longest possible match" rule forces the parse in which the MapKeyExpr is a:b, a:*, or *:b (respectively) and the MapValueExpr is c. To achieve the alternative parse (in which the MapKeyExpr is merely a or *), insert whitespace before and/or after the first colon.

See A.2 Lexical structure.

The value of the expression is a map whose entries correspond to the key-value pairs obtained by evaluating the successive MapKeyExpr and MapValueExpr expressions.

Each MapKeyExpr expression is evaluated and atomized; a type error [err:XPTY0004] occurs if the result is not a single atomic value. The associated value is the result of evaluating the corresponding MapValueExpr. If the MapValueExpr evaluates to a node, the associated value is the node itself, not a new node with the same values.

Note:

XPath 4.0 has no operators that can distinguish a map or array from another map or array with the same values. Future versions of the XQuery Update Facility, on the other hand, will expose this difference, and need to be clear about the data model instance that is constructed.

In some existing implementations that support updates via proprietary extensions, if the MapValueExpr evaluates to a map or array, the associated value is a new map or array with the same values.

[Definition: Two atomic values K1 and K2 have the same key value if op:same-key(K1, K2) returns true, as specified in Section 17.1.1 op:same-key FO31 ] If two or more entries have the same key value then a dynamic error is raised [err:XQDY0137].

Example:

The following expression constructs a map with seven entries:

map {
  "Su" : "Sunday",
  "Mo" : "Monday",
  "Tu" : "Tuesday",
  "We" : "Wednesday",
  "Th" : "Thursday",
  "Fr" : "Friday",
  "Sa" : "Saturday"
}

Maps can nest, and can contain any XDM value. Here is an example of a nested map with values that can be string values, numeric values, or arrays:

map {
    "book": map {
        "title": "Data on the Web",
        "year": 2000,
        "author": [
            map {
                "last": "Abiteboul",
                "first": "Serge"
            },
            map {
                "last": "Buneman",
                "first": "Peter"
            },
            map {
                "last": "Suciu",
                "first": "Dan"
            }
        ],
        "publisher": "Morgan Kaufmann Publishers",
        "price": 39.95
    }
}
    
4.14.1.2 Map Lookup using Function Call Syntax

Maps are functions, and function calls can be used to look up the value associated with a key in a map. If $map is a map and $key is a key, then $map($key) is equivalent to map:get($map, $key). The semantics of such a function call are formally defined in Section 17.1.6 map:get FO31.

Examples:

Note:

XPath 4.0 also provides an alternate syntax for map and array lookup that is more terse, supports wildcards, and allows lookup to iterate over a sequence of maps or arrays. See 4.14.3 The Lookup Operator ("?") for Maps and Arrays for details.

Map lookups can be chained.

Examples: (These examples assume that $b is bound to the books map from the previous section)

  • The expression $b("book")("title") returns the string Data on the Web.

  • The expression $b("book")("author") returns the array of authors.

  • The expression $b("book")("author")(1)("last") returns the string Abiteboul.

    (This example combines 4.14.2.2 Array Lookup using Function Call Syntax with map lookups.)

4.14.2 Arrays

4.14.2.1 Array Constructors

[Definition: An array is a function that associates a set of positions, represented as positive integer keys, with values.] The first position in an array is associated with the integer 1. [Definition: The values of an array are called its members.] In the type hierarchy, array has a distinct type, which is derived from function. Atomization converts arrays to sequences (see Atomization).

An array is created using an ArrayConstructor.

[88]    ArrayConstructor    ::=    SquareArrayConstructor | CurlyArrayConstructor
[89]    SquareArrayConstructor    ::=    "[" (ExprSingle ("," ExprSingle)*)? "]"
[90]    CurlyArrayConstructor    ::=    "array" EnclosedExpr

If a member of an array is a node, its node identity is preserved. In both forms of an ArrayConstructor, if a member expression evaluates to a node, the associated value is the node itself, not a new node with the same values. If the member expression evaluates to a map or array, the associated value is a new map or array with the same values.

A SquareArrayConstructor consists of a comma-delimited set of argument expressions. It returns an array in which each member contains the value of the corresponding argument expression.

Examples:

  • [ 1, 2, 5, 7 ] creates an array with four members: 1, 2, 5, and 7.

  • [ (), (27, 17, 0)] creates an array with two members: () and the sequence (27, 17, 0).

  • [ $x, local:items(), <tautology>It is what it is.</tautology> ] creates an array with three members: the value of $x, the result of evaluating the function call, and a tautology element.

A CurlyArrayConstructor can use any expression to create its members. It evaluates its operand expression to obtain a sequence of items and creates an array with these items as members. Unlike a SquareArrayConstructor, a comma in a CurlyArrayConstructor is the comma operator, not a delimiter.

Examples:

  • array { $x } creates an array with one member for each item in the sequence to which $x is bound.

  • array { local:items() } creates an array with one member for each item in the sequence to which local:items() evaluates.

  • array { 1, 2, 5, 7 } creates an array with four members: 1, 2, 5, and 7.

  • array { (), (27, 17, 0) } creates an array with three members: 27, 17, and 0.

  • array{ $x, local:items(), <tautology>It is what it is.</tautology> } creates an array with the following members: the items to which $x is bound, followed by the items to which local:items() evaluates, followed by a tautology element.

Note:

XPath 4.0 does not provide explicit support for sparse arrays. Use integer-valued maps to represent sparse arrays, e.g. map { 27 : -1, 153 : 17 } .

4.14.2.2 Array Lookup using Function Call Syntax

Arrays are functions, and function calls can be used to look up the value associated with position in an array. If $array is an array and $index is an integer corresponding to a position in the array, then $array($key) is equivalent to array:get($array, $key). The semantics of such a function call are formally defined in Section 17.3.2 array:get FO31.

Examples:

  • [ 1, 2, 5, 7 ](4) evaluates to 7.

  • [ [1, 2, 3], [4, 5, 6]](2) evaluates to [4, 5, 6].

  • [ [1, 2, 3], [4, 5, 6]](2)(2) evaluates to 5.

  • [ 'a', 123, <name>Robert Johnson</name> ](3) evaluates to <name>Robert Johnson</name>.

  • array { (), (27, 17, 0) }(1) evaluates to 27.

  • array { (), (27, 17, 0) }(2) evaluates to 17.

  • array { "licorice", "ginger" }(20) raises a dynamic error [err:FOAY0001]FO31.

Note:

XPath 4.0 also provides an alternate syntax for map and array lookup that is more terse, supports wildcards, and allows lookup to iterate over a sequence of maps or arrays. See 4.14.3 The Lookup Operator ("?") for Maps and Arrays for details.

4.14.3 The Lookup Operator ("?") for Maps and Arrays

XPath 4.0 provides a lookup operator for maps and arrays that is more convenient for some common cases. It provides a terse syntax for simple strings as keys in maps or integers as keys in arrays, supports wildcards, and iterates over sequences of maps and arrays.

4.14.3.1 Unary Lookup
[91]    UnaryLookup    ::=    "?" KeySpecifier
[66]    KeySpecifier    ::=    NCName | IntegerLiteral | StringLiteral | VarRef | ParenthesizedExpr | "*"

Unary lookup is used in predicates (e.g. $map[?name='Mike'] or with the simple map operator (e.g. $maps ! ?name='Mike'). See 4.14.3.2 Postfix Lookup for the postfix lookup operator.

UnaryLookup returns a sequence of values selected from the context item, which must be a map or array. If the context item is not a map or an array, a type error is raised [err:XPTY0004].

If the context item is a map:

  1. If the KeySpecifier is an NCName or a StringLiteral , the UnaryLookup operator is equivalent to .(KS), where KS is the value of the NCName or StringLiteral.

  2. If the KeySpecifier is an IntegerLiteral, the UnaryLookup operator is equivalent to .(KS), where KS is the value of the IntegerLiteral.

  3. If the KeySpecifier is a ParenthesizedExpr or a VarRef the UnaryLookup operator is equivalent to the following expression, where KS is the value of the ParenthesizedExpr or VarRef :

    for $k in fn:data(KS)
    return .($k)  
    
  4. If the KeySpecifier is a wildcard ("*"), the UnaryLookup operator is equivalent to the following expression:

    for $k in map:keys(.)
    return .($k)
    

    Note:

    The order of keys in map:keys() is implementation-dependent, so the order of values in the result sequence is also implementation-dependent.

If the context item is an array:

  1. If the KeySpecifier is an IntegerLiteral, the UnaryLookup operator is equivalent to .(KS), where KS is the value of the IntegerLiteral.

  2. If the KeySpecifier is an NCName or StringLiteral , the UnaryLookup operator raises a type error [err:XPTY0004].

  3. If the KeySpecifier is a ParenthesizedExpr or a VarRef , the UnaryLookup operator is equivalent to the following expression, where KS is the value of the ParenthesizedExpr or VarRef :

    for $k in fn:data(KS)
    return .($k)  
    
  4. If the KeySpecifier is a wildcard ("*"), the UnaryLookup operator is equivalent to the following expression:

    for $k in 1 to array:size(.)
    return .($k)
    

    Note:

    Note that array items are returned in order.

Examples:

  • ?name is equivalent to .("name"), an appropriate lookup for a map.

  • ?2 is equivalent to .(2), an appropriate lookup for an array or an integer-valued map.

  • ?"first name" is equivalent to .("first name")

  • ?($a) and ?$a are equivalent to for $k in $a return .($k), allowing keys for an array or map to be passed using a variable.

  • ?(2 to 4) is equivalent to for $k in (2,3,4) return .($k), a convenient way to return a range of values from an array.

  • ?(3.5) raises a type error if the context item is an array because the parameter must be an integer.

  • ([1,2,3], [1,2,5], [1,2])[?3 = 5] raises an error because ?3 on one of the items in the sequence fails.

  • If $m is bound to the weekdays map described in 4.14.1 Maps, then $m?* returns the values ("Sunday","Monday","Tuesday","Wednesday", "Thursday", "Friday","Saturday"), in implementation-dependent order.

  • [1, 2, 5, 7]?* evaluates to (1, 2, 5, 7).

  • [[1, 2, 3], [4, 5, 6]]?* evaluates to ([1, 2, 3], [4, 5, 6])

4.14.3.2 Postfix Lookup
[65]    Lookup    ::=    "?" KeySpecifier

The semantics of a Postfix Lookup expression depend on the form of the KeySpecifier, as follows:

  • If the KeySpecifier is an NCName, StringLiteral, VarRef, IntegerLiteral, or Wildcard ("*"), then the expression E?S is equivalent to E!?S. (That is, the semantics of the postfix lookup operator are defined in terms of the unary lookup operator).

  • If the KeySpecifier is a ParenthesizedExpr, then the expression E?(S) is equivalent to

    for $e in E, $s in fn:data(S) return $e($s)

    Note:

    The focus for evaluating S is the same as the focus for the Lookup expression itself.

Examples:

  • map { "first" : "Jenna", "last" : "Scott" }?first evaluates to "Jenna"

  • map { "first name" : "Jenna", "last name" : "Scott" }?"first name" evaluates to "Jenna"

  • [4, 5, 6]?2 evaluates to 5.

  • (map {"first": "Tom"}, map {"first": "Dick"}, map {"first": "Harry"})?first evaluates to the sequence ("Tom", "Dick", "Harry").

  • ([1,2,3], [4,5,6])?2 evaluates to the sequence (2, 5).

  • ["a","b"]?3 raises a dynamic error [err:FOAY0001]FO31

4.15 Conditional Expressions

XPath 4.0 provides a conditional expression based on the keywords if, then, and else.

In addition, it provides a more concise syntax as a ternary expression using the operators ?? and !!

[20]    IfExpr    ::=    "if" "(" Expr ")" "then" ExprSingle "else" ExprSingle
[11]    TernaryConditionalExpr    ::=    OrExpr ("??" TernaryConditionalExpr "!!" TernaryConditionalExpr)?

Both constructs have the same semantics. There are three expressions, called the test expression, the then-expression, and the the else-expression.

With the keyword syntax, the format is:

if (test-expression) then then-expression else else-expression

With the ternary operator syntax, the format is:

test-expression ?? then-expression !! else-expression

Note:

The ternary operator syntax is borrowed from Perl6.

The first step in processing a conditional expression is to find the effective boolean value of the test expression, as defined in 2.4.3 Effective Boolean Value.

The value of a conditional expression is defined as follows: If the effective boolean value of the test expression is true, the value of the then-expression is returned. If the effective boolean value of the test expression is false, the value of the else-expression is returned.

Conditional expressions have a special rule for propagating dynamic errors. If the effective value of the test expression is true, the conditional expression ignores (does not raise) any dynamic errors encountered in the else-expression. In this case, since the else-expression can have no observable effect, it need not be evaluated. Similarly, if the effective value of the test expression is false, the conditional expression ignores any dynamic errors encountered in the then-expression, and the then-expression need not be evaluated.

Here are some examples of conditional expressions:

  • In this example, the test expression is a comparison expression:

    if ($widget1/unit-cost &lt; $widget2/unit-cost)
      then $widget1
      else $widget2
  • In this example, the test expression tests for the existence of an attribute named discounted, independently of its value:

    if ($part/@discounted)
      then $part/wholesale
      else $part/retail
  • The above example can instead be written:

    $part/(@discounted ?? wholesale !! retail)

    (Note: the equivalence holds only if $part is a single item.)

4.16 Otherwise Expression

[28]    OtherwiseExpr    ::=    UnionExpr ( "otherwise" UnionExpr )*

The otherwise expression returns the value of its first operand, unless this is an empty sequence, in which case it returns the value of its second operand.

For example, @price - (@discount otherwise 0) returns the value of @price - @discount, if the attribute @discount exists, or the value of @price if the @discount attribute is absent.

To prevent spurious errors, the right hand operand must not be evaluated unless the left-hand operand returns an empty sequence.

Note:

The operator is associative (even under error conditions): A otherwise (B otherwise C) returns the same result as (A otherwise B) otherwise C.

4.17 Quantified Expressions

Quantified expressions support existential and universal quantification. The value of a quantified expression is always true or false.

[18]    QuantifiedExpr    ::=    ("some" | "every") QuantifierBinding ("," QuantifierBinding)* "satisfies" ExprSingle
[19]    QuantifierBinding    ::=    "$" VarName "in" ExprSingle

A quantified expression begins with a quantifier, which is the keyword some or every, followed by one or more in-clauses that are used to bind variables, followed by the keyword satisfies and a test expression. Each in-clause associates a variable with an expression that returns a sequence of items, called the binding sequence for that variable. The value of the quantified expression is defined by the following rules:

  1. If the QuantifiedExpr contains more than one QuantifierBinding, then it is equivalent to the expression obtained by replacing each comma with satisfies some or satisfies every respectively. For example, the expression some $x in X, $y in Y satisfies $x = $y is equivalent to some $x in X satisfies some $y in Y satisfies $x = $y, while the expression every $x in X, $y in Y satisfies $x lt $y is equivalent to every $x in X satisfies every $y in Y satisfies $x lt $y

  2. If the quantifier is some, the QuantifiedExpr returns true if at least one evaluation of the test expression has the effective boolean value true; otherwise it returns false. In consequence, if the binding sequence is empty, the result of the QuantifiedExpr is false.

  3. If the quantifier is every, the QuantifiedExpr returns true if every evaluation of the test expression has the effective boolean value true; otherwise it returns false. In consequence, if the binding sequence is empty, the result of the QuantifiedExpr is true.

The scope of a variable bound in a quantified expression comprises all subexpressions of the quantified expression that appear after the variable binding. The scope does not include the expression to which the variable is bound.

The order in which test expressions are evaluated for the various binding tuples is implementation-dependent. If the quantifier is some, an implementation may return true as soon as it finds one binding tuple for which the test expression has an effective boolean value of true, and it may raise a dynamic error as soon as it finds one binding tuple for which the test expression raises an error. Similarly, if the quantifier is every, an implementation may return false as soon as it finds one binding tuple for which the test expression has an effective boolean value of false, and it may raise a dynamic error as soon as it finds one binding tuple for which the test expression raises an error. As a result of these rules, the value of a quantified expression is not deterministic in the presence of errors, as illustrated in the examples below.

Here are some examples of quantified expressions:

  • This expression is true if every part element has a discounted attribute (regardless of the values of these attributes):

    every $part in /parts/part satisfies $part/@discounted
  • This expression is true if at least one employee element satisfies the given comparison expression:

    some $emp in /emps/employee satisfies
         ($emp/bonus &gt; 0.25 * $emp/salary)
  • This expression is true if at every employee element has at least one salary child with the attribute current="true":

    every $emp in /emps/employee satisfies
         some $sal in $emp/salary satisfies $sal/@current='true'

    Note:

    Like many quantified expressions, this can be simplified. This example can be written every $emp in /emps/employee satisfies $emp/salary[@current='true'], or even more concisely as empty(/emps/employee[not(salary/@current='true')].

    Another alternative in XPath 4.0 4.0 is to use the higher-order functions fn:some and fn:all. This example can be written fn:all(/emps/employee, ->(){salary/@current='true'})

  • In the following examples, each quantified expression evaluates its test expression over nine pairs of variable bindings, formed from the Cartesian product of the sequences (1, 2, 3) and (2, 3, 4). The expression beginning with some evaluates to true, and the expression beginning with every evaluates to false.

    some $x in (1, 2, 3), $y in (2, 3, 4)
    satisfies $x + $y = 4
    every $x in (1, 2, 3), $y in (2, 3, 4)
    satisfies $x + $y = 4
  • This quantified expression may either return true or raise a type error, since its test expression returns true for one variable binding and raises a type error for another:

    some $x in (1, 2, "cat") satisfies $x * 2 = 4
  • This quantified expression may either return false or raise a type error, since its test expression returns false for one variable binding and raises a type error for another:

    every $x in (1, 2, "cat") satisfies $x * 2 = 4

4.18 Expressions on SequenceTypes

The instance of, cast, castable, and treat expressions are used to test whether a value conforms to a given type or to convert it to an instance of a given type.

4.18.1 Instance Of

[31]    InstanceofExpr    ::=    TreatExpr ( "instance" "of" SequenceType )?

The boolean operator instance of returns true if the value of its first operand matches the SequenceType in its second operand, according to the rules for SequenceType matching; otherwise it returns false. For example:

  • 5 instance of xs:integer

    This example returns true because the given value is an instance of the given type.

  • 5 instance of xs:decimal

    This example returns true because the given value is an integer literal, and xs:integer is derived by restriction from xs:decimal.

  • (5, 6) instance of xs:integer+

    This example returns true because the given sequence contains two integers, and is a valid instance of the specified type.

  • . instance of element()

    This example returns true if the context item is an element node or false if the context item is defined but is not an element node. If the context item is absentDM31, a dynamic error is raised [err:XPDY0002].

4.18.2 Cast

[34]    CastExpr    ::=    ArrowExpr ( "cast" "as" SingleType )?
[92]    SingleType    ::=    (SimpleTypeName | LocalUnionType) "?"?
[127]    LocalUnionType    ::=    "union" "(" ItemType ("," ItemType)* ")"

Sometimes it is necessary to convert a value to a specific datatype. For this purpose, XPath 4.0 provides a cast expression that creates a new value of a specific type based on an existing value. A cast expression takes two operands: an input expression and a target type. The type of the atomized value of the input expression is called the input type. The target type must be either of:

  • The name of a type defined in the in-scope schema types, which must be a simple type [err:XQST0052]. In addition, the target type cannot be xs:NOTATION, xs:anySimpleType, or xs:anyAtomicType

  • A LocalUnionType such as union(xs:date, xs:dateTime).

[err:XPST0080]. The optional occurrence indicator "?" denotes that an empty sequence is permitted. If the target type is a lexical QName that has no namespace prefix, it is considered to be in the default type namespace.

Casting a node to xs:QName can cause surprises because it uses the static context of the cast expression to provide the namespace bindings for this operation. Instead of casting to xs:QName, it is generally preferable to use the fn:QName function, which allows the namespace context to be taken from the document containing the QName.

The semantics of the cast expression are as follows:

  1. The input expression is evaluated.

  2. The result of the first step is atomized.

  3. If the result of atomization is a sequence of more than one atomic value, a type error is raised [err:XPTY0004].

  4. If the result of atomization is an empty sequence:

    1. If ? is specified after the target type, the result of the cast expression is an empty sequence.

    2. If ? is not specified after the target type, a type error is raised [err:XPTY0004].

  5. If the result of atomization is a single atomic value, the result of the cast expression is determined by casting to the target type as described in Section 19 Casting FO31. When casting, an implementation may need to determine whether one type is derived by restriction from another. An implementation can determine this either by examining the in-scope schema definitions or by using an alternative, implementation-dependent mechanism such as a data dictionary. The result of a cast expression is one of the following:

    1. A value of the target type (or, in the case of list types, a sequence of values that are instances of the item type of the list type).

    2. A type error, if casting from the source type to the target type is not supported (for example attempting to convert an integer to a date).

    3. A dynamic error, if the particular input value cannot be converted to the target type (for example, attempting to convert the string "three" to an integer).

4.18.3 Castable

[33]    CastableExpr    ::=    CastExpr ( "castable" "as" SingleType )?
[92]    SingleType    ::=    (SimpleTypeName | LocalUnionType) "?"?
[127]    LocalUnionType    ::=    "union" "(" ItemType ("," ItemType)* ")"

XPath 4.0 provides an expression that tests whether a given value is castable into a given target type. The target type must be either of:

  • The name of a type defined in the in-scope schema types, which must be a simple type [err:XQST0052]. In addition, the target type cannot be xs:NOTATION, xs:anySimpleType, or xs:anyAtomicType

  • A LocalUnionType such as union(xs:date, xs:dateTime).

The expression E castable as T returns true if the result of evaluating E can be successfully cast into the target type T by using a cast expression; otherwise it returns false. If evaluation of E fails with a dynamic error or if the value of E cannot be atomized, the castable expression as a whole fails. The castable expression can be used as a predicate to avoid errors at evaluation time. It can also be used to select an appropriate type for processing of a given value, as illustrated in the following example:

if ($x castable as hatsize)
   then $x cast as hatsize
   else if ($x castable as IQ)
   then $x cast as IQ
   else $x cast as xs:string

4.18.4 Constructor Functions

For every simple type in the in-scope schema types (except xs:NOTATION and xs:anyAtomicType, and xs:anySimpleType, which are not instantiable), a constructor function is implicitly defined. In each case, the name of the constructor function is the same as the name of its target type (including namespace). The signature of the constructor function for a given type depends on the type that is being constructed, and can be found in Section 18 Constructor functions FO31.

[Definition: The constructor function for a given type is used to convert instances of other simple types into the given type. The semantics of the constructor function call T($arg) are defined to be equivalent to the expression (($arg) cast as T?).]

The following examples illustrate the use of constructor functions:

  • This example is equivalent to ("2000-01-01" cast as xs:date?).

    xs:date("2000-01-01")
  • This example is equivalent to (($floatvalue * 0.2E-5) cast as xs:decimal?).

    xs:decimal($floatvalue * 0.2E-5)
  • This example returns an xs:dayTimeDuration value equal to 21 days. It is equivalent to ("P21D" cast as xs:dayTimeDuration?).

    xs:dayTimeDuration("P21D")
  • If usa:zipcode is a user-defined atomic type in the in-scope schema types, then the following expression is equivalent to the expression ("12345" cast as usa:zipcode?).

    usa:zipcode("12345")

Note:

An instance of an atomic type that is not in a namespace can be constructed by using a URIQualifiedName in either a cast expression or a constructor function call. Examples:

17 cast as Q{}apple
Q{}apple(17)

In either context, using an unqualified NCName might not work: in a cast expression, an unqualified name is resolved using the default type namespace, while an unqualified name in a constructor function call is resolved using the function name resolver which will typically assume a default namespace.

4.18.5 Treat

[32]    TreatExpr    ::=    CastableExpr ( "treat" "as" SequenceType )?

XPath 4.0 provides an expression called treat that can be used to modify the static type of its operand.

Like cast, the treat expression takes two operands: an expression and a SequenceType. Unlike cast, however, treat does not change the dynamic type or value of its operand. Instead, the purpose of treat is to ensure that an expression has an expected dynamic type at evaluation time.

The semantics of expr1 treat as type1 are as follows:

  • During static analysis:

    The static type of the treat expression is type1 . This enables the expression to be used as an argument of a function that requires a parameter of type1 .

  • During expression evaluation:

    If expr1 matches type1 , using the rules for SequenceType matching, the treat expression returns the value of expr1 ; otherwise, it raises a dynamic error [err:XPDY0050]. If the value of expr1 is returned, the identity of any nodes in the value is preserved. The treat expression ensures that the value of its expression operand conforms to the expected type at run-time.

  • Example:

    $myaddress treat as element(*, USAddress)

    The static type of $myaddress may be element(*, Address), a less specific type than element(*, USAddress). However, at run-time, the value of $myaddress must match the type element(*, USAddress) using rules for SequenceType matching; otherwise a dynamic error is raised [err:XPDY0050].

4.19 Simple map operator (!)

[43]    SimpleMapExpr    ::=    PathExpr ("!" PathExpr)*

A mapping expression S!E evaluates the expression E once for every item in the sequence obtained by evaluating S. The simple mapping operator "!" can be applied to any sequence, regardless of the types of its items, and it can deliver a mixed sequence of nodes, atomic values, and functions. Unlike the similar "/" operator, it does not sort nodes into document order or eliminate duplicates.

Each operation E1!E2 is evaluated as follows: Expression E1 is evaluated to a sequence S. Each item in S then serves in turn to provide an inner focus (the item as the context item, its position in S as the context position, the length of S as the context size) for an evaluation of E2 in the dynamic context. The sequences resulting from all the evaluations of E2 are combined as follows: Every evaluation of E2 returns a (possibly empty) sequence of items. These sequences are concatenated and returned. The returned sequence preserves the orderings within and among the subsequences generated by the evaluations of E2 .

Simple map operators have functionality similar to 4.6.1.1 Path operator (/). The following table summarizes the differences between these two operators

Operator Path operator (E1 / E2) Simple map operator (E1 ! E2)
E1 Any sequence of nodes Any sequence of items
E2 Either a sequence of nodes or a sequence of non-node items A sequence of items
Additional processing Duplicate elimination and document ordering Simple sequence concatenation

The following examples illustrate the use of simple map operators combined with path expressions.

  • child::div1 / child::para / string() ! concat("id-", .)

    Selects the para element children of the div1 element children of the context node; that is, the para element grandchildren of the context node that have div1 parents. It then outputs the strings obtained by prepending "id-" to each of the string values of these grandchildren.

  • $emp ! (@first, @middle, @last)

    Returns the values of the attributes first, middle, and last for element $emp, in the order given. (The / operator here returns the attributes in an unpredictable order.)

  • $docs ! ( //employee)

    Returns all the employees within all the documents identified by the variable docs, in document order within each document, but retaining the order of documents.

  • avg( //employee / salary ! translate(., '$', '') ! number(.))

    Returns the average salary of the employees, having converted the salary to a number by removing any $ sign and then converting to a number. (The second occurrence of ! could not be written as / because the left-hand operand of / cannot be an atomic value.)

  • fn:string-join((1 to $n)!"*")

    Returns a string containing $n asterisks.

  • $values!(.*.) => fn:sum()

    Returns the sum of the squares of a sequence of numbers.

  • string-join(ancestor::*!name(), '/')

    Returns a path containing the names of the ancestors of an element, separated by "/" characters.

4.20 Arrow Expressions

[35]    ArrowExpr    ::=    UnaryExpr ( (FatArrowTarget | ThinArrowTarget) )*
[38]    FatArrowTarget    ::=    "=>" ((ArrowStaticFunction ArgumentList) | (ArrowDynamicFunction PositionalArgumentList))
[39]    ThinArrowTarget    ::=    "->" ((ArrowStaticFunction ArgumentList) | (ArrowDynamicFunction PositionalArgumentList) | EnclosedExpr)
[67]    ArrowStaticFunction    ::=    EQName
[68]    ArrowDynamicFunction    ::=    VarRef | ParenthesizedExpr
[58]    ArgumentList    ::=    "(" ((PositionalArguments ("," KeywordArguments)?) | KeywordArguments)? ")"
[59]    PositionalArgumentList    ::=    "(" PositionalArguments? ")"

[Definition: An arrow operator applies a function to the value of an expression, using the value as the first argument to the function.]

The fat arrow operator => is defined as follows:

The thin arrow operator -> is defined as follows:

  • If the arrow is followed by an ArrowStaticFunction:

    Given a UnaryExpr U, an ArrowStaticFunction F, and an ArgumentList (A, B, C...), the expression U -> F(A, B, C...) is equivalent to the expression (U ! F(., A, B, C...)).

  • If the arrow is followed by an ArrowDynamicFunction:

    Given a UnaryExpr U, an ArrowDynamicFunction F, and an PositionalArgumentList (A, B, C...), the expression U -> F(A, B, C...) is equivalent to the expression (U ! F(., A, B, C...)).

  • If the arrow is followed by an EnclosedExpr:

    Given a UnaryExpr U, and an EnclosedExpr {E}, the expression U -> {E} is equivalent to the expression (U) ! (E).

    For example, the expression $x -> {.+1} is equivalent to ($x)!(.+1).

    Note:

    The precedence of the ! operator is higher than that of ->, so $x -> f() -> {.+1} is equivalent to ($x -> f()) ! (.+1). Using the -> operator in such a pipeline expression, in preference to !, can therefore reduce the need for parentheses.

    Note:

    The expression $x -> {.+1} can be considered as an abbreviation for $x -> (->{.+1})(): that is, it invokes the anonymous function ->{.+1} once for each item in $x.

The fat arrow operator thus applies the supplied function to the result of the left-hand operand as a whole, while the thin arrow operator applies the function (or enclosed expression) to each item in the value of the left-hand operand individually. In the case where the result of the left-hand operand is a single item, the two operators have almost the same effect; the only difference is that the thin arrow binds the focus.

This syntax is particularly helpful when applying multiple functions to a value in turn. For example, the following expression invites syntax errors due to misplaced parentheses:

tokenize((normalize-unicode(upper-case($string))),"\s+")

In the following reformulation, it is easier to see that the parentheses are balanced:

$string -> upper-case() -> normalize-unicode() -> tokenize("\s+")

Assuming that $string is a single string, the above example could equally be written:

$string => upper-case() => normalize-unicode() => tokenize("\s+")

The difference between the two operators is seen when the left-hand operand evaluates to a sequence:

"The cat sat on the mat" => tokenize() -> concat(".") -> upper-case() => string-join(" ")

which returns "THE. CAT. SAT. ON. THE. MAT.". The first arrow could be written either as => or -> because the operand is a singleton; the next two arrows have to be -> because the function is applied to each item in the tokenized sequence individually; the final arrow must be => because the string-join function applies to the sequence as a whole.

Note:

It may be useful to think of this as a map/reduce pipeline. The functions introduced by -> are mapping operations; the function introduced by => is a reduce operation.

The following example introduces an enclosed expression to the pipeline:

(1 to 5) -> xs:double() -> math:sqrt() -> {.+1} => sum()

This is equivalent to sum((1 to 5) ! (math:sqrt(xs:double(.))+1)).

Note:

The ArgumentList may include PlaceHolders, though this is not especially useful. For example, the expression "$" -> concat(?) is equivalent to concat("$", ?): its value is a function that prepends a supplied string with a "$" symbol.

Note:

The ArgumentList may include keyword arguments if the function is identified statically (that is, by name). For example, the following is valid: $xml => xml-to-json(indent:=true()) => parse-json(escape:=false()).

5 Conformance

This section defines the conformance criteria for an XPath 4.0 processor. In this section, the following terms are used to indicate the requirement levels defined in [RFC2119]. [Definition: MUST means that the item is an absolute requirement of the specification.] [Definition: MUST NOT means that the item is an absolute prohibition of the specification.] [Definition: MAY means that an item is truly optional.]

XPath is intended primarily as a component that can be used by other specifications. Therefore, XPath relies on specifications that use it (such as [XPointer] and [XSL Transformations (XSLT) Version 3.0]) to specify conformance criteria for XPath in their respective environments. Specifications that set conformance criteria for their use of XPath MUST NOT change the syntactic or semantic definitions of XPath as given in this specification, except by subsetting and/or compatible extensions.

If a language is described as an extension of XPath, then every expression that conforms to the XPath grammar MUST behave as described in this specification.

5.1 Static Typing Feature

[Definition: The Static Typing Feature is an optional feature of XPath that provides support for static semantics, and requires implementations to detect and report type errors during the static analysis phase.] Specifications that use XPath MAY specify conformance criteria for use of the Static Typing Feature.

If an implementation does not support the Static Typing Feature, but can nevertheless determine during the static analysis phase that an XPath expression, if evaluated, would necessarily raise a dynamic error or that an expression, if evaluated, would necessarily raise a type error, the implementation MAY raise that error during the static analysis phase. The choice of whether to raise such an error at analysis time is implementation dependent.

A XPath 4.0 Grammar

A.1 EBNF

The grammar of XPath 4.0 uses the same simple Extended Backus-Naur Form (EBNF) notation as [XML 1.0] with the following minor differences.

  • All named symbols have a name that begins with an uppercase letter.

  • It adds a notation for referring to productions in external specifications.

  • Comments or extra-grammatical constraints on grammar productions are between '/*' and '*/' symbols.

    • A 'xgc:' prefix is an extra-grammatical constraint, the details of which are explained in A.1.2 Extra-grammatical Constraints

    • A 'ws:' prefix explains the whitespace rules for the production, the details of which are explained in A.2.4 Whitespace Rules

    • A 'gn:' prefix means a 'Grammar Note', and is meant as a clarification for parsing rules, and is explained in A.1.3 Grammar Notes. These notes are not normative.

The terminal symbols for this grammar include the quoted strings used in the production rules below, and the terminal symbols defined in section A.2.1 Terminal Symbols.

The EBNF notation is described in more detail in A.1.1 Notation.

[1]    XPath    ::=    Expr
[2]    FunctionSignature    ::=    "(" ParamList? ")" TypeDeclaration?
[3]    ParamList    ::=    Param ("," Param)*
[4]    Param    ::=    "$" EQName TypeDeclaration?
[5]    FunctionBody    ::=    EnclosedExpr
[6]    EnclosedExpr    ::=    "{" Expr? "}"
[7]    Expr    ::=    ExprSingle ("," ExprSingle)*
[8]    ExprSingle    ::=    WithExpr
| ForExpr
| LetExpr
| QuantifiedExpr
| IfExpr
| TernaryConditionalExpr
[9]    WithExpr    ::=    "with" NamespaceDeclaration ("," NamespaceDeclaration)* EnclosedExpr
[10]    NamespaceDeclaration    ::=    QName "=" StringLiteral
[11]    TernaryConditionalExpr    ::=    OrExpr ("??" TernaryConditionalExpr "!!" TernaryConditionalExpr)?
[12]    ForExpr    ::=    SimpleForClause "return" ExprSingle
[13]    SimpleForClause    ::=    "for" "member"? SimpleForBinding ("," SimpleForBinding)*
[14]    SimpleForBinding    ::=    "$" VarName "in" ExprSingle
[15]    LetExpr    ::=    SimpleLetClause "return" ExprSingle
[16]    SimpleLetClause    ::=    "let" SimpleLetBinding ("," SimpleLetBinding)*
[17]    SimpleLetBinding    ::=    "$" VarName ":=" ExprSingle
[18]    QuantifiedExpr    ::=    ("some" | "every") QuantifierBinding ("," QuantifierBinding)* "satisfies" ExprSingle
[19]    QuantifierBinding    ::=    "$" VarName "in" ExprSingle
[20]    IfExpr    ::=    "if" "(" Expr ")" "then" ExprSingle "else" ExprSingle
[21]    OrExpr    ::=    AndExpr ( "or" AndExpr )*
[22]    AndExpr    ::=    ComparisonExpr ( "and" ComparisonExpr )*
[23]    ComparisonExpr    ::=    StringConcatExpr ( (ValueComp
| GeneralComp
| NodeComp) StringConcatExpr )?
[24]    StringConcatExpr    ::=    RangeExpr ( "||" RangeExpr )*
[25]    RangeExpr    ::=    AdditiveExpr ( "to" AdditiveExpr )?
[26]    AdditiveExpr    ::=    MultiplicativeExpr ( ("+" | "-") MultiplicativeExpr )*
[27]    MultiplicativeExpr    ::=    OtherwiseExpr ( ("*" | "div" | "idiv" | "mod") OtherwiseExpr )*
[28]    OtherwiseExpr    ::=    UnionExpr ( "otherwise" UnionExpr )*
[29]    UnionExpr    ::=    IntersectExceptExpr ( ("union" | "|") IntersectExceptExpr )*
[30]    IntersectExceptExpr    ::=    InstanceofExpr ( ("intersect" | "except") InstanceofExpr )*
[31]    InstanceofExpr    ::=    TreatExpr ( "instance" "of" SequenceType )?
[32]    TreatExpr    ::=    CastableExpr ( "treat" "as" SequenceType )?
[33]    CastableExpr    ::=    CastExpr ( "castable" "as" SingleType )?
[34]    CastExpr    ::=    ArrowExpr ( "cast" "as" SingleType )?
[35]    ArrowExpr    ::=    UnaryExpr ( (FatArrowTarget | ThinArrowTarget) )*
[36]    UnaryExpr    ::=    ("-" | "+")* ValueExpr
[37]    ValueExpr    ::=    SimpleMapExpr
[38]    FatArrowTarget    ::=    "=>" ((ArrowStaticFunction ArgumentList) | (ArrowDynamicFunction PositionalArgumentList))
[39]    ThinArrowTarget    ::=    "->" ((ArrowStaticFunction ArgumentList) | (ArrowDynamicFunction PositionalArgumentList) | EnclosedExpr)
[40]    GeneralComp    ::=    "=" | "!=" | "<" | "<=" | ">" | ">="
[41]    ValueComp    ::=    "eq" | "ne" | "lt" | "le" | "gt" | "ge"
[42]    NodeComp    ::=    "is" | "<<" | ">>"
[43]    SimpleMapExpr    ::=    PathExpr ("!" PathExpr)*
[44]    PathExpr    ::=    ("/" RelativePathExpr?)
| ("//" RelativePathExpr)
| RelativePathExpr
/* xgc: leading-lone-slash */
[45]    RelativePathExpr    ::=    StepExpr (("/" | "//") StepExpr)*
[46]    StepExpr    ::=    PostfixExpr | AxisStep
[47]    AxisStep    ::=    (ReverseStep | ForwardStep) PredicateList
[48]    ForwardStep    ::=    (ForwardAxis NodeTest) | AbbrevForwardStep
[49]    ForwardAxis    ::=    ("child" "::")
| ("descendant" "::")
| ("attribute" "::")
| ("self" "::")
| ("descendant-or-self" "::")
| ("following-sibling" "::")
| ("following" "::")
| ("namespace" "::")
[50]    AbbrevForwardStep    ::=    "@"? NodeTest
[51]    ReverseStep    ::=    (ReverseAxis NodeTest) | AbbrevReverseStep
[52]    ReverseAxis    ::=    ("parent" "::")
| ("ancestor" "::")
| ("preceding-sibling" "::")
| ("preceding" "::")
| ("ancestor-or-self" "::")
[53]    AbbrevReverseStep    ::=    ".."
[54]    NodeTest    ::=    KindTest | NameTest
[55]    NameTest    ::=    EQName | Wildcard
[56]    Wildcard    ::=    "*"
| (NCName ":*")
| ("*:" NCName)
| (BracedURILiteral "*")
/* ws: explicit */
[57]    PostfixExpr    ::=    PrimaryExpr (Predicate | PositionalArgumentList | Lookup)*
[58]    ArgumentList    ::=    "(" ((PositionalArguments ("," KeywordArguments)?) | KeywordArguments)? ")"
[59]    PositionalArgumentList    ::=    "(" PositionalArguments? ")"
[60]    PositionalArguments    ::=    Argument ("," Argument)*
[61]    KeywordArguments    ::=    KeywordArgument ("," KeywordArgument)*
[62]    KeywordArgument    ::=    NCName ":=" ExprSingle
[63]    PredicateList    ::=    Predicate*
[64]    Predicate    ::=    "[" Expr "]"
[65]    Lookup    ::=    "?" KeySpecifier
[66]    KeySpecifier    ::=    NCName | IntegerLiteral | StringLiteral | VarRef | ParenthesizedExpr | "*"
[67]    ArrowStaticFunction    ::=    EQName
[68]    ArrowDynamicFunction    ::=    VarRef | ParenthesizedExpr
[69]    PrimaryExpr    ::=    Literal
| VarRef
| ParenthesizedExpr
| ContextItemExpr
| FunctionCall
| FunctionItemExpr
| MapConstructor
| ArrayConstructor
| UnaryLookup
[70]    Literal    ::=    NumericLiteral | StringLiteral
[71]    NumericLiteral    ::=    IntegerLiteral | DecimalLiteral | DoubleLiteral
[72]    VarRef    ::=    "$" VarName
[73]    VarName    ::=    EQName
[74]    ParenthesizedExpr    ::=    "(" Expr? ")"
[75]    ContextItemExpr    ::=    "."
[76]    FunctionCall    ::=    EQName ArgumentList /* xgc: reserved-function-names */
/* gn: parens */
[77]    Argument    ::=    ExprSingle | ArgumentPlaceholder
[78]    ArgumentPlaceholder    ::=    "?"
[79]    LocalNamespaceDecls    ::=    LocalNamespaceDecl*
[80]    LocalNamespaceDecl    ::=    "namespace" NCName "{" URILiteral "}"
[81]    FunctionItemExpr    ::=    NamedFunctionRef | InlineFunctionExpr
[82]    NamedFunctionRef    ::=    EQName "#" IntegerLiteral /* xgc: reserved-function-names */
[83]    InlineFunctionExpr    ::=    (("function" FunctionSignature) | ("->" FunctionSignature?)) FunctionBody
[84]    MapConstructor    ::=    "map" "{" (MapConstructorEntry ("," MapConstructorEntry)*)? "}"
[85]    MapConstructorEntry    ::=    MapKeyExpr ":" MapValueExpr
[86]    MapKeyExpr    ::=    ExprSingle
[87]    MapValueExpr    ::=    ExprSingle
[88]    ArrayConstructor    ::=    SquareArrayConstructor | CurlyArrayConstructor
[89]    SquareArrayConstructor    ::=    "[" (ExprSingle ("," ExprSingle)*)? "]"
[90]    CurlyArrayConstructor    ::=    "array" EnclosedExpr
[91]    UnaryLookup    ::=    "?" KeySpecifier
[92]    SingleType    ::=    (SimpleTypeName | LocalUnionType) "?"?
[93]    TypeDeclaration    ::=    "as" SequenceType
[94]    SequenceType    ::=    ("empty-sequence" "(" ")")
| (ItemType OccurrenceIndicator?)
[95]    OccurrenceIndicator    ::=    "?" | "*" | "+" /* xgc: occurrence-indicators */
[96]    ItemType    ::=    AnyItemTest | TypeName | KindTest | FunctionTest | MapTest | ArrayTest | AtomicOrUnionType | RecordTest | LocalUnionType | EnumerationType | ParenthesizedItemType
[97]    AnyItemTest    ::=    "item" "(" ")"
[98]    AtomicOrUnionType    ::=    EQName
[99]    KindTest    ::=    DocumentTest
| ElementTest
| AttributeTest
| SchemaElementTest
| SchemaAttributeTest
| PITest
| CommentTest
| TextTest
| NamespaceNodeTest
| AnyKindTest
[100]    AnyKindTest    ::=    "node" "(" ")"
[101]    DocumentTest    ::=    "document-node" "(" (ElementTest | SchemaElementTest)? ")"
[102]    TextTest    ::=    "text" "(" ")"
[103]    CommentTest    ::=    "comment" "(" ")"
[104]    NamespaceNodeTest    ::=    "namespace-node" "(" ")"
[105]    PITest    ::=    "processing-instruction" "(" (NCName | StringLiteral)? ")"
[106]    AttributeTest    ::=    "attribute" "(" (NameTest ("," TypeName)?)? ")"
[107]    SchemaAttributeTest    ::=    "schema-attribute" "(" AttributeDeclaration ")"
[108]    AttributeDeclaration    ::=    AttributeName
[109]    ElementTest    ::=    "element" "(" (NameTest ("," TypeName "?"?)?)? ")"
[110]    SchemaElementTest    ::=    "schema-element" "(" ElementDeclaration ")"
[111]    ElementDeclaration    ::=    ElementName
[112]    AttributeName    ::=    EQName
[113]    ElementName    ::=    EQName
[114]    SimpleTypeName    ::=    TypeName | LocalUnionType
[115]    TypeName    ::=    EQName
[116]    FunctionTest    ::=    AnyFunctionTest
| TypedFunctionTest
[117]    AnyFunctionTest    ::=    "function" "(" "*" ")"
[118]    TypedFunctionTest    ::=    "function" "(" (SequenceType ("," SequenceType)*)? ")" "as" SequenceType
[119]    MapTest    ::=    AnyMapTest | TypedMapTest
[120]    AnyMapTest    ::=    "map" "(" "*" ")"
[121]    TypedMapTest    ::=    "map" "(" ItemType "," SequenceType ")"
[122]    RecordTest    ::=    "record" "(" FieldDeclaration ("," FieldDeclaration)* ExtensibleFlag? ")"
[123]    FieldDeclaration    ::=    FieldName "?"? ("as" (SequenceType | SelfReference))?
[124]    FieldName    ::=    NCName | StringLiteral
[125]    SelfReference    ::=    ".." OccurrenceIndicator?
[126]    ExtensibleFlag    ::=    "," "*"
[127]    LocalUnionType    ::=    "union" "(" ItemType ("," ItemType)* ")"
[128]    EnumerationType    ::=    "enum" "(" StringLiteral ("," StringLiteral)* ")"
[129]    ArrayTest    ::=    AnyArrayTest | TypedArrayTest
[130]    AnyArrayTest    ::=    "array" "(" "*" ")"
[131]    TypedArrayTest    ::=    "array" "(" SequenceType ")"
[132]    ParenthesizedItemType    ::=    "(" ItemType ")"
[133]    URILiteral    ::=    StringLiteral
[134]    EQName    ::=    QName | URIQualifiedName

A.1.1 Notation

[Definition: Each rule in the grammar defines one symbol, using the following format:

symbol ::= expression

]

[Definition: A terminal is a symbol or string or pattern that can appear in the right-hand side of a rule, but never appears on the left-hand side in the main grammar, although it may appear on the left-hand side of a rule in the grammar for terminals.] The following constructs are used to match strings of one or more characters in a terminal:

[a-zA-Z]

matches any Char with a value in the range(s) indicated (inclusive).

[abc]

matches any Char with a value among the characters enumerated.

[^abc]

matches any Char with a value not among the characters given.

"string"

matches the sequence of characters that appear inside the double quotes.

'string'

matches the sequence of characters that appear inside the single quotes.

[http://www.w3.org/TR/REC-example/#NT-Example]

matches any string matched by the production defined in the external specification as per the provided reference.

Patterns (including the above constructs) can be combined with grammatical operators to form more complex patterns, matching more complex sets of character strings. In the examples that follow, A and B represent (sub-)patterns.

(A)

A is treated as a unit and may be combined as described in this list.

A?

matches A or nothing; optional A.

A B

matches A followed by B. This operator has higher precedence than alternation; thus A B | C D is identical to (A B) | (C D).

A | B

matches A or B but not both.

A - B

matches any string that matches A but does not match B.

A+

matches one or more occurrences of A. Concatenation has higher precedence than alternation; thus A+ | B+ is identical to (A+) | (B+).

A*

matches zero or more occurrences of A. Concatenation has higher precedence than alternation; thus A* | B* is identical to (A*) | (B*)

A.1.2 Extra-grammatical Constraints

This section contains constraints on the EBNF productions, which are required to parse syntactically valid sentences. The notes below are referenced from the right side of the production, with the notation: /* xgc: <id> */.

Constraint: leading-lone-slash

A single slash may appear either as a complete path expression or as the first part of a path expression in which it is followed by a RelativePathExpr. In some cases, the next token after the slash is insufficient to allow a parser to distinguish these two possibilities: the * token and keywords like union could be either an operator or a NameTest . For example, without lookahead the first part of the expression / * 5 is easily taken to be a complete expression, / *, which has a very different interpretation (the child nodes of /).

If the token immediately following a slash can form the start of a RelativePathExpr, then the slash must be the beginning of a PathExpr, not the entirety of it.

A single slash may be used as the left-hand argument of an operator by parenthesizing it: (/) * 5. The expression 5 * /, on the other hand, is syntactically valid without parentheses.

Constraint: xml-version

The version of XML and XML Names (e.g. [XML 1.0] and [XML Names], or [XML 1.1] and [XML Names 1.1]) is implementation-defined. It is recommended that the latest applicable version be used (even if it is published later than this specification). The EBNF in this specification links only to the 1.0 versions. Note also that these external productions follow the whitespace rules of their respective specifications, and not the rules of this specification, in particular A.2.4.1 Default Whitespace Handling. Thus prefix : localname is not a syntactically valid lexical QName for purposes of this specification, just as it is not permitted in a XML document. Also, comments are not permissible on either side of the colon. Also extra-grammatical constraints such as well-formedness constraints must be taken into account.

Constraint: reserved-function-names

Unprefixed function names spelled the same way as language keywords could make the language impossible to parse. For instance, element(foo) could be taken either as a FunctionCall or as an ElementTest. Therefore, an unprefixed function name must not be any of the names in A.3 Reserved Function Names.

A function named "if" can be called by binding its namespace to a prefix and using the prefixed form: "library:if(foo)" instead of "if(foo)".

Constraint: occurrence-indicators

As written, the grammar in A XPath 4.0 Grammar is ambiguous for some forms using the '+' and '*' occurrence indicators. The ambiguity is resolved as follows: these operators are tightly bound to the SequenceType expression, and have higher precedence than other uses of these symbols. Any occurrence of '+' and '*', as well as '?', following a sequence type is assumed to be an occurrence indicator, which binds to the last ItemType in the SequenceType.

Thus, 4 treat as item() + - 5 must be interpreted as (4 treat as item()+) - 5, taking the '+' as an OccurrenceIndicator and the '-' as a subtraction operator. To force the interpretation of "+" as an addition operator (and the corresponding interpretation of the "-" as a unary minus), parentheses may be used: the form (4 treat as item()) + -5 surrounds the SequenceType expression with parentheses and leads to the desired interpretation.

function () as xs:string * is interpreted as function () as (xs:string *), not as (function () as xs:string) *. Parentheses can be used as shown to force the latter interpretation.

This rule has as a consequence that certain forms which would otherwise be syntactically valid and unambiguous are not recognized: in "4 treat as item() + 5", the "+" is taken as an OccurrenceIndicator, and not as an operator, which means this is not a syntactically valid expression.

A.1.3 Grammar Notes

This section contains general notes on the EBNF productions, which may be helpful in understanding how to interpret and implement the EBNF. These notes are not normative. The notes below are referenced from the right side of the production, with the notation: /* gn: <id> */.

Note:

grammar-note: parens

Look-ahead is required to distinguish FunctionCall from a EQName or keyword followed by a Comment. For example: address (: this may be empty :) may be mistaken for a call to a function named "address" unless this lookahead is employed. Another example is for (: whom the bell :) $tolls in 3 return $tolls, where the keyword "for" must not be mistaken for a function name.

grammar-note: comments

Comments are allowed everywhere that ignorable whitespace is allowed, and the Comment symbol does not explicitly appear on the right-hand side of the grammar (except in its own production). See A.2.4.1 Default Whitespace Handling.

A comment can contain nested comments, as long as all "(:" and ":)" patterns are balanced, no matter where they occur within the outer comment.

Note:

Lexical analysis may typically handle nested comments by incrementing a counter for each "(:" pattern, and decrementing the counter for each ":)" pattern. The comment does not terminate until the counter is back to zero.

Some illustrative examples:

  • (: commenting out a (: comment :) may be confusing, but often helpful :) is a syntactically valid Comment, since balanced nesting of comments is allowed.

  • "this is just a string :)" is a syntactically valid expression. However, (: "this is just a string :)" :) will cause a syntax error. Likewise, "this is another string (:" is a syntactically valid expression, but (: "this is another string (:" :) will cause a syntax error. It is a limitation of nested comments that literal content can cause unbalanced nesting of comments.

  • for (: set up loop :) $i in $x return $i is syntactically valid, ignoring the comment.

  • 5 instance (: strange place for a comment :) of xs:integer is also syntactically valid.

A.2 Lexical structure

The terminal symbols assumed by the grammar above are described in this section.

Quoted strings appearing in production rules are terminal symbols.

Other terminal symbols are defined in A.2.1 Terminal Symbols.

Some productions are defined by reference to the XML and XML Names specifications (e.g. [XML 1.0] and [XML Names], or [XML 1.1] and [XML Names 1.1] . A host language may choose which version of these specifications is used; it is recommended that the latest applicable version be used (even if it is published later than this specification).

A host language may choose whether the lexical rules of [XML 1.0] and [XML Names] are followed, or alternatively, the lexical rules of [XML 1.1] and [XML Names 1.1] are followed.

When tokenizing, the longest possible match that is consistent with the EBNF is used.

All keywords are case sensitive. Keywords are not reserved—that is, any lexical QName may duplicate a keyword except as noted in A.3 Reserved Function Names.

A.2.1 Terminal Symbols

[135]    IntegerLiteral    ::=    Digits
[136]    DecimalLiteral    ::=    ("." Digits) | (Digits "." [0-9]*) /* ws: explicit */
[137]    DoubleLiteral    ::=    (("." Digits) | (Digits ("." [0-9]*)?)) [eE] [+-]? Digits /* ws: explicit */
[138]    StringLiteral    ::=    ('"' (EscapeQuot | [^"])* '"') | ("'" (EscapeApos | [^'])* "'") /* ws: explicit */
[139]    URIQualifiedName    ::=    BracedURILiteral NCName /* ws: explicit */
[140]    BracedURILiteral    ::=    "Q" "{" [^{}]* "}" /* ws: explicit */
[141]    EscapeQuot    ::=    '""'
[142]    EscapeApos    ::=    "''"
[143]    Comment    ::=    "(:" (CommentContents | Comment)* ":)" /* ws: explicit */
/* gn: comments */
[144]    QName    ::=    [http://www.w3.org/TR/REC-xml-names/#NT-QName]Names /* xgc: xml-version */
[145]    NCName    ::=    [http://www.w3.org/TR/REC-xml-names/#NT-NCName]Names /* xgc: xml-version */
[146]    Char    ::=    [http://www.w3.org/TR/REC-xml#NT-Char]XML /* xgc: xml-version