Please check the errata for any errors or issues reported since publication.
See also translations.
This document is also available in these nonnormative formats: Specification in XML format using HTML5 vocabulary, XML function catalog, and HTML with change markings relative to version 3.0.
Copyright © 2000 W3C^{®} (MIT, ERCIM, Keio, Beihang). W3C liability, trademark and document use rules apply.
This document defines constructor functions, operators, and functions on the datatypes defined in [XML Schema Part 2: Datatypes Second Edition] and the datatypes defined in [XQuery and XPath Data Model (XDM) 3.1]. It also defines functions and operators on nodes and node sequences as defined in the [XQuery and XPath Data Model (XDM) 3.1]. These functions and operators are defined for use in [XML Path Language (XPath) 3.1] and [XQuery 3.1: An XML Query Language] and [XSL Transformations (XSLT) Version 3.0] and other related XML standards. The signatures and summaries of functions defined in this document are available at: http://www.w3.org/2005/xpathfunctions/.
This document is a proposal by the editor, with no official standing, to create a new version 4.0 of the function library, with additional convenience functions.
A summary of changes since version 3.1 is provided at F Changes since version 3.1.
This is a first proposal by the editor, with no official standing whatsoever. Comments are invited.
The purpose of this document is to propose functions and operators to be included in XPath 4.0, XQuery 4.0, and XSLT 4.0. Note that this proposal has no official standing at the time of publication. The exact syntax used to call these functions and operators is specified in [XML Path Language (XPath) 3.1], [XQuery 3.1: An XML Query Language] and [XSL Transformations (XSLT) Version 3.0].
This document defines three classes of functions:
General purpose functions, available for direct use in userwritten queries, stylesheets, and XPath expressions, whose arguments and results are values defined by the [XQuery and XPath Data Model (XDM) 3.1].
Constructor functions, used for creating instances of a datatype from values of (in general) a different datatype. These functions are also available for general use; they are named after the datatype that they return, and they always take a single argument.
Functions that specify the semantics of operators defined in [XML Path Language (XPath) 3.1] and [XQuery 3.1: An XML Query Language]. These exist for specification purposes only, and are not intended for direct calling from userwritten code.
[XML Schema Part 2: Datatypes Second Edition] defines a number of primitive and derived datatypes, collectively known as builtin datatypes. This document defines functions and operations on these datatypes as well as the other types (for example, nodes and sequences of nodes) defined in Section 2.7 Schema Information ^{DM31} of the [XQuery and XPath Data Model (XDM) 3.1]. These functions and operations are available for use in [XML Path Language (XPath) 3.1], [XQuery 3.1: An XML Query Language] and any other host language that chooses to reference them. In particular, they may be referenced in future versions of XSLT and related XML standards.
[Schema 1.1 Part 2] adds to the datatypes defined
in [XML Schema Part 2: Datatypes Second Edition]. It introduces a new derived type xs:dateTimeStamp
, and it
incorporates as builtin types the two types xs:yearMonthDuration
and xs:dayTimeDuration
which were previously XDM additions to the type system. In addition, XSD 1.1 clarifies
and updates many
aspects of the definitions of the existing datatypes: for example, it extends the
value space of
xs:double
to allow both positive and negative zero, and extends the lexical space to allow
+INF
;
it modifies the value space of xs:Name
to permit additional Unicode characters; it allows year zero and disallows leap seconds
in xs:dateTime
values; and it allows any character string to appear as the value of an xs:anyURI
item.
Implementations of this specification may support either XSD 1.0 or XSD 1.1 or both.
References to specific sections of some of the above documents are indicated by crossdocument links in this document. Each such link consists of a pointer to a specific section followed a superscript specifying the linked document. The superscripts have the following meanings: 'XQ' [XQuery 3.1: An XML Query Language], 'XT' [XSL Transformations (XSLT) Version 3.0], 'XP' [XML Path Language (XPath) 3.1], and 'DM' [XQuery and XPath Data Model (XDM) 3.1].
This recommendation contains a set of function specifications. It defines conformance at the level of individual functions. An implementation of a function conforms to a function specification in this recommendation if all the following conditions are satisfied:
For all combinations of valid inputs to the function (both explicit arguments and implicit context dependencies), the result of the function meets the mandatory requirements of this specification.
For all invalid inputs to the function, the implementation signals (in some way appropriate to the calling environment) that a dynamic error has occurred.
For a sequence of calls within the same ·execution scope·, the requirements of this recommendation regarding the ·determinism· of results are satisfied (see 1.7.4 Properties of functions).
Other recommendations ("host languages") that reference this document may dictate:
Subsets or supersets of this set of functions to be available in particular environments;
Mechanisms for invoking functions, supplying arguments, initializing the static and dynamic context, receiving results, and handling errors;
A concrete realization of concepts such as ·execution scope·;
Which versions of other specifications referenced herein (for example, XML, XSD, or Unicode) are to be used.
Any behavior that is discretionary (implementationdefined or implementationdependent) in this specification may be constrained by a host language.
Note:
Adding such constraints in a host language, however, is discouraged because it makes it difficult to reuse implementations of the function library across host languages.
This specification allows flexibility in the choice of versions of specifications on which it depends:
It is ·implementationdefined· which version of Unicode is supported, but it is recommended that the most recent version of Unicode be used.
It is ·implementationdefined· whether the type system is based on XML Schema 1.0 or XML Schema 1.1.
It is ·implementationdefined· whether definitions that rely on XML (for example, the set of valid XML characters) should use the definitions in XML 1.0 or XML 1.1.
Note:
The XML Schema 1.1 recommendation
introduces one new concrete datatype: xs:dateTimeStamp
; it also incorporates
the types xs:dayTimeDuration
, xs:yearMonthDuration
,
and xs:anyAtomicType
which were previously defined in earlier versions of [XQuery and XPath Data Model (XDM) 3.1].
Furthermore, XSD 1.1
includes the option of supporting revised definitions of types such as xs:NCName
based on the rules in XML 1.1 rather than 1.0.
In this document, text labeled as an example or as a Note is provided for explanatory purposes and is not normative.
The functions and operators defined in this document are contained in one of
several namespaces (see [Namespaces in XML]) and referenced using an
xs:QName
.
This document uses conventional prefixes to refer to these namespaces. Userwritten
applications can choose a different prefix to refer to the namespace, so long as it
is
bound to the correct URI. The host language may also define a default namespace for
function calls, in which case function names in that namespace need not be prefixed
at all. In many cases the default namespace will be
http://www.w3.org/2005/xpathfunctions
, allowing a call on the fn:name
function (for example) to be written as name()
rather than fn:name()
;
in this document, however, all example function calls are explicitly prefixed.
The URIs of the namespaces and the conventional prefixes associated with them are:
http://www.w3.org/2001/XMLSchema
for constructors —
associated with xs
.
The section 18 Constructor functions defines
constructor functions for the builtin datatypes defined
in [XML Schema Part 2: Datatypes Second Edition] and in Section
2.7 Schema Information
^{DM31}
of [XQuery and XPath Data Model (XDM) 3.1]. These datatypes and the corresponding constructor functions
are in the XML Schema namespace, http://www.w3.org/2001/XMLSchema
,
and are named in this document using the xs
prefix.
http://www.w3.org/2005/xpathfunctions
for functions — associated with fn
.
The namespace
prefix used in this document for most functions that are available to users is
fn
.
http://www.w3.org/2005/xpathfunctions/math
for functions — associated with math
.
This namespace is used for some mathematical functions. The namespace
prefix used in this document for these functions is math
.
These functions are available to users in exactly the same way as those in the
fn
namespace.
http://www.w3.org/2005/xpathfunctions/map
for functions — associated with map
.
This namespace is used for some functions that manipulate maps (see
17.1 Functions that Operate on Maps). The namespace
prefix used in this document for these functions is map
.
These functions are available to users in exactly the same way as those in the
fn
namespace.
http://www.w3.org/2005/xpathfunctions/array
for functions — associated with array
.
This namespace is used for some functions that manipulate maps (see
17.3 Functions that Operate on Arrays). The namespace
prefix used in this document for these functions is array
.
These functions are available to users in exactly the same way as those in the
fn
namespace.
http://www.w3.org/2005/xqterrors
— associated with
err
.
There are no functions in this namespace; it is used for error codes.
This document uses the prefix err
to represent the namespace URI
http://www.w3.org/2005/xqterrors
, which is the namespace for all XPath
and XQuery error codes and messages. This namespace prefix is not predeclared and
its use in this document is not normative.
http://www.w3.org/2010/xsltxqueryserialization
— associated with
output
.
There are no functions in this namespace: it is used for serialization parameters, as described in [XSLT and XQuery Serialization 3.1]
Functions defined with the op
prefix are described here to
underpin the definitions of the operators in [XML Path Language (XPath) 3.1], [XQuery 3.1: An XML Query Language]
and [XSL Transformations (XSLT) Version 3.0]. These functions are not available
directly to users, and there is no requirement that implementations should
actually provide these functions. For this reason, no namespace is associated
with the op
prefix. For example, multiplication is generally
associated with the *
operator, but it is described as a function
in this document:
op:numericmultiply
($arg1
as
xs:numeric
, $arg2
as
xs:numeric
) as
xs:numeric
Note:
The above namespace URIs are not expected to change from one version of this document to another. The contents of these namespaces may be extended to allow additional functions (and errors, and serialization parameters) to be defined.
A function is uniquely defined by its name and arity (number of arguments); it is
therefore
not possible to have two different functions that have the same name and arity, but
different
types in their signature. That is, function overloading in this sense of the term
is not permitted.
Consequently, functions such as fn:string
which accept arguments of many different
types have a signature that defines a very general argument type, in this case item()?
which accepts any single item; supplying an inappropriate item (such as a function
item) causes
a dynamic error.
Some functions on numeric types include the type xs:numeric
in their signature
as an argument or result type. In this version of the specification, xs:numeric
has been redefined as a builtin union type representing the union of
xs:decimal
, xs:float
, xs:double
(and thus automatically
accepting types derived from these, including xs:integer
).
Operators such as "+" may be overloaded: they map to different underlying functions depending on the dynamic types of the supplied operands.
It is possible for two functions to have the same name provided they have different arity (number of arguments). For the functions defined in this specification, where two functions have the same name and different arity, they also have closely related behavior, so they are defined in the same section of this document.
Each function (or group of functions having the same name) is defined in this specification using a standard proforma.
The function name is a QName
as defined in [XML Schema Part 2: Datatypes Second Edition]
and must adhere to its syntactic conventions. Following the precedent set by [XML Path Language (XPath) Version 1.0],
function names are generally composed of English words separated by hyphens ("").
Abbreviations are
used only where there is a strong precedent in other programming languages (as with
math:sin
and
math:cos
for sine and cosine). If a
function name contains a [XML Schema Part 2: Datatypes Second Edition] datatype name, it may have
intercapitalized spelling and is used in the function name as such. An example is
fn:timezonefromdateTime
.
The first section in the proforma is a short summary of what the function does. This is intended to be informative rather than normative.
Each function is then defined by specifying its signature, which defines the types of the parameters and of the result value.
Each function's signature is presented in a form like this:
fn:functionname
($parametername
as
parametertype
, ...) as
returntype
In this notation, functionname, in boldface, is the name of the
function whose signature is being specified. If the function takes no
parameters, then the name is followed by an empty parameter list:
"()
"; otherwise, the name is followed by a parenthesized list of
parameter declarations, in which each declaration specifies the static type of the
parameter, in italics, and a descriptive, but nonnormative, name. If there are
two or more parameter declarations, they are separated by a comma. The
returntype
, also in italics, specifies the static type of the value returned by the
function. The dynamic type of the value returned by the function is the same as its
static
type or derived from the static type. All parameter types and return types are
specified using the SequenceType notation defined in Section
2.5.4 SequenceType Syntax
^{XP31}.
One function, fn:concat
, has a variable number of arguments (two or more).
More strictly, there is an infinite set of functions having the name fn:concat
, with arity
ranging from 2 to infinity. For this special case, a single function signature is
given, with an ellipsis
indicating an indefinite number of arguments.
The next section in the proforma defines the semantics of the function as a set of rules. The order in which the rules appear is significant; they are to be applied in the order in which they are written. Error conditions, however, are generally listed in a separate section that follows the main rules, and take precedence over nonerror rules except where otherwise stated. The principles outlined in Section 2.3.4 Errors and Optimization ^{XP31} apply by default: to paraphrase, if the result of the function can be determined without evaluating all its arguments, then it is not necessary to evaluate the remaining arguments merely in order to determine whether any error conditions apply.
Where the proforma includes sections headed Notes or Examples, these are nonnormative.
Rules for passing parameters to operators are described in the relevant sections
of [XQuery 3.1: An XML Query Language] and [XML Path Language (XPath) 3.1]. For example, the rules for
passing parameters to arithmetic operators are described in Section
3.5 Arithmetic Expressions
^{XP31}. Specifically, rules for parameters of
type xs:untypedAtomic
and the empty sequence are specified in this section.
As is customary, the parameter type name indicates that the function or operator
accepts arguments of that type, or types derived from it, in that position. This
is called subtype substitution (See Section
2.5.5 SequenceType Matching
^{XP31}). In addition, numeric type instances and
instances of type xs:anyURI
can be promoted to produce an argument
of the required type. (See Section
B.1 Type Promotion
^{XP31}).
Subtype Substitution: A derived type may substitute for
its base type. In particular, xs:integer
may be used
where xs:decimal
is expected.
Numeric Type Promotion: xs:decimal
may be
promoted to xs:float
or xs:double
.
Promotion to xs:double
should be done directly, not via
xs:float
, to avoid loss of precision.
anyURI Type Promotion: A value of
type xs:anyURI
can be promoted to the
type xs:string
.
Some functions accept a single value or the empty sequence as an argument and
some may return a single value or the empty sequence. This is indicated in the
function signature by following the parameter or return type name with a
question mark: "?
", indicating that either a single value or the
empty sequence must appear. See below.
fn:functionname
($parametername
as
parametertype?
) as
returntype?
Note that this function signature is different from a signature in which the
parameter is omitted. See, for example, the two signatures
for fn:string
. In the first signature, the parameter is omitted
and the argument defaults to the context item, referred to as .
.
In the second signature, the argument must be present but may be the empty
sequence, written as ()
.
Some functions accept a sequence of zero or more values as an argument. This is
indicated by following the name of the type of the items in the sequence with
*
. The sequence may contain zero or more items of the named type.
For example, the function below accepts a sequence of xs:double
and
returns a xs:double
or the empty sequence.
fn:median
($arg
as
xs:double*
) as
xs:double?
In XPath 4.0, the arguments in a function call can be supplied by
keyword as an alternative to supplying them positionally. For example the call
resolveuri(@href, staticbaseuri())
can now be written
resolveuri(base: staticbaseuri(), relative: @href)
. The order in which
arguments are supplied can therefore differ from the order in which they are declared.
The specification, however, continues to use phrases such as "the second argument"
as a
convenient shorthand for "the value of the argument that is bound to the second parameter
declaration".
As a matter of convention, a number of functions defined in this document take a parameter whose value is a map, defining options controlling the detail of how the function is evaluated. Maps are a new datatype introduced in XPath 3.1.
For example, the function fn:xmltojson
has an options parameter
allowing specification of whether the output is to be indented. A call might be written:
fn:xmltojson($input, map{'indent':true()})
[Definition] Functions that take an options parameter adopt common conventions on how the options are used. These are referred to as the option parameter conventions. These rules apply only to functions that explicitly refer to them.
Where a function adopts the ·option parameter conventions·, the following rules apply:
The value of the relevant argument must be a map. The entries in the map are
referred to as options: the key of the entry is called the option name, and the
associated value is the option value. Option names defined in this specification
are always strings (single xs:string
values). Option values may
be of any type.
The type of the options parameter in the function signature is always
given as map(*)
.
Although option names are described above as strings, the actual key may be
any value that compares equal to the required string (using the eq
operator
with Unicode codepoint collation; or equivalently, the op:samekey
relation).
For example, instances of xs:untypedAtomic
or xs:anyURI
are equally acceptable.
Note:
This means that the implementation of the function can check for the
presence and value of particular options using the functions map:contains
and/or map:get
.
It is not an error if the options map contains options with names other than those
described in this specification. Implementations may attach an
·implementationdefined· meaning to such entries,
and may define errors that arise if such entries are present with invalid values.
Implementations must ignore such entries unless they have a specific
·implementationdefined· meaning.
Implementations that define additional options in this way should
use values of type xs:QName
as the option names, using an appropriate namespace.
All entries in the options map are optional, and supplying an empty map has the same effect as omitting the relevant argument in the function call, assuming this is permitted.
For each named option, the function specification defines a required type for the option value. The value that is actually supplied in the map is converted to this required type using the function conversion rules^{XP31}. This will result in an error (typically [err:XPTY0004]^{XP} or [err:FORG0001]^{FO}) if conversion of the supplied value to the required type is not possible. A type error also occurs if this conversion delivers a coerced function whose invocation fails with a type error. A dynamic error occurs if the supplied value after conversion is not one of the permitted values for the option in question: the error codes for this error are defined in the specification of each function.
Note:
It is the responsibility of each function implementation to invoke this conversion; it does not happen automatically as a consequence of the function calling rules.
In cases where an option is listvalued, by convention the value may be supplied
either as a sequence or as an array. Accepting a sequence is convenient if the
value is generated programmatically using an XPath expression; while accepting an
array
allows the options to be held in an external file in JSON format, to be read using
a call on the fn:jsondoc
function.
In cases where the value of an option is itself a map, the specification of the particular function must indicate whether or not these rules apply recursively to the contents of that map.
The diagrams in this section show how nodes, functions, primitive simple types, and user defined types fit together into a type system. This type system comprises two distinct subsystems that both include the primitive atomic types. In the diagrams, connecting lines represent relationships between derived types and the types from which they are derived; the arrowheads point toward the type from which they are derived. The dashed line represents relationships not present in this diagram, but that appear in one of the other diagrams. Dotted lines represent additional relationships that follow an evident pattern. The information that appears in each diagram is recapitulated in tabular form.
The xs:IDREFS
, xs:NMTOKENS
,
xs:ENTITIES
types, and xs:numeric
and both the
userdefined list types
and
userdefined union types
are special types in that these types are lists or unions
rather than types derived by extension or restriction.
The first diagram and its corresponding table illustrate the relationship of various item types.
Item types are used to characterize the various types of item that can appear in a sequence (nodes, atomic values, and functions), and they are therefore used in declaring the types of variables or the argument types and result types of functions.
Item types in the data model
form a directed graph, rather than a hierarchy or lattice: in the relationship defined
by the derivedfrom(A, B)
function, some types are derived
from more than one other type. Examples include functions (function(xs:string) as xs:int
is substitutable for function(xs:NCName) as xs:int
and also for
function(xs:string) as xs:decimal
), and union types (A
is substitutable for union(A, B)
and also for union(A, C)
.
In XDM, item types include node types, function types, and builtin atomic types.
The diagram, which shows only hierarchic relationships, is therefore a simplification
of
the full model.
In the table, each type whose name is indented is derived from the type whose name appears nearest above it with one less level of indentation.
item  
xs:anyAtomicType  
node  
attribute  
userdefined attribute types  
comment  
document  
userdefined document types  
element  
userdefined element types  
namespace  
processinginstruction  
text  
function(*)  
array(*)  
map(*) 
The next diagram and table illustrate the schema type subsystem, in which
all types are derived from the distinguished type xs:anyType
.
Schema types include builtin types defined in the XML Schema specification, and userdefined types defined using mechanisms described in the XML Schema specification. Schema types define the permitted contents of nodes. The main categories are complex types, which define the permitted content of elements, and simple types, which can be used to constrain the values of both elements and attributes.
In the table, each type whose name is indented is derived from the type whose name appears nearest above it with one less level of indentation.
xs:anyType  
xs:anySimpleType  
xs:anyAtomicType  
list types  
xs:IDREFS  
xs:NMTOKENS  
xs:ENTITIES  
userdefined list types  
union types  
xs:numeric  
userdefined union types  
complex types  
xs:untyped  
userdefined complex types 
The final diagram and table show all of the atomic types, including the primitive simple types and the builtin types derived from the primitive simple types. This includes all the builtin datatypes defined in [XML Schema Part 2: Datatypes Second Edition].
Atomic types are both item types and schema types, so the root type xs:anyAtomicType
may be found
in both the previous diagrams.
In the table, each type whose name is indented is derived from the type whose name appears nearest above it with one less level of indentation.
xs:untypedAtomic  
xs:dateTime  
xs:dateTimeStamp  
xs:date  
xs:time  
xs:duration  
xs:yearMonthDuration  
xs:dayTimeDuration  
xs:float  
xs:double  
xs:decimal  
xs:integer  
xs:nonPositiveInteger  
xs:negativeInteger  
xs:long  
xs:int  
xs:short  
xs:byte  
xs:nonNegativeInteger  
xs:unsignedLong  
xs:unsignedInt  
xs:unsignedShort  
xs:unsignedByte  
xs:positiveInteger  
xs:gYearMonth  
xs:gYear  
xs:gMonthDay  
xs:gDay  
xs:gMonth  
xs:string  
xs:normalizedString  
xs:token  
xs:language  
xs:NMTOKEN  
xs:Name  
xs:NCName  
xs:ID  
xs:IDREF  
xs:ENTITY  
xs:boolean  
xs:base64Binary  
xs:hexBinary  
xs:anyURI  
xs:QName  
xs:NOTATION 
The terminology used to describe the functions and operators on types defined in [XML Schema Part 2: Datatypes Second Edition] is defined in the body of this specification. The terms defined in this section are used in building those definitions.
Note:
Following in the tradition of [XML Schema Part 2: Datatypes Second Edition], the terms type and datatype are used interchangeably.
This document uses the terms string
, character
, and codepoint
with meanings that are normatively defined in [XQuery and XPath Data Model (XDM) 3.1], and which are paraphrased here
for ease of reference:
[Definition] A character is an instance of the Char^{XML} production of [Extensible Markup Language (XML) 1.0 (Fifth Edition)].
Note:
This definition excludes Unicode characters in the surrogate blocks as well as xFFFE and xFFFF, while including characters with codepoints greater than xFFFF which some programming languages treat as two characters. The valid characters are defined by their codepoints, and include some whose codepoints have not been assigned by the Unicode consortium to any character.
[Definition] A string is a sequence of zero or more
·characters·, or equivalently,
a value in the value space of the xs:string
datatype.
[Definition] A codepoint is an integer assigned to a ·character· by the Unicode consortium, or reserved for future assignment to a character.
Note:
The set of codepoints is thus wider than the set of characters.
This specification spells "codepoint" as one word; the Unicode specification spells it as "code point". Equivalent terms found in other specifications are "character number" or "code position". See [Character Model for the World Wide Web 1.0: Fundamentals]
Because these terms appear so frequently, they are hyperlinked to the definition only when there is a particular desire to draw the reader's attention to the definition; the absence of a hyperlink does not mean that the term is being used in some other sense.
It is ·implementationdefined· which version of [The Unicode Standard] is supported, but it is recommended that the most recent version of Unicode be used.
Unless explicitly stated, the xs:string
values returned by the
functions in this document are not normalized in the sense of [Character Model for the World Wide Web 1.0: Fundamentals].
Notes:
In functions that involve character counting such
as fn:substring
, fn:stringlength
and
fn:translate
, what is counted is the number of XML ·characters·
in the string (or equivalently, the number of Unicode codepoints). Some
implementations may represent a codepoint above xFFFF using two 16bit
values known as a surrogate pair. A surrogate pair counts as one character, not two.
This document uses the phrase "namespace URI" to identify the concept identified in [Namespaces in XML] as "namespace name", and the phrase "local name" to identify the concept identified in [Namespaces in XML] as "local part".
It also uses the term "expandedQName" defined below.
[Definition] An expandedQName
is a value in the value space of the xs:QName
datatype as defined in the XDM data model
(see [XQuery and XPath Data Model (XDM) 3.1]): that is, a triple containing namespace prefix (optional), namespace URI (optional),
and local name. Two expanded QNames are equal if the namespace URIs are the same (or
both absent)
and the local names are the same. The prefix plays no part in the comparison, but
is used only
if the expanded QName needs to be converted back to a string.
The term URI is used as follows:
[Definition] Within this specification, the term URI refers to Universal Resource Identifiers as
defined in [RFC 3986] and extended in [RFC 3987] with a new name IRI. The term URI
Reference, unless otherwise stated, refers to a string in the lexical space of the xs:anyURI
datatype
as defined in [XML Schema Part 2: Datatypes Second Edition].
Note:
Note that this means, in practice, that where this
specification requires a "URI Reference", an IRI as defined in [RFC 3987] will be
accepted, provided that other relevant specifications also permit an 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 also
that the
definition of xs:anyURI
is a wider definition than the definition in [RFC 3987];
for example it does not require nonASCII characters to be escaped.
In this specification:
The auxiliary verb must, when rendered in small capitals, indicates a precondition for conformance.
When the sentence relates to an implementation of a function (for example "All implementations must recognize URIs of the form ...") then an implementation is not conformant unless it behaves as stated.
When the sentence relates to the result of a function (for example "The result must have the same type as
$arg
") then the implementation is not conformant unless it delivers a result as stated.
When the sentence relates to the arguments to a function (for example "The value of
$arg
must
be a valid regular expression") then the implementation is not conformant unless it
enforces the condition by raising a dynamic error
whenever the condition is not satisfied.
The auxiliary verb may, when rendered in small capitals, indicates optional or discretionary behavior. The statement "An implementation may do X" implies that it is implementationdependent whether or not it does X.
The auxiliary verb should, when rendered in small capitals, indicates desirable or recommended behavior. The statement "An implementation should do X" implies that it is desirable to do X, but implementations may choose to do otherwise if this is judged appropriate.
[Definition] Where behavior is described as implementationdefined, variations between processors are permitted, but a conformant implementation must document the choices it has made.
[Definition] Where behavior is described as implementationdependent, variations between processors are permitted, and conformant implementations are not required to document the choices they have made.
Note:
Where this specification states that something is implementationdefined or implementationdependent, it is open to host languages to place further constraints on the behavior.
This section is concerned with the question of whether two calls on a function, with the same arguments, may produce different results.
[Definition] An execution scope is a sequence of
calls to the function library during which certain aspects of the state are required
to remain invariant.
For example, two calls to fn:currentdateTime
within the same execution scope will return the same result.
The execution scope is defined by the host language that invokes the function library.
In XSLT, for example, any two function calls executed during
the same transformation are in the same execution scope (except that static expressions,
such as those used in
usewhen
attributes, are in a separate execution scope).
The following definition explains more precisely what it means for two function calls to return the same result:
[Definition] Two values are defined to be identical if they contain the same number of items and the items are pairwise identical. Two items are identical if and only if one of the following conditions applies:
Both items are atomic values, of precisely the same type, and the values are equal
as defined using the eq
operator,
using the Unicode codepoint collation when comparing strings.
Both items are nodes, and represent the same node.
Both items are maps, both maps have the same number of entries, and for every entry E1 in the first map there is an entry E2 in the second map such that the keys of E1 and E2 are ·the same key·, and the corresponding values V1 and V2 are ·identical·.
Both items are arrays, both arrays have the same number of members, and the members are pairwise ·identical·.
Both items are function items, neither item is a map or array, and all the following conditions apply:
Either both functions have the same name, or both names are absent^{DM31}.
Both functions have the same arity.
Both functions have the same function signature. Two
function signatures are defined to be the same if the declared result types are identical
and the declared
argument types are pairwise identical. Two types S and T are defined to be
identical if and only if subtype(S, T)
and subtype(T, S)
both hold, where the subtype relation is defined in Section
2.5.6.1 The judgement subtype(A, B)
^{XP31}.
Note:
Under this definition, a union type with memberTypes="xs:double xs:decimal"
is identical to a union type with memberTypes="xs:decimal xs:double"
. However, two functions
whose signatures differ in this way will probably be deemed nonidentical under rule
(e) below, because they are likely to
have different effect when invoked with an argument of type xs:untypedAtomic
.
Both functions have the same nonlocal variable bindings (sometimes called the function's closure).
The processor is able to determine that the implementations of the two functions are equivalent, in the sense that for all possible combinations of arguments, the two functions have the same effect.
Note:
There is no function or operator defined in the specification that tests whether two function items are identical. Where the specification requires two function items to be identical, for example in the results of repeated calls of a function whose result is a function, then the processor must ensure that it returns functions that are indistinguishable in their observable effect. Where the specification defines behavior conditional on two function items being identical, the determination of identity is to some degree implementationdependent. There are cases where function items are definitely not identical (for example if they have different name or arity), but positive determination of identity is possible only using implementationdependent techniques, for example when both items contain references to the same piece of code representing the function's implementation.
Some functions produce results that depend not only on their explicit arguments, but also on the static and dynamic context.
[Definition] A function may have the property of being contextdependent: the result of such a function depends on the values of properties in the static and dynamic evaluation context as well as on the actual supplied arguments (if any).
[Definition] A function that is not ·contextdependent· is called contextindependent.
A function that is contextdependent can be used as a named
function reference, can be partially applied, and can be found using fn:functionlookup
.
The principle in such cases is that the static context used for the function evaluation
is taken from the static context of the named function reference, partial function
application, or the call
on fn:functionlookup
; and the dynamic context for the function evaluation is taken from the dynamic
context of the evaluation of the named function reference, partial function application,
or the call
of fn:functionlookup
. In effect, the static and dynamic part of the context thus act
as part of the closure of the function item.
Contextdependent functions fall into a number of categories:
The functions fn:currentdate
, fn:currentdateTime
, fn:currenttime
,
fn:defaultlanguage
, fn:implicittimezone
,
fn:adjustdatetotimezone
, fn:adjustdateTimetotimezone
, and
fn:adjusttimetotimezone
depend on properties of the dynamic context that are
fixed within the ·execution scope·. The same applies to a
number of functions in the op:
namespace that manipulate dates and times and
that make use of the implicit timezone. These functions will return the same
result if called repeatedly during a single ·execution scope·.
A number of functions including fn:baseuri#0
, fn:data#0
,
fn:documenturi#0
, fn:elementwithid#1
, fn:id#1
,
fn:idref#1
, fn:lang#1
, fn:last#0
, fn:localname#0
,
fn:name#0
, fn:namespaceuri#0
, fn:normalizespace#0
,
fn:number#0
, fn:path#0
, fn:position#0
,
fn:root#0
, fn:string#0
, and
fn:stringlength#0
depend on the focus^{XP31}.
These functions will in general return
different results on different calls if the focus is different.
[Definition] A function is focusdependent if its result depends on the focus^{XP31} (that is, the context item, position, or size).
[Definition] A function that is not ·focusdependent· is called focusindependent
The function fn:defaultcollation
and many stringhandling operators and functions depend
on the default collation and the inscope collations, which are both properties
of the static context. If a particular call of one of these functions is
evaluated twice with the same arguments then it will return the same result
each time (because the static context, by definition, does not change at run
time). However, two distinct calls (that is, two calls on the function
appearing in different places in the source code) may produce different results
even if the explicit arguments are the same.
Functions such as fn:staticbaseuri
, fn:doc
, and fn:collection
depend on
other aspects of the static context. As with functions that depend on
collations, a single call will produce the same results on each call if the
explicit arguments are the same, but two calls appearing in different places in
the source code may produce different results.
The fn:functionlookup
function is a special case because it is
potentially dependent on everything in the static and dynamic context. This is because
the static and dynamic
context of the call to fn:functionlookup
are used as the static and dynamic context of the
function that fn:functionlookup
returns.
[Definition] For a ·contextdependent· function, the parts of the context on which it depends are referred to as implicit arguments.
[Definition] A function that is guaranteed to produce ·identical· results from repeated calls within a single ·execution scope· if the explicit and implicit arguments are identical is referred to as deterministic.
[Definition] A function that is not ·deterministic· is referred to as nondeterministic.
All functions defined in this specification are ·deterministic· unless otherwise stated. Exceptions include the following:
[Definition] Some
functions (such as fn:distinctvalues
, fn:unordered
, map:keys
,
and map:foreach
) produce results in an
·implementationdefined· or
·implementationdependent· order.
In such cases two calls with the same arguments are not guaranteed to produce the
results in the same order. These functions are
said to be nondeterministic with respect to ordering.
Some functions (such as fn:analyzestring
,
fn:parsexml
, fn:parsexmlfragment
, and fn:jsontoxml
)
construct a tree of nodes to
represent their results. There is no guarantee that repeated calls with the same
arguments will return the same identical node (in the sense of the is
operator). However, if nonidentical nodes are returned, their content will be the
same in the sense of the fn:deepequal
function. Such a function is said
to be nondeterministic with respect to node identity.
Some functions (such as fn:doc
and fn:collection
) create new nodes by reading external
documents. Such functions are guaranteed to be ·deterministic· with the exception that
an implementation is allowed to make them nondeterministic as a user option.
Where the results of a function are described as being (to a greater or lesser extent) ·implementationdefined· or ·implementationdependent·, this does not by itself remove the requirement that the results should be deterministic: that is, that repeated calls with the same explicit and implicit arguments must return identical results.
Accessors and their semantics are described in [XQuery and XPath Data Model (XDM) 3.1]. Some of these accessors are exposed to the user through the functions described below.
Each of these functions has an arityzero signature which is equivalent to the arityone
form, with the context item supplied as the implicit first argument. In addition,
each of the
arityone functions accepts an empty sequence as the argument, in which case it generally
delivers
an empty sequence as the result: the exception is fn:string
, which delivers
a zerolength string.
Function  Accessor  Accepts  Returns 

fn:nodename

nodename

node (optional)  xs:QName (optional)

fn:nilled

nilled

node (optional)  xs:boolean (optional)

fn:string

stringvalue

item (optional) 
xs:string

fn:data

typedvalue

zero or more items  a sequence of atomic values 
fn:baseuri

baseuri

node (optional)  xs:anyURI (optional)

fn:documenturi

documenturi

node (optional)  xs:anyURI (optional)

Returns the name of a node, as an xs:QName
.
fn:nodename
() as
xs:QName?
fn:nodename
($node
as
node()?
) as
xs:QName?
The zeroargument form of this function is ·deterministic·, ·contextdependent·, and ·focusdependent·.
The oneargument form of this function is ·deterministic·, ·contextindependent·, and ·focusindependent·.
If the argument is omitted, it defaults to the context item (.
). The
behavior of the function if the argument is omitted is exactly the same as if the
context item had been passed as the argument.
If $node
is the empty sequence, the empty sequence is returned.
Otherwise, the function returns the result of the dm:nodename
accessor as
defined in [XQuery and XPath Data Model (XDM) 3.1] (see Section
5.10 nodename Accessor
^{DM31}).
The following errors may be raised when $node
is omitted:
If the context item is absent^{DM31}, dynamic error [err:XPDY0002]^{XP}
If the context item is not a node, type error [err:XPTY0004]^{XP}.
For element and attribute nodes, the name of the node is returned as an
xs:QName
, retaining the prefix, namespace URI, and local part.
For processing instructions, the name of the node is returned as an
xs:QName
in which the prefix and namespace URI are absent^{DM31}.
For a namespace node, the function returns an empty sequence if the node represents
the
default namespace; otherwise it returns an xs:QName
in which prefix and
namespace URI are absent^{DM31} and the local
part is the namespace prefix being bound.
For all other kinds of node, the function returns the empty sequence.
Returns true for an element that is nilled.
fn:nilled
() as
xs:boolean?
fn:nilled
($node
as
node()?
) as
xs:boolean?
The zeroargument form of this function is ·deterministic·, ·contextdependent·, and ·focusdependent·.
The oneargument form of this function is ·deterministic·, ·contextindependent·, and ·focusindependent·.
If the argument is omitted, it defaults to the context item (.
). The
behavior of the function if the argument is omitted is exactly the same as if the
context item had been passed as the argument.
If $node
is the empty sequence, the function returns the empty sequence.
Otherwise the function returns the result of the dm:nilled
accessor as
defined in [XQuery and XPath Data Model (XDM) 3.1] (see Section
5.8 nilled Accessor
^{DM31}).
The following errors may be raised when $node
is omitted:
If the context item is absent^{DM31}, dynamic error [err:XPDY0002]^{XP}
If the context item is not a node, type error [err:XPTY0004]^{XP}.
If $node
is not an element node, the function returns the empty
sequence.
If $node
is an untyped element node, the function returns false.
In practice, the function returns true
only for an element node that has
the attribute xsi:nil="true"
and that is successfully validated against a
schema that defines the element to be nillable; the detailed rules, however, are defined
in [XQuery and XPath Data Model (XDM) 3.1].
Returns the value of $item
represented as an xs:string
.
fn:string
() as
xs:string
fn:string
($item
as
item()?
) as
xs:string
The zeroargument form of this function is ·deterministic·, ·contextdependent·, and ·focusdependent·.
The oneargument form of this function is ·deterministic·, ·contextindependent·, and ·focusindependent·.
In the zeroargument version of the function, $item
defaults to the context
item. That is, calling fn:string()
is equivalent to calling
fn:string(.)
.
If $item
is the empty sequence, the function returns the zerolength
string.
If $item
is a node, the function returns the string value of the node, as obtained using the
dm:stringvalue
accessor defined in [XQuery and XPath Data Model (XDM) 3.1] (see Section
5.12 stringvalue Accessor
^{DM31}).
If $item
is an atomic value, the function returns the result of the expression $item cast
as xs:string
(see 19 Casting).
In all other cases, a dynamic error occurs (see below).
A dynamic error is raised [err:XPDY0002]^{XP} by the zeroargument version of the function if the context item is absent^{DM31}.
A type error is raised [err:FOTY0014] if
$item
is a function item (this includes maps and arrays).
Every node has a string value, even an element with elementonly content (which has no typed value). Moreover, casting an atomic value to a string always succeeds. Functions, maps, and arrays have no string value, so these are the only arguments that satisfy the type signature but cause failure.
The expression string(23)
returns "23"
.
The expression string(false())
returns "false"
.
The expression string("Paris")
returns "Paris"
.
The expression string((1, 2, 3))
raises error XPTY0004
.
The expression string([[1, 2], [3, 4]])
raises error FOTY0014
.
The expression string(abs#1)
raises error FOTY0014
.
let $para := <para>In a hole in the ground there lived a <term author="Tolkien">hobbit</term>.</para>
The expression string($para)
returns "In a hole in the ground there lived a hobbit."
.
Returns the result of atomizing a sequence. This process flattens arrays, and replaces nodes by their typed values.
fn:data
() as
xs:anyAtomicType*
fn:data
($input
as
item()*
) as
xs:anyAtomicType*
The zeroargument form of this function is ·deterministic·, ·contextdependent·, and ·focusdependent·.
The oneargument form of this function is ·deterministic·, ·contextindependent·, and ·focusindependent·.
If the argument is omitted, it defaults to the context item (.
). The
behavior of the function if the argument is omitted is exactly the same as if the
context item had been passed as the argument.
The result of fn:data
is the sequence of atomic values produced by
applying the following rules to each item in $input
:
If the item is an atomic value, it is appended to the result sequence.
If the item is a node, the typed value of the node is appended to the result
sequence. The typed value is a sequence of zero or more atomic values:
specifically, the result of the dm:typedvalue
accessor as defined in
[XQuery and XPath Data Model (XDM) 3.1] (See Section
5.14 typedvalue Accessor
^{DM31}).
If the item is an array, the result of applying fn:data
to
each member of the array, in order, is appended to the result sequence.
A type error is raised [err:FOTY0012] if an item in the
sequence $input
is a node that does not have a typed value.
A type error is raised [err:FOTY0013] if an item in
the sequence $input
is a function item other than
an array.
A dynamic error is raised if $input
is omitted and the context item is
absent^{DM31}.
The process of applying the fn:data
function to a sequence is referred to
as atomization
. In many cases an explicit call on fn:data
is
not required, because atomization is invoked implicitly when a node or sequence of
nodes
is supplied in a context where an atomic value or sequence of atomic values is
required.
The result of atomizing an empty sequence is an empty sequence.
The result of atomizing an empty array is an empty sequence.
The expression data(123)
returns 123
.
The expression data((123, 456))
returns 123, 456
.
The expression data([[1,2],[3,4]])
returns 1, 2, 3, 4
.
let $para := <para>In a hole in the ground there lived a <term author="Tolkien">hobbit</term>.</para>
The expression data($para)
returns xs:untypedAtomic("In a hole in the ground there lived a hobbit.")
.
The expression data($para/term/@author)
returns xs:untypedAtomic("Tolkien")
.
The expression data(abs#1)
raises error FOTY0013
.
Returns the base URI of a node.
fn:baseuri
() as
xs:anyURI?
fn:baseuri
($node
as
node()?
) as
xs:anyURI?
The zeroargument form of this function is ·deterministic·, ·contextdependent·, and ·focusdependent·.
The oneargument form of this function is ·deterministic·, ·contextindependent·, and ·focusindependent·.
The zeroargument version of the function returns the base URI of the context node:
it
is equivalent to calling fn:baseuri(.)
.
The singleargument version of the function behaves as follows:
$node
is the empty sequence, the function returns the empty
sequence.
dm:baseuri
accessor
applied to the node $node
. This accessor is defined, for each kind of
node, in the XDM specification (See Section
5.2 baseuri Accessor
^{DM31}).
Note:
As explained in XDM, document, element and processinginstruction nodes have a baseuri property which may be empty. The baseuri property for all other node kinds is the empty sequence. The dm:baseuri accessor returns the baseuri property of a node if it exists and is nonempty; otherwise it returns the result of applying the dm:baseuri accessor to its parent, recursively. If the node does not have a parent, or if the recursive ascent up the ancestor chain encounters a parentless node whose baseuri property is empty, the empty sequence is returned. In the case of namespace nodes, however, the result is always an empty sequence — it does not depend on the base URI of the parent element.See also fn:staticbaseuri
.
The following errors may be raised when $node
is omitted:
If the context item is absent^{DM31}, dynamic error [err:XPDY0002]^{XP}
If the context item is not a node, type error [err:XPTY0004]^{XP}.
Returns the URI of a resource where a document can be found, if available.
fn:documenturi
() as
xs:anyURI?
fn:documenturi
($node
as
node()?
) as
xs:anyURI?
The zeroargument form of this function is ·deterministic·, ·contextdependent·, and ·focusdependent·.
The oneargument form of this function is ·deterministic·, ·contextindependent·, and ·focusindependent·.
If the argument is omitted, it defaults to the context item (.
). The
behavior of the function if the argument is omitted is exactly the same as if the
context item had been passed as the argument.
If $node
is the empty sequence, the function returns the empty sequence.
If $node
is not a document node, the function returns the empty
sequence.
Otherwise, the function returns the value of the documenturi
accessor
applied to $node
, as defined in [XQuery and XPath Data Model (XDM) 3.1] (See
Section
6.1.2 Accessors
^{DM31}).
The following errors may be raised when $node
is omitted:
If the context item is absent^{DM31}, dynamic error [err:XPDY0002]^{XP}
If the context item is not a node, type error [err:XPTY0004]^{XP}.
In the case of a document node $D
returned by the fn:doc
function, or a document node at the root of a tree containing a node returned by the
fn:collection
function, it will always be true that either
fn:documenturi($D)
returns the empty sequence, or that the following
expression is true: fn:doc(fn:documenturi($D))
is $D
. It is
·implementationdefined· whether this guarantee also holds for
document nodes obtained by other means, for example a document node passed as the
initial context node of a query or transformation.
A consequence of these rules is that it is not possible (within the
execution scope of a transformation) for two different documents to have the same
value for their documenturi
property. This means that in situations where
URI stability is not guaranteed (for example, with streamed input documents in XSLT,
or for documents returned by fn:collection
if document stability has been
disabled), the documenturi
property should be absent, and
fn:documenturi
should return an empty sequence.
In this document, as well as in [XQuery 3.1: An XML Query Language] and [XML Path Language (XPath) 3.1],
the phrase "an error is raised"
is used. Raising an error is equivalent to calling the fn:error
function defined in this section with the provided error code. Except
where otherwise
specified, errors defined in this specification are dynamic errors.
Some errors,
however, are classified as type errors. Type errors are typically
used where the presence
of the error can be inferred from knowledge of the type of the actual arguments
to a function, for
example with a call such as fn:string(fn:abs#1)
. Host languages may allow type errors
to be reported statically if they are discovered during static analysis.
When function specifications indicate that an error is to be raised, the notation
"[error code]". os used to specify an error code. Each error defined
in this document is identified by an xs:QName
that is in the
http://www.w3.org/2005/xqterrors
namespace, represented in this document by the err
prefix. It is this
xs:QName
that is actually passed as an argument to the
fn:error
function. Calling this function raises an error. For a
more detailed treatment of error handing, see Section
2.3.3 Handling Dynamic Errors
^{XP31}.
The fn:error
function is a general function that may be called as above
but may also be called from [XQuery 3.1: An XML Query Language] or [XML Path Language (XPath) 3.1]
applications with, for example, an xs:QName
argument.
Calling the fn:error
function raises an applicationdefined error.
fn:error
() as
none
fn:error
($code
as
xs:QName?
) as
none
fn:error
($code
as
xs:QName?
, $description
as
xs:string
) as
none
fn:error (

$code 
as xs:QName? ,

$description 
as xs:string ,


$errorobject 
as item()* ) as none 
This function is ·nondeterministic·, ·contextindependent·, and ·focusindependent·.
This function never returns a value. Instead it always raises an error. The effect of the error is identical to the effect of dynamic errors raised implicitly, for example when an incorrect argument is supplied to a function.
The parameters to the fn:error
function supply information that is
associated with the error condition and that is made available to a caller that asks
for
information about the error. The error may be caught either by the host language (using
a try/catch construct in XSLT or XQuery, for example), or by the calling application
or
external processing environment. The way in which error information is returned to
the
external processing environment is ·implementationdependent·.
There are three pieces of information that may be associated with an error:
The $code
is an error code that distinguishes this error from others.
It is an xs:QName
; the namespace URI conventionally identifies the
component, subsystem, or authority responsible for defining the meaning of the
error code, while the local part identifies the specific error condition. The
namespace URI http://www.w3.org/2005/xqterrors
is used for errors
defined in this specification; other namespace URIs may be used for errors defined
by the application.
If the external processing environment expects the error code to be returned as a
URI or a string rather than as an xs:QName
, then an error code with
namespace URI NS
and local part LP
will be returned in
the form NS#LP
. The namespace URI part of the error code should
therefore not include a fragment identifier.
If no value is supplied for the $code
argument (that is,
if the function is called with no arguments or if the first argument is an empty sequence),
the effective value of the error code is fn:QName('http://www.w3.org/2005/xqterrors', 'err:FOER0000')
.
The $description
is a naturallanguage description of the error
condition.
If no value is supplied for the $description
argument (that is, if the function is called with less than two arguments), then the
effective value of the description is ·implementationdependent·.
The $errorobject
is an arbitrary value used to convey additional
information about the error, and may be used in any way the application
chooses.
If no value is supplied for the $errorobject
argument (that is, if the function is called with less than three arguments), then
the
effective value of the error object is ·implementationdependent·.
This function always raises a dynamic error. By default, it raises [err:FOER0000]
The value of the $description
parameter may need to be localized.
The type "none" is a special type defined in [XQuery 1.0 and XPath 2.0 Formal Semantics] and is not available to the user. It indicates that the function never returns and ensures that it has the correct static type.
Any QName may be used as an error code; there are no reserved names or namespaces. The error is always classified as a dynamic error, even if the error code used is one that is normally used for static errors or type errors.
The expression fn:error()
raises error FOER0000
. (This returns the URI
http://www.w3.org/2005/xqterrors#FOER0000
(or the corresponding
xs:QName
) to the external processing environment, unless the error
is caught using a try/catch construct in the host language.)
The expression fn:error(fn:QName('http://www.example.com/HR', 'myerr:toohighsal'),
'Does not apply because salary is too high')
raises error myerr:toohighsal
. (This returns http://www.example.com/HR#toohighsal
and the
xs:string
"Does not apply because salary is too high"
(or the corresponding
xs:QName
) to the external processing environment, unless the error
is caught using a try/catch construct in the host language.)
Provides an execution trace intended to be used in debugging queries.
fn:trace
($value
as
item()*
) as
item()*
fn:trace
($value
as
item()*
, $label
as
xs:string
) as
item()*
This function is ·deterministic·, ·contextindependent·, and ·focusindependent·.
The function returns $value
, unchanged.
In addition, the values of $value
, converted to an xs:string
,
and $label
(if supplied)
may be directed to a trace data set. The destination of the trace
output is ·implementationdefined·. The format of the trace output is
·implementationdependent·. The ordering of output from calls of the
fn:trace
function is ·implementationdependent·.
Sometimes there is a need to output trace information unrelated to a specific value.
In such cases it can be useful to set $value
to an empty string or an empty
sequence, and to compute the value of the $label
argument:
fn:trace((), "Processing item "  $i)
.
Consider a situation in which a user wants to investigate the actual value passed
to
a function. Assume that in a particular execution, $v
is an
xs:decimal
with value 124.84
. Writing fn:trace($v,
'the value of $v is:')
will put the strings "124.84"
and
"the value of $v is:"
in the trace data set in implementation
dependent order.
Returns implementationdependent information about the current state of execution.
fn:stacktrace
() as
xs:string
The result of the function is an implementationdependent string containing diagnostic information about the current state of execution.
The function is nondeterministic: multiple calls will typically produce different results.
The function will typically be called to assist in diagnosing dynamic errors.
This section specifies arithmetic operators on the numeric datatypes defined in [XML Schema Part 2: Datatypes Second Edition].
The operators described in this section are defined on the following atomic types. Each type whose name is indented is derived from the type whose name appears nearest above with one less level of indentation.
xs:decimal  
xs:integer  
xs:float  
xs:double 
They also apply to types derived by restriction from the above types.
The type xs:numeric
is defined as a union type whose member types are
(in order) xs:double
, xs:float
, and xs:decimal
. This type is implicitly imported
into the static context, so it can also be used in defining the signature of userwritten
functions. Apart from the fact that
it is implicitly imported, it behaves exactly like a userdefined type with the same
definition. This means, for example:
If the expected type of a function parameter is given as xs:numeric
, the actual value supplied
can be an instance of any of these three types, or any type derived from these three
by restriction (this includes the builtin
type xs:integer
, which is derived from xs:decimal
).
If the expected type of a function parameter is given as xs:numeric
, and the actual value supplied
is xs:untypedAtomic
(or a node whose atomized value is xs:untypedAtomic
), then it will
be cast to the union type xs:numeric
using the rules in 19.3.5 Casting to union types.
Because the lexical space of xs:double
subsumes the lexical space of the other member types, and
xs:double
is listed first, the effect is that if the untyped atomic value is in the lexical
space of
xs:double
, it will be converted to an xs:double
, and if not, a dynamic error occurs.
When the return type of a function is given as xs:numeric
, the actual value returned will be
an instance of one of the three member types (and perhaps also of types derived from
these by restriction). The rules
for the particular function will specify how the type of the result depends on the
values supplied as arguments.
In many cases, for the functions in this specification, the result is defined to be
the same type as the first
argument.
Note:
This specification uses [IEEE 7542008] arithmetic for xs:float
and xs:double
values.
One consequence of this is that some operations result in the value NaN
(nota number), which
has the unusual property that it is not equal to itself. Another consequence is that
some operations return the value negative zero.
This differs from [XML Schema Part 2: Datatypes Second Edition] which defines
NaN
as being equal to itself and defines only a single zero in the value space.
The text accompanying several functions defines behavior for both positive and negative
zero inputs and outputs
in the interest of alignment with [IEEE 7542008]. A conformant implementation must
respect these semantics. In consequence, the expression 0.0e0
(which is actually a unary minus operator
applied to an xs:double
value) will always return negative zero: see 4.2.8 op:numericunaryminus.
As a concession to implementations that rely on implementations of XSD 1.0, however,
when casting from string to double
the lexical form 0
may be converted to positive zero, though negative zero
is recommended.
XML Schema 1.1 introduces support for positive and negative zero as distinct values,
and also uses the [IEEE 7542008]
semantics for comparisons involving NaN
.
The following functions define the semantics of arithmetic operators defined in [XQuery 3.1: An XML Query Language] and [XML Path Language (XPath) 3.1] on these numeric types.
Operator  Meaning 

op:numericadd

Addition 
op:numericsubtract

Subtraction 
op:numericmultiply

Multiplication 
op:numericdivide

Division 
op:numericintegerdivide

Integer division 
op:numericmod

Modulus 
op:numericunaryplus

Unary plus 
op:numericunaryminus

Unary minus (negation) 
The parameters and return types for the above operators are in most cases declared
to be of type
xs:numeric
, which permits the basic numeric
types: xs:integer
, xs:decimal
, xs:float
and xs:double
, and types derived from them.
In general the twoargument functions require that both arguments are of the same
primitive type,
and they return a value of this same type.
The exceptions are op:numericdivide
, which returns
an xs:decimal
if called with two xs:integer
operands,
and op:numericintegerdivide
which always returns an xs:integer
.
If the two operands of an arithmetic expression are not of the same type, subtype substitution and numeric type promotion are used to obtain two operands of the same type. Section B.1 Type Promotion ^{XP31} and Section B.2 Operator Mapping ^{XP31} describe the semantics of these operations in detail.
The result type of operations depends on their argument datatypes and is defined in the following table:
Operator  Returns 

op:operation(xs:integer, xs:integer)

xs:integer (except for op:numericdivide(integer,
integer) , which returns xs:decimal )

op:operation(xs:decimal, xs:decimal)

xs:decimal

op:operation(xs:float, xs:float)

xs:float

op:operation(xs:double, xs:double)

xs:double

op:operation(xs:integer)

xs:integer

op:operation(xs:decimal)

xs:decimal

op:operation(xs:float)

xs:float

op:operation(xs:double)

xs:double

These rules define any operation on any pair of arithmetic types. Consider the following example:
op:operation(xs:int, xs:double) => op:operation(xs:double, xs:double)
For this operation, xs:int
must be converted to
xs:double
. This can be done, since by the rules above:
xs:int
can be substituted for xs:integer
,
xs:integer
can be substituted for xs:decimal
,
xs:decimal
can be promoted to xs:double
. As far as possible, the promotions should be done in a
single step. Specifically, when an xs:decimal
is promoted to an
xs:double
, it should not be converted to an xs:float
and then to xs:double
, as this risks loss of precision.
As another example, a user may define height
as a derived type of
xs:integer
with a minimum value of 20 and a maximum value of 100.
They may then derive fenceHeight
using an enumeration to restrict the
permitted set of values to, say, 36, 48 and 60.
op:operation(fenceHeight, xs:integer) => op:operation(xs:integer, xs:integer)
fenceHeight
can be substituted for its base type
height
and height
can be substituted for its base type
xs:integer
.
The basic rules for addition, subtraction, and multiplication
of ordinary numbers are not set out in this specification; they are taken as given.
In the case of xs:double
and xs:float
the rules are as defined in [IEEE 7542008]. The rules for handling
division and modulus operations, as well as the rules for handling special values
such as infinity and NaN
,
and exception conditions such as overflow and underflow, are described more explicitly
since they are not necessarily obvious.
On overflow and underflow situations during arithmetic operations conforming implementations must behave as follows:
For xs:float
and xs:double
operations, overflow
behavior must be conformant with [IEEE 7542008]. This specification allows the following options:
Raising a dynamic error [err:FOAR0002] via an overflow trap.
Returning INF
or INF
.
Returning the largest (positive or negative) noninfinite number.
For xs:float
and xs:double
operations,
underflow behavior must be conformant with [IEEE 7542008]. This specification allows the following options:
Raising a dynamic error [err:FOAR0002] via an underflow trap.
Returning 0.0E0
or +/ 2**Emin
or a
denormalized value; where Emin
is the smallest
possible xs:float
or xs:double
exponent.
For xs:decimal
operations, overflow behavior must
raise a dynamic error [err:FOAR0002]. On
underflow, 0.0
must be returned.
For xs:integer
operations, implementations that support
limitedprecision integer operations must select from
the following options:
They may choose to always raise a dynamic error [err:FOAR0002].
They may provide an ·implementationdefined· mechanism that allows users to choose between raising an error and returning a result that is modulo the largest representable integer value. See [ISO 10967].
The functions op:numericadd
, op:numericsubtract
,
op:numericmultiply
, op:numericdivide
,
op:numericintegerdivide
and op:numericmod
are each
defined for pairs of numeric operands, each of which has the same
type:xs:integer
, xs:decimal
, xs:float
, or
xs:double
. The functions op:numericunaryplus
and
op:numericunaryminus
are defined for a single operand whose type
is one of those same numeric types.
For xs:float
and xs:double
arguments, if either
argument is NaN
, the result is NaN
.
For xs:decimal
values, let N be the number of digits
of precision supported by the implementation, and let M (M <= N
) be the minimum limit on the number of digits
required for conformance (18 digits for XSD 1.0, 16 digits for XSD 1.1). Then for
addition, subtraction, and multiplication
operations, the returned result should be accurate to N digits of precision, and for division and modulus operations,
the returned result should be accurate to at least M digits of precision.
The actual precision is ·implementationdefined·. If the number
of digits in the mathematical result exceeds the number of digits that the implementation
retains for that operation, the result is truncated or rounded in an ·implementationdefined· manner.
Note:
This Recommendation does not specify whether xs:decimal
operations are fixed point or floating point.
In an implementation using floating point it is possible for very simple operations
to require more digits of precision than
are available; for example adding 1e100
to 1e100
requires 200 digits of precision for an
accurate representation of the result.
The [IEEE 7542008] specification also describes handling of
two exception conditions called divideByZero
and invalidOperation
. The
IEEE divideByZero
exception is raised not only by a direct attempt to divide by zero, but also by
operations such as log(0)
. The IEEE invalidOperation
exception is raised by
attempts to call a function with an argument that is outside the function's domain
(for example,
sqrt(1)
or log(1)
).
Although IEEE defines these as exceptions, it also defines "default nonstop exception
handling" in
which the operation returns a defined result, typically positive or negative infinity,
or NaN. With this
function library,
these IEEE exceptions do not cause a dynamic error
at the application level; rather they result in the relevant function or operator
returning
the defined nonerror result.
The underlying IEEE exception may be notified to the application
or to the user by some ·implementationdefined·
warning condition, but the observable effect on an application
using the functions and operators defined in this specification is simply to return
the defined result (typically INF, +INF, or NaN) with no error.
The [IEEE 7542008] specification distinguishes two NaN values,
a quiet NaN and a signaling NaN. These two values are not distinguishable in the XDM
model:
the value spaces of xs:float
and xs:double
each include only a single
NaN
value. This does not prevent the implementation distinguishing them internally,
and triggering different ·implementationdefined·
warning conditions, but such distinctions do not affect the observable behavior of
an application
using the functions and operators defined in this specification.
Returns the arithmetic sum of its operands: ($arg1 + $arg2
).
Defines the semantics of the "+" operator when applied to two numeric values
op:numericadd
($arg1
as
xs:numeric
, $arg2
as
xs:numeric
) as
xs:numeric
General rules: see 4.2 Arithmetic operators on numeric values.
For xs:float
or xs:double
values, if one of the operands is a
zero or a finite number and the other is INF
or INF
,
INF
or INF
is returned. If both operands are
INF
, INF
is returned. If both operands are
INF
, INF
is returned. If one of the operands is
INF
and the other is INF
, NaN
is
returned.
Returns the arithmetic difference of its operands: ($arg1  $arg2
).
Defines the semantics of the "" operator when applied to two numeric values.
op:numericsubtract
($arg1
as
xs:numeric
, $arg2
as
xs:numeric
) as
xs:numeric
General rules: see 4.2 Arithmetic operators on numeric values.
For xs:float
or xs:double
values, if one of the operands is a
zero or a finite number and the other is INF
or INF
, an
infinity of the appropriate sign is returned. If both operands are INF
or
INF
, NaN
is returned. If one of the operands is
INF
and the other is INF
, an infinity of the appropriate
sign is returned.
Returns the arithmetic product of its operands: ($arg1 * $arg2
).
Defines the semantics of the "*" operator when applied to two numeric values.
op:numericmultiply
($arg1
as
xs:numeric
, $arg2
as
xs:numeric
) as
xs:numeric
General rules: see 4.2 Arithmetic operators on numeric values.
For xs:float
or xs:double
values, if one of the operands is a
zero and the other is an infinity, NaN
is returned. If one of the operands
is a nonzero number and the other is an infinity, an infinity with the appropriate
sign
is returned.
Returns the arithmetic quotient of its operands: ($arg1 div $arg2
).
Defines the semantics of the "div" operator when applied to two numeric values.
op:numericdivide
($arg1
as
xs:numeric
, $arg2
as
xs:numeric
) as
xs:numeric
General rules: see 4.2 Arithmetic operators on numeric values.
As a special case, if the types of both $arg1
and $arg2
are
xs:integer
, then the return type is xs:decimal
.
A dynamic error is raised [err:FOAR0001] for xs:decimal
and xs:integer
operands, if the divisor is (positive or negative) zero.
For xs:float
and xs:double
operands, floating point division
is performed as specified in [IEEE 7542008]. A positive number divided by
positive zero returns INF
. A negative number divided by positive zero
returns INF
. Division by negative zero returns INF
and
INF
, respectively. Positive or negative zero divided by positive or
negative zero returns NaN
. Also, INF
or INF
divided by INF
or INF
returns NaN
.
Performs an integer division.
Defines the semantics of the "idiv" operator when applied to two numeric values.
op:numericintegerdivide (

$arg1 
as xs:numeric ,

$arg2 
as xs:numeric ) as xs:integer 
General rules: see 4.2 Arithmetic operators on numeric values.
If $arg2
is INF
or INF
, and $arg1
is not INF
or INF
, then the result is zero.
Otherwise, subject to limits of precision and overflow/underflow conditions, the result
is the largest (furthest from zero) xs:integer
value $N
such
that the following expression is true:
fn:abs($N * $arg2) le fn:abs($arg1) and fn:compare($N * $arg2, 0) eq fn:compare($arg1, 0).
Note:
The second term in this condition ensures that the result has the correct sign.
The implementation may adopt a different algorithm provided that it is equivalent
to
this formulation in all cases where ·implementationdependent· or ·implementationdefined· behavior does not affect the outcome, for example,
the implementationdefined precision of the result of xs:decimal
division.
A dynamic error is raised [err:FOAR0001] if the divisor is (positive or negative) zero.
A dynamic error is raised [err:FOAR0002] if either operand is
NaN
or if $arg1
is INF
or
INF
.
Except in situations involving errors, loss of precision, or overflow/underflow, the
result of $a idiv $b
is the same as ($a div $b) cast as
xs:integer
.
The semantics of this function are different from integer division as defined in programming languages such as Java and C++.
The expression op:numericintegerdivide(10,3)
returns 3
.
The expression op:numericintegerdivide(3,2)
returns 1
.
The expression op:numericintegerdivide(3,2)
returns 1
.
The expression op:numericintegerdivide(3,2)
returns 1
.
The expression op:numericintegerdivide(9.0,3)
returns 3
.
The expression op:numericintegerdivide(3.5,3)
returns 1
.
The expression op:numericintegerdivide(3.0,4)
returns 0
.
The expression op:numericintegerdivide(3.1E1,6)
returns 5
.
The expression op:numericintegerdivide(3.1E1,7)
returns 4
.
Returns the remainder resulting from dividing $arg1
, the dividend, by
$arg2
, the divisor.
Defines the semantics of the "mod" operator when applied to two numeric values.
op:numericmod
($arg1
as
xs:numeric
, $arg2
as
xs:numeric
) as
xs:numeric
General rules: see 4.2 Arithmetic operators on numeric values.
The operation a mod b
for operands that are xs:integer
or
xs:decimal
, or types derived from them, produces a result such that
(a idiv b)*b+(a mod b)
is equal to a
and the magnitude of
the result is always less than the magnitude of b
. This identity holds even
in the special case that the dividend is the negative integer of largest possible
magnitude for its type and the divisor is 1 (the remainder is 0). It follows from
this
rule that the sign of the result is the sign of the dividend.
For xs:float
and xs:double
operands the following rules
apply:
If either operand is NaN
, the result is NaN
.
If the dividend is positive or negative infinity, or the divisor is positive or
negative zero (0), or both, the result is NaN
.
If the dividend is finite and the divisor is an infinity, the result equals the dividend.
If the dividend is positive or negative zero and the divisor is finite, the result is the same as the dividend.
In the remaining cases, where neither positive or negative infinity, nor positive
or negative zero, nor NaN
is involved, the result obeys (a idiv
b)*b+(a mod b)
= a
.
Division is truncating division, analogous to integer division, not [IEEE 7542008] rounding division i.e. additional digits are truncated,
not rounded to the required precision.
A dynamic error is raised [err:FOAR0001] for xs:integer
and xs:decimal
operands, if $arg2
is zero.
The expression op:numericmod(10,3)
returns 1
.
The expression op:numericmod(6,2)
returns 0
.
The expression op:numericmod(4.5,1.2)
returns 0.9
.
The expression op:numericmod(1.23E2, 0.6E1)
returns 3.0E0
.
Returns its operand with the sign unchanged: (+ $arg
).
Defines the semantics of the unary "+" operator applied to a numeric value.
op:numericunaryplus
($arg
as
xs:numeric
) as
xs:numeric
General rules: see 4.2 Arithmetic operators on numeric values.
The returned value is equal to $arg
, and is an instance of
xs:integer
, xs:decimal
, xs:double
, or
xs:float
depending on the type of $arg
.
Because function conversion rules are applied in the normal way, the unary
+
operator can be used to force conversion of an untyped node to a
number: the result of +@price
is the same as xs:double(@price)
if the type of @price
is xs:untypedAtomic
.
Returns its operand with the sign reversed: ( $arg
).
Defines the semantics of the unary "" operator when applied to a numeric value.
op:numericunaryminus
($arg
as
xs:numeric
) as
xs:numeric
General rules: see 4.2 Arithmetic operators on numeric values.
The returned value is an instance of xs:integer
, xs:decimal
,
xs:double
, or xs:float
depending on the type of
$arg
.
For xs:integer
and xs:decimal
arguments, 0
and
0.0
return 0
and 0.0
, respectively. For
xs:float
and xs:double
arguments, NaN
returns
NaN
, 0.0E0
returns 0.0E0
and vice versa.
INF
returns INF
. INF
returns
INF
.
The six value comparison operators eq
, ne
, lt
,
le
, gt
, and ge
are defined in terms of two
underlying functions: op:numericequal
and op:numericlessthan
.
These functions are defined to operate on values of the same type.
If the arguments are of different types, then one of them is converted to the type of the other using the following rules, in order:
If one operand is xs:float
then it is converted to xs:double
.
If one operand is xs:double
and the other is xs:decimal
, then:
If the xs:double
operand is INF
, +INF
, or NaN
,
then the xs:decimal
value is cast to xs:double
and the values are compared
as doubles.
Otherwise, the xs:double
value is converted to a decimal number with no rounding
or loss of precision and the values are compared acccording to their mathematical
values.
Note:
Every instance of xs:float
, xs:double
, and xs:decimal
,
other than the values INF
, +INF
, and NaN
, can be represented
exactly as a decimal number provided enough digits are available both before and after
the decimal
point. The effect of this rule is that the comparison operators are transitive.
In edge cases this rule may give a different result from earlier releases. For example
in XPath 3.1 (depending on the implementationdefined precision), the values
xs:decimal('1.0000000000100000000001')
and xs:double('1.00000000001')
might compare as equal; in this version of the specification, they are not equal.
This change removes the problems caused for fn:distinctvalues
and
xsl:foreachgroup
as a result of nontransitivity, and it aligns the semantics
of the eq
operator (used also in fn:distinctvalues
, fn:indexof
,
and fn:deepequal
) with the semantics of the op:samekey
comparison
used for maps.
This specification defines the following comparison operators on numeric values.
Each comparison operator returns a boolean
value. If either, or both, operands are NaN
, false
is
returned.
Function  Meaning 

op:numericequal 
Returns true if and only if the value of $arg1 is equal to the value of
$arg2 .

op:numericlessthan 
Returns true if and only if $arg1 is numerically less than
$arg2 .

Returns true if and only if the value of $arg1
is equal to the value of
$arg2
.
Defines the semantics of the "eq" operator when applied to two numeric values, and is also used in defining the semantics of "ne", "le" and "ge".
op:numericequal
($arg1
as
xs:numeric
, $arg2
as
xs:numeric
) as
xs:boolean
General rules: see 4.3 Comparison operators on numeric values.
The two arguments will always have been converted so they have the same primitive
type
(both xs:float
, both xs:double
, or both xs:decimal
.
The values are compared using the equality rules defined in [XSD11].
Positive and negative zero compare equal.
If $arg1
or $arg2
is
NaN
, the function returns false
.
Returns true
if and only if $arg1
is numerically less than
$arg2
.
Defines the semantics of the
lt
operator when applied to two numeric values, and is also used in defining the
semantics of le
, gt
, and ge
.
op:numericlessthan
($arg1
as
xs:numeric
, $arg2
as
xs:numeric
) as
xs:boolean
General rules: see 4.3 Comparison operators on numeric values.
The two arguments will always have been converted so they have the same primitive
type
(both xs:float
, both xs:double
, or both xs:decimal
.
The values are compared using the ordering rules defined in [XSD11]. If the
ordering relation of the two values is imcomparable
(which happens when one or both
of them is NaN
, then the result is false.
For xs:float
and xs:double
values, positive infinity is
greater than all other nonNaN
values; negative infinity is less than all
other nonNaN
values. Positive and negative zero compare equal.
If $arg1
or $arg2
is
NaN
, the function returns false
.
The following functions are defined on numeric types. Each function returns a value of the same type as the type of its argument.
If the argument is the empty sequence, the empty sequence is returned.
For xs:float
and xs:double
arguments, if the
argument is "NaN", "NaN" is returned.
Except for fn:abs
, for xs:float
and
xs:double
arguments, if the argument is positive or
negative infinity, positive or negative infinity is returned.
Function  Meaning 

fn:abs 
Returns the absolute value of $value .

fn:ceiling 
Rounds $value upwards to a whole number.

fn:floor 
Rounds $value downwards to a whole number.

fn:round 
Rounds a value to a specified number of decimal places, rounding upwards if two such values are equally near. 
fn:roundhalftoeven 
Rounds a value to a specified number of decimal places, rounding to make the last digit even if two such values are equally near. 
fn:isNaN 
Returns true if the argument is the xs:float or xs:double value NaN.

Note:
fn:round
and fn:roundhalftoeven
produce the same result in all cases
except when the argument is exactly midway between two values with the required precision.
Other ways of rounding midway values can be achieved as follows:
Towards negative infinity: fn:round($x)
Away from zero: fn:round(fn:abs($x))*fn:compare($x,0)
Towards zero: fn:abs(fn:round($x))*fn:compare($x,0)
Returns the absolute value of $value
.
fn:abs
($value
as
xs:numeric?
) as
xs:numeric?
This function is ·deterministic·, ·contextindependent·, and ·focusindependent·.
General rules: see 4.4 Functions on numeric values.
If $value
is negative the function returns $value
, otherwise it
returns $value
.
For the four types xs:float
,
xs:double
, xs:decimal
and xs:integer
, it is
guaranteed that if the type of $value
is an instance of type T then
the result will also be an instance of T. The result may
also be an instance of a type derived from one of these four by restriction. For example,
if
$value
is an instance of xs:positiveInteger
then the value of
$value
may be returned unchanged.
For xs:float
and xs:double
arguments, if the argument is
positive zero or negative zero, then positive zero is returned. If the argument is
positive or negative infinity, positive infinity is returned.
The expression fn:abs(10.5)
returns 10.5
.
The expression fn:abs(10.5)
returns 10.5
.
Rounds $value
upwards to a whole number.
fn:ceiling
($value
as
xs:numeric?
) as
xs:numeric?
This function is ·deterministic·, ·contextindependent·, and ·focusindependent·.
General rules: see 4.4 Functions on numeric values.
The function returns the smallest (closest to negative infinity) number with no
fractional part that is not less than $value
.
For the four types xs:float
,
xs:double
, xs:decimal
and xs:integer
, it is
guaranteed that if the type of $value
is an instance of type T then
the result will also be an instance of T. The result may
also be an instance of a type derived from one of these four by restriction. For example,
if
$value
is an instance of xs:decimal
then the result may
be an instance of xs:integer
.
For xs:float
and xs:double
arguments, if the argument is
positive zero, then positive zero is returned. If the argument is negative zero, then
negative zero is returned. If the argument is less than zero and greater than 1,
negative zero is returned.
The expression fn:ceiling(10.5)
returns 11
.
The expression fn:ceiling(10.5)
returns 10
.
Rounds $value
downwards to a whole number.
fn:floor
($value
as
xs:numeric?
) as
xs:numeric?
This function is ·deterministic·, ·contextindependent·, and ·focusindependent·.
General rules: see 4.4 Functions on numeric values.
The function returns the largest (closest to positive infinity) number with no
fractional part that is not greater than $value
.
For the four types xs:float
,
xs:double
, xs:decimal
and xs:integer
, it is
guaranteed that if the type of $value
is an instance of type T then
the result will also be an instance of T. The result may
also be an instance of a type derived from one of these four by restriction. For example,
if
$value
is an instance of xs:decimal
then the result may
be an instance of xs:integer
.
For xs:float
and xs:double
arguments, if the argument is
positive zero, then positive zero is returned. If the argument is negative zero, then
negative zero is returned.
The expression fn:floor(10.5)
returns 10
.
The expression fn:floor(10.5)
returns 11
.
Rounds a value to a specified number of decimal places, rounding upwards if two such values are equally near.
fn:round
($value
as
xs:numeric?
) as
xs:numeric?
fn:round
($value
as
xs:numeric?
, $precision
as
xs:integer
) as
xs:numeric?
This function is ·deterministic·, ·contextindependent·, and ·focusindependent·.
General rules: see 4.4 Functions on numeric values.
The function returns the nearest (that is, numerically closest) value to
$value
that is a multiple of ten to the power of minus
$precision
. If two such values are equally near (for example, if the
fractional part in $value
is exactly .5), the function returns the one that
is closest to positive infinity.
For the four types xs:float
,
xs:double
, xs:decimal
and xs:integer
, it is
guaranteed that if the type of $value
is an instance of type T then
the result will also be an instance of T. The result may
also be an instance of a type derived from one of these four by restriction. For example,
if
$value
is an instance of xs:decimal
and $precision
is
less than one, then the result may
be an instance of xs:integer
.
The singleargument version of this function produces the same result as the
twoargument version with $precision=0
(that is, it rounds to a whole
number).
When $value
is of type xs:float
and xs:double
:
If $value
is NaN, positive or negative zero, or positive or negative
infinity, then the result is the same as the argument.
For other values, the argument is cast to xs:decimal
using an
implementation of xs:decimal
that imposes no limits on the number of
digits that can be represented. The function is applied to this
xs:decimal
value, and the resulting xs:decimal
is
cast back to xs:float
or xs:double
as appropriate to
form the function result. If the resulting xs:decimal
value is zero,
then positive or negative zero is returned according to the sign of
$value
.
This function is typically used with a nonzero $precision
in financial
applications where the argument is of type xs:decimal
. For arguments of
type xs:float
and xs:double
the results may be
counterintuitive. For example, consider round(35.425e0, 2)
. The result is
not 35.43, as might be expected, but 35.42. This is because the xs:double
written as 35.425e0 has an exact value equal to 35.42499999999..., which is closer
to
35.42 than to 35.43.
The expression fn:round(2.5)
returns 3.0
.
The expression fn:round(2.4999)
returns 2.0
.
The expression fn:round(2.5)
returns 2.0
. (Not the possible alternative, 3
).
The expression fn:round(1.125, 2)
returns 1.13
.
The expression fn:round(8452, 2)
returns 8500
.
The expression fn:round(3.1415e0, 2)
returns 3.14e0
.
Rounds a value to a specified number of decimal places, rounding to make the last digit even if two such values are equally near.
fn:roundhalftoeven
($value
as
xs:numeric?
) as
xs:numeric?
fn:roundhalftoeven (

$value 
as xs:numeric? ,

$precision 
as xs:integer ) as xs:numeric? 
This function is ·deterministic·, ·contextindependent·, and ·focusindependent·.
General rules: see 4.4 Functions on numeric values.
The function returns the nearest (that is, numerically closest) value to
$value
that is a multiple of ten to the power of minus
$precision
. If two such values are equally near (e.g. if the fractional
part in $value
is exactly .500...), the function returns the one whose least
significant digit is even.
For the four types xs:float
,
xs:double
, xs:decimal
and xs:integer
, it is
guaranteed that if the type of $value
is an instance of type T then
the result will also be an instance of T. The result may
also be an instance of a type derived from one of these four by restriction. For example,
if
$value
is an instance of xs:decimal
and $precision
is less than one, then the result may
be an instance of xs:integer
.
The first signature of this function produces the same result as the second signature
with $precision=0
.
For arguments of type xs:float
and xs:double
:
If the argument is NaN
, positive or negative zero, or positive or
negative infinity, then the result is the same as the argument.
In all other cases, the argument is cast to xs:decimal
using an
implementation of xs:decimal
that imposes no limits on the number of digits that
can be represented. The function is applied to this xs:decimal
value,
and the resulting xs:decimal
is cast back to xs:float
or
xs:double
as appropriate to form the function result. If the
resulting xs:decimal
value is zero, then positive or negative zero is
returned according to the sign of the original argument.
This function is typically used in financial applications where the argument is of
type
xs:decimal
. For arguments of type xs:float
and
xs:double
the results may be counterintuitive. For example, consider
roundhalftoeven(xs:float(150.015), 2)
. The result is not 150.02 as
might be expected, but 150.01. This is because the conversion of the
xs:float
value represented by the literal 150.015 to an
xs:decimal
produces the xs:decimal
value 150.014999389...,
which is closer to 150.01 than to 150.02.
The expression fn:roundhalftoeven(0.5)
returns 0.0
.
The expression fn:roundhalftoeven(1.5)
returns 2.0
.
The expression fn:roundhalftoeven(2.5)
returns 2.0
.
The expression fn:roundhalftoeven(3.567812e+3, 2)
returns 3567.81e0
.
The expression fn:roundhalftoeven(4.7564e3, 2)
returns 0.0e0
.
The expression fn:roundhalftoeven(35612.25, 2)
returns 35600
.
Returns true if the argument is the xs:float
or xs:double
value NaN.
fn:isNaN
($value
as
xs:anyAtomicType
) as
xs:boolean
This function is ·deterministic·, ·contextindependent·, and ·focusindependent·.
The function returns true if the argument is the xs:float
or xs:double
value NaN;
otherwise it returns false.
The expression fn:isNaN(23)
returns false()
.
The expression fn:isNaN("NaN")
returns false()
.
The expression fn:isNaN(fn:number("twentythree"))
returns true()
.
The expression fn:isNaN(math:sqrt(1))
returns true()
.
It is possible to convert strings to values of type xs:integer
,
xs:float
, xs:decimal
, or xs:double
using the constructor functions described in 18 Constructor functions
or using cast
expressions as described in 19 Casting.
In addition the fn:number
function is available to convert strings
to values of type xs:double
. It differs from the xs:double
constructor function in that any value outside the lexical space of the xs:double
datatype is converted to the xs:double
value NaN
.
Function  Meaning 

fn:number 
Returns the value indicated by $value or, if $value is not
specified, the context item after atomization, converted to an xs:double .

Returns the value indicated by $value
or, if $value
is not
specified, the context item after atomization, converted to an xs:double
.
fn:number
() as
xs:double
fn:number
($value
as
xs:anyAtomicType?
) as
xs:double
The zeroargument form of this function is ·deterministic·, ·contextdependent·, and ·focusdependent·.
The oneargument form of this function is ·deterministic·, ·contextindependent·, and ·focusindependent·.
Calling the zeroargument version of the function is defined to give the same result
as
calling the singleargument version with the context item (.
). That is,
fn:number()
is equivalent to fn:number(.)
, as defined by
the rules that follow.
If $value
is the empty sequence or if $value
cannot be converted
to an xs:double
, the xs:double
value NaN
is
returned.
Otherwise, $value
is converted to an xs:double
following the
rules of 19.1.2.2 Casting to xs:double. If the conversion to xs:double
fails, the xs:double
value NaN
is returned.
A dynamic error is raised [err:XPDY0002]^{XP}
if $value
is omitted and the context item is absent^{DM31}.
As a consequence of the rules given above, a type error occurs if the context item cannot be atomized, or if the result of atomizing the context item is a sequence containing more than one atomic value.
XSD 1.1 allows the string +INF
as a representation of positive infinity;
XSD 1.0 does not. It is ·implementationdefined· whether XSD 1.1 is
supported.
Generally fn:number
returns NaN
rather than raising a dynamic
error if the argument cannot be converted to xs:double
. However, a type
error is raised in the usual way if the supplied argument cannot be atomized or if
the
result of atomization does not match the required argument type.
The expression fn:number($item1/quantity)
returns 5.0e0
.
The expression fn:number($item2/description)
returns xs:double('NaN')
.
Assume that the context item is the xs:string
value "15
".
Then fn:number()
returns 1.5e1
.
Function  Meaning 

fn:formatinteger 
Formats an integer according to a given picture string, using the conventions of a given natural language if specified. 
Formats an integer according to a given picture string, using the conventions of a given natural language if specified.
fn:formatinteger
($value
as
xs:integer?
, $picture
as
xs:string
) as
xs:string
fn:formatinteger (

$value 
as xs:integer? ,

$picture 
as xs:string ,


$lang 
as xs:string? ) as xs:string 
The twoargument form of this function is ·deterministic·, ·contextdependent·, and ·focusindependent·. It depends on default language.
The threeargument form of this function is ·deterministic·, ·contextindependent·, and ·focusindependent·.
If $value
is an empty sequence, the function returns a zerolength
string.
In all other cases, the $picture
argument describes the format in which
$value
is output.
The rules that follow describe how nonnegative numbers are output. If the value of
$value
is negative, the rules below are applied to the absolute value of
$value
, and a minus sign is prepended to the result.
The value of $picture
consists of a primary format token, optionally
followed by a format modifier. The primary format token is always present and
must not be zerolength. If the string contains one or more
semicolons then everything that precedes the last semicolon is taken as the primary
format token and everything that follows is taken as the format modifier; if the string
contains no semicolon then the entire picture is taken as the primary format token,
and
the format modifier is taken to be absent (which is equivalent to supplying a
zerolength string).
The primary format token is classified as one of the following:
A decimaldigitpattern made up of optionaldigitsigns, mandatorydigitsigns, and groupingseparatorsigns.
The optionaldigitsign is the character "#".
A mandatorydigitsign is a ·character· in Unicode category Nd. All
mandatorydigitsigns within the format token
must be from the same digit family, where a digit
family is a sequence of ten consecutive characters in Unicode category Nd,
having digit values 0 through 9. Within the format token, these digits are
interchangeable: a threedigit number may thus be indicated equivalently by
000
, 001
, or 999
.
a groupingseparatorsign is a nonalphanumeric character, that is a ·character· whose Unicode category is other than Nd, Nl, No, Lu, Ll, Lt, Lm or Lo.
If the primary format token contains at least one Unicode digit then it is taken
as a decimal digit pattern, and in this case it must match the
regular expression ^((\p{Nd}#[^\p{N}\p{L}])+?)$
. If it contains a
digit but does not match this pattern, a dynamic error is raised [err:FODF1310].
Note:
If a semicolon is to be used as a grouping separator, then the primary format token as a whole must be followed by another semicolon, to ensure that the grouping separator is not mistaken as a separator between the primary format token and the format modifier.
There must be at least one mandatorydigitsign. There may be zero or more optionaldigitsigns, and (if present) these must precede all mandatorydigitsigns. There may be zero or more groupingseparatorsigns. A groupingseparatorsign must not appear at the start or end of the decimaldigitpattern, nor adjacent to another groupingseparatorsign.
The corresponding output format is a decimal number, using this digit family, with
at least as many digits as there are mandatorydigitsigns in the
format token. Thus, a format token 1
generates the sequence 0 1
2 ... 10 11 12 ...
, and a format token 01
(or equivalently,
00
or 99
) generates the sequence 00 01 02 ...
09 10 11 12 ... 99 100 101
. A format token of ١
(ArabicIndic digit one) generates the sequence ١
then ٢
then ٣
...
The groupingseparatorsigns are handled as follows:
The position of grouping separators within the format token, counting backwards from the last digit, indicates the position of grouping separators to appear within the formatted number, and the character used as the groupingseparatorsign within the format token indicates the character to be used as the corresponding grouping separator in the formatted number.
More specifically, the position of a grouping separator is the number of optionaldigitsigns and mandatorydigitsigns appearing between the grouping separator and the righthand end of the primary format token.
Grouping separators are defined to be regular if the following conditions apply:
There is at least one grouping separator.
Every grouping separator is the same character (call it C).
There is a positive integer G (the grouping size) such that:
The position of every grouping separator is an integer multiple of G, and
Every positive integer multiple of G that is less than the number of optionaldigitsigns and mandatorydigitsigns in the primary format token is the position of a grouping separator.
The grouping separator template is a (possibly infinite) set of (position, character) pairs.
If grouping separators are regular, then the grouping separator template contains
one pair of the form (n×G, C)
for every positive integer n where G is the grouping size and C is the grouping character.
Otherwise (when grouping separators are not regular), the grouping separator template
contains one pair of the form
(P, C)
for every grouping separator found in the primary formatting token, where C is the grouping
separator character and P is its position.
Note:
If there are no grouping separators, then the grouping separator template is an empty set.
The number is formatted as follows:
Let S_{1} be the result of formatting the supplied number in decimal notation as if by casting
it to xs:string
.
Let S_{2} be the result of padding S_{1} on the left with as many leading zeroes as are needed to ensure that it contains at least as many digits as the number of mandatorydigitsigns in the primary format token.
Let S_{3} be the result of replacing all decimal digits (09) in S_{2} with the corresponding digits from the selected digit family.
Let S_{4} be the result of inserting grouping separators into S_{3}: for every (position P, character C) pair in the grouping separator template where P is less than the number of digits in S_{3}, insert character C into S_{3} at position P, counting from the righthand end.
Let S_{5} be the result of converting S_{4} into ordinal form, if an ordinal modifier is present, as described below.
The result of the function is then S_{5}.
The format token A
, which generates the sequence A B C ... Z AA
AB AC...
.
The format token a
, which generates the sequence a b c ... z aa
ab ac...
.
The format token i
, which generates the sequence i ii iii iv v
vi vii viii ix x ...
.
The format token I
, which generates the sequence I II III IV V
VI VII VIII IX X ...
.
The format token w
, which generates numbers written as lowercase
words, for example in English, one two three four ...
The format token W
, which generates numbers written as uppercase
words, for example in English, ONE TWO THREE FOUR ...
The format token Ww
, which generates numbers written as titlecase
words, for example in English, One Two Three Four ...
Any other format token, which indicates a numbering sequence in which that token
represents the number 1 (one) (but see the note below).
It is ·implementationdefined· which
numbering sequences, additional to those listed above, are supported. If an
implementation does not support a numbering sequence represented by the given
token, it must use a format token of 1
.
Note:
In some traditional numbering sequences additional signs are added to denote that the letters should be interpreted as numbers; these are not included in the format token. An example (see also the example below) is classical Greek where a dexia keraia (x0374, ʹ) and sometimes an aristeri keraia (x0375, ͵) is added.
For all format tokens other than a decimaldigitpattern, there
may be ·implementationdefined· lower and upper bounds on the range of numbers that
can be formatted using this format token; indeed, for some numbering sequences there
may
be intrinsic limits. For example, the format token ①
(circled
digit one, ①) has a range imposed by the Unicode character repertoire — zero to 20
in Unicode versions prior to 3.2, or zero to 50 in subsequent versions. For the numbering
sequences described above any upper bound imposed by the implementation must
not be less than 1000 (one thousand) and any lower bound must not be
greater than 1. Numbers that fall outside this range must be
formatted using the format token 1
.
The above expansions of numbering sequences for format tokens such as a
and
i
are indicative but not prescriptive. There are various conventions in
use for how alphabetic sequences continue when the alphabet is exhausted, and differing
conventions for how roman numerals are written (for example, IV
versus
IIII
as the representation of the number 4). Sometimes alphabetic
sequences are used that omit letters such as i
and o
. This
specification does not prescribe the detail of any sequence other than those sequences
consisting entirely of decimal digits.
Many numbering sequences are languagesensitive. This applies especially to the sequence
selected by the tokens w
, W
and Ww
. It also
applies to other sequences, for example different languages using the Cyrillic alphabet
use different sequences of characters, each starting with the letter #x410 (Cyrillic
capital letter A). In such cases, the $lang
argument specifies which
language's conventions are to be used. If the argument is specified, the value
should be either an empty sequence or a value that would be valid
for the xml:lang
attribute (see [Extensible Markup Language (XML) 1.0 (Fifth Edition)]). Note that this
permits the identification of sublanguages based on country codes (from ISO 31661)
as
well as identification of dialects and regions within a country.
The set of languages for which numbering is supported is ·implementationdefined·. If the $lang
argument is absent, or is
set to an empty sequence, or is invalid, or is not a language supported by the
implementation, then the number is formatted using the default language from the dynamic
context.
The format modifier must be a string that matches the regular
expression ^([co](\(.+\))?)?[at]?$
. That is, if it is present it must
consist of one or more of the following, in order:
either c
or o
, optionally followed by a sequence of
characters enclosed between parentheses, to indicate cardinal or ordinal numbering
respectively, the default being cardinal numbering
either a
or t
, to indicate alphabetic or traditional
numbering respectively, the default being ·implementationdefined·.
If the o
modifier is present, this indicates a request to output ordinal
numbers rather than cardinal numbers. For example, in English, when used with the
format
token 1
, this outputs the sequence 1st 2nd 3rd 4th ...
, and
when used with the format token w
outputs the sequence first second
third fourth ...
.
The string of characters between the parentheses, if present, is used to select between other possible variations of cardinal or ordinal numbering sequences. The interpretation of this string is ·implementationdefined·. No error occurs if the implementation does not define any interpretation for the defined string.
It is ·implementationdefined· what combinations of values of the format token, the language, and the cardinal/ordinal modifier are supported. If ordinal numbering is not supported for the combination of the format token, the language, and the string appearing in parentheses, the request is ignored and cardinal numbers are generated instead.
The use of the a
or t
modifier disambiguates between numbering
sequences that use letters. In many languages there are two commonly used numbering
sequences that use letters. One numbering sequence assigns numeric values to letters
in
alphabetic sequence, and the other assigns numeric values to each letter in some other
manner traditional in that language. In English, these would correspond to the numbering
sequences specified by the format tokens a
and i
. In some
languages, the first member of each sequence is the same, and so the format token
alone
would be ambiguous. In the absence of the a
or t
modifier, the
default is ·implementationdefined·.
A dynamic error is raised [err:FODF1310] if the format token is invalid, that is, if it violates any mandatory rules (indicated by an emphasized must or required keyword in the above rules). For example, the error is raised if the primary format token contains a digit but does not match the required regular expression.
Note the careful distinction between conditions that are errors and conditions where fallback occurs. The principle is that an error in the syntax of the format picture will be reported by all processors, while a construct that is recognized by some implementations but not others will never result in an error, but will instead cause a fallback representation of the integer to be used.
The following notes apply when a decimaldigitpattern is used:
If groupingseparatorsigns
appear at regular intervals within the format token, then the sequence is extrapolated
to
the left, so grouping separators will be used in the formatted number at every
multiple of N. For example, if the format token is 0'000
then the number one million will be formatted as 1'000'000
, while the
number fifteen will be formatted as 0'015
.
The only purpose of optionaldigitsigns is to mark the position of
groupingseparatorsigns. For example, if the format token is
#'##0
then the number one million will be formatted as
1'000'000
, while the number fifteen will be formatted as
15
. A grouping separator is included in the formatted number only
if there is a digit to its left, which will only be the case if either (a) the
number is large enough to require that digit, or (b) the number of
mandatorydigitsigns in the format token requires insignificant
leading zeros to be present.
Grouping separators are not designed for effects such as
formatting a US telephone number as (365)1239876
. In general they are not
suitable for such purposes because (a) only single characters are allowed, and (b)
they
cannot appear at the beginning or end of the number.
Numbers will never be truncated. Given the decimaldigitpattern
01
, the number three hundred will be output as 300
,
despite the absence of any optionaldigitsign.
The following notes apply when ordinal numbering is selected using the o
modifier.
In some languages, the form of numbers (especially ordinal numbers) varies depending
on the grammatical context: they may have different genders and may decline with the
noun that they qualify. In such cases the string appearing in parentheses after the
letter c
or o
may be used to indicate the variation of the
cardinal or ordinal number required.
The way in which the variation is indicated will depend on the conventions of the language.
For inflected languages that vary the ending of the word, the approach recommended
in the previous version of this specification was to indicate the required ending,
preceded by a hyphen: for example in German, appropriate values might be
o(e)
, o(er)
, o(es)
, o(en)
.
Another approach, which might usefully be adopted by an implementation based on the
opensource ICU localization library [ICU], or any other library making use of the
Unicode Common Locale Data Repository [Unicode CLDR], is to allow the value in parentheses
to be the name of a registered numbering rule set for the language in question,
conventionally prefixed with a percent sign: for example,
o(%spelloutordinalmasculine)
, or c(%spelloutcardinalyear)
.
The expression formatinteger(123, '0000')
returns "0123"
.
formatinteger(123, 'w')
might return "one hundred and
twentythree"
Ordinal numbering in Italian: The specification "1;o(º)"
with $lang
equal to
it
, if supported, should produce the sequence:
1º 2º 3º 4º ...
The specification "Ww;o"
with $lang
equal to
it
, if supported, should produce the sequence:
Primo Secondo Terzo Quarto Quinto ...
The expression formatinteger(21, '1;o', 'en')
returns "21st"
.
formatinteger(14, 'Ww;o(e)', 'de')
might return
"Vierzehnte"
The expression formatinteger(7, 'a')
returns "g"
.
The expression formatinteger(57, 'I')
returns "LVII"
.
The expression formatinteger(1234, '#;##0;')
returns "1;234"
.
This section defines a function for formatting decimal and floating point numbers.
Function  Meaning 

fn:formatnumber 
Returns a string containing a number formatted according to a given picture string, taking account of decimal formats specified in the static context. 
Note:
This function can be used to format any numeric quantity, including an integer. For
integers, however,
the fn:formatinteger
function offers additional possibilities. Note also that the picture
strings used by the two functions are not 100% compatible, though they
share some options in common.
Decimal formats are defined in the static context, and the way they are defined is therefore outside the scope of this specification. XSLT and XQuery both provide custom syntax for creating a decimal format.
The static context provides a set of decimal formats. One of the decimal formats is unnamed, the others (if any) are identified by a QName. There is always an unnamed decimal format available, but its contents are ·implementationdefined·.
Each decimal format provides a set of named properties, described in the following table:
Name  Type  Usage (nonnormative) 

decimalseparator 
A single ·character·  Defines the character used to represent the decimal point (typically ".") both in the picture string and in the formatted number. 
groupingseparator 
A single ·character·  Defines the character used to separate groups of digits (typically ",") both in the picture string and in the formatted number. 
exponentseparator 
A single ·character·  Defines the character used to separate the mantissa from the exponent in scientific notation (typically "e") both in the picture string and in the formatted number. 
infinity 
A ·string·  Defines the string used to represent the value positive or negative infinity in the formatted number (typically "Infinity") 
minussign 
A single ·character·  Defines the character used as a minus sign in the formatted number if there is no subpicture for formatting negative numbers (typically "", x2D) 
NaN 
A ·string·  Defines the string used to represent the value NaN in the formatted number

percent 
A single ·character·  Defines the character used as a percent sign (typically "%") both in the picture string and in the formatted number 
permille 
A single ·character·  Defines the character used as a permille sign (typically "‰", x2030) both in the picture string and in the formatted number 
zerodigit 
A single ·character·, which must be a character in Unicode category Nd with decimal digit value 0 (zero)  Defines the characters used in the picture string to represent a mandatory digit: for example, if the zerodigit is "0" then any of the digits "0" to "9" may be used (interchangeably) in the picture string to represent a mandatory digit, and in the formatted number the characters "0" to "9" will be used to represent the digits zero to nine. 
digit 
A single ·character·  Defines the character used in the picture string to represent an optional digit (typically "#") 
patternseparator 
A single ·character·  Defines the character used in the picture string to separate the positive and negative subpictures (typically ";") 
Note:
A phrase such as "The minussign^{XP31} character" is to be read as "the character assigned to the minussign^{XP31} property in the relevant decimal format within the static context".
[Definition] The decimal digit family of a decimal format is the sequence of ten digits with consecutive Unicode ·codepoints· starting with the character that is the value of the zerodigit^{XP31} property.
[Definition] The optional digit character is the character that is the value of the digit^{XP31} property.
For any named or unnamed decimal format, the properties representing characters used in a ·picture string· must have distinct values. These properties are decimalseparator^{XP31} , groupingseparator^{XP31}, exponentseparator^{XP31}, percent^{XP31}, permille^{XP31}, digit^{XP31}, and patternseparator^{XP31}. Furthermore, none of these properties may be equal to any ·character· in the ·decimal digit family·.
Returns a string containing a number formatted according to a given picture string, taking account of decimal formats specified in the static context.
fn:formatnumber
($value
as
xs:numeric?
, $picture
as
xs:string
) as
xs:string
fn:formatnumber (

$value 
as xs:numeric? ,

$picture 
as xs:string ,


$decimalformatname 
as union(xs:string, xs:QName)? ) as xs:string 
The twoargument form of this function is ·deterministic·, ·contextindependent·, and ·focusindependent·.
The threeargument form of this function is ·deterministic·, ·contextdependent·, and ·focusindependent·. It depends on decimal formats, and namespaces.
The effect of the twoargument form of the function is equivalent to calling the threeargument form with an empty sequence as the value of the third argument.
The function formats $value
as a string using the ·picture string· specified by the
$picture
argument and the decimalformat named by the
$decimalformatname
argument, or the unnamed decimalformat, if there
is no $decimalformatname
argument. The syntax of the picture string is
described in 4.7.3 Syntax of the picture string.
The $value
argument may be of any numeric data type
(xs:double
, xs:float
, xs:decimal
, or their
subtypes including xs:integer
). Note that if an xs:decimal
is
supplied, it is not automatically promoted to an xs:double
, as such
promotion can involve a loss of precision.
If the supplied value of the $value
argument is an empty sequence, the
function behaves as if the supplied value were the xs:double
value
NaN
.
The value of $decimalformatname
, if present and nonempty,
must be either an xs:QName
,
or a string which after removal of leading and trailing
whitespace is in the form of an EQName
as defined in the XPath 4.0
grammar, that is one of the following:
A lexical QName, which is expanded using the statically known namespaces. The default namespace is not used (no prefix means no namespace).
A URIQualifiedName
using the syntax Q{uri}local
, where
the URI can be zerolength to indicate a name in no namespace.
The decimal format that is used is the decimal format in the static context whose
name
matches $decimalformatname
if supplied, or the unnamed decimal format in
the static context otherwise.
The evaluation of the fn:formatnumber
function takes place in two
phases, an analysis phase described in 4.7.4 Analyzing the picture string and a
formatting phase described in 4.7.5 Formatting the number.
The analysis phase takes as its inputs the ·picture string· and the variables derived from the relevant decimal format in the static context, and produces as its output a number of variables with defined values. The formatting phase takes as its inputs the number to be formatted and the variables produced by the analysis phase, and produces as its output a string containing a formatted representation of the number.
The result of the function is the formatted string representation of the supplied number.
A dynamic error is raised [err:FODF1280]
if
the $decimalformatname
argument is supplied as an xs:string
that is neither a valid lexical QName nor a
valid URIQualifiedName
, or if it uses a prefix that is not found in the
statically known namespaces, or if the static context does not contain a declaration
of
a decimalformat with a matching expanded QName. If the processor is able to detect
the
error statically (for example, when the argument is supplied as a string literal),
then
the processor may optionally signal this as a static error.
A string is an ordered sequence of characters, and this specification uses terms such as "left" and "right", "preceding" and "following" in relation to this ordering, irrespective of the position of the characters when visually rendered on some output medium. Both in the picture string and in the result string, digits with higher significance (that is, representing higher powers of ten) always precede digits with lower significance, even when the rendered text flow is from right to left.
The following examples assume a default decimal format in which the chosen digits are the ASCII digits 09, the decimal separator is ".", the grouping separator is ",", the minussign is "", and the percentsign is "%".
The expression formatnumber(12345.6, '#,###.00')
returns "12,345.60"
.
The expression formatnumber(12345678.9, '9,999.99')
returns "12,345,678.90"
.
The expression formatnumber(123.9, '9999')
returns "0124"
.
The expression formatnumber(0.14, '01%')
returns "14%"
.
The expression formatnumber(6, '000')
returns "006"
.
The following example assumes the existence of a decimal format named 'ch' in which
the grouping separator is ʹ
and the decimal separator is
·
:
The expression formatnumber(1234.5678, '#ʹ##0·00',
'ch')
returns "1ʹ234·57"
.
The following examples assume that the exponent separator is in decimal format 'fortran' is 'E':
The expression formatnumber(1234.5678, '00.000E0', 'fortran')
returns "12.346E2"
.
The expression formatnumber(0.234, '0.0E0', 'fortran')
returns "2.3E1"
.
The expression formatnumber(0.234, '#.00E0', 'fortran')
returns "0.23E0"
.
The expression formatnumber(0.234, '.00E0', 'fortran')
returns ".23E0"
.
Note:
This differs from the formatnumber
function previously defined in XSLT 2.0 in that
any digit can be used in the picture string to represent a mandatory digit:
for example the picture
strings '000', '001', and '999' are equivalent. The digits will all be from
the same decimal digit family,
specifically, the sequence of ten consecutive digits starting with the digit
assigned to the zerodigit property.
This change is to align formatnumber
(which previously used '000') with formatdateTime
(which used '001').
[Definition] The formatting of a number is controlled by a picture string. The picture string is a sequence of ·characters·, in which the characters assigned to the properties decimalseparator^{XP31} , exponentseparator^{XP31}, groupingseparator^{XP31}, and digit^{XP31}, and patternseparator^{XP31} and the members of the ·decimal digit family·, are classified as active characters, and all other characters (including the values of the properties percent^{XP31} and permille^{XP31}) are classified as passive characters.
A dynamic error is raised [err:FODF1310] if the ·picture string· does not conform to the following rules. Note that in these rules the words "preceded" and "followed" refer to characters anywhere in the string, they are not to be read as "immediately preceded" and "immediately followed".
A picturestring consists either of a subpicture, or of two subpictures separated by the patternseparator^{XP31} character. A picturestring must not contain more than one instance of the patternseparator^{XP31} character. If the picturestring contains two subpictures, the first is used for positive and unsigned zero values and the second for negative values.
A subpicture must not contain more than one instance of the decimalseparator^{XP31} character.
A subpicture must not contain more than one instance of the percent^{XP31} or permille^{XP31} characters, and it must not contain one of each.
The mantissa part of a subpicture (defined below) must contain at least one character that is either an ·optional digit character· or a member of the ·decimal digit family·.
A subpicture must not contain a passive character that is preceded by an active character and that is followed by another active character.
A subpicture must not contain a groupingseparator^{XP31} character that appears adjacent to a decimalseparator^{XP31} character, or in the absence of a decimalseparator^{XP31} character, at the end of the integer part.
A subpicture must not contain two adjacent instances of the groupingseparator^{XP31} character.
The integer part of a subpicture (defined below) must not contain a member of the ·decimal digit family· that is followed by an instance of the ·optional digit character·. The fractional part of a subpicture (defined below) must not contain an instance of the ·optional digit character· that is followed by a member of the ·decimal digit family·.
A character that matches the exponentseparator^{XP31} property is treated as an exponentseparatorsign if it is both preceded and followed within the subpicture by an active character. Otherwise, it is treated as a passive character. A subpicture must not contain more than one character that is treated as an exponentseparatorsign.
A subpicture that contains a percent^{XP31} or permille^{XP31} character must not contain a character treated as an exponentseparatorsign.
If a subpicture contains a character treated as an exponentseparatorsign then this must be followed by one or more characters that are members of the ·decimal digit family·, and it must not be followed by any active character that is not a member of the ·decimal digit family·.
The mantissa part of the subpicture is defined as the part that appears to the left of the exponentseparatorsign if there is one, or the entire subpicture otherwise. The exponent part of the subpicture is defined as the part that appears to the right of the exponentseparatorsign; if there is no exponentseparatorsign then the exponent part is absent.
The integer part of the subpicture is defined as the part that appears to the left of the decimalseparator^{XP31} character if there is one, or the entire mantissa part otherwise.
The fractional part of the subpicture is defined as that part of the mantissa part that appears to the right of the decimalseparator^{XP31} character if there is one, or the part that appears to the right of the rightmost active character otherwise. The fractional part may be zerolength.
This phase of the algorithm analyzes the ·picture string· and the properties from the selected decimal format in the static context, and it has the effect of setting the values of various variables, which are used in the subsequent formatting phase. These variables are listed below. Each is shown with its initial setting and its datatype.
Several variables are associated with each subpicture. If there are two subpictures, then these rules are applied to one subpicture to obtain the values that apply to positive and unsigned zero numbers, and to the other to obtain the values that apply to negative numbers. If there is only one subpicture, then the values for both cases are derived from this subpicture.
The variables are as follows:
The integerpartgroupingpositions is a sequence of integers representing the positions of grouping separators within the integer part of the subpicture. For each groupingseparator^{XP31} character that appears within the integer part of the subpicture, this sequence contains an integer that is equal to the total number of ·optional digit character· and ·decimal digit family· characters that appear within the integer part of the subpicture and to the right of the groupingseparator^{XP31} character.
The grouping is defined to be regular if the following conditions apply:
There is an least one groupingseparator in the integer part of the subpicture.
There is a positive integer G (the grouping size) such that the position of every groupingseparator in the integer part of the subpicture is a positive integer multiple of G.
Every position in the integer part of the subpicture that is a positive integer multiple of G is occupied by a groupingseparator.
If the grouping is regular, then the integerpartgroupingpositions sequence contains all integer multiples of G as far as necessary to accommodate the largest possible number.
The minimumintegerpartsize is an integer indicating the minimum number of digits that will appear to the left of the decimalseparator character. It is initially set to the number of ·decimal digit family· characters found in the integer part of the subpicture, but may be adjusted as described below.
Note:
There is no maximum integer part size. All significant digits in the integer part of the number will be displayed, even if this exceeds the number of ·optional digit character· and ·decimal digit family· characters in the subpicture.
The scaling factor is a nonnegative integer used to determine the scaling of the mantissa in exponential notation. It is set to the number of ·decimal digit family· characters found in the integer part of the subpicture.
The prefix is set to contain all passive characters in the subpicture to the left of the leftmost active character. If the picture string contains only one subpicture, the prefix for the negative subpicture is set by concatenating the minussign^{XP31} character and the prefix for the positive subpicture (if any), in that order.
The fractionalpartgroupingpositions is a sequence of integers representing the positions of grouping separators within the fractional part of the subpicture. For each groupingseparator^{XP31} character that appears within the fractional part of the subpicture, this sequence contains an integer that is equal to the total number of ·optional digit character· and ·decimal digit family· characters that appear within the fractional part of the subpicture and to the left of the groupingseparator^{XP31} character.
Note:
There is no need to extrapolate grouping positions on the fractional side, because the number of digits in the output will never exceed the number of ·optional digit character· and ·decimal digit family· characters in the fractional part of the subpicture.
The minimumfractionalpartsize is set to the number of ·decimal digit family· characters found in the fractional part of the subpicture.
The maximumfractionalpartsize is set to the total number of ·optional digit character· and ·decimal digit family· characters found in the fractional part of the subpicture.
If the effect of the above rules is that minimumintegerpartsize and maximumfractionalpartsize are both zero, then an adjustment is applied as follows:
If an exponent separator is present then:
minimumfractionalpartsize is changed to 1 (one).
maximumfractionalpartsize is changed to 1 (one).
Note:
This has the effect that with the picture #.e9
, the value 0.123
is formatted as 0.1e0
Otherwise:
minimumintegerpartsize is changed to 1 (one).
Note:
This has the effect that with the picture #
, the value 0.23
is formatted
as 0
If all the following conditions are true:
An exponent separator is present
The minimumintegerpartsize is zero
There is at least one ·optional digit character· in the integer part of the subpicture
then the minimumintegerpartsize is changed to 1 (one).
Note:
This has the effect that with the picture .9e9
, the value 0.1
is formatted
as .1e0
, while with the picture #.9e9
, it is formatted as 0.1e0
If (after making the above adjustments) the minimumintegerpartsize and the minimumfractionalpartsize are both zero, then the minimumfractionalpartsize is set to 1 (one).
The minimumexponentsize is set to the number of ·decimal digit family· characters found in the exponent part of the subpicture if present, or zero otherwise.
Note:
The rules for the syntax of the picture string ensure that if an exponent separator is present, then the minimumexponentsize will always be greater than zero.
The suffix is set to contain all passive characters to the right of the rightmost active character in the subpicture.
Note:
If there is only one subpicture, then all variables for positive numbers and negative numbers will be the same, except for prefix: the prefix for negative numbers will be preceded by the minussign^{XP31} character.
This section describes the second phase of processing of the
fn:formatnumber
function. This phase takes as input a number to be formatted
(referred to as the input number), and the variables set up by
analyzing the decimal format in the static context and the
·picture string·, as described above.
The result of this phase is a string, which forms the return value of
the fn:formatnumber
function.
The algorithm for this second stage of processing is as follows:
If the input number is NaN (not a number), the result is the value of the pattern separator^{XP31} property (with no prefix or suffix).
In the rules below, the positive subpicture and its associated variables are used
if the input number is positive, and the negative subpicture and its associated
variables are used if it is negative. For xs:double
and xs:float
,
negative zero is taken as negative, positive zero as positive. For xs:decimal
and xs:integer
, the positive subpicture is used for zero.
The adjusted number is determined as follows:
If the subpicture contains a percent^{XP31} character, the adjusted number is the input number multiplied by 100.
If the subpicture contains a permille^{XP31} character, the adjusted number is the input number multiplied by 1000.
Otherwise, the adjusted number is the input number.
If the multiplication causes numeric overflow, no error occurs, and the adjusted number is positive or negative infinity as appropriate.
If the adjusted number is positive or negative infinity, the result is the concatenation of the appropriate prefix, the value of the infinity^{XP31} property, and the appropriate suffix.
If the minimum exponent size is nonzero, and the adjusted number is nonzero, then the adjusted number is scaled to establish a mantissa and an integer exponent. The mantissa and exponent are chosen such that all the following conditions are true:
The primitive type of the mantissa is the same as the primitive type of the adjusted number (integer, decimal, float, or double).
The mantissa multiplied by ten to the power of the exponent is equal to the adjusted number.
The mantissa is less than 10^{N}, and at least 10^{N1}, where N is the scaling factor.
If the minimum exponent size is zero, then the mantissa is the adjusted number and there is no exponent.
If the minimum exponent size is nonzero and the adjusted number is zero, then the mantissa is the adjusted number and the exponent is zero.
The mantissa is converted (if necessary) to
an xs:decimal
value,
using an implementation of xs:decimal
that imposes no limits on the
totalDigits
or fractionDigits
facets. If there are several
such values that
are numerically equal to the mantissa (bearing in mind that if the
mantissa is an xs:double
or xs:float
, the comparison will be done by
converting the decimal value back to an xs:double
or xs:float
), the one that
is chosen should be one with the smallest possible number of digits
not counting leading or trailing zeroes (whether significant or insignificant).
For example, 1.0 is preferred to
0.9999999999, and 100000000 is preferred to 100000001. This value is then
rounded so that it uses no more than maximumfractionalpartsize
digits in
its fractional part. The rounded number is defined to be the result of
converting the mantissa to an xs:decimal
value, as described above,
and then calling the function fn:roundhalftoeven
with this converted number
as the first argument and the maximumfractionalpartsize
as the second
argument, again with no limits on the totalDigits
or fractionDigits
in the
result.
The absolute value of the rounded number is converted to a string in decimal notation, using the digits in the ·decimal digit family· to represent the ten decimal digits, and the decimalseparator^{XP31} character to separate the integer part and the fractional part. This string must always contain a decimalseparator^{XP31}, and it must contain no leading zeroes and no trailing zeroes. The value zero will at this stage be represented by a decimalseparator^{XP31} on its own.
If the number of digits to the left of the decimalseparator^{XP31} character is less than minimumintegerpartsize, leading zero digit^{XP31} characters are added to pad out to that size.
If the number of digits to the right of the decimalseparator^{XP31} character is less than minimumfractionalpartsize, trailing zero digit^{XP31} characters are added to pad out to that size.
For each integer N in the integerpartgroupingpositions list, a groupingseparator^{XP31} character is inserted into the string immediately after that digit that appears in the integer part of the number and has N digits between it and the decimalseparator^{XP31} character, if there is such a digit.
For each integer N in the fractionalpartgroupingpositions list, a groupingseparator^{XP31} character is inserted into the string immediately before that digit that appears in the fractional part of the number and has N digits between it and the decimalseparator^{XP31} character, if there is such a digit.
If there is no decimalseparator^{XP31} character in the subpicture, or if there are no digits to the right of the decimalseparator character in the string, then the decimalseparator character is removed from the string (it will be the rightmost character in the string).
If an exponent exists, then the string produced from the mantissa as described above is extended with the following, in order: (a) the exponentseparator^{XP31} character; (b) if the exponent is negative, the minussign^{XP31} character; (c) the value of the exponent represented as a decimal integer, extended if necessary with leading zeroes to make it up to the minimum exponent size, using digits taken from the ·decimal digit family·.
The result of the function is the concatenation of the appropriate prefix, the string conversion of the number as obtained above, and the appropriate suffix.
The functions in this section perform trigonometric and other mathematical calculations
on xs:double
values. They
are provided primarily for use in applications performing geometrical computation,
for example when generating
SVG graphics.
Functions are provided to support the six most commonly used trigonometric calculations: sine, cosine and tangent, and their inverses arc sine, arc cosine, and arc tangent. Other functions such as secant, cosecant, and cotangent are not provided because they are easily computed in terms of these six.
The functions in this section (with the exception of math:pi
)
are specified by reference to [IEEE 7542008], where
they appear as Recommended operations in section 9. IEEE defines
these functions for a variety of floating point formats; this specification
defines them only for xs:double
values. The IEEE specification
applies with the following caveats:
IEEE states that the preferred quantum is languagedefined. In this specification, it is ·implementationdefined·.
IEEE states that certain functions should raise the inexact exception if the result is inexact. In this specification, this exception if it occurs does not result in an error. Any diagnostic information is outside the scope of this specification.
IEEE defines various rounding algorithms for inexact results, and states that the choice of rounding direction, and the mechanisms for influencing this choice, are languagedefined. In this specification, the rounding direction and any mechanisms for influencing it are ·implementationdefined·.
Certain operations (such as taking the square root of a negative number)
are defined in IEEE to signal the invalid operation exception and return
a
quiet NaN. In this specification, such operations return NaN
and do not raise an error. The same policy applies to operations (such
as taking
the logarithm of zero) that raise a dividebyzero exception. Any diagnostic
information is outside the scope of this specification.
Operations whose mathematical result is greater than the largest finite xs:double
value are defined in IEEE to signal the overflow exception; operations
whose mathematical
result is closer to zero than the smallest nonzero xs:double
value are similarly
defined in IEEE to signal the underflow exception. The treatment of these
exceptions in
this specification is defined in 4.2 Arithmetic operators on numeric values.
Function  Meaning 

math:pi 
Returns an approximation to the mathematical constant π. 
math:exp 
Returns the value of e^{x} where x is the argument value. 
math:exp10 
Returns the value of 10 ^{x}, where x is the supplied argument value.

math:log 
Returns the natural logarithm of the argument. 
math:log10 
Returns the baseten logarithm of the argument. 
math:pow 
Returns the result of raising the first argument to the power of the second. 
math:sqrt 
Returns the nonnegative square root of the argument. 
math:sin 
Returns the sine of the argument. The argument is an angle in radians. 
math:cos 
Returns the cosine of the argument. The argument is an angle in radians. 
math:tan 
Returns the tangent of the argument. The argument is an angle in radians. 
math:asin 
Returns the arc sine of the argument. 
math:acos 
Returns the arc cosine of the argument. 
math:atan 
Returns the arc tangent of the argument. 
math:atan2 
Returns the angle in radians subtended at the origin by the point on a plane with coordinates (x, y) and the positive xaxis. 
Returns an approximation to the mathematical constant π.
math:pi
() as
xs:double
This function is ·deterministic·, ·contextindependent·, and ·focusindependent·.
This function returns the xs:double
value whose lexical representation is
3.141592653589793e0
The expression 2*math:pi()
returns 6.283185307179586e0
.
The expression 60 * (math:pi() div 180)
converts an angle of 60 degrees
to radians.
Returns the value of e^{x} where x is the argument value.
math:exp
($value
as
xs:double?
) as
xs:double?
This function is ·deterministic·, ·contextindependent·, and ·focusindependent·.
If $value
is the empty sequence, the function returns the empty sequence.
Otherwise the result is the mathematical constant e raised to the power of
$value
, as defined in the [IEEE 7542008] specification of
the exp
function applied to 64bit binary floating point values.
The treatment of overflow and underflow is defined in 4.2 Arithmetic operators on numeric values.
The expression math:exp(())
returns ()
.
The expression math:exp(0)
returns 1.0e0
.
The expression math:exp(1)
returns 2.7182818284590455e0
(approximately).
The expression math:exp(2)
returns 7.38905609893065e0
.
The expression math:exp(1)
returns 0.36787944117144233e0
.
The expression math:exp(math:pi())
returns 23.140692632779267e0
.
The expression math:exp(xs:double('NaN'))
returns xs:double('NaN')
.
The expression math:exp(xs:double('INF'))
returns xs:double('INF')
.
The expression math:exp(xs:double('INF'))
returns 0.0e0
.
Returns the value of 10
^{x}, where x is the supplied argument value.
math:exp10
($value
as
xs:double?
) as
xs:double?
This function is ·deterministic·, ·contextindependent·, and ·focusindependent·.
If $value
is the empty sequence, the function returns the empty sequence.
Otherwise the result is ten raised to the power of $value
, as defined in the
[IEEE 7542008] specification of the exp10
function applied
to 64bit binary floating point values.
The treatment of overflow and underflow is defined in 4.2 Arithmetic operators on numeric values.
The expression math:exp10(())
returns ()
.
The expression math:exp10(0)
returns 1.0e0
.
The expression math:exp10(1)
returns 1.0e1
.
The expression math:exp10(0.5)
returns 3.1622776601683795e0
.
The expression math:exp10(1)
returns 1.0e1
.
The expression math:exp10(xs:double('NaN'))
returns xs:double('NaN')
.
The expression math:exp10(xs:double('INF'))
returns xs:double('INF')
.
The expression math:exp10(xs:double('INF'))
returns 0.0e0
.
Returns the natural logarithm of the argument.
math:log
($value
as
xs:double?
) as
xs:double?
This function is ·deterministic·, ·contextindependent·, and ·focusindependent·.
If $value
is the empty sequence, the function returns the empty sequence.
Otherwise the result is the natural logarithm of $value
, as defined in the
[IEEE 7542008] specification of the log
function applied
to 64bit binary floating point values.
The treatment of divideByZero
and invalidOperation
exceptions
is defined in 4.2 Arithmetic operators on numeric values. The effect is that if the argument is
zero, the result is INF
, and if it is negative, the result is NaN
.
The expression math:log(())
returns ()
.
The expression math:log(0)
returns xs:double('INF')
.
The expression math:log(math:exp(1))
returns 1.0e0
.
The expression math:log(1.0e3)
returns 6.907755278982137e0
.
The expression math:log(2)
returns 0.6931471805599453e0
.
The expression math:log(1)
returns xs:double('NaN')
.
The expression math:log(xs:double('NaN'))
returns xs:double('NaN')
.
The expression math:log(xs:double('INF'))
returns xs:double('INF')
.
The expression math:log(xs:double('INF'))
returns xs:double('NaN')
.
Returns the baseten logarithm of the argument.
math:log10
($value
as
xs:double?
) as
xs:double?
This function is ·deterministic·, ·contextindependent·, and ·focusindependent·.
If $value
is the empty sequence, the function returns the empty sequence.
Otherwise the result is the base10 logarithm of $value
, as defined in the
[IEEE 7542008] specification of the log10
function applied
to 64bit binary floating point values.
The treatment of divideByZero
and invalidOperation
exceptions
is defined in 4.2 Arithmetic operators on numeric values. The effect is that if the argument is
zero, the result is INF
, and if it is negative, the result is NaN
.
The expression math:log10(())
returns ()
.
The expression math:log10(0)
returns xs:double('INF')
.
The expression math:log10(1.0e3)
returns 3.0e0
.
The expression math:log10(1.0e3)
returns 3.0e0
.
The expression math:log10(2)
returns 0.3010299956639812e0
.
The expression math:log10(1)
returns xs:double('NaN')
.
The expression math:log10(xs:double('NaN'))
returns xs:double('NaN')
.
The expression math:log10(xs:double('INF'))
returns xs:double('INF')
.
The expression math:log10(xs:double('INF'))
returns xs:double('NaN')
.
Returns the result of raising the first argument to the power of the second.
math:pow
($x
as
xs:double?
, $y
as
xs:numeric
) as
xs:double?
This function is ·deterministic·, ·contextindependent·, and ·focusindependent·.
If $x
is the empty sequence, the function returns the empty sequence.
If $y
is an instance of xs:integer
, the result is
$x
raised to the power of $y
as defined in the [IEEE 7542008] specification of the pown
function applied to a
64bit binary floating point value and an integer.
Otherwise $y
is converted to an xs:double
by numeric
promotion, and the result is $x
raised to the power of
$y
as defined in the [IEEE 7542008] specification of the
pow
function applied to two 64bit binary floating point values.
The treatment of the divideByZero
and invalidOperation
exceptions is defined in 4.2 Arithmetic operators on numeric values. Some of the consequences are
illustrated in the examples below.
The expression math:pow((), 93.7)
returns ()
.
The expression math:pow(2, 3)
returns 8.0e0
.
The expression math:pow(2, 3)
returns 8.0e0
.
The expression math:pow(2, 3)
returns 0.125e0
.
The expression math:pow(2, 3)
returns 0.125e0
.
The expression math:pow(2, 0)
returns 1.0e0
.
The expression math:pow(0, 0)
returns 1.0e0
.
The expression math:pow(xs:double('INF'), 0)
returns 1.0e0
.
The expression math:pow(xs:double('NaN'), 0)
returns 1.0e0
.
The expression math:pow(math:pi(), 0)
returns 1.0e0
.
The expression math:pow(0e0, 3)
returns 0.0e0
.
The expression math:pow(0e0, 4)
returns 0.0e0
.
The expression math:pow(0e0, 3)
returns 0.0e0
.
The expression math:pow(0, 4)
returns 0.0e0
.
The expression math:pow(0e0, 3)
returns xs:double('INF')
.
The expression math:pow(0e0, 4)
returns xs:double('INF')
.
The expression math:pow(0e0, 3)
returns xs:double('INF')
.
The expression math:pow(0, 4)
returns xs:double('INF')
.
The expression math:pow(16, 0.5e0)
returns 4.0e0
.
The expression math:pow(16, 0.25e0)
returns 2.0e0
.
The expression math:pow(0e0, 3.0e0)
returns xs:double('INF')
.
The expression math:pow(0e0, 3.0e0)
returns xs:double('INF')
. (Oddvalued whole numbers are treated specially).
The expression math:pow(0e0, 3.1e0)
returns xs:double('INF')
.
The expression math:pow(0e0, 3.1e0)
returns xs:double('INF')
.
The expression math:pow(0e0, 3.0e0)
returns 0.0e0
.
The expression math:pow(0e0, 3.0e0)
returns 0.0e0
. (Oddvalued whole numbers are treated specially).
The expression math:pow(0e0, 3.1e0)
returns 0.0e0
.
The expression math:pow(0e0, 3.1e0)
returns 0.0e0
.
The expression math:pow(1, xs:double('INF'))
returns 1.0e0
.
The expression math:pow(1, xs:double('INF'))
returns 1.0e0
.
The expression math:pow(1, xs:double('INF'))
returns 1.0e0
.
The expression math:pow(1, xs:double('INF'))
returns 1.0e0
.
The expression math:pow(1, xs:double('NaN'))
returns 1.0e0
.
The expression math:pow(2.5e0, 2.0e0)
returns 6.25e0
.
The expression math:pow(2.5e0, 2.00000001e0)
returns xs:double('NaN')
.
Returns the nonnegative square root of the argument.
math:sqrt
($value
as
xs:double?
) as
xs:double?
This function is ·deterministic·, ·contextindependent·, and ·focusindependent·.
If $value
is the empty sequence, the function returns the empty sequence.
Otherwise the result is the mathematical nonnegative square root of $value
as defined in the [IEEE 7542008] specification of the
squareRoot
function applied to 64bit binary floating point values.
The treatment of the invalidOperation
exception is defined in 4.2 Arithmetic operators on numeric values. The effect is that if the argument is less than zero, the result
is NaN
.
If $value
is positive or negative zero, positive infinity, or
NaN
, then the result is $value
. (Negative zero is the only
case where the result can have negative sign)
The expression math:sqrt(())
returns ()
.
The expression math:sqrt(0.0e0)
returns 0.0e0
.
The expression math:sqrt(0.0e0)
returns 0.0e0
.
The expression math:sqrt(1.0e6)
returns 1.0e3
.
The expression math:sqrt(2.0e0)
returns 1.4142135623730951e0
.
The expression math:sqrt(2.0e0)
returns xs:double('NaN')
.
The expression math:sqrt(xs:double('NaN'))
returns xs:double('NaN')
.
The expression math:sqrt(xs:double('INF'))
returns xs:double('INF')
.
The expression math:sqrt(xs:double('INF'))
returns xs:double('NaN')
.
Returns the sine of the argument. The argument is an angle in radians.
math:sin
($radians
as
xs:double?
) as
xs:double?
This function is ·deterministic·, ·contextindependent·, and ·focusindependent·.
If $radians
is the empty sequence, the function returns the empty
sequence.
Otherwise the result is the sine of $radians
(which is treated as an angle in
radians) as defined in the [IEEE 7542008] specification of the
sin
function applied to 64bit binary floating point values.
The treatment of the invalidOperation
and underflow
exceptions
is defined in 4.2 Arithmetic operators on numeric values.
If $radians
is positive or negative zero, the result is
$radians
.
If $radians
is positive or negative infinity, or NaN
,
then the result is NaN
.
Otherwise the result is always in the range 1.0e0 to +1.0e0
The expression math:sin(())
returns ()
.
The expression math:sin(0)
returns 0.0e0
.
The expression math:sin(0.0e0)
returns 0.0e0
.
The expression math:sin(math:pi() div 2)
returns 1.0e0
(approximately).
The expression math:sin(math:pi() div 2)
returns 1.0e0
(approximately).
The expression math:sin(math:pi())
returns 0.0e0
(approximately).
The expression math:sin(xs:double('NaN'))
returns xs:double('NaN')
.
The expression math:sin(xs:double('INF'))
returns xs:double('NaN')
.
The expression math:sin(xs:double('INF'))
returns xs:double('NaN')
.
Returns the cosine of the argument. The argument is an angle in radians.
math:cos
($radians
as
xs:double?
) as
xs:double?
This function is ·deterministic·, ·contextindependent·, and ·focusindependent·.
If $radians
is the empty sequence, the function returns the empty
sequence.
If $radians
is positive or negative infinity, or NaN
,
then the result is NaN
.
Otherwise the result is the cosine of $
θ (which is treated as an angle in
radians) as defined in the [IEEE 7542008] specification of the
cos
function applied to 64bit binary floating point values.
The treatment of the invalidOperation
exception is defined in 4.2 Arithmetic operators on numeric values.
If $radians
is positive or negative zero, the result is
$radians
.
If $radians
is positive or negative infinity, or NaN
,
then the result is NaN
.
Otherwise the result is always in the range 1.0e0 to +1.0e0
The expression math:cos(())
returns ()
.
The expression math:cos(0)
returns 1.0e0
.
The expression math:cos(0.0e0)
returns 1.0e0
.
The expression math:cos(math:pi() div 2)
returns 0.0e0
(approximately).
The expression math:cos(math:pi() div 2)
returns 0.0e0
(approximately).
The expression math:cos(math:pi())
returns 1.0e0
(approximately).
The expression math:cos(xs:double('NaN'))
returns xs:double('NaN')
.
The expression math:cos(xs:double('INF'))
returns xs:double('NaN')
.
The expression math:cos(xs:double('INF'))
returns xs:double('NaN')
.
Returns the tangent of the argument. The argument is an angle in radians.
math:tan
($radians
as
xs:double?
) as
xs:double?
This function is ·deterministic·, ·contextindependent·, and ·focusindependent·.
If $radians
is the empty sequence, the function returns the empty
sequence.
Otherwise the result is the tangent of $radians
(which is treated as an angle
in radians) as defined in the [IEEE 7542008] specification of the
tan
function applied to 64bit binary floating point values.
The treatment of the invalidOperation
and underflow
exceptions
is defined in 4.2 Arithmetic operators on numeric values.
If $radians
is positive or negative infinity, or NaN
,
then the result is NaN
.
The expression math:tan(())
returns ()
.
The expression math:tan(0)
returns 0.0e0
.
The expression math:tan(0.0e0)
returns 0.0e0
.
The expression math:tan(math:pi() div 4)
returns 1.0e0
(approximately).
The expression math:tan(math:pi() div 4)
returns 1.0e0
(approximately).
The expression 1 div math:tan(math:pi() div 2)
returns 0.0e0
(approximately). (Mathematically, tan(π/2) is positive infinity. But because math:pi() div 2
returns an approximation, the result of math:tan(math:pi() div 2)
will be a large
but finite number.)
The expression 1 div math:tan(math:pi() div 2)
returns 0.0e0
(approximately). (Mathematically, tan(π/2) is negative infinity. But because math:pi() div 2
returns an approximation, the result of math:tan(math:pi() div 2)
will be a large
but finite negative number.)
The expression math:tan(math:pi())
returns 0.0e0
(approximately).
The expression math:tan(xs:double('NaN'))
returns xs:double('NaN')
.
The expression math:tan(xs:double('INF'))
returns xs:double('NaN')
.
The expression math:tan(xs:double('INF'))
returns xs:double('NaN')
.
Returns the arc sine of the argument.
math:asin
($value
as
xs:double?
) as
xs:double?
This function is ·deterministic·, ·contextindependent·, and ·focusindependent·.
If $value
is the empty sequence, the function returns the empty sequence.
Otherwise the result is the arc sine of $value
as defined in the [IEEE 7542008] specification of the
asin
function applied to 64bit binary floating point values.
The result is in the range π/2 to +π/2 radians.
The treatment of the invalidOperation
and underflow
exceptions
is defined in 4.2 Arithmetic operators on numeric values.
If $value
is positive or negative zero, the result is $value
.
If $value
is NaN
, or if its absolute value is greater than one,
then the result is NaN
.
In other cases the result is an xs:double
value representing an angle
θ in radians in the range π/2 <=
θ <= +
π/2
.
The expression math:asin(())
returns ()
.
The expression math:asin(0)
returns 0.0e0
.
The expression math:asin(0.0e0)
returns 0.0e0
.
The expression math:asin(1.0e0)
returns 1.5707963267948966e0
(approximately).
The expression math:asin(1.0e0)
returns 1.5707963267948966e0
(approximately).
The expression math:asin(2.0e0)
returns xs:double('NaN')
.
The expression math:asin(xs:double('NaN'))
returns xs:double('NaN')
.
The expression math:asin(xs:double('INF'))
returns xs:double('NaN')
.
The expression math:asin(xs:double('INF'))
returns xs:double('NaN')
.
Returns the arc cosine of the argument.
math:acos
($value
as
xs:double?
) as
xs:double?
This function is ·deterministic·, ·contextindependent·, and ·focusindependent·.
If $value
is the empty sequence, the function returns the empty sequence.
Otherwise the result is the arc cosine of $value
, as defined in the [IEEE 7542008] specification of the
acos
function applied to 64bit binary floating point values.
The result is in the range zero to +π radians.
The treatment of the invalidOperation
exception is defined in 4.2 Arithmetic operators on numeric values.
If $value
is NaN
, or if its absolute value is greater than one,
then the result is NaN
.
In other cases the result is an xs:double
value representing an angle
θ in radians in the range 0 <=
θ <=
+
π.
The expression math:acos(())
returns ()
.
The expression math:acos(0)
returns 1.5707963267948966e0
(approximately).
The expression math:acos(0.0e0)
returns 1.5707963267948966e0
(approximately).
The expression math:acos(1.0e0)
returns 0.0e0
.
The expression math:acos(1.0e0)
returns 3.141592653589793e0
(approximately).
The expression math:acos(2.0e0)
returns xs:double('NaN')
.
The expression math:acos(xs:double('NaN'))
returns xs:double('NaN')
.
The expression math:acos(xs:double('INF'))
returns xs:double('NaN')
.
The expression math:acos(xs:double('INF'))
returns xs:double('NaN')
.
Returns the arc tangent of the argument.
math:atan
($value
as
xs:double?
) as
xs:double?
This function is ·deterministic·, ·contextindependent·, and ·focusindependent·.
If $value
is the empty sequence, the function returns the empty sequence.
Otherwise the result is the arc tangent of $value
, as defined
in the [IEEE 7542008] specification of the
atan
function applied to 64bit binary floating point values.
The result is in the range π/2
to +π/2 radians.
The treatment of the underflow
exception is defined in 4.2 Arithmetic operators on numeric values.
If $value
is positive or negative zero, the result is $value
.
If $value
is NaN
then the result is NaN
.
In other cases the result is an xs:double
value representing an angle
θ in radians in the range π/2 <=
θ <= +
π/2
.
The expression math:atan(())
returns ()
.
The expression math:atan(0)
returns 0.0e0
.
The expression math:atan(0.0e0)
returns 0.0e0
.
The expression math:atan(1.0e0)
returns 0.7853981633974483e0
(approximately).
The expression math:atan(1.0e0)
returns 0.7853981633974483e0
(approximately).
The expression math:atan(xs:double('NaN'))
returns xs:double('NaN')
.
The expression math:atan(xs:double('INF'))
returns 1.5707963267948966e0
(approximately).
The expression math:atan(xs:double('INF'))
returns 1.5707963267948966e0
(approximately).
Returns the angle in radians subtended at the origin by the point on a plane with coordinates (x, y) and the positive xaxis.
math:atan2
($y
as
xs:double
, $x
as
xs:double
) as
xs:double
This function is ·deterministic·, ·contextindependent·, and ·focusindependent·.
The result is the value of atan2(y, x)
as defined in the [IEEE 7542008] specification of the atan2
function applied to
64bit binary floating point values. The result is in the range π
to +π radians.
The treatment of the underflow
exception is defined in 4.2 Arithmetic operators on numeric values.
If either argument is NaN
then the result is NaN
.
If $y
is positive and $x
is positive and finite, then (subject
to rules for overflow, underflow and approximation) the value of atan2($y,
$x)
is atan($y div $x)
.
If $y
is positive and $x
is negative and finite, then (subject
to the same caveats) the value of atan2($y, $x)
is π
 atan($y div $x)
.
Some results for special values of the arguments are shown in the examples below.
The expression math:atan2(+0.0e0, 0.0e0)
returns 0.0e0
.
The expression math:atan2(0.0e0, 0.0e0)
returns 0.0e0
.
The expression math:atan2(+0.0e0, 0.0e0)
returns 3.141592653589793e0
.
The expression math:atan2(0.0e0, 0.0e0)
returns 3.141592653589793e0
.
The expression math:atan2(1, 0.0e0)
returns 1.5707963267948966e0
.
The expression math:atan2(+1, 0.0e0)
returns 1.5707963267948966e0
.
The expression math:atan2(0.0e0, 1)
returns 3.141592653589793e0
.
The expression math:atan2(+0.0e0, 1)
returns 3.141592653589793e0
.
The expression math:atan2(0.0e0, +1)
returns 0.0e0
.
The expression math:atan2(+0.0e0, +1)
returns +0.0e0
.
Function  Meaning 

fn:randomnumbergenerator 
Returns a random number generator, which can be used to generate sequences of random numbers. 
Returns a random number generator, which can be used to generate sequences of random numbers.
fn:randomnumbergenerator
() as
itemtype(rng)
fn:randomnumbergenerator
($seed
as
xs:anyAtomicType?
) as
itemtype(rng)
This function is ·deterministic·, ·contextindependent·, ·focusindependent·, and ·higherorder·.
The function returns a random number generator. A random number generator is represented
as a value of type
rng
, defined as follows:
record( number as xs:double, next as (function() as record(number, next, permute, *)), permute as (function(item()*) as item()*), * )
That is, the result of the function is a map containing three entries. The keys of each entry are strings:
The entry with key "number"
holds a random number; it is an xs:double
greater than or equal
to zero (0.0e0), and less than one (1.0e0).
The entry with key "next"
is a zeroarity function that can be called to return another random number
generator.
The properties of this function are as follows:
name: absent
parameter names: ()
signature: () => map(xs:string, item())
nonlocal variable bindings: none
implementation: implementationdependent
The entry with key "permute"
is a function with arity 1 (one), which takes an arbitrary sequence
as its argument, and returns a random permutation of that sequence.
The properties of this function are as follows:
name: absent
parameter names: ("arg")
signature: (item()*) => item()*
nonlocal variable bindings: none
implementation: implementationdependent
Calling the fn:randomnumbergenerator
function with no arguments is equivalent to calling the singleargument
form of the function with an implementationdependent seed.
Calling the fn:randomnumbergenerator
function with an empty sequence as $seed
is equivalent to calling the singleargument form of the function with an implementationdependent
seed.
If a $seed
is supplied, it may be an atomic value of any type.
Both forms of the function are ·deterministic·: calling the function twice with the same arguments, within a single ·execution scope·, produces the same results.
The value of the number
entry should be such that all eligible xs:double
values are equally likely to be chosen.
The function returned in the permute
entry should be such that all permutations
of the supplied sequence are equally likely to be chosen.
The map returned by the fn:randomnumbergenerator
function may contain additional entries beyond
those specified here, but it must match the type
itemtype(rng)
defined above. The meaning of any additional entries
is ·implementationdefined·. To avoid conflict with any future version of this specification, the keys of any
such entries should start with an underscore character.
It is not meaningful to ask whether the functions returned in the next
and permute
functions resulting from two separate calls with the same seed are "the same function",
but the functions must be equivalent in the sense
that calling them produces the same sequence of random numbers.
The repeatability of the results of function calls in different execution scopes is
outside the scope of this
specification. It is recommended that when the same seed is provided explicitly, the same random number sequence
should be delivered even in different execution scopes; while if no seed is provided,
the processor should choose a seed
that is likely to be different from one execution scope to another. (The same effect
can be achieved explicitly by using
fn:currentdateTime()
as a seed.)
The specification does not place strong conformance requirements on the actual randomness of the result; this is left to the implementation. It is desirable, for example, when generating a sequence of random numbers that the sequence should not get into a repeating loop; but the specification does not attempt to dictate this.
The following example returns a random permutation of the integers in the range 1
to 100:
fn:randomnumbergenerator()?permute(1 to 100)
The following example returns a 10% sample of the items in an input sequence $seq
, chosen at random:
fn:randomnumbergenerator()?permute($seq)[position() = 1 to (count($seq) idiv 10)]
The following code defines a function that can be called to produce a random sequence
of xs:double
values in the range zero to one, of specified length:
declare %public function r:randomsequence($length as xs:integer) as xs:double* { r:randomsequence($length, fn:randomnumbergenerator()) }; declare %private function r:randomsequence($length as xs:integer, $G as record(number as xs:double, next as function(*), *)) { if ($length eq 0) then () else ($G?number, r:randomsequence($length  1, $G?next())) }; r:randomsequence(200);
This section specifies functions and operators on the [XML Schema Part 2: Datatypes Second Edition]
xs:string
datatype and the datatypes derived from it.
The operators described in this section are defined on the following types. Each type whose name is indented is derived from the type whose name appears nearest above with one less level of indentation.
xs:string  
xs:normalizedString  
xs:token  
xs:language  
xs:NMTOKEN  
xs:Name  
xs:NCName  
xs:ID  
xs:IDREF  
xs:ENTITY 
They also apply to userdefined types derived by restriction from the above types.
Function  Meaning 

fn:codepointstostring 
Returns an xs:string whose characters have supplied ·codepoints·.

fn:stringtocodepoints 
Returns the sequence of ·codepoints· that constitute an
xs:string value.

Returns an xs:string
whose characters have supplied ·codepoints·.
fn:codepointstostring
($values
as
xs:integer*
) as
xs:string
This function is ·deterministic·, ·contextindependent·, and ·focusindependent·.
The function returns the string made up from the ·characters· whose Unicode ·codepoints· are
supplied in $values
. This will be the zerolength string if $values
is the empty sequence.
A dynamic error is raised [err:FOCH0001] if any of the codepoints in
$values
is not a permitted XML character.
The expression fn:codepointstostring((66, 65, 67, 72))
returns "BACH"
.
The expression fn:codepointstostring((2309, 2358, 2378, 2325))
returns "अशॊक"
.
The expression fn:codepointstostring(())
returns ""
.
The expression fn:codepointstostring(0)
raises error FOCH0001
.
Returns the sequence of ·codepoints· that constitute an
xs:string
value.
fn:stringtocodepoints
($value
as
xs:string?
) as
xs:integer*
This function is ·deterministic·, ·contextindependent·, and ·focusindependent·.
The function returns a sequence of integers, each integer being the Unicode ·codepoint· of the corresponding ·character· in $value
.
If $value
is a zerolength string or the empty sequence, the function returns
the empty sequence.
The expression fn:stringtocodepoints("Thérèse")
returns (84, 104, 233, 114, 232, 115, 101)
.
Function  Meaning 

fn:compare 
Returns 1, 0, or 1, depending on whether $value1 collates before,
equal to, or after $value2 according to the rules of a selected
collation.

fn:codepointequal 
Returns true if two strings are equal, considered codepointbycodepoint. 
fn:collationkey 
Given a string value and a collation, generates an internal value called a collation key, with the property that the matching and ordering of collation keys reflects the matching and ordering of strings under the specified collation. 
fn:containstoken 
Determines whether or not any of the supplied strings, when tokenized at whitespace boundaries, contains the supplied token, under the rules of the supplied collation. 
A collation is a specification of the manner in which ·strings· are
compared and, by extension, ordered. When values whose type is
xs:string
or a type derived from xs:string
are
compared (or, equivalently, sorted), the comparisons are inherently
performed according to some collation (even if that collation is defined
entirely on codepoint values). The [Character Model for the World Wide Web 1.0: Fundamentals] observes that
some applications may require different comparison and ordering behaviors
than other applications. Similarly, some users having particular linguistic
expectations may require different behaviors than other users. Consequently,
the collation must be taken into account when comparing strings in any
context. Several functions in this and the following section make use of a
collation.
Collations can indicate that two different codepoints are, in fact, equal for comparison purposes (e.g., "v" and "w" are considered equivalent in some Swedish collations). Strings can be compared codepointbycodepoint or in a linguistically appropriate manner, as defined by the collation.
Some collations, especially those based on the Unicode Collation Algorithm (see [UTS #10]) can be "tailored" for various purposes. This document does not discuss such tailoring, nor does it provide a mechanism to perform tailoring. Instead, it assumes that the collation argument to the various functions below is a tailored and named collation.
The ·Unicode codepoint collation· is a collation available in every implementation, which sorts based on codepoint values. For further details see 5.3.2 The Unicode Codepoint Collation.
Collations may or may not perform Unicode normalization on strings before comparing them.
This specification assumes that collations are named and that the collation
name may be provided as an argument to string functions. Functions that
allow specification of a collation do so with an argument whose type is
xs:string
but whose lexical form must conform to an
xs:anyURI
. If the collation is specified using a relative URI reference,
it is resolved relative to the value of the
static base URI property from the static context.
This specification also defines the manner in which a
default collation is determined if the collation argument is not specified
in calls of functions that use a collation but allow it to be omitted.
This specification does not define whether or not the collation URI is dereferenced. The collation URI may be an abstract identifier, or it may refer to an actual resource describing the collation. If it refers to a resource, this specification does not define the nature of that resource. One possible candidate is that the resource is a locale description expressed using the Locale Data Markup Language: see [UTS #35].
Functions such as fn:compare
and fn:max
that
compare xs:string
values use a single collation URI to identify
all aspects of the collation rules. This means that any parameters such as
the strength of the collation must be specified as part of the collation
URI. For example, suppose there is a collation
http://www.example.com/collations/French
that refers to a French collation that compares on the basis of
base characters. Collations that use the same basic rules, but with higher
strengths, for example, base characters and accents, or base characters,
accents and case, would need to be given different names, say
http://www.example.com/collations/French1
and
http://www.example.com/collations/French2
.
Note that some specifications use the term collation to refer to
an algorithm that can be parameterized, but in this specification, each
possible parameterization is considered to be a distinct collation.
The XQuery/XPath static context includes a provision for a default collation that can be used for string comparisons and ordering operations. See the description of the static context in Section 2.1.1 Static Context ^{XP31}. If the default collation is not specified by the user or the system, the default collation is the ·Unicode codepoint collation·.
Note:
XML allows elements to specify the xml:lang
attribute to
indicate the language associated with the content of such an element.
This specification does not use xml:lang
to identify the
default collation because using
xml:lang
does not produce desired effects when the two
strings to be compared have different xml:lang
values or
when a string is multilingual.
[Definition] The collation URI
http://www.w3.org/2005/xpathfunctions/collation/codepoint
identifies
a collation which must be recognized by every implementation: it is referred to as
the Unicode codepoint collation (not to be confused with the Unicode collation algorithm).
The Unicode codepoint collation does not perform any normalization on the supplied strings.
The collation is defined as follows. Each of the two strings is
converted to a sequence of integers using the fn:stringtocodepoints
function. These two sequences $A
and $B
are then compared as follows:
If both sequences are empty, the strings are equal.
If one sequence is empty and the other is not, then the string corresponding to the empty sequence is less than the other string.
If the first integer in $A
is less than the first integer in $B
, then
the string corresponding to $A
is less than the string corresponding to
$B
.
If the first integer in $A
is greater than the first integer in $B
, then
the string corresponding to $A
is greater than the string corresponding to
$B
.
Otherwise (the first pair of integers are equal), the result is obtained
by applying the same rules recursively to fn:tail($A)
and
fn:tail($B)
Note:
While the Unicode codepoint collation does not produce results suitable for quality publishing of printed indexes or directories, it is adequate for many purposes where a restricted alphabet is used, such as sorting of vehicle registrations.
This specification defines a family of collation URIs representing tailorings of the Unicode Collation Algorithm (UCA) as defined in [UTS #10]. The parameters used for tailoring the UCA are based on the parameters defined in the Locale Data Markup Language (LDML), defined in [UTS #35].
This family of URIs use the scheme and path http://www.w3.org/2013/collation/UCA
followed by an optional query part. The query part, if present, consists of a question
mark followed
by a sequence of zero or more semicolonseparated parameters. Each parameter is a
keywordvalue pair, the
keyword and value being separated by an equals sign.
All implementations must recognize URIs in this family in the collation
argument of functions that
take a collation argument.
If the fallback
parameter is
present with the value no
, then the implementation must either use a collation that conforms with
the rules in the Unicode specifications for the requested tailoring, or fail with
a static or dynamic error indicating that it
does not provide the collation (the error code should be the same as if the collation
URI were not recognized).
If the fallback
parameter
is omitted or takes the value yes
, and if the collation URI is wellformed according to the rules in this section,
then the implementation must accept the collation URI, and should use the available
collation that most closely reflects the user's intentions. For example, if the collation
URI requested is
http://www.w3.org/2013/collation/UCA?lang=se;fallback=yes
and the implementation does not include a fully
conformant version of the UCA tailored for Swedish, then it may choose to use a Swedish collation that is known to differ
from the UCA definition, or one whose conformance has not been established. It might
even, as a last resort, fall back to using
codepoint collation.
If two query parameters use the same keyword then the last one wins. If a query parameter
uses a keyword or value which is not
defined in this specification then the meaning is ·implementationdefined·. If the implementation recognizes
the meaning of the keyword and value then it should interpret it accordingly; if it does not recognize
the keyword or value then if the fallback
parameter is present with the value no
it should reject
the collation as unsupported, otherwise it should ignore the unrecognized parameter.
The following query parameters are defined. If any parameter is absent, the default is ·implementationdefined· except where otherwise stated. The meaning given for each parameter is nonnormative; the normative specification is found in [UTS #35].
Keyword  Values  Meaning 

fallback  yes  no (default yes)  Determines whether the processor uses a fallback collation if a conformant collation is not available. 
lang  language code: a string in the lexical space of xs:language .

The language whose collation conventions are to be used. 
version  string  The version number of the UCA to be used. 
strength (default tertiary)  primary  secondary  tertiary  quaternary  identical, or 12345 as synonyms  The collation strength as defined in UCA. Primary
strength takes only the base form of the character into account (so A=a=Ä=ä); secondary
strength ignores case but considers accents
and diacritics as significant (so A=a and Ä=ä but ä≠a); tertiary considers case as
significant (A≠a≠Ä≠ä); quaternary considers
spaces and punctuation that would otherwise be ignored (for example database =database ).

maxVariable  space  punct  symbol  currency (default punct) 
Indicates that all characters in the specified group and earlier groups are treated
as "noise" characters
to be handled as defined by the alternate parameter. For example, maxVariable=punct indicates
that characters classified as whitespace or punctuation get this treatment.

alternate  nonignorable  shifted  blanked (default nonignorable)  Controls the handling of characters such as spaces and hyphens;
specifically, the "noise" characters in the groups selected by the maxVariable parameter. The value nonignorable
indicates that such characters are treated as distinct at the primary level (so data base sorts before datatype );
shifted indicates that they are used to differentiate two strings only at the quaternary level,
and blanked indicates that they are taken into account only at the identical level.

backwards  yes  no (default no)  The value backwards=yes indicates that the last accent in the
string is the most significant.

normalization  yes  no (default no)  Indicates whether strings are converted to normalization form D. 
caseLevel  yes  no (default no)  When used with primary strength, setting caseLevel=yes has the effect of ignoring accents
while taking account of case.

caseFirst  upper  lower  Indicates whether uppercase precedes lowercase or vice versa. 
numeric  yes  no (default no)  When numeric=yes is specified, a sequence of consecutive digits is interpreted as a number,
for example chap2 sorts before chap12 .

reorder  a commaseparated sequence of reorder codes, where a reorder code is one of space , punct ,
symbol , currency , digit , or a fourletter script code defined in [ISO 15924 Register], the register
of scripts maintained by the Unicode Consortium in its capacity as registration authority
for [ISO 15924].

Determines the relative ordering of text in different scripts; for example the value
digit,Grek,Latn indicates
that digits precede Greek letters, which precede Latin letters.

Note:
This list excludes parameters that are inconvenient to express in a URI, or that are applicable only to substring matching.
The collation URI http://www.w3.org/2005/xpathfunctions/collation/htmlasciicaseinsensitive
must be recognized
by every implementation. It is used
to refer to the HTML ASCII caseinsensitive collation as defined in [HTML5: A vocabulary and associated APIs for HTML and XHTML] (section 2.5, Case sensitivity and
string comparison). It is used, for example, when matching HTML class
attribute values.
Note:
The definition of the collation is paraphrased here for convenience:
Comparing two strings in an ASCII caseinsensitive manner means comparing them exactly, codepoint for codepoint, except that the characters in the range x41 to x5A (AZ) and the corresponding characters in the range x61 to x7A (az) are considered to also match.
HTML5 defines the semantics of equality matching using this collation; it does not
define rules for ordering. If the collation
is used for ordering, the results are ·implementationdefined·. The collation supports collation units and can therefore
be used with functions such as fn:contains
; each Unicode codepoint is a single collation unit.
Many functions have two signatures, where one signature includes a $collation
argument and the other omits this argument.
The collation to use for these functions is determined by the following rules:
If the function specifies an explicit collation, CollationA (e.g., if
the optional collation argument is specified in a call of the
fn:compare
function), then:
If CollationA is supported by the implementation, then CollationA is used.
Otherwise, a dynamic error is raised [err:FOCH0002].
If no collation is explicitly specified for the function and the default collation in the XQuery/XPath static context is CollationB, then:
If CollationB is supported by the implementation, then CollationB is used.
Otherwise, a dynamic error is raised [err:FOCH0002].
Note:
Because the set of collations that are supported is ·implementationdefined·, an implementation has the option to support all collation URIs, in which case it will never raise this error.
If the value of the collation argument is a relative URI reference, it is resolved against the baseURI from the static context. If it is a relative URI reference and cannot be resolved, perhaps because the baseURI property in the static context is absent, a dynamic error is raised [err:FOCH0002].
Note:
There is no explicit requirement that the string used as a collation URI be a valid URI. Implementations will in many cases reject such strings on the grounds that do not identify a supported collation; they may also cause an error if they cannot be resolved against the static base URI.
Returns 1, 0, or 1, depending on whether $value1
collates before,
equal to, or after $value2
according to the rules of a selected
collation.
fn:compare
($value1
as
xs:string?
, $value2
as
xs:string?
) as
xs:integer?
fn:compare (

$value1 
as xs:string? ,

$value2 
as xs:string? ,


$collation 
as xs:string ) as xs:integer? 
The twoargument form of this function is ·deterministic·, ·contextdependent·, and ·focusindependent·. It depends on collations.
The threeargument form of this function is ·deterministic·, ·contextdependent·, and ·focusindependent·. It depends on collations, and static base URI.
Returns 1, 0, or 1, depending on whether $value1
is
respectively less than, equal to, or greater than $value2
,
according to the rules of the collation that is used.
The collation used by this function is determined according to the rules in 5.3.5 Choosing a collation.
If either $value1
or $value2
is the empty sequence,
the function returns the empty sequence.
This function, called with the first signature, defines the semantics of the "eq",
"ne",
"gt", "lt", "le" and "ge" operators on xs:string
values.
The expression fn:compare('abc', 'abc')
returns 0
.
The expression fn:compare('Strasse', 'Straße')
returns 0
. (Assuming the default collation includes provisions that equate
"ss" and the (German) character "ß"
("sharps"). Otherwise, the returned value depends on the
semantics of the default collation.)
The expression fn:compare('Strasse', 'Straße',
'http://www.w3.org/2013/collation/UCA?lang=de;strength=primary')
returns 0
. (The specified collation equates
"ss" and the (German) character "ß"
("sharps").)
The expression fn:compare('Strassen', 'Straße')
returns 1
. (Assuming the default collation includes provisions that treat
differences between "ss" and the (German) character "ß"
("sharps") with less strength than the differences between the
base characters, such as the final "n". ).
Returns true if two strings are equal, considered codepointbycodepoint.
fn:codepointequal
($value1
as
xs:string?
, $value2
as
xs:string?
) as
xs:boolean?
This function is ·deterministic·, ·contextindependent·, and ·focusindependent·.
If either argument is the empty sequence, the function returns the empty sequence.
Otherwise, the function returns true
or false
depending on
whether $value1
is equal to
$value2
, according to the Unicode codepoint collation
(http://www.w3.org/2005/xpathfunctions/collation/codepoint
).
This function allows xs:anyURI
values to be compared without having to
specify the Unicode codepoint collation.
The expression fn:codepointequal("abcd", "abcd")
returns true()
.
The expression fn:codepointequal("abcd", "abcd ")
returns false()
.
The expression fn:codepointequal("", "")
returns true()
.
The expression fn:codepointequal("", ())
returns ()
.
The expression fn:codepointequal((), ())
returns ()
.
Given a string value and a collation, generates an internal value called a collation key, with the property that the matching and ordering of collation keys reflects the matching and ordering of strings under the specified collation.
fn:collationkey
($value
as
xs:string
) as
xs:base64Binary
fn:collationkey (

$value 
as xs:string ,

$collation 
as xs:string ) as xs:base64Binary 
This function is ·deterministic·, ·contextdependent·, and ·focusindependent·. It depends on collations.
Calling the oneargument version of this function is equivalent to calling the twoargument version supplying the default collation as the second argument.
The function returns an ·implementationdependent·
value with the property that,
for any two strings $K1
and $K2
:
collationkey($K1, $C) eq collationkey($K2, $C)
if and only if
compare($K1, $K2, $C) eq 0
collationkey($K1, $C) lt collationkey($K2, $C)
if and only if
compare($K1, $K2, $C) lt 0
The collation used by this function is determined according to the rules in 5.3.5 Choosing a collation. Collation keys are defined as xs:base64Binary
values
to ensure unambiguous and contextfree comparison semantics.
An implementation is free to generate a collation key in any convenient way provided that it always generates the same collation key for two strings that are equal under the collation, and different collation keys for strings that are not equal. This holds only within a single ·execution scope·; an implementation is under no obligation to generate the same collation keys during a subsequent unrelated query or transformation.
It is possible to define collations that do not have the ability to generate collation keys. Supplying such a collation will cause the function to fail. The ability to generate collation keys is an ·implementationdefined· property of the collation.
An error is raised [err:FOCH0004] if the specified collation does not support the generation of collation keys.
The function is provided primarily for use with maps. If a map is required where
codepoint equality is inappropriate for comparing keys, then a common technique is
to
normalize the key so that equality matching becomes feasible. There are many ways
keys can be normalized, for example by use of functions such as
fn:uppercase
, fn:lowercase
,
fn:normalizespace
, or fn:normalizeunicode
, but this
function provides a way of normalizing them according to the rules of a specified
collation. For example, if the collation ignores accents, then the function will
generate the same collation key for two input strings that differ only in their use
of
accents.
The result of the function is defined to be an xs:base64Binary
value. Binary values
are chosen because they have unambiguous and contextfree comparison semantics, because
the value space
is unbounded, and because the ordering rules are such that between any two values
in the ordered value space, an
arbitrary number of further values can be interpolated. The choice between xs:base64Binary
and xs:hexBinary
is arbitrary; the only operation that behaves differently between the two binary
data types is conversion to/from a string, and this operation is not one that is normally
required for
effective use of collation keys.
For collations based on the Unicode Collation Algorithm, an algorithm for computing collation keys is provided in [UTS #10]. Implementations are not required to use this algorithm.
The fact that collation keys are ordered can be exploited in XQuery, whose order by
clause does not allow the collation to be selected dynamically. This restriction can
be circumvented
by rewriting the clause order by $e/@key collation "URI"
as order by fn:collationkey($e/@key, $collation)
,
where $collation
allows the collation to be chosen dynamically.
Note that xs:base64Binary
becomes an ordered type
in XPath 3.1, making binary collation keys possible.
let $C := 'http://www.w3.org/2013/collation/UCA?strength=primary'
The expression map:merge((map{collationkey("A", $C):1}, map{collationkey("a",
$C):2}), map{"duplicates":"uselast"})(collationkey("A", $C))
returns 2
. (Given that the keys of the two entries are equal under the rules of
the chosen collation, only one of the entries can appear in the result; the one
that is chosen is the one from the last map in the input sequence.)
The expression let $M := map{collationkey("A", $C):1, collationkey("B", $C):2}
return $M(collationkey("a", $C))
returns 1
. (The strings "A" and "a" have the same collation key under this
collation.)
As the above examples illustrate, it is important that when the
collationkey
function is used to add entries to a map, then it must
also be used when retrieving entries from the map. This process can be made less
errorprone by encapsulating the map within a function: function($k)
{$M(collationkey($k, $collation)}
.
Determines whether or not any of the supplied strings, when tokenized at whitespace boundaries, contains the supplied token, under the rules of the supplied collation.
fn:containstoken
($value
as
xs:string*
, $token
as
xs:string
) as
xs:boolean
fn:containstoken (

$value 
as xs:string* ,

$token 
as xs:string ,


$collation 
as xs:string ) as xs:boolean 
The twoargument form of this function is ·deterministic·, ·contextdependent·, and ·focusindependent·. It depends on collations.
The threeargument form of this function is ·deterministic·, ·contextdependent·, and ·focusindependent·. It depends on collations, and static base URI.
If $value
is the empty sequence, the function returns false
.
Leading and trailing whitespace is trimmed from $token
.
If the trimmed value of $token
is a zerolength string, the function returns false
.
The collation used by this function is determined according to the rules in 5.3.5 Choosing a collation.
The function returns true if and only if there is string in $value
which,
after tokenizing at whitespace boundaries, contains a token
that is equal to the trimmed value of $token
under
the rules of the selected collation.
That is, the function returns the value of the expression:
some $t in $input!fn:tokenize(.) satisfies compare($t, fn:replace($token, '^\s*\s*$', ''), $collation) eq 0)
Interior whitespace within $token
will cause the function to return false
,
unless such whitespace is ignored by the selected collation.
This function can be used for processing spaceseparated attribute values (for example, the XHTML and DITA class attribute), where one often needs to test for the presence of a single token in a spaceseparated list. The function is designed to work both when the attribute has been validated against an XSD list type, and when it appears as a single untyped string. It differs from the HTML 5 definition in that HTML 5 recognizes form feed (x0C) as a separator. To reproduce the HTML token matching behavior, the HTML ASCII caseinsensitive collation should be used: see 5.3.4 The HTML ASCII CaseInsensitive Collation.
The expression fn:containstoken("red green blue ", "red")
returns true()
.
The expression fn:containstoken(("red", "green", "blue"), " red ")
returns true()
.
The expression fn:containstoken("red, green, blue", "red")
returns false()
.
The expression fn:containstoken("red green blue", "RED", "http://www.w3.org/2005/xpathfunctions/collation/htmlasciicaseinsensitive")
returns true()
.
The following functions are defined on values of type xs:string
and
types derived from it.
Function  Meaning 

fn:characters 
Splits the supplied string into a sequence of singlecharacter strings. 
fn:concat 
Returns the concatenation of the string values of the arguments. 
fn:stringjoin 
Returns a string created by concatenating the items in a sequence, with a defined separator between adjacent items. 
fn:substring 
Returns the part of $value beginning at the position
indicated by $start and continuing for the number of ·characters· indicated by $length .

fn:stringlength 
Returns the number of ·characters· in a string. 
fn:normalizespace 
Returns $value with leading and trailing whitespace removed, and
sequences of internal whitespace reduced to a single space character.

fn:normalizeunicode 
Returns $value after applying Unicode normalization.

fn:uppercase 
Converts a string to upper case. 
fn:lowercase 
Converts a string to lower case. 
fn:translate 
Returns $value modified by replacing or removing individual
characters.

Notes:
When the above operators and functions are applied to datatypes derived from
xs:string
, they are guaranteed to return values that are instances of
xs:string
, but the value might or might not be an instance of the
particular subtype of xs:string
to which they were applied.
The strings returned by fn:concat
and fn:stringjoin
are not guaranteed to be normalized.
But see note in fn:concat
.
Splits the supplied string into a sequence of singlecharacter strings.
fn:characters
($value
as
xs:string?
) as
xs:string*
This function is ·deterministic·, ·contextindependent·, and ·focusindependent·.
The function returns a sequence of strings, each string having length 1, containing
the corresponding ·character· in $value
.
If $value
is a zerolength string or the empty sequence, the function returns
the empty sequence.
The expression fn:characters("Thérèse")
returns ("T", "h", "é", "r", "è", "s", "e")
.
The expression fn:characters("")
returns ()
.
The expression fn:characters(())
returns ()
.
The expression fn:characters("Banana") => fn:indexof("a")
returns (2, 4, 6)
.
The expression fn:characters("stretch") => fn:stringjoin("")
returns "stretch"
.
The expression "Banana" => fn:characters() => fn:reverse() => fn:stringjoin()
returns "ananaB"
.
Returns the concatenation of the string values of the arguments.
The twoargument form of this function defines the semantics of the "" operator.
fn:concat (

$value1 
as xs:anyAtomicType? ,

$value2 
as xs:anyAtomicType? ,


...  ) as xs:string 
This function is ·deterministic·, ·contextindependent·, and ·focusindependent·.
This function accepts two or more xs:anyAtomicType
arguments and casts each
one to xs:string
. The function returns the xs:string
that is
the concatenation of the values of its arguments after conversion. If any argument
is
the empty sequence, that argument is treated as the zerolength string.
The fn:concat
function is specified to allow two or more arguments, which
are concatenated together. This is the only function specified in this document that
allows a variable number of arguments. This capability is retained for compatibility
with [XML Path Language (XPath) Version 1.0].
As mentioned in 5.1 String types Unicode normalization is not automatically
applied to the result of fn:concat
. If a normalized result is required,
fn:normalizeunicode
can be applied to the xs:string
returned by fn:concat
. The following XQuery:
let $v1 := "I plan to go to Mu" let $v2 := "?nchen in September" return concat($v1, $v2)
where the "?" represents either the actual Unicode character COMBINING DIARESIS (Unicode codepoint U+0308) or "̈", will return:
"I plan to go to Mu?nchen in September"
where the "?" represents either the actual Unicode character COMBINING DIARESIS (Unicode codepoint U+0308) or "̈". It is worth noting that the returned value is not normalized in NFC; however, it is normalized in NFD.
However, the following XQuery:
let $v1 := "I plan to go to Mu" let $v2 := "?nchen in September" return normalizeunicode(concat($v1, $v2))
where the "?" represents either the actual Unicode character COMBINING DIARESIS (Unicode codepoint U+0308) or "̈", will return:
"I plan to go to München in September"
This returned result is normalized in NFC.
The expression fn:concat('un', 'grateful')
returns "ungrateful"
.
The expression fn:concat('Thy ', (), 'old ', "groans", "", ' ring',
' yet', ' in', ' my', ' ancient',' ears.')
returns "Thy old groans ring yet in my ancient ears."
.
The expression fn:concat('Ciao!',())
returns "Ciao!"
.
The expression fn:concat('Ingratitude, ', 'thou ', 'marblehearted', ' fiend!')
returns "Ingratitude, thou marblehearted fiend!"
.
The expression fn:concat(01, 02, 03, 04, true())
returns "1234true"
.
The expression 10  '/'  6
returns "10/6"
.
Returns a string created by concatenating the items in a sequence, with a defined separator between adjacent items.
fn:stringjoin
($values
as
xs:anyAtomicType*
) as
xs:string
fn:stringjoin (

$values 
as xs:anyAtomicType* ,

$separator 
as xs:string ) as xs:string 
This function is ·deterministic·, ·contextindependent·, and ·focusindependent·.
The effect of calling the singleargument version of this function is the same as
calling the twoargument version with $separator
set to a zerolength
string.
The function returns an xs:string
created by casting each item
in the sequence $values
to an xs:string
,
and then concatenating the result strings in order,
using the value of $separator
as a
separator between adjacent strings. If $separator
is the zerolength
string, then the items in $values
are concatenated without a separator.
If $values
is the empty sequence, the function returns the
zerolength string.
The expression fn:stringjoin(1 to 9)
returns "123456789"
.
The expression fn:stringjoin(('Now', 'is', 'the', 'time', '...'),
' ')
returns "Now is the time ..."
.
The expression fn:stringjoin(('Blow, ', 'blow, ', 'thou ', 'winter ', 'wind!'),
'')
returns "Blow, blow, thou winter wind!"
.
The expression fn:stringjoin((), 'separator')
returns ""
.
The expression fn:stringjoin(1 to 5, ', ')
returns "1, 2, 3, 4, 5"
.
let $doc := <doc> <chap> <section xml:id="xyz"/> </chap> </doc>
The expression $doc//@xml:id ! fn:stringjoin((nodename(), '="', ., '"'))
returns 'xml:id="xyz"'
.
The expression $doc//section ! fn:stringjoin(ancestororself::*/name(), '/')
returns "doc/chap/section"
.
Returns the part of $value
beginning at the position
indicated by $start
and continuing for the number of ·characters· indicated by $length
.
fn:substring
($value
as
xs:string?
, $start
as
xs:double
) as
xs:string
fn:substring (

$value 
as xs:string? ,

$start 
as xs:double ,


$length 
as xs:double ) as xs:string 
This function is ·deterministic·, ·contextindependent·, and ·focusindependent·.
If $value
is the empty sequence, the function returns
the zerolength string.
Otherwise, the function returns a string comprising those ·characters· of $value
whose index position (counting
from one) is greater than or equal to $start
(rounded to an
integer), and (if $length
is specified) less than the sum of
$start
and $length
(both rounded to integers).
The characters returned do not extend beyond $value
. If
$start
is zero or negative, only those characters in positions greater
than zero are returned.
More specifically, the three argument version of the function returns the characters
in
$value
whose position $p
satisfies:
fn:round($start) <= $p and $p < fn:round($start) + fn:round($length)
The two argument version of the function assumes that $length
is infinite
and thus returns the ·characters· in
$value
whose position $p
satisfies:
fn:round($start) <= $p
In the above computations, the rules for op:numericlessthan
and
op:numericgreaterthan
apply.
The first character of a string is located at position 1, not position 0.
The second and third arguments allow xs:double
values (rather than
requiring xs:integer
) in order to achieve compatibility with XPath 1.0.
A surrogate pair counts as one character, not two.
The consequences of supplying values such as NaN
or positive or negative
infinity for the $start
or $length
arguments follow from the
above rules, and are not always intuitive.
The expression fn:substring("motor car", 6)
returns " car"
. (Characters starting at position 6 to the end of
$sourceString
are selected.)
The expression fn:substring("metadata", 4, 3)
returns "ada"
. (Characters at positions greater than or equal to 4 and less than 7 are
selected.)
The expression fn:substring("12345", 1.5, 2.6)
returns "234"
. (Characters at positions greater than or equal to 2 and less than 5 are
selected.)
The expression fn:substring("12345", 0, 3)
returns "12"
. (Characters at positions greater than or equal to 0 and less than 3 are
selected. Since the first position is 1, these are the characters at positions 1
and 2.)
The expression fn:substring("12345", 5, 3)
returns ""
. (Characters at positions greater than or equal to 5 and less than 2 are
selected.)
The expression fn:substring("12345", 3, 5)
returns "1"
. (Characters at positions greater than or equal to 3 and less than 2
are selected. Since the first position is 1, this is the character at position
1.)
The expression fn:substring("12345", 0 div 0E0, 3)
returns ""
. (Since 0 div 0E0
returns NaN
, and
NaN
compared to any other number returns false
, no
characters are selected.)
The expression fn:substring("12345", 1, 0 div 0E0)
returns ""
. (As above.)
The expression fn:substring((), 1, 3)
returns ""
.
The expression fn:substring("12345", 42, 1 div 0E0)
returns "12345"
. (Characters at positions greater than or equal to 42 and less than
INF
are selected.)
The expression fn:substring("12345", 1 div 0E0, 1 div 0E0)
returns ""
. (Since the value of INF + INF
is NaN
, no
characters are selected.)
Returns the number of ·characters· in a string.
fn:stringlength
() as
xs:integer
fn:stringlength
($value
as
xs:string?
) as
xs:integer
The zeroargument form of this function is ·deterministic·, ·contextdependent·, and ·focusdependent·.
The oneargument form of this function is ·deterministic·, ·contextindependent·, and ·focusindependent·.
The function returns an xs:integer
equal to the length in ·characters· of $value
.
Calling the zeroargument version of the function is equivalent to calling
fn:stringlength(fn:string(.))
.
If $value
is the empty sequence, the function returns the
xs:integer
value zero (0).
If $value
is not specified and the context item is absent^{DM31}, a dynamic error is raised: [err:XPDY0002]^{XP}.
Unlike some programming languages, a ·codepoint· greater than 65535 counts as one character, not two.
There are situations where fn:stringlength()
has a different effect
from fn:stringlength(.)
. For example, if the context item
is an attribute node typed as an xs:integer
with the string value 000001
,
then fn:stringlength()
returns 6 (the length of the string value of the node), while
fn:stringlength(.)
raises a type error (because the result of atomization
is not an xs:string
).
The expression fn:stringlength("Harp not on that string, madam; that is past.")
returns 45
.
The expression fn:stringlength(())
returns 0
.
Returns $value
with leading and trailing whitespace removed, and
sequences of internal whitespace reduced to a single space character.
fn:normalizespace
() as
xs:string
fn:normalizespace
($value
as
xs:string?
) as
xs:string
The zeroargument form of this function is ·deterministic·, ·contextdependent·, and ·focusdependent·.
The oneargument form of this function is ·deterministic·, ·contextindependent·, and ·focusindependent·.
If $value
is the empty sequence, the function returns the
zerolength string.
The function returns a string constructed by stripping leading and trailing whitespace
from $value
, and replacing sequences of one or more adjacent
whitespace characters with a single space, #x20
.
The whitespace characters are defined in the metasymbol S (Production 3) of [Extensible Markup Language (XML) 1.0 (Fifth Edition)].
If no argument is supplied, then $value
defaults to the string value
(calculated using fn:string
) of the context item (.
).
If no argument is supplied and the context item is absent^{DM31} then a dynamic error is raised: [err:XPDY0002]^{XP}.
The definition of whitespace is unchanged in [Extensible Markup Language (XML) 1.1 Recommendation]. It is repeated here for convenience:
S ::= (#x20  #x9  #xD  #xA)+
The expression fn:normalizespace(" The wealthy curled darlings
of our nation. ")
returns "The wealthy curled darlings of our nation."
.
The expression fn:normalizespace(())
returns ""
.
Returns $value
after applying Unicode normalization.
fn:normalizeunicode
($value
as
xs:string?
) as
xs:string
fn:normalizeunicode
($value
as
xs:string?
, $form
as
xs:string
) as
xs:string
This function is ·deterministic·, ·contextindependent·, and ·focusindependent·.
If $value
is the empty sequence, the function returns the
zerolength string.
If the singleargument version of the function is used, the result is the same as
calling the twoargument version with $form
set to the string
"NFC".
Otherwise, the function returns $value
normalized according to
the rules of the normalization form identified by the value of
$form
.
The effective value of $form
is the value of the expression
fn:uppercase(fn:normalizespace($form))
.
If the effective value of $form
is "NFC",
then the function returns $value
converted to Unicode
Normalization Form C (NFC).
If the effective value of $form
is "NFD",
then the function returns $value
converted to Unicode
Normalization Form D (NFD).
If the effective value of $form
is "NFKC",
then the function returns $value
in Unicode Normalization
Form KC (NFKC).
If the effective value of $form
is "NFKD",
then the function returns $value
converted to Unicode
Normalization Form KD (NFKD).
If the effective value of $form
is
"FULLYNORMALIZED", then the function returns
$value
converted to fully normalized form.
If the effective value of $form
is the zerolength
string, no normalization is performed and $value
is returned.
Normalization forms NFC, NFD, NFKC, and NFKD, and the algorithms to be used for converting a string to each of these forms, are defined in [UAX #15].
The motivation for normalization form FULLYNORMALIZED is explained in [Character Model for the World Wide Web 1.0: Normalization]. However, as that specification did not progress beyond working draft status, the normative specification is as follows:
A string is fullynormalized if (a) it is in normalization form NFC as defined in [UAX #15], and (b) it does not start with a composing character.
A composing character is a character that is one or both of the following:
the second character in the canonical decomposition mapping of some character that is not listed in the Composition Exclusion Table defined in [UAX #15];
of nonzero canonical combining class (as defined in [The Unicode Standard]).
A string is converted to FULLYNORMALIZED form as follows:
if the first character in the string is a composing character, prepend a single space (x20);
convert the resulting string to normalization form NFC.
Conforming implementations must support normalization form "NFC" and may support normalization forms "NFD", "NFKC", "NFKD", and "FULLYNORMALIZED". They may also support other normalization forms with ·implementationdefined· semantics.
It is ·implementationdefined· which
version of Unicode (and therefore, of the normalization algorithms and their underlying
data) is supported by the implementation. See [UAX #15] for
details of the stability policy regarding changes to the normalization rules in future
versions of Unicode. If the input string contains codepoints that are unassigned in
the
relevant version of Unicode, or for which no normalization rules are defined, the
fn:normalizeunicode
function leaves such codepoints unchanged. If the
implementation supports the requested normalization form then it must
be able to handle every input string without raising an error.
A dynamic error is raised [err:FOCH0003] if the
effective value of the $form
argument is not one of the values
supported by the implementation.
Converts a string to upper case.
fn:uppercase
($value
as
xs:string?
) as
xs:string
This function is ·deterministic·, ·contextindependent·, and ·focusindependent·.
If $value
is the empty sequence, the zerolength string is
returned.
Otherwise, the function returns $value
after translating every
·character· to its uppercase correspondent as
defined in the appropriate case mappings section in the Unicode standard [The Unicode Standard]. For versions of Unicode beginning with the 2.1.8 update, only
localeinsensitive case mappings should be applied. Beginning with version 3.2.0 (and
likely future versions) of Unicode, precise mappings are described in default case
operations, which are full case mappings in the absence of tailoring for particular
languages and environments. Every lowercase character that does not have an uppercase
correspondent, as well as every uppercase character, is included in the returned
value
in its original form.
Case mappings may change the length of a string. In general, the
fn:uppercase
and fn:lowercase
functions are not inverses
of each other: fn:lowercase(fn:uppercase($s))
is not guaranteed to
return $s
, nor is fn:uppercase(fn:lowercase($s))
. The
Latin small letter dotless i (as used in Turkish) is perhaps the most prominent
lowercase letter which will not roundtrip. The Latin capital letter i with dot above
is the most prominent uppercase letter which will not round trip; there are others,
such as Latin capital letter Sharp S (#1E9E) which was introduced in Unicode 5.1.
These functions may not always be linguistically appropriate (e.g. Turkish i without dot) or appropriate for the application (e.g. titlecase). In cases such as Turkish, a simple translation should be used first.
Because the function is not sensitive to locale, results will not always match user expectations. In Quebec, for example, the standard uppercase equivalent of "è" is "È", while in metropolitan France it is more commonly "E"; only one of these is supported by the functions as defined.
Many characters of class Ll lack uppercase equivalents in the Unicode case mapping tables; many characters of class Lu lack lowercase equivalents.
The expression fn:uppercase("abCd0")
returns "ABCD0"
.
Converts a string to lower case.
fn:lowercase
($value
as
xs:string?
) as
xs:string
This function is ·deterministic·, ·contextindependent·, and ·focusindependent·.
If t$value
is the empty sequence, the zerolength string is
returned.
Otherwise, the function returns $value
after translating every
·character· to its lowercase correspondent as
defined in the appropriate case mappings section in the Unicode standard [The Unicode Standard]. For versions of Unicode beginning with the 2.1.8 update, only
localeinsensitive case mappings should be applied. Beginning with version 3.2.0 (and
likely future versions) of Unicode, precise mappings are described in default case
operations, which are full case mappings in the absence of tailoring for particular
languages and environments. Every uppercase character that does not have a lowercase
correspondent, as well as every lowercase character, is included in the returned
value
in its original form.
Case mappings may change the length of a string. In general, the
fn:uppercase
and fn:lowercase
functions are not inverses
of each other: fn:lowercase(fn:uppercase($s))
is not guaranteed to
return $s
, nor is fn:uppercase(fn:lowercase($s))
. The
Latin small letter dotless i (as used in Turkish) is perhaps the most prominent
lowercase letter which will not roundtrip. The Latin capital letter i with dot above
is the most prominent uppercase letter which will not round trip; there are others,
such as Latin capital letter Sharp S (#1E9E) which was introduced in Unicode 5.1.
These functions may not always be linguistically appropriate (e.g. Turkish i without dot) or appropriate for the application (e.g. titlecase). In cases such as Turkish, a simple translation should be used first.
Because the function is not sensitive to locale, results will not always match user expectations. In Quebec, for example, the standard uppercase equivalent of "è" is "È", while in metropolitan France it is more commonly "E"; only one of these is supported by the functions as defined.
Many characters of class Ll lack uppercase equivalents in the Unicode case mapping tables; many characters of class Lu lack lowercase equivalents.
The expression fn:lowercase("ABc!D")
returns "abc!d"
.
Returns $value
modified by replacing or removing individual
characters.
fn:translate (

$value 
as xs:string? ,

$replace 
as xs:string ,


$with 
as xs:string ) as xs:string 
This function is ·deterministic·, ·contextindependent·, and ·focusindependent·.
If $value
is the empty sequence, the function returns the
zerolength string.
Otherwise, the function returns a result string constructed by processing each ·character· in $value
, in order,
according to the following rules:
If the character does not appear in $replace
then it
is added to the result string unchanged.
If the character first appears in $replace
at some
position M, where the value of $with
is
M or more characters in length, then the character at position
M in $with
is added to the result string.
If the character first appears in $replace
at some
position M, where $with
is less than
M characters in length, then the character is omitted from the
result string.
If $replace
is the zerolength string then the function returns
$value
unchanged.
If a character occurs more than once in $replace
, then the first
occurrence determines the action taken.
If $with
is longer than $replace
, the excess
characters are ignored.
The expression fn:translate("bar","abc","ABC")
returns "BAr"
.
The expression fn:translate("aaa","abc","ABC")
returns "AAA"
.
The expression fn:translate("abcdabc", "abc", "AB")
returns "ABdAB"
.
The functions described in the section examine a string $arg1
to see
whether it contains another string $arg2
as a substring. The result
depends on whether $arg2
is a substring of $arg1
, and
if so, on the range of ·characters· in $arg1
which $arg2
matches.
When the ·Unicode codepoint collation·
is used, this simply involves determining whether $arg1
contains a
contiguous sequence of characters whose ·codepoints· are the same, one for one,
with the codepoints of the characters in $arg2
.
When a collation is specified, the rules are more complex.
All collations support the capability of deciding whether two ·strings· are
considered equal, and if not, which of the strings should be regarded as
preceding the other. For functions such as fn:compare
, this is
all that is required. For other functions, such as fn:contains
,
the collation needs to support an additional property: it must be able to
decompose the string into a sequence of collation units, each unit consisting of
one or more characters, such that two strings can be compared by pairwise
comparison of these units. ("collation unit" is equivalent to "collation
element" as defined in [UTS #10].) The string
$arg1
is then considered to contain $arg2
as a
substring if the sequence of collation units corresponding to $arg2
is a subsequence of the sequence of the collation units corresponding to
$arg1
. The characters in $arg1
that match are the
characters corresponding to these collation units.
This rule may occasionally lead to surprises. For example, consider a collation
that treats "Jaeger" and "Jäger" as equal. It might do this by
treating "ä" as representing two collation units, in which case the
expression fn:contains("Jäger", "eg")
will return
true
. Alternatively, a collation might treat "ae" as a single
collation unit, in which case the expression fn:contains("Jaeger",
"eg")
will return false
. The results of these functions thus
depend strongly on the properties of the collation that is used.
In addition,
collations may specify that some collation units should be ignored during matching.
If hyphen is an ignored
collation unit, then fn:contains("codepoint", "codepoint")
will be true,
and fn:contains("codepoint", "")
will also be true.
In the definitions below, we refer to the terms match and minimal match as defined in definitions DS2 and DS4 of [UTS #10]. In applying these definitions:
C is the collation; that is, the value of the $collation
argument if specified, otherwise the default collation.
P is the (candidate) substring $arg2
Q is the (candidate) containing string $arg1
The boundary condition B is satisfied at the start and end of a string, and between any two characters that belong to different collation units ("collation elements" in the language of [UTS #10]). It is not satisfied between two characters that belong to the same collation unit.
It is possible to define collations that do not have the ability to decompose a string into units suitable for substring matching. An argument to a function defined in this section may be a URI that identifies a collation that is able to compare two strings, but that does not have the capability to split the string into collation units. Such a collation may cause the function to fail, or to give unexpected results or it may be rejected as an unsuitable argument. The ability to decompose strings into collation units is an ·implementationdefined· property of the collation.
Function  Meaning 

fn:contains 
Returns true if the string $value contains $substring as a
substring, taking collations into account.

fn:startswith 
Returns true if the string $value contains $substring as a leading
substring, taking collations into account.

fn:endswith 
Returns true if the string $value contains $substring as a trailing
substring, taking collations into account.

fn:substringbefore 
Returns the part of $value that precedes the first occurrence of
$substring , taking collations into account.

fn:substringafter 
Returns the part of $value that follows the first occurrence of
$substring , taking collations into account.

Returns true if the string $value
contains $substring
as a
substring, taking collations into account.
fn:contains
($value
as
xs:string?
, $substring
as
xs:string?
) as
xs:boolean
fn:contains (

$value 
as xs:string? ,

$substring 
as xs:string? ,


$collation 
as xs:string ) as xs:boolean 
The twoargument form of this function is ·deterministic·, ·contextdependent·, and ·focusindependent·. It depends on collations.
The threeargument form of this function is ·deterministic·, ·contextdependent·, and ·focusindependent·. It depends on collations, and static base URI.
If $value
or $substring
is the empty sequence, or
contains only ignorable collation units, it is interpreted as the zerolength
string.
If $substring
is the zerolength string, then the function returns
true
.
If $value
is the zerolength string, the function returns
false
.
The collation used by this function is determined according to the rules in 5.3.5 Choosing a collation.
The function returns an xs:boolean
indicating whether or not
$value
contains (at the beginning, at the end, or anywhere within) at
least one sequence of collation units that provides a minimal match to the
collation units in $substring
, according to the collation that is
used.
Note:
Minimal match is defined in [UTS #10].
A dynamic error may be raised [err:FOCH0004] if the specified collation does not support collation units.
The collation used in these examples, http://example.com/CollationA
is a
collation in which both "" and "*" are ignorable collation units.
"Ignorable collation unit" is equivalent to "ignorable collation element" in [UTS #10].
The expression fn:contains ( "tattoo", "t")
returns true()
.
The expression fn:contains ( "tattoo", "ttt")
returns false()
.
The expression fn:contains ( "", ())
returns true()
. (The first rule is applied, followed by the second
rule.)
The expression fn:contains ( "abcdefghi", "def",
"http://www.w3.org/2013/collation/UCA?lang=en;alternate=blanked;strength=primary")
returns true()
.
The expression fn:contains ( "a*b*c*d*e*f*g*h*i*", "def",
"http://www.w3.org/2013/collation/UCA?lang=en;alternate=blanked;strength=primary")
returns true()
.
The expression fn:contains ( "abcd***ef**ghi", "def",
"http://www.w3.org/2013/collation/UCA?lang=en;alternate=blanked;strength=primary")
returns true()
.
The expression fn:contains ( (), "****",
"http://www.w3.org/2013/collation/UCA?lang=en;alternate=blanked;strength=primary")
returns true()
. (The second argument contains only ignorable collation units and is
equivalent to the zerolength string.)
Returns true if the string $value
contains $substring
as a leading
substring, taking collations into account.
fn:startswith
($value
as
xs:string?
, $substring
as
xs:string?
) as
xs:boolean
fn:startswith (

$value 
as xs:string? ,

$substring 
as xs:string? ,


$collation 
as xs:string ) as xs:boolean 
The twoargument form of this function is ·deterministic·, ·contextdependent·, and ·focusindependent·. It depends on collations.
The threeargument form of this function is ·deterministic·, ·contextdependent·, and ·focusindependent·. It depends on collations, and static base URI.
If $value
or $substring
is the empty sequence, or
contains only ignorable collation units, it is interpreted as the zerolength
string.
If $substring
is the zerolength string, then the function returns
true
. If $value
is the zerolength string and
$substring
is not the zerolength string, then the function returns
false
.
The collation used by this function is determined according to the rules in 5.3.5 Choosing a collation.
The function returns an xs:boolean
indicating whether or not
$value
starts with a sequence of collation units that provides a
match to the collation units of $substring
according to the
collation that is used.
Note:
Match is defined in [UTS #10].
A dynamic error may be raised [err:FOCH0004] if the specified collation does not support collation units.
The collation used in these examples, http://example.com/CollationA
is a
collation in which both "" and "*" are ignorable collation units.
"Ignorable collation unit" is equivalent to "ignorable collation element" in [UTS #10].
The expression fn:startswith("tattoo", "tat")
returns true()
.
The expression fn:startswith ( "tattoo", "att")
returns false()
.
The expression fn:startswith ((), ())
returns true()
.
The expression fn:startswith ( "abcdefghi", "abc",
"http://www.w3.org/2013/collation/UCA?lang=en;alternate=blanked;strength=primary")
returns true()
.
The expression fn:startswith ( "a*b*c*d*e*f*g*h*i*", "abc",
"http://www.w3.org/2013/collation/UCA?lang=en;alternate=blanked;strength=primary")
returns true()
.
The expression fn:startswith ( "abcd***ef**ghi", "abcdef",
"http://www.w3.org/2013/collation/UCA?lang=en;alternate=blanked;strength=primary")
returns true()
.
The expression fn:startswith ( (), "****",
"http://www.w3.org/2013/collation/UCA?lang=en;alternate=blanked;strength=primary")
returns true()
. (The second argument contains only ignorable collation units and is
equivalent to the zerolength string.)
The expression fn:startswith ( "abcdefghi", "abc",
"http://www.w3.org/2013/collation/UCA?lang=en;alternate=blanked;strength=primary")
returns true()
.
Returns true if the string $value
contains $substring
as a trailing
substring, taking collations into account.
fn:endswith
($value
as
xs:string?
, $substring
as
xs:string?
) as
xs:boolean
fn:endswith (

$value 
as xs:string? ,

$substring 
as xs:string? ,


$collation 
as xs:string ) as xs:boolean 
The twoargument form of this function is ·deterministic·, ·contextdependent·, and ·focusindependent·. It depends on collations.
The threeargument form of this function is ·deterministic·, ·contextdependent·, and ·focusindependent·. It depends on collations, and static base URI.
If $value
or $substring
is the empty sequence, or
contains only ignorable collation units, it is interpreted as the zerolength
string.
If $substring
is the zerolength string, then the function returns
true
. If $value
is the zerolength string and
the value of $substring
is not the zerolength string, then the function returns
false
.
The collation used by this function is determined according to the rules in 5.3.5 Choosing a collation.
The function returns an xs:boolean
indicating whether or not
$value
ends with a sequence of collation units that provides a
match to the collation units of $substring
according to the
collation that is used.
Note:
Match is defined in [UTS #10].
A dynamic error may be raised [err:FOCH0004] if the specified collation does not support collation units.
The collation used in these examples, http://example.com/CollationA
is a
collation in which both "" and "*" are ignorable collation units.
"Ignorable collation unit" is equivalent to "ignorable collation element" in [UTS #10].
The expression fn:endswith ( "tattoo", "tattoo")
returns true()
.
The expression fn:endswith ( "tattoo", "atto")
returns false()
.
The expression fn:endswith ((), ())
returns true()
.
The expression fn:endswith ( "abcdefghi", "ghi",
"http://www.w3.org/2013/collation/UCA?lang=en;alternate=blanked;strength=primary")
returns true()
.
The expression fn:endswith ( "abcd***ef**ghi", "defghi",
"http://www.w3.org/2013/collation/UCA?lang=en;alternate=blanked;strength=primary")
returns true()
.
The expression fn:endswith ( "abcd***ef**ghi", "defghi",
"http://www.w3.org/2013/collation/UCA?lang=en;alternate=blanked;strength=primary")
returns true()
.
The expression fn:endswith ( (), "****",
"http://www.w3.org/2013/collation/UCA?lang=en;alternate=blanked;strength=primary")
returns true()
. (The second argument contains only ignorable collation units and is
equivalent to the zerolength string.)
The expression fn:endswith ( "abcdefghi", "ghi",
"http://www.w3.org/2013/collation/UCA?lang=en;alternate=blanked;strength=primary")
returns true()
.
Returns the part of $value
that precedes the first occurrence of
$substring
, taking collations into account.
fn:substringbefore (

$value 
as xs:string? ,

$substring 
as xs:string? ) as xs:string 
fn:substringbefore (

$value 
as xs:string? ,

$substring 
as xs:string? ,


$collation 
as xs:string ) as xs:string 
The twoargument form of this function is ·deterministic·, ·contextdependent·, and ·focusindependent·. It depends on collations.
The threeargument form of this function is ·deterministic·, ·contextdependent·, and ·focusindependent·. It depends on collations, and static base URI.
If $value
or $substring
is the empty sequence, or
contains only ignorable collation units, it is interpreted as the zerolength
string.
If $substring
is the zerolength string, then the function returns
the zerolength string.
If $value
does not contain a string that is equal to
$substring
, then the function returns the zerolength string.
The collation used by this function is determined according to the rules in 5.3.5 Choosing a collation.
The function returns the substring of $value
that precedes in
$value
the first occurrence of a sequence of collation units
that provides a minimal match to the collation units of $substring
according to the collation that is used.
Note:
Minimal match is defined in [UTS #10].
A dynamic error may be raised [err:FOCH0004] if the specified collation does not support collation units.
The collation used in these examples, http://example.com/CollationA
is a
collation in which both "" and "*" are ignorable collation units.
"Ignorable collation unit" is equivalent to "ignorable collation element" in [UTS #10].
The expression fn:substringbefore ( "tattoo", "attoo")
returns "t"
.
The expression fn:substringbefore ( "tattoo", "tatto")
returns ""
.
The expression fn:substringbefore ((), ())
returns ""
.
The expression fn:substringbefore ( "abcdefghi", "de",
"http://www.w3.org/2013/collation/UCA?lang=en;alternate=blanked;strength=primary")
returns "abc"
.
The expression fn:substringbefore ( "abcdefghi", "de",
"http://www.w3.org/2013/collation/UCA?lang=en;alternate=blanked;strength=primary")
returns "abc"
.
The expression fn:substringbefore ( "a*b*c*d*e*f*g*h*i*", "***cde",
"http://www.w3.org/2013/collation/UCA?lang=en;alternate=blanked;strength=primary")
returns "a*b*"
.
The expression fn:substringbefore ( "Eureka!", "****",
"http://www.w3.org/2013/collation/UCA?lang=en;alternate=blanked;strength=primary")
returns ""
. (The second argument contains only ignorable collation units and is
equivalent to the zerolength string.)
Returns the part of $value
that follows the first occurrence of
$substring
, taking collations into account.
fn:substringafter
($value
as
xs:string?
, $substring
as
xs:string?
) as
xs:string
fn:substringafter (

$value 
as xs:string? ,

$substring 
as xs:string? ,


$collation 
as xs:string ) as xs:string 
The twoargument form of this function is ·deterministic·, ·contextdependent·, and ·focusindependent·. It depends on collations.
The threeargument form of this function is ·deterministic·, ·contextdependent·, and ·focusindependent·. It depends on collations, and static base URI.
If $value
or $substring
is the empty sequence, or
contains only ignorable collation units, it is interpreted as the zerolength
string.
If $substring
is the zerolength string, then the function returns
the value of $value
.
If $value
does not contain a string that is equal to
$substring
, then the function returns the zerolength string.
The collation used by this function is determined according to the rules in 5.3.5 Choosing a collation.
The function returns the substring of $value
that follows in
$value
the first occurrence of a sequence of collation units
that provides a minimal match to the collation units of $substring
according to the collation that is used.
Note:
Minimal match is defined in [UTS #10].
A dynamic error may be raised [err:FOCH0004] if the specified collation does not support collation units.
The collation used in these examples, http://example.com/CollationA
is a
collation in which both "" and "*" are ignorable collation units.
"Ignorable collation unit" is equivalent to "ignorable collation element" in [UTS #10].
The expression fn:substringafter("tattoo", "tat")
returns "too"
.
The expression fn:substringafter("tattoo", "tattoo")
returns ""
.
The expression fn:substringafter((), ())
returns ""
.
The expression fn:substringafter("abcdefghi", "de",
"http://www.w3.org/2013/collation/UCA?lang=en;alternate=blanked;strength=primary")
returns "fghi"
.
The expression fn:substringafter("abcdefghi", "de",
"http://www.w3.org/2013/collation/UCA?lang=en;alternate=blanked;strength=primary")
returns "fghi"
.
The expression fn:substringafter ( "a*b*c*d*e*f*g*h*i*", "***cde***",
"http://www.w3.org/2013/collation/UCA?lang=en;alternate=blanked;strength=primary")
returns "*f*g*h*i*"
.
The expression fn:substringafter ( "Eureka!", "****",
"http://www.w3.org/2013/collation/UCA?lang=en;alternate=blanked;strength=primary")
returns "Eureka!"
. (The second argument contains only ignorable collation units and is
equivalent to the zerolength string.)
The three functions described in this section make use of a regular expression syntax for pattern matching. This is described below.
Function  Meaning 

fn:matches 
Returns true if the supplied string matches a given regular expression. 
fn:replace 
Returns a string produced from the input string by replacing any substrings that match a given regular expression with a supplied replacement string, provided either literally, or by invoking a supplied function. 
fn:tokenize 
Returns a sequence of strings constructed by splitting the input wherever a separator is found; the separator is any substring that matches a given regular expression. 
fn:analyzestring 
Analyzes a string using a regular expression, returning an XML structure that identifies which parts of the input string matched or failed to match the regular expression, and in the case of matched substrings, which substrings matched each capturing group in the regular expression. 
The regular expression syntax used by these functions is defined in terms of the regular expression syntax specified in XML Schema (see [XML Schema Part 2: Datatypes Second Edition]), which in turn is based on the established conventions of languages such as Perl. However, because XML Schema uses regular expressions only for validity checking, it omits some facilities that are widelyused with languages such as Perl. This section, therefore, describes extensions to the XML Schema regular expressions syntax that reinstate these capabilities.
Note:
It is recommended that implementers consult [UTS #18] for information on using regular expression processing on Unicode characters.
The regular expression syntax and semantics are identical to those defined in [XML Schema Part 2: Datatypes Second Edition] with the additions described in the following subsections.
Note:
In [Schema 1.1 Part 2] there are no substantive technical changes to the syntax or semantics of regular expressions relative to XSD 1.0, but a number of errors and ambiguities have been resolved. For example, the rules for the interpretation of hyphens within square brackets in a regular expression have been clarified; and the semantics of regular expressions are no longer tied to a specific version of Unicode.
Implementers, even in cases where XSD 1.1 is not supported, are advised to consult the XSD 1.1 regular expression specification for guidance on how to handle cases where the XSD 1.0 specification is unclear or inconsistent.
Two metacharacters, ^
and $
are
added. By default, the metacharacter ^
matches the
start of the entire string, while $
matches the end
of the entire string. In multiline mode, ^
matches
the start of any line (that is, the start of the entire string,
and the position immediately after a newline character), while
$
matches the end of any line (that is, the end of
the entire string, and the position immediately before a newline
character). Newline here means the character #x0A
only.
This means that the production in [XML Schema Part 2: Datatypes Second Edition]:
[10] Char ::= [^.\?*+()#x5B#x5D]
is modified to read:
[10] Char ::= [^.\?*+{}()^$#x5B#x5D]
The XSD 1.1 grammar for regular expressions uses the same
production rule, but renumbered and renamed [73] NormalChar
; it
is affected in the same way.
The characters #x5B
and #x5D
correspond
to "[
" and "]
" respectively.
Note:
The definition of Char (production [10]) in [XML Schema Part 2: Datatypes Second Edition] has a known error in which it omits the left brace ("{") and right brace ("}"). That error is corrected here.
The following production:
[11] charClass ::= charClassEsc  charClassExpr  WildCardEsc
is modified to read:
[11] charClass ::= charClassEsc  charClassExpr 
WildCardEsc  "^"  "$"
Using XSD 1.1 as the baseline the equivalent is to change the production:
[74] charClass ::= SingleCharEsc  charClassEsc  charClassExpr  WildCardEsc
to read:
[74] charClass ::= SingleCharEsc  charClassEsc  charClassExpr 
WildCardEsc  "^"  "$"
Single character escapes are extended to allow the
$
character to be escaped. The following production
is changed:
[24]SingleCharEsc ::= '\' [nrt\.?*+(){}#x2D#x5B#x5D#x5E]
to
[24]SingleCharEsc ::= '\' [nrt\.?*+(){}$#x2D#x5B#x5D#x5E]
(In the XSD 1.1 version of the regular expression grammar, the production rule
for SingleCharEsc
is unchanged, but is renumbered [84])
Reluctant quantifiers are supported. They are
indicated by a
?
following a quantifier. Specifically:
X??
matches X, once or not at all
X*?
matches X, zero or more times
X+?
matches X, one or more times
X{n}?
matches X, exactly n times
X{n,}?
matches X, at least n times
X{n,m}?
matches X, at least n times, but
not more than m times
The effect of these quantifiers is that the regular expression
matches the shortest possible substring consistent
with the match as a whole succeeding. Without the
?
, the regular expression matches the
longest possible substring.
To achieve this, the production in [XML Schema Part 2: Datatypes Second Edition]:
[4] quantifier ::= [?*+]  ( '{' quantity '}' )
is changed to:
[4] quantifier ::= ( [?*+]  ( '{' quantity '}' ) ) '?'?
(In the XSD 1.1 version of the regular expression grammar, this rule is unchanged, but is renumbered [67])
Note:
Reluctant quantifiers have no effect on the results of the
boolean fn:matches
function, since this
function is only interested in discovering whether a match
exists, and not where it exists.
Subexpressions (groups) within the regular expression are
recognized. The regular expression syntax defined by [XML Schema Part 2: Datatypes Second Edition]
allows a regular expression to contain parenthesized subexpressions,
but attaches no special
significance to them. Some operations associated with regular expressions (for example,
backreferences, and the fn:replace
function) allow access to the parts of the
input string that matched a subexpression (called captured substrings).
[Definition] A
left parenthesis is recognized as a capturing left parenthesis provided
it is not immediately followed by ?:
(see below), is not within a character group (square brackets),
and is not escaped with a backslash. The subexpression enclosed by a capturing left
parenthesis and its matching right parenthesis is referred to as a capturing subexpression.
More specifically, the ·capturing subexpression· enclosed by the Nth capturing left parenthesis within the regular expression (determined by its character position in lefttoright order, and counting from one) is referred to as the Nth capturing subexpression.
For example, in the regular expression A(BC(?:D(EF(GH[()]))))
, the string matched
by the subexpression BC(?:D(EF(GH[()])))
is capturing subexpression 1, the string
matched by EF(GH[()])
is capturing subexpression 2, and the string matched by
GH[()]
is capturing subexpression 3.
When, in the course of evaluating a regular expression, a particular substring of the input matches a capturing subexpression, that substring becomes available as a captured substring. The string matched by the Nth capturing subexpression is referred to as the Nth captured substring. By convention, the substring captured by the entire regular expression is treated as captured substring 0 (zero).
When a ·capturing subexpression· is matched
more than once (because it is within a construct that allows repetition), then
only the last substring that it matched will be captured. Note that this rule
is not sufficient in all cases to ensure an unambiguous result, especially in
cases where (a) the regular expression contains nested repeating constructs,
and/or (b) the repeating construct matches a zerolength string. In such cases
it is implementationdependent which substring is captured. For example given
the regular expression (a*)+
and the input string "aaaa"
, an implementation
might legitimately capture either "aaaa"
or a zero length string as the content
of the captured subgroup.
Parentheses that are required to group terms within the regular expression, but which
are
not required for capturing of substrings, can be represented using
the syntax (?:xxxx)
. To achieve this, the production rule for atom
in [XML Schema Part 2: Datatypes Second Edition] is changed to replace the alternative:
( '(' regExp ')' )
with:
( '(' '?:'? regExp ')' )
(For the new versions of the XSD 1.0 and XSD 1.1 production rules for
atom
, see below.)
In the absence of backreferences (see below),
the presence of the optional ?:
has no effect on the set of strings
that match the regular expression, but causes the left parenthesis not to be counted
by operations (such as fn:replace
and backreferences) that number the capturing subexpressions
within a regular expression.
Backreferences are allowed
outside a character class expression.
A backreference is an additional kind of atom.
The construct \N
where
N
is a single digit is always recognized as a
backreference; if this is followed by further digits, these
digits are taken to be part of the backreference if and only if
the resulting number NN is such that
the backreference is preceded by the opening parenthesis of the NNth
capturing left parenthesis.
The regular expression is invalid if a backreference refers to a
capturing subexpression that does not exist or whose
closing right parenthesis occurs after the backreference.
A backreference with number N matches a string that is the same as
the value of the N
th captured substring.
For example, the regular expression
('").*\1
matches a sequence of characters
delimited either by an apostrophe at the start and end, or by a
quotation mark at the start and end.
If no string has been matched by the N
th capturing
subexpression, the backreference is interpreted as matching
a zerolength string.
Combining this change with the introduction of noncapturing groups (see above), backreferences change the following production:
[9] atom ::= Char  charClass  ( '(' regExp ')' )
to
[9] atom ::= Char  charClass  ( '(' '?:'? regExp ')' )  backReference
[9a] backReference ::= "\" [19][09]*
With respect to the XSD 1.1 version of the regular expression grammar, the effect is to change:
[72] atom ::= NormalChar  charClass  ( '(' regExp ')' )
to
[72] atom ::= NormalChar  charClass  ( '(' '?:'? regExp ')' )  backReference
[72a] backReference ::= "\" [19][09]*
Note:
Within a character class expression,
\
followed by a digit is invalid.
Some other regular expression languages interpret this as an octal character reference.
A regular expression that uses a Unicode block name that is not defined in the version(s)
of Unicode
supported by the processor (for example \p{IsBadBlockName}
) is deemed to be invalid
[err:FORX0002].
Note:
XSD 1.0 does not say how this situation should be handled; XSD 1.1 says that it should be handled by treating all characters as matching.
All these functions provide an optional parameter, $flags
,
to set options for the interpretation of the regular expression. The
parameter accepts a xs:string
, in which individual letters
are used to set options. The presence of a letter within the string
indicates that the option is on; its absence indicates that the option
is off. Letters may appear in any order and may be repeated. If there
are characters present that are not defined here as flags, then a dynamic error
is raised [err:FORX0001].
The following options are defined:
s
: If present, the match operates in "dotall"
mode. (Perl calls this the singleline mode.) If the
s
flag is not specified, the metacharacter
.
matches any character except a newline
(#x0A
) or carriage return (#x0D
)
character. In dotall mode, the
metacharacter .
matches any character whatsoever.
Suppose the input contains "hello" and "world" on two lines.
This will not be matched by the regular expression
"hello.*world" unless dotall mode is enabled.
m
: If present, the match operates in multiline
mode. By default, the metacharacter ^
matches the
start of the entire string, while $ matches the end of the
entire string. In multiline mode, ^
matches the
start of any line (that is, the start of the entire string, and
the position immediately after a newline character
other than a newline
that appears as the last character in the string), while
$
matches the end of any line
(that is, the position immediately
before a newline character, and the end of the entire string if there
is no
newline character at the end of the string).
Newline here means the character #x0A
only.
i
: If present, the match operates in
caseinsensitive mode. The detailed rules are as follows.
In these
rules, a character C2 is considered to be a casevariant of
another character C1 if the following XPath expression returns
true
when the two characters
are considered as strings of length one, and the
·Unicode codepoint collation· is used:
fn:lowercase(C1) eq fn:lowercase(C2) or
fn:uppercase(C1) eq fn:uppercase(C2)
Note that the casevariants of a character under this definition are always single characters.
When a normal character (Char
) is used as an atom,
it represents
the set containing that character and all its casevariants.
For example, the regular expression "z" will match both "z" and
"Z".
A character range (production charRange
in the XSD 1.0 grammar, replaced by productions charRange
and singleChar
in XSD 1.1) represents the set
containing all the characters that it would match in the absence
of the "i
" flag, together with their casevariants.
For example,
the regular expression "[AZ]" will match all
the letters AZ and all the letters az. It will also match
certain other characters such as #x212A
(KELVIN SIGN), since
fn:lowercase("#x212A")
is "k".
This rule applies also to a character range used in a character
class subtraction (charClassSub
): thus [AZ[IO]] will match
characters such as "A", "B", "a", and "b", but will not match
"I", "O", "i", or "o".
The rule also applies to a character range used as part of a negative character group: thus [^Q] will match every character except "Q" and "q" (these being the only casevariants of "Q" in Unicode).
A backreference is compared using caseblind comparison:
that is, each character must either be the same as the
corresponding character of the previously matched string, or must
be a casevariant of that character. For example, the strings
"Mum", "mom", "Dad", and "DUD" all match the regular
expression "([md])[aeiou]\1" when the "i
" flag is used.
All other constructs are unaffected by the "i
" flag.
For example,
"\p{Lu}" continues to match uppercase letters only.
x
: If present, whitespace characters
(#x9, #xA, #xD and #x20) in the regular
expression are removed prior to matching with one exception:
whitespace characters within character class expressions
(charClassExpr
) are not removed. This flag can be used,
for example, to break up long regular expressions into readable lines.
Examples:
fn:matches("helloworld", "hello world", "x")
returns true()
fn:matches("helloworld", "hello[ ]world", "x")
returns false()
fn:matches("hello world", "hello\ sworld", "x")
returns true()
fn:matches("hello world", "hello world", "x")
returns false()
q
: if present, all characters in the regular expression
are treated as representing themselves, not as metacharacters. In effect, every
character that would normally have a special meaning in a regular expression is implicitly
escaped
by preceding it with a backslash.
Furthermore, when this flag is present, the characters $
and
\
have no special significance when used in the replacement string
supplied to the fn:replace
function.
This flag can be used in conjunction with the i
flag. If it is used
together with the m
, s
, or x
flag, that flag
has no effect.
Examples:
fn:tokenize("12.3.5.6", ".", "q")
returns ("12", "3", "5", "6")
fn:replace("a\b\c", "\", "\\", "q")
returns "a\\b\\c"
fn:replace("a/b/c", "/", "$", "q")
returns "a$b$c"
fn:matches("abcd", ".*", "q")
returns false()
fn:matches("Mr. B. Obama", "B. OBAMA", "iq")
returns true()
Returns true if the supplied string matches a given regular expression.
fn:matches
($value
as
xs:string?
, $pattern
as
xs:string
) as
xs:boolean
fn:matches (

$value 
as xs:string? ,

$pattern 
as xs:string ,


$flags 
as xs:string ) as xs:boolean 
This function is ·deterministic·, ·contextindependent·, and ·focusindependent·.
The effect of calling the first version of this function (omitting the argument
$flags
) is the same as the effect of calling the second version with the
$flags
argument set to a zerolength string. Flags are defined in
5.6.2 Flags.
If $value
is the empty sequence, it is interpreted as the zerolength
string.
The function returns true
if $value
or some substring of
$value
matches the regular expression supplied as $pattern
.
Otherwise, the function returns false
. The matching rules are influenced by
$flags
if present.
A dynamic error is raised [err:FORX0002] if
$pattern
is invalid according to the rules described in 5.6.1 Regular expression syntax.
A dynamic error is raised [err:FORX0001] if
$flags
is invalid according to the rules described in 5.6.2 Flags.
Unless the metacharacters ^
and $
are used as anchors, the
string is considered to match the pattern if any substring matches the pattern. But
if
anchors are used, the anchors must match the start/end of the string (in string mode),
or the start/end of a line (in multiline mode).
This is different from the behavior of patterns in [XML Schema Part 2: Datatypes Second Edition], where regular expressions are implicitly anchored.
Regular expression matching is defined on the basis of Unicode code points; it takes no account of collations.
The expression fn:matches("abracadabra", "bra")
returns true()
.
The expression fn:matches("abracadabra", "^a.*a$")
returns true()
.
The expression fn:matches("abracadabra", "^bra")
returns false()
.
Given the source document:
let $poem := <poem author="Wilhelm Busch"> Kaum hat dies der Hahn gesehen, Fängt er auch schon an zu krähen: Kikeriki! Kikikerikih!! Tak, tak, tak!  da kommen sie. </poem>
the following function calls produce the following results, with the
poem
element as the context node:
The expression fn:matches($poem, "Kaum.*krähen")
returns false()
.
The expression fn:matches($poem, "Kaum.*krähen", "s")
returns true()
.
The expression fn:matches($poem, "^Kaum.*gesehen,$", "m")
returns true()
.
The expression fn:matches($poem, "^Kaum.*gesehen,$")
returns false()
.
The expression fn:matches($poem, "kiki", "i")
returns true()
.
Returns a string produced from the input string by replacing any substrings that match a given regular expression with a supplied replacement string, provided either literally, or by invoking a supplied function.
fn:replace (

$value 
as xs:string? ,

$pattern 
as xs:string ,


$replacement 
as xs:string? ,


$flags 
as xs:string? ,


$action 
as (function(xs:string, xs:string*) as xs:string?)? ) as xs:string 
This function is ·deterministic·, ·contextindependent·, and ·focusindependent·.
If the $flags
argument is omitted, the effect is the same as supplying
a zerolength string. Flags are defined in 5.6.2 Flags. The $flags
argument is interpreted in the same manner as for the fn:matches
function.
The replacement string is determined by the values of the $replacement
and/or $action
arguments. If both these arguments are present and nonempty,
an error is reported.
If $value
is the empty sequence, it is interpreted as the zerolength
string.
The function returns the xs:string
that is obtained by replacing each
nonoverlapping substring of $value
that matches the given
$pattern
with a replacement string.
If two overlapping substrings of $value
both match the
$pattern
, then only the first one (that is, the one whose first ·character· comes first in the $value
string) is
replaced.
The replacement string is determined as follows:
If the $replacement
argument is present and is not an empty sequence,
then the value of $replacement
.
If the $action
argument is present and is not an empty sequence,
then the string obtained by calling the $action
function.
The first argument to the $action
function is the string to be replaced.
The second argument to the $action
function is the sequence of captured
substrings. The Nth
item in this sequence is the substring captured by
the Nth
parenthesized subexpression. If the
Nth
parenthesized subexpression was not matched, the Nth
item
will be the zerolength string.
Note that the rules for function coercion mean that the function actually
supplied for the $action
parameter may be an arity1 function: the
second argument does not need to be declared if it is not used.
If the function returns an empty sequence, then the replacement string is the zerolength string.
If neither of the $replacement
or $action
arguments
is present, or if both are empty, then the replacement string is the zerolength string.
If the q
flag is present, or if the replacement string was obtained
by calling the $action
function, then the replacement string is used
as is.
Otherwise, within the replacement string, a variable $N
may
be used to refer to the substring captured by the Nth parenthesized subexpression
in
the regular expression. For each match of the pattern, these variables are assigned
the
value of the content matched by the relevant subexpression, and the modified
replacement string is then substituted for the ·characters· in $value
that matched the pattern.
$0
refers to the substring captured by the regular expression as a
whole.
More specifically, the rules are as follows, where S
is the number of
parenthesized subexpressions in the regular expression, and N
is the
decimal number formed by taking all the digits that consecutively follow the
$
character:
If N
=0
, then the variable is replaced by the substring
matched by the regular expression as a whole.
If 1
<=N
<=S
, then the variable is
replaced by the substring captured by the Nth parenthesized subexpression. If the
Nth
parenthesized subexpression was not matched, then the
variable is replaced by the zerolength string.
If S
<N
<=9
, then the variable is
replaced by the zerolength string.
Otherwise (if N
>S
and
N
>9
), the last digit of N
is taken to
be a literal character to be included "as is" in the replacement string, and the
rules are reapplied using the number N
formed by stripping off this
last digit.
For example, if the replacement string is
"$23"
and there are 5 substrings, the result contains the value of the substring that
matches the second subexpression, followed by the digit
3
.
Unless the q
flag is used, a literal $
character within the
replacement string must be written as \$
, and a literal \
character must be written as \\
.
If two alternatives within the pattern both match at the same position in the
$input
, then the match that is chosen is the one matched by the first
alternative. For example:
fn:replace("abcd", "(ab)(a)", "[1=$1][2=$2]") returns "[1=ab][2=]cd"
A dynamic error is raised [err:FORX0002] if the value of
$pattern
is invalid according to the rules described in section 5.6.1 Regular expression syntax.
A dynamic error is raised [err:FORX0001] if the value of
$flags
is invalid according to the rules described in section 5.6.2 Flags.
A dynamic error is raised [err:FORX0003] if the pattern matches a
zerolength string, that is, if the expression fn:matches("", $pattern,
$flags)
returns true
. It is not an error, however, if a captured
substring is zerolength.
In the absence of the q
flag,
a dynamic error is raised [err:FORX0004] if the value of
$replacement
contains a dollar sign ($
) character that is not
immediately followed by a digit 09
and not immediately preceded by a
backslash (\
).
In the absence of the q
flag,
a dynamic error is raised [err:FORX0004] if the value of
$replacement
contains a backslash (\
) character that is not part of a
\\
pair, unless it is immediately followed by a dollar sign ($
)
character.
A dynamic error is raised [ERROR 0005 NOT FOUND] if both the $replacement
and $action
arguments are supplied, and neither is an empty sequence.
If the input string contains no substring that matches the regular expression, the result of the function is a single string identical to the input string.
The expression fn:replace("abracadabra", "bra", "*")
returns "a*cada*"
.
The expression fn:replace("abracadabra", "a.*a", "*")
returns "*"
.
The expression fn:replace("abracadabra", "a.*?a", "*")
returns "*c*bra"
.
The expression fn:replace("abracadabra", "a", "")
returns "brcdbr"
.
The expression fn:replace("abracadabra", "a(.)", "a$1$1")
returns "abbraccaddabbra"
.
The expression fn:replace("AAAA", "A+", "b")
returns "b"
.
The expression fn:replace("AAAA", "A+?", "b")
returns "bbbb"
.
The expression fn:replace("darted", "^(.*?)d(.*)$", "$1c$2")
returns "carted"
. (The first d
is replaced.)
The expression fn:replace("abracadabra", "bra", action: >{"*"})
returns "a*cada*"
.
The expression fn:replace("abracadabra", "bra", action: fn:uppercase#1)
returns aBRAcadaBRA
.
The expression fn:replace("Chapter 9", "[09]+", action: >{string(number(.)+1)})
returns "Chapter 10"
.
The expression fn:replace("LHR to LAX", "[AZ]{3}", action: map{'LAX': 'Los Angeles', 'LHR': 'London'})
returns "London to Los Angeles"
.
The expression fn:replace("57°43′30″", "([09]+)°([09]+)′([09]+)″)", action: >($s, $groups){string(number($groups[1])
+ number($groups[2])÷60 + number($groups[3])÷3600)'°'})
returns "57.725°"
.
The expression fn:replace("abracadabra", ".*?", "$1")
raises an error,
because the pattern matches the zerolength string
Returns a sequence of strings constructed by splitting the input wherever a separator is found; the separator is any substring that matches a given regular expression.
fn:tokenize
($value
as
xs:string?
) as
xs:string*
fn:tokenize
($value
as
xs:string?
, $pattern
as
xs:string
) as
xs:string*
fn:tokenize (

$value 
as xs:string? ,

$pattern 
as xs:string ,


$flags 
as xs:string ) as xs:string* 
This function is ·deterministic·, ·contextindependent·, and ·focusindependent·.
The oneargument form of this function
splits the supplied string at whitespace boundaries. More specifically, calling fn:tokenize($value)
is equivalent to calling fn:tokenize(fn:normalizespace($value), ' '))
where the second argument
is a single space character (x20).
The effect of calling the twoargument form of this function (omitting the argument
$flags
) is the same as the effect of calling the threeargument version with the
$flags
argument set to a zerolength string. Flags are defined in
5.6.2 Flags.
The following rules apply to the threeargument form of the function:
The $flags
argument is interpreted in the same way as for the
fn:matches
function.
If $value
is the empty sequence, or if $value
is the
zerolength string, the function returns the empty sequence.
The function returns a sequence of strings formed by breaking the $value
string into a sequence of strings, treating any substring that matches
$pattern
as a separator. The separators themselves are not returned.
Except with the oneargument form of the function,
if a separator occurs at the start of the $value
string, the result
sequence will start with a zerolength string. Similarly, zerolength strings will
also occur in
the result sequence if a separator occurs at the end of the $value
string,
or if two adjacent substrings match the supplied $pattern
.
If two alternatives within the supplied $pattern
both match at the same
position in the $value
string, then the match that is chosen is the first.
For example:
fn:tokenize("abracadabra", "(ab)(a)") returns ("", "r", "c", "d", "r", "")
A dynamic error is raised [err:FORX0002] if the value of
$pattern
is invalid according to the rules described in section 5.6.1 Regular expression syntax.
A dynamic error is raised [err:FORX0001] if the value of
$flags
is invalid according to the rules described in section 5.6.2 Flags.
A dynamic error is raised [err:FORX0003] if the supplied
$pattern
matches a zerolength string, that is, if fn:matches("",
$pattern, $flags)
returns true
.
If the input string is not zero length, and no separators are found in the input string, the result of the function is a single string identical to the input string.
The oneargument form of the function has a similar effect to
the twoargument form with \s+
as the separator pattern, except that the oneargument
form strips leading and trailing whitespace, whereas the twoargument form delivers
an extra
zerolength token if leading or trailing whitespace is present.
The function returns no information about the separators that were found
in the string. If this information is required, the fn:analyzestring
function
can be used instead.
The separator used by the oneargument form of the function is any sequence of tab (x09), newline (x0A), carriage return (x0D) or space (x20) characters. This is the same as the separator recognized by listvalued attributes as defined in XSD. It is not the same as the separator recognized by listvalued attributes in HTML5, which also treats formfeed (x0C) as whitespace. If it is necessary to treat formfeed as a separator, an explicit separator pattern should be used.
The expression fn:tokenize(" red green blue ")
returns ("red", "green", "blue")
.
The expression fn:tokenize("The cat sat on the mat", "\s+")
returns ("The", "cat", "sat", "on", "the", "mat")
.
The expression fn:tokenize(" red green blue ", "\s+")
returns ("", "red", "green", "blue", "")
.
The expression fn:tokenize("1, 15, 24, 50", ",\s*")
returns ("1", "15", "24", "50")
.
The expression fn:tokenize("1,15,,24,50,", ",")
returns ("1", "15", "", "24", "50", "")
.
fn:tokenize("abba", ".?")
raises the dynamic error [err:FORX0003].
The expression fn:tokenize("Some unparsed <br> HTML <BR> text",
"\s*<br>\s*", "i")
returns ("Some unparsed", "HTML", "text")
.
Analyzes a string using a regular expression, returning an XML structure that identifies which parts of the input string matched or failed to match the regular expression, and in the case of matched substrings, which substrings matched each capturing group in the regular expression.
fn:analyzestring (

$value 
as xs:string? ,

$pattern 
as xs:string ) as element(fn:analyzestringresult) 
fn:analyzestring (

$value 
as xs:string? ,

$pattern 
as xs:string ,


$flags 
as xs:string ) as element(fn:analyzestringresult) 
This function is ·nondeterministic·, ·contextindependent·, and ·focusindependent·.
The effect of calling the first version of this function (omitting the argument
$flags
) is the same as the effect of calling the second version with the
$flags
argument set to a zerolength string. Flags are defined in
5.6.2 Flags.
The $flags
argument is interpreted in the same way as for the
fn:matches
function.
If $value
is the empty sequence the function behaves as if
$value
were the zerolength string. In this situation the result will be
an element node with no children.
The function returns an element node whose local name is
analyzestringresult
. This element and all its descendant elements have
the namespace URI http://www.w3.org/2005/xpathfunctions
. The namespace
prefix is ·implementationdependent·. The children of this element are a
sequence of fn:match
and fn:nonmatch
elements. This sequence
is formed by breaking the $value
string into a sequence of strings,
returning any substring that matches $pattern
as the content of a
match
element, and any intervening substring as the content of a
nonmatch
element.
More specifically, the function starts at the beginning of the input string and attempts
to find the first substring that matches the regular expression. If there are several
matches, the first match is defined to be the one whose starting position comes first
in
the string. If several alternatives within the regular expression both match at the
same
position in the input string, then the match that is chosen is the first alternative
that matches. For example, if the input string is The quick brown fox jumps
and the regular expression is jumpjumps
, then the match that is chosen is
jump
.
Having found the first match, the instruction proceeds to find the second and subsequent matches by repeating the search, starting at the first ·character· that was not included in the previous match.
The input string is thus partitioned into a sequence of substrings, some of which
match
the regular expression, others which do not match it. Each substring will contain
at
least one character. This sequence is represented in the result by the sequence of
fn:match
and fn:nonmatch
children of the returned element
node; the string value of the fn:match
or fn:nonmatch
element
will be the corresponding substring of $input
, and the string value of the
returned element node will therefore be the same as $input
.
The content of an fn:nonmatch
element is always a single text node.
The content of a fn:match
element, however, is in general a sequence of
text nodes and fn:group
element children. An fn:group
element
with a nr
attribute having the integer value N identifies the
substring captured by the Nth parenthesized subexpression in the regular
expression. For each capturing subexpression there will be at most one corresponding
fn:group
element in each fn:match
element in the
result.
If the function is called twice with the same arguments, it is ·implementationdependent· whether the two calls return the same element node or distinct (but deep equal) element nodes. In this respect it is ·nondeterministic with respect to node identity·.
The base URI of the element nodes in the result is ·implementationdependent·.
A schema is defined for the structure of the returned element: see C.1 Schema for the result of fn:analyzestring.
The result of the function will always be such that validation against this schema would succeed. However, it is ·implementationdefined· whether the result is typed or untyped, that is, whether the elements and attributes in the returned tree have type annotations that reflect the result of validating against this schema.
A dynamic error is raised [err:FORX0002] if the value of
$pattern
is invalid according to the rules described in section 5.6.1 Regular expression syntax.
A dynamic error is raised [err:FORX0001] if the value of
$flags
is invalid according to the rules described in section 5.6.2 Flags.
A dynamic error is raised [err:FORX0003] if the supplied
$pattern
matches a zerolength string, that is, if fn:matches("",
$pattern, $flags)
returns true
.
It is recommended that a processor that implements schema awareness should return typed nodes. The concept of "schema awareness", however, is a matter for host languages to define and is outside the scope of the function library specification.
The declarations and definitions in the schema are not automatically available in
the static context of the fn:analyzestring
call (or of any other
expression). The contents of the static context are hostlanguage defined, and in
some
host languages are implementationdefined.
The schema defines the outermost element, analyzestringresult
, in such
a way that mixed content is permitted. In fact the element will only have element
nodes (match
and nonmatch
) as its children, never text nodes. Although this might have originally been an
oversight, defining the analyzestringresult
element with mixed="true"
allows it
to be atomized, which is potentially useful (the atomized value will be the original
input string),
and the capability has therefore been retained for compatibility with the 3.0 version
of this
specification.
In the following examples, the result document is shown in serialized form, with whitespace between the element nodes. This whitespace is not actually present in the result.
The expression fn:analyzestring("The cat sat on the mat.", "\w+")
returns (with whitespace added for legibility):
<analyzestringresult xmlns="http://www.w3.org/2005/xpathfunctions"> <match>The</match> <nonmatch> </nonmatch> <match>cat</match> <nonmatch> </nonmatch> <match>sat</match> <nonmatch> </nonmatch> <match>on</match> <nonmatch> </nonmatch> <match>the</match> <nonmatch> </nonmatch> <match>mat</match> <nonmatch>.</nonmatch> </analyzestringresult>
The expression fn:analyzestring("20081203",
"^(\d+)\(\d+)\(\d+)$")
returns (with whitespace added for legibility):
<analyzestringresult xmlns="http://www.w3.org/2005/xpathfunctions"> <match><group nr="1">2008</group><group nr="2" >12</group><group nr="3">03</group></match> </analyzestringresult>
The expression fn:analyzestring("A1,C15,,D24, X50,",
"([AZ])([09]+)")
returns (with whitespace added for legibility):
<analyzestringresult xmlns="http://www.w3.org/2005/xpathfunctions"> <match><group nr="1">A</group><group nr="2">1</group></match> <nonmatch>,</nonmatch> <match><group nr="1">C</group><group nr="2">15</group></match> <nonmatch>,,</nonmatch> <match><group nr="1">D</group><group nr="2">24</group></match> <nonmatch>, </nonmatch> <match><group nr="1">X</group><group nr="2">50</group></match> <nonmatch>,</nonmatch> </analyzestringresult>
This section specifies functions that manipulate URI values, either as instances
of xs:anyURI
or as strings.
Function  Meaning 

fn:resolveuri 
Resolves a relative IRI reference against an absolute IRI. 
fn:encodeforuri 
Encodes reserved characters in a string that is intended to be used in the path segment of a URI. 
fn:iritouri 
Converts a string containing an IRI into a URI according to the rules of [RFC 3987]. 
fn:escapehtmluri 
Escapes a URI in the same way that HTML user agents handle attribute values expected to contain URIs. 
Resolves a relative IRI reference against an absolute IRI.
fn:resolveuri
($relative
as
xs:string?
) as
xs:anyURI?
fn:resolveuri
($relative
as
xs:string?
, $base
as
xs:string
) as
xs:anyURI?
The oneargument form of this function is ·deterministic·, ·contextdependent·, and ·focusindependent·. It depends on static base URI.
The twoargument form of this function is ·deterministic·, ·contextindependent·, and ·focusindependent·.
The function is defined to operate on IRI references as defined in [RFC 3987], and the implementation must permit all arguments that are valid according to that specification. In addition, the implementation may accept some or all strings that conform to the rules for (absolute or relative) Legacy Extended IRI references as defined in [Legacy extended IRIs for XML resource identification]. For the purposes of this section, the terms IRI and IRI reference include these extensions, insofar as the implementation chooses to support them.
The following rules apply in order:
If $relative
is the empty sequence, the function returns the empty
sequence.
If $relative
is an absolute IRI (as defined above), then it is returned
unchanged.
If the $base
argument is not supplied, then:
If the static base URI in the static context is not absent, it is used as the effective
value of $base
.
Otherwise, a dynamic error is raised: [err:FONS0005].
The function resolves the relative IRI reference $relative
against the base IRI $base
using the algorithm defined in [RFC 3986], adapted by treating any ·character·
that would not be valid in an RFC3986 URI or relative reference in the same way that
RFC3986 treats unreserved characters. No percentencoding takes place.
The first form of this function resolves $relative
against the value of the
baseuri property from the static context. A dynamic error is raised [err:FONS0005] if the baseuri property is not initialized in the static
context.
A dynamic error is raised [err:FORG0002] if $relative
is not a valid IRI according to the rules of RFC3987, extended with an
implementationdefined subset of the extensions permitted in LEIRI, or if it is not
a
suitable relative reference to use as input to the RFC3986 resolution algorithm extended
to handle additional unreserved characters.
A dynamic error is raised [err:FORG0002] if $base
is
not a valid IRI according to the rules of RFC3987, extended with an
implementationdefined subset of the extensions permitted in LEIRI, or if it is not
a
suitable IRI to use as input to the chosen resolution algorithm (for example, if it
is a
relative IRI reference, if it is a nonhierarchic URI, or if it contains a fragment
identifier).
A dynamic error is raised [err:FORG0009] if the chosen resolution algorithm fails for any other reason.
Resolving a URI does not dereference it. This is merely a syntactic operation on two ·strings·.
The algorithms in the cited RFCs include some variations that are optional or recommended rather than mandatory; they also describe some common practices that are not recommended, but which are permitted for backwards compatibility. Where the cited RFCs permit variations in behavior, so does this specification.
Throughout this family of specifications, the phrase "resolving a relative URI (or IRI) reference" should be understood as using the rules of this function, unless otherwise stated.
RFC3986 defines an algorithm for resolving relative references in the context of the URI syntax defined in that RFC. RFC3987 describes a modification to that algorithm to make it applicable to IRIs (specifically: additional characters permitted in an IRI are handled the same way that RFC3986 handles unreserved characters). The LEIRI specification does not explicitly define a resolution algorithm, but suggests that it should not be done by converting the LEIRI to a URI, and should not involve percentencoding. This specification fills this gap by defining resolution for LEIRIs in the same way that RFC3987 defines resolution for IRIs, that is by specifying that additional characters are handled as unreserved characters.
Encodes reserved characters in a string that is intended to be used in the path segment of a URI.
fn:encodeforuri
($value
as
xs:string?
) as
xs:string
This function is ·deterministic·, ·contextindependent·, and ·focusindependent·.
If $value
is the empty sequence, the function returns the zerolength
string.
This function applies the URI escaping rules defined in section 2 of [RFC 3986] to the xs:string
supplied as $value
. The
effect of the function is to escape reserved characters. Each such character in the
string is replaced with its percentencoded form as described in [RFC 3986].
Since [RFC 3986] recommends that, for consistency, URI producers and normalizers should use uppercase hexadecimal digits for all percentencodings, this function must always generate hexadecimal values using the uppercase letters AF.
All characters are escaped except those identified as "unreserved" by [RFC 3986], that is the upper and lowercase letters AZ, the digits 09, HYPHENMINUS (""), LOW LINE ("_"), FULL STOP ".", and TILDE "~".
This function escapes URI delimiters and therefore cannot be used indiscriminately to encode "invalid" characters in a path segment.
This function is invertible but not idempotent. This is because a string containing
a
percent character will be modified by applying the function: for example
100%
becomes 100%25
, while 100%25
becomes
100%2525
.
The expression fn:encodeforuri("http://www.example.com/00/Weather/CA/Los%20Angeles#ocean")
returns "http%3A%2F%2Fwww.example.com%2F00%2FWeather%2FCA%2FLos%2520Angeles%23ocean"
. (This is probably not what the user intended because all of the
delimiters have been encoded.)
The expression concat("http://www.example.com/",
encodeforuri("~bébé"))
returns "http://www.example.com/~b%C3%A9b%C3%A9"
.
The expression concat("http://www.example.com/", encodeforuri("100% organic"))
returns "http://www.example.com/100%25%20organic"
.
Converts a string containing an IRI into a URI according to the rules of [RFC 3987].
fn:iritouri
($value
as
xs:string?
) as
xs:string
This function is ·deterministic·, ·contextindependent·, and ·focusindependent·.
If $value
is the empty sequence, the function returns the zerolength
string.
Otherwise, the function converts $value
into a URI according to
the rules given in Section 3.1 of [RFC 3987] by percentencoding characters
that are allowed in an IRI but not in a URI. If $value
contains a character
that is invalid in an IRI, such as the space character (see note below), the invalid
character is replaced by its percentencoded form as described in [RFC 3986] before the conversion is performed.
Since [RFC 3986] recommends that, for consistency, URI producers and normalizers should use uppercase hexadecimal digits for all percentencodings, this function must always generate hexadecimal values using the uppercase letters AF.
The function is idempotent but not invertible. Both the inputs My Documents
and My%20Documents
will be converted to the output
My%20Documents
.
This function does not check whether $iri
is a valid IRI. It treats it as
an ·string· and operates on the ·characters· in the string.
The following printable ASCII characters are invalid in an IRI: "<", ">", "
" " (double quote), space, "{", "}", "", "\", "^", and "`". Since these
characters should not appear in an IRI, if they do appear in $iri
they will
be percentencoded. In addition, characters outside the range x20x7E will be
percentencoded because they are invalid in a URI.
Since this function does not escape the PERCENT SIGN "%" and this character is not allowed in data within a URI, users wishing to convert character strings (such as file names) that include "%" to a URI should manually escape "%" by replacing it with "%25".
The expression fn:iritouri
("http://www.example.com/00/Weather/CA/Los%20Angeles#ocean")
returns "http://www.example.com/00/Weather/CA/Los%20Angeles#ocean"
.
The expression fn:iritouri ("http://www.example.com/~bébé")
returns "http://www.example.com/~b%C3%A9b%C3%A9"
.
Escapes a URI in the same way that HTML user agents handle attribute values expected to contain URIs.
fn:escapehtmluri
($value
as
xs:string?
) as
xs:string
This function is ·deterministic·, ·contextindependent·, and ·focusindependent·.
If $value
is the empty sequence, the function returns the zerolength
string.
Otherwise, the function escapes all ·characters· except
printable characters of the USASCII coded character set, specifically the ·codepoints· between 32 and 126 (decimal) inclusive. Each
character in $uri
to be escaped is replaced by an escape sequence, which is
formed by encoding the character as a sequence of octets in UTF8, and then representing
each of these octets in the form %HH, where HH is the hexadecimal representation of
the
octet. This function must always generate hexadecimal values using the uppercase
letters AF.
The behavior of this function corresponds to the recommended handling of nonASCII characters in URI attribute values as described in [HTML 4.0] Appendix B.2.1.
The expression fn:escapehtmluri("http://www.example.com/00/Weather/CA/Los Angeles#ocean")
returns "http://www.example.com/00/Weather/CA/Los Angeles#ocean"
.
The expression fn:escapehtmluri("javascript:if (navigator.browserLanguage == 'fr') window.open('http://www.example.com/~bébé');")
returns "javascript:if (navigator.browserLanguage == 'fr') window.open('http://www.example.com/~b%C3%A9b%C3%A9');"
.
This section defines functions and operators on the xs:boolean
datatype.
Since no literals are defined in XPath to reference the constant boolean values true and false, two functions are provided for the purpose.
Function  Meaning 

fn:true 
Returns the xs:boolean value true .

fn:false 
Returns the xs:boolean value false .

Returns the xs:boolean
value true
.
fn:true
() as
xs:boolean
This function is ·deterministic·, ·contextindependent·, and ·focusindependent·.
The result is equivalent to xs:boolean("1")
.
The expression fn:true()
returns xs:boolean(1)
.
Returns the xs:boolean
value false
.
fn:false
() as
xs:boolean
This function is ·deterministic·, ·contextindependent·, and ·focusindependent·.
The result is equivalent to xs:boolean("0")
.
The expression fn:false()
returns xs:boolean(0)
.
The following functions define the semantics of operators on boolean values in [XQuery 3.1: An XML Query Language] and [XML Path Language (XPath) 3.1]:
Function  Meaning 

op:booleanequal 
Returns true if the two arguments are the same boolean value.

op:booleanlessthan 
Returns true if the first argument is false and the second is true. 
The ordering operator op:booleanlessthan
is provided for application purposes
and for compatibility with [XML Path Language (XPath) Version 1.0]. The [XML Schema Part 2: Datatypes Second Edition]
datatype xs:boolean
is not ordered.
Returns true
if the two arguments are the same boolean value.
Defines the semantics of the "eq"
operator when applied to two xs:boolean
values.
op:booleanequal
($value1
as
xs:boolean
, $value2
as
xs:boolean
) as
xs:boolean
The function returns true
if both arguments are true
or if
both arguments are false
. It returns false
if one of the
arguments is true
and the other argument is false
.
Returns true if the first argument is false and the second is true.
Defines the
semantics of the "lt" operator when applied to two xs:boolean
values. Also
used in the definition of the "ge" operator.
op:booleanlessthan
($arg1
as
xs:boolean
, $arg2
as
xs:boolean
) as
xs:boolean
The function returns true
if $arg1
is false
and
$arg2
is true
. Otherwise, it returns
false
.
The following functions are defined on boolean values:
Function  Meaning 

fn:boolean 
Computes the effective boolean value of the sequence $input .

fn:not 
Returns true if the effective boolean value of $input is
false , or false if it is true .

Computes the effective boolean value of the sequence $input
.
fn:boolean
($input
as
item()*
) as
xs:boolean
The function computes the effective boolean value of a sequence, defined according to the following rules. See also Section 2.4.3 Effective Boolean Value ^{XP31}.
If $input
is the empty sequence, fn:boolean
returns
false
.
If $input
is a sequence whose first item is a node,
fn:boolean
returns true
.
If $input
is a singleton value of type xs:boolean
or a
derived from xs:boolean
, fn:boolean
returns
$input
.
If $input
is a singleton value of type xs:string
or a type
derived from xs:string
, xs:anyURI
or a type derived from
xs:anyURI
, or xs:untypedAtomic
,
fn:boolean
returns false
if the operand value has
zero length; otherwise it returns true
.
If $input
is a singleton value of any numeric type or a type 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
.
In all cases other than those listed above, fn:boolean
raises a type error [err:FORG0006].
The result of this function is not necessarily the same as $input cast as
xs:boolean
. For example, fn:boolean("false")
returns the value
true
whereas "false" cast as xs:boolean
(which can also be
written xs:boolean("false")
) returns false
.
let $abc := ("a", "b", "")
fn:boolean($abc)
raises a type error [err:FORG0006].
The expression fn:boolean($abc[1])
returns true()
.
The expression fn:boolean($abc[0])
returns false()
.
The expression fn:boolean($abc[3])
returns false()
.
fn:boolean([])
raises a type error [err:FORG0006].
Returns true
if the effective boolean value of $input
is
false
, or false
if it is true
.
fn:not
($input
as
item()*
) as
xs:boolean
This function is ·deterministic·, ·contextindependent·, and ·focusindependent·.
The value of $input
is first reduced to an effective boolean value by
applying the fn:boolean()
function. The function returns true
if the effective boolean value is false
, or false
if the
effective boolean value is true
.
The expression fn:not(fn:true())
returns false()
.
The expression fn:not(())
returns true()
.
The expression fn:not("false")
returns false()
.
fn:not(1 to 10)
raises a type error [err:FORG0006].
Operators are defined on the following type:
xs:duration
and on the two defined subtypes (see 8.1 Two totally ordered subtypes of duration):
xs:yearMonthDuration
xs:dayTimeDuration
No ordering relation is defined on xs:duration
values.
Two xs:duration
values may however be compared for equality.
Operations on durations (including equality comparison, casting to string, and extraction of components) all treat the duration as normalized. This means that the seconds and minutes components will always be less than 60, the hours component less than 24, and the months component less than 12. Thus, for example, a duration of 120 seconds always gives the same result as a duration of two minutes.
Conditions such as underflow and overflow may occur with arithmetic on durations: see 9.7.1 Limits and precision
Note:
This means that in practice, the information content of an xs:duration
value can be reduced to an xs:integer
number of months, and an xs:decimal
number of seconds. For the two defined subtypes this is further simplified so that
one of these two
components is fixed at zero. Operations such as comparison of durations and arithmetic
on durations
can be expressed in terms of numeric operations applied to these two components.
Two subtypes of xs:duration
, namely xs:yearMonthDuration
and xs:dayTimeDuration
, are defined in [Schema 1.1 Part 2]. These types must
be available in the data model whether or not the implementation supports other aspects
of XSD 1.1.
The significance of these subtypes is that arithmetic and ordering become well defined;
this is not the
case for xs:duration
values in general, because of the variable number of days in a month. For this reason,
many of the functions
and operators on durations require the arguments/operands to belong to these two subtypes.
Function  Meaning 

op:yearMonthDurationlessthan 
Returns true if $arg1 is a shorter duration than $arg2 .

op:dayTimeDurationlessthan 
Returns true if $arg1 is a shorter duration than $arg2 .

op:durationequal 
Returns true if $arg1 and $arg2 are durations of the same
length.

The following comparison operators are defined on the [XML Schema Part 2: Datatypes Second Edition]
duration datatypes. Each operator takes two operands of the same
type and returns an xs:boolean
result. As discussed in [XML Schema Part 2: Datatypes Second Edition], the
order relation on xs:duration
is a partial order rather than
a total order. For this reason, only equality is defined on xs:duration
.
A full complement of comparison and
arithmetic functions are defined on the two subtypes of duration described in
8.1 Two totally ordered subtypes of duration which do have a total order.
Returns true if $arg1
is a shorter duration than $arg2
.
Defines
the semantics of the "lt" operator when applied to two xs:yearMonthDuration
values. Also used in the definition of the "ge" operator.
op:yearMonthDurationlessthan (

$arg1 
as xs:yearMonthDuration ,

$arg2 
as xs:yearMonthDuration ) as xs:boolean 
If the number of months in $arg1
is numerically less than the
number of months in $arg2
, the function returns true.
Otherwise, the function returns false.
Either or both durations may be negative.
Returns true if $arg1
is a shorter duration than $arg2
.
Defines the
semantics of the "lt" operator when applied to two xs:dayTimeDuration
values.
Also used in the definition of the "ge" operator.
op:dayTimeDurationlessthan (

$arg1 
as xs:dayTimeDuration ,

$arg2 
as xs:dayTimeDuration ) as xs:boolean 
If the number of seconds in $arg1
is numerically less than the
number of seconds in $arg2
, the function returns true.
Otherwise, the function returns false.
Either or both durations may be negative
Returns true if $arg1
and $arg2
are durations of the same
length.
Defines the
semantics of the "eq" operators when applied to two xs:duration
values. Also
used in the definition of the "ne" operator.
op:durationequal
($arg1
as
xs:duration
, $arg2
as
xs:duration
) as
xs:boolean
If the xs:yearMonthDuration
components of $arg1
and
$arg2
are equal and the xs:dayTimeDuration
components of
$arg1
and $arg2
are equal, the function returns
true
.
Otherwise, the function returns false.
The semantics of this function are:
xs:yearMonthDuration($arg1) div xs:yearMonthDuration('P1M') eq xs:yearMonthDuration($arg2) div xs:yearMonthDuration('P1M') and xs:dayTimeDuration($arg1) div xs:dayTimeDuration('PT1S') eq xs:dayTimeDuration($arg2) div xs:dayTimeDuration('PT1S')
that is, the function returns true
if the months and seconds values of the
two durations are equal.
Note that this function, like any other, may be applied to arguments that are derived
from the types given in the function signature, including the two subtypes
xs:dayTimeDuration
and xs:yearMonthDuration
. With the
exception of the zerolength duration, no instance of xs:dayTimeDuration
can ever be equal to an instance of xs:yearMonthDuration
.
The expression op:durationequal(xs:duration("P1Y"),
xs:duration("P12M"))
returns true()
.
The expression op:durationequal(xs:duration("PT24H"),
xs:duration("P1D"))
returns true()
.
The expression op:durationequal(xs:duration("P1Y"),
xs:duration("P365D"))
returns false()
.
The expression op:durationequal(xs:yearMonthDuration("P0Y"),
xs:dayTimeDuration("P0D"))
returns true()
.
The expression op:durationequal(xs:yearMonthDuration("P1Y"),
xs:dayTimeDuration("P365D"))
returns false()
.
The expression op:durationequal(xs:yearMonthDuration("P2Y"),
xs:yearMonthDuration("P24M"))
returns true()
.
The expression op:durationequal(xs:dayTimeDuration("P10D"),
xs:dayTimeDuration("PT240H"))
returns true()
.
The expression op:durationequal(xs:duration("P2Y0M0DT0H0M0S"),
xs:yearMonthDuration("P24M"))
returns true()
.
The expression op:durationequal(xs:duration("P0Y0M10D"),
xs:dayTimeDuration("PT240H"))
returns true()
.
The duration datatype may be considered to be a composite datatypes
in that it contains distinct properties or components. The extraction functions specified
below extract a single component from a duration value.
For xs:duration
and its subtypes, including the two subtypes xs:yearMonthDuration
and
xs:dayTimeDuration
, the components are normalized: this means that the seconds and minutes
components will always be less than 60, the hours component less than 24, and the
months component less than 12.
Function  Meaning 

fn:yearsfromduration 
Returns the number of years in a duration. 
fn:monthsfromduration 
Returns the number of months in a duration. 
fn:daysfromduration 
Returns the number of days in a duration. 
fn:hoursfromduration 
Returns the number of hours in a duration. 
fn:minutesfromduration 
Returns the number of minutes in a duration. 
fn:secondsfromduration 
Returns the number of seconds in a duration. 
Returns the number of years in a duration.
fn:yearsfromduration
($value
as
xs:duration?
) as
xs:integer?
This function is ·deterministic·, ·contextindependent·, and ·focusindependent·.
If $value
is the empty sequence, the function returns the empty sequence.
Otherwise, the function returns an xs:integer
representing the years
component in $value
. Given that a duration
is a ($months, $seconds)
tuple, the result is the value of ($months idiv 12)
.
If $value
is a negative duration then the result will be negative.
If $value
is an xs:dayTimeDuration
the function returns 0.
The expression fn:yearsfromduration(xs:yearMonthDuration("P20Y15M"))
returns 21
.
The expression fn:yearsfromduration(xs:yearMonthDuration("P15M"))
returns 1
.
The expression fn:yearsfromduration(xs:dayTimeDuration("P2DT15H"))
returns 0
.
Returns the number of months in a duration.
fn:monthsfromduration
($value
as
xs:duration?
) as
xs:integer?
This function is ·deterministic·, ·contextindependent·, and ·focusindependent·.
If $value
is the empty sequence, the function returns the empty sequence.
Otherwise, the function returns an xs:integer
representing the months
component in $value
. Given that a duration
is a ($months, $seconds)
tuple, the result is the value of ($months mod 12)
.
If $value
is a negative duration then the result will be negative.
If $value
is an xs:dayTimeDuration
the function returns 0.
The expression fn:monthsfromduration(xs:yearMonthDuration("P20Y15M"))
returns 3
.
The expression fn:monthsfromduration(xs:yearMonthDuration("P20Y18M"))
returns 6
.
The expression fn:monthsfromduration(xs:dayTimeDuration("P2DT15H0M0S"))
returns 0
.
Returns the number of days in a duration.
fn:daysfromduration
($value
as
xs:duration?
) as
xs:integer?
This function is ·deterministic·, ·contextindependent·, and ·focusindependent·.
If $value
is the empty sequence, the function returns the empty sequence.
Otherwise, the function returns an xs:integer
representing the days
component in $value
. Given that a duration
is a ($months, $seconds)
tuple, the result is ($seconds idiv 86400)
.
If $value
is a negative duration then the result will be negative.
If $value
is an xs:yearMonthDuration
the function returns 0.
The expression fn:daysfromduration(xs:dayTimeDuration("P3DT10H"))
returns 3
.
The expression fn:daysfromduration(xs:dayTimeDuration("P3DT55H"))
returns 5
.
The expression fn:daysfromduration(xs:yearMonthDuration("P3Y5M"))
returns 0
.
Returns the number of hours in a duration.
fn:hoursfromduration
($value
as
xs:duration?
) as
xs:integer?
This function is ·deterministic·, ·contextindependent·, and ·focusindependent·.
If $value
is the empty sequence, the function returns the empty sequence.
Otherwise, the function returns an xs:integer
representing the hours
component in $value
. Given that a duration
is a ($months, $seconds)
tuple, the result is the value of ($seconds mod 86400) idiv 3600
.
If $value
is a negative duration then the result will be negative.
If $value
is an xs:yearMonthDuration
the function returns 0.
The expression fn:hoursfromduration(xs:dayTimeDuration("P3DT10H"))
returns 10
.
The expression fn:hoursfromduration(xs:dayTimeDuration("P3DT12H32M12S"))
returns 12
.
The expression fn:hoursfromduration(xs:dayTimeDuration("PT123H"))
returns 3
.
The expression fn:hoursfromduration(xs:dayTimeDuration("P3DT10H"))
returns 10
.
Returns the number of minutes in a duration.
fn:minutesfromduration
($value
as
xs:duration?
) as
xs:integer?
This function is ·deterministic·, ·contextindependent·, and ·focusindependent·.
If $value
is the empty sequence, the function returns the empty sequence.
Otherwise, the function returns an xs:integer
representing the minutes
component in $value
. Given that a duration
is a ($months, $seconds)
tuple, the result is the value of ($seconds mod 3600) idiv 60
.
If $value
is a negative duration then the result will be negative.
If $value
is an xs:yearMonthDuration
the function returns 0.
The expression fn:minutesfromduration(xs:dayTimeDuration("P3DT10H"))
returns 0
.
The expression fn:minutesfromduration(xs:dayTimeDuration("P5DT12H30M"))
returns 30
.
Returns the number of seconds in a duration.
fn:secondsfromduration
($value
as
xs:duration?
) as
xs:decimal?
This function is ·deterministic·, ·contextindependent·, and ·focusindependent·.
If $value
is the empty sequence, the function returns the empty sequence.
Otherwise, the function returns an xs:decimal
representing the seconds
component in $value
. Given that a duration
is a ($months, $seconds)
tuple, the result is the value of ($seconds mod 60)
as an xs:decimal
.
If $value
is a negative duration then the result will be negative.
If $value
is an xs:yearMonthDuration
the function returns 0.
The expression fn:secondsfromduration(xs:dayTimeDuration("P3DT10H12.5S"))
returns 12.5
.
The expression fn:secondsfromduration(xs:dayTimeDuration("PT256S"))
returns 16.0
.
Function  Meaning 

op:addyearMonthDurations 
Returns the result of adding two xs:yearMonthDuration values.

op:subtractyearMonthDurations 
Returns the result of subtracting one xs:yearMonthDuration value from
another.

op:multiplyyearMonthDuration 
Returns the result of multiplying $arg1 by $arg2 .
The result is rounded to the nearest month.

op:divideyearMonthDuration 
Returns the result of dividing $arg1 by $arg2 .
The result is rounded to the nearest month.

op:divideyearMonthDurationbyyearMonthDuration 
Returns the ratio of two xs:yearMonthDuration values.

op:adddayTimeDurations 
Returns the sum of two xs:dayTimeDuration values.

op:subtractdayTimeDurations 
Returns the result of subtracting one xs:dayTimeDuration from another.

op:multiplydayTimeDuration 
Returns the result of multiplying a xs:dayTimeDuration by a number.

op:dividedayTimeDuration 
Returns the result of multiplying a xs:dayTimeDuration by a number.

op:dividedayTimeDurationbydayTimeDuration 
Returns the ratio of two xs:dayTimeDuration values, as a decimal
number.

For operators that combine a duration and a date/time value, see 9.7 Arithmetic operators on durations, dates and times.
Returns the result of adding two xs:yearMonthDuration
values.
Defines the semantics of the
"+" operator when applied to two xs:yearMonthDuration
values.
op:addyearMonthDurations (

$arg1 
as xs:yearMonthDuration ,

$arg2 
as xs:yearMonthDuration ) as xs:yearMonthDuration 
The function returns the result of adding $arg1
to $arg2
.
The result will be an xs:yearMonthDuration
whose
length in months is equal to the length in months of $arg1
plus the length
in months of $arg2
.
For handling of overflow, see 9.7.1 Limits and precision.
Either duration (and therefore the result) may be negative.
The expression op:addyearMonthDurations(xs:yearMonthDuration("P2Y11M"),
xs:yearMonthDuration("P3Y3M"))
returns xs:yearMonthDuration("P6Y2M")
.
Returns the result of subtracting one xs:yearMonthDuration
value from
another.
Defines the semantics of the
"" operator when applied to two xs:yearMonthDuration
values.
op:subtractyearMonthDurations (

$arg1 
as xs:yearMonthDuration ,

$arg2 
as xs:yearMonthDuration ) as xs:yearMonthDuration 
The function returns the result of subtracting $arg2
from
$arg1
. The result will be an xs:yearMonthDuration
whose length in months is equal to the length in months of $arg1
minus the
length in months of $arg2
.
For handling of overflow, see 9.7.1 Limits and precision.
Either duration (and therefore the result) may be negative.
The expression op:subtractyearMonthDurations(xs:yearMonthDuration("P2Y11M"),
xs:yearMonthDuration("P3Y3M"))
returns xs:yearMonthDuration("P4M")
.
Returns the result of multiplying $arg1
by $arg2
.
The result is rounded to the nearest month.
Defines the semantics of the
"*" operator when applied to an xs:yearMonthDuration
and a numeric
value.
op:multiplyyearMonthDuration (

$arg1 
as xs:yearMonthDuration ,

$arg2 
as xs:double ) as xs:yearMonthDuration 
The result is the xs:yearMonthDuration
whose length in months is equal to
the result of applying the fn:round
function to the value obtained by
multiplying the length in months of $arg1
by the value of
$arg2
.
If $arg2
is positive or negative zero, the result is a zerolength
duration. If $arg2
is positive or negative infinity, the result overflows
and is handled as described in 9.7.1 Limits and precision.
For handling of overflow and underflow, see 9.7.1 Limits and precision.
A dynamic error is raised [err:FOCA0005] if $arg2
is
NaN
.
Either duration (and therefore the result) may be negative.
The expression op:multiplyyearMonthDuration(xs:yearMonthDuration("P2Y11M"),
2.3)
returns xs:yearMonthDuration("P6Y9M")
.
Returns the result of dividing $arg1
by $arg2
.
The result is rounded to the nearest month.
Defines the semantics of the
"div" operator when applied to an xs:yearMonthDuration
and a numeric
value.
op:divideyearMonthDuration (

$arg1 
as xs:yearMonthDuration ,

$arg2 
as xs:double ) as xs:yearMonthDuration 
The result is the xs:yearMonthDuration
whose length in months is equal to
the result of applying the fn:round
function to the value obtained by
dividing the length in months of $arg1
by the value of
$arg2
.
If $arg2
is positive or negative infinity, the result is a zerolength
duration. If $arg2
is positive or negative zero, the result overflows and
is handled as described in 9.7.1 Limits and precision.
For handling of overflow and underflow, see 9.7.1 Limits and precision.
A dynamic error is raised [err:FOCA0005] if $arg2
is
NaN
.
Either operand (and therefore the result) may be negative.
The expression op:divideyearMonthDuration(xs:yearMonthDuration("P2Y11M"),
1.5)
returns xs:yearMonthDuration("P1Y11M")
.
Returns the ratio of two xs:yearMonthDuration
values.
Defines the semantics of the
"div" operator when applied to two xs:yearMonthDuration
values.
op:divideyearMonthDurationbyyearMonthDuration (

$arg1 
as xs:yearMonthDuration ,

$arg2 
as xs:yearMonthDuration ) as xs:decimal 
The function returns the result of dividing the length in months of $arg1
by the length in months of $arg2
, according to the rules of the
op:numericdivide
function for integer operands.
For handling of overflow and underflow, see 9.7.1 Limits and precision.
Either duration (and therefore the result) may be negative.
The expression op:divideyearMonthDurationbyyearMonthDuration(xs:yearMonthDuration("P3Y4M"),
xs:yearMonthDuration("P1Y4M"))
returns 2.5
.
The following example demonstrates how to calculate the length of an
xs:yearMonthDuration
value in months:
The expression op:divideyearMonthDurationbyyearMonthDuration(xs:yearMonthDuration("P3Y4M"),
xs:yearMonthDuration("P1M"))
returns 40
.
Returns the sum of two xs:dayTimeDuration
values.
Defines the semantics of the "+"
operator when applied to two xs:dayTimeDuration
values.
op:adddayTimeDurations (

$arg1 
as xs:dayTimeDuration ,

$arg2 
as xs:dayTimeDuration ) as xs:dayTimeDuration 
The function returns the result of adding $arg1
to
$arg2
. The result is the xs:dayTimeDuration
whose length in
seconds is equal to the sum of the length in seconds of the two input durations.
For handling of overflow, see 9.7.1 Limits and precision.
Either duration (and therefore the result) may be negative.
The expression op:adddayTimeDurations(xs:dayTimeDuration("P2DT12H5M"),
xs:dayTimeDuration("P5DT12H"))
returns xs:dayTimeDuration('P8DT5M')
.
Returns the result of subtracting one xs:dayTimeDuration
from another.
Defines the semantics of the ""
operator when applied to two xs:dayTimeDuration
values.
op:subtractdayTimeDurations (

$arg1 
as xs:dayTimeDuration ,

$arg2 
as xs:dayTimeDuration ) as xs:dayTimeDuration 
The function returns the result of subtracting $arg2
from
$arg1
. The result is the xs:dayTimeDuration
whose
length in seconds is equal to the length in seconds of $arg1
minus the
length in seconds of $arg2
.
For handling of overflow, see 9.7.1 Limits and precision.
Either duration (and therefore the result) may be negative.
The expression op:subtractdayTimeDurations(xs:dayTimeDuration("P2DT12H"),
xs:dayTimeDuration("P1DT10H30M"))
returns xs:dayTimeDuration('P1DT1H30M')
.
Returns the result of multiplying a xs:dayTimeDuration
by a number.
Defines the semantics of the "*"
operator when applied to an xs:dayTimeDuration
and a numeric
value.
op:multiplydayTimeDuration (

$arg1 
as xs:dayTimeDuration ,

$arg2 
as xs:double ) as xs:dayTimeDuration 
The function returns the result of multiplying $arg1
by
$arg2
. The result is the xs:dayTimeDuration
whose length in
seconds is equal to the length in seconds of $arg1
multiplied by the
numeric value $arg2
.
If $arg2
is positive or negative zero, the result is a zerolength
duration. If $arg2
is positive or negative infinity, the result overflows
and is handled as described in 9.1.1 Limits and precision.
For handling of overflow and underflow, see 9.7.1 Limits and precision.
A dynamic error is raised [err:FOCA0005] if $arg2
is
NaN
.
Either operand (and therefore the result) may be negative.
The expression op:multiplydayTimeDuration(xs:dayTimeDuration("PT2H10M"),
2.1)
returns xs:dayTimeDuration('PT4H33M')
.
Returns the result of multiplying a xs:dayTimeDuration
by a number.
Defines the semantics of the
"div" operator when applied to two xs:dayTimeDuration
values.
op:dividedayTimeDuration (

$arg1 
as xs:dayTimeDuration ,

$arg2 
as xs:double ) as xs:dayTimeDuration 
The function returns the result of dividing $arg1
by
$arg2
. The result is the xs:dayTimeDuration
whose length in
seconds is equal to the length in seconds of $arg1
divided by the numeric
value $arg2
.
If $arg2
is positive or negative infinity, the result is a zerolength
duration. If $arg2
is positive or negative zero, the result overflows and
is handled as described in 9.1.1 Limits and precision.
For handling of overflow and underflow, see 9.7.1 Limits and precision.
A dynamic error is raised [err:FOCA0005] if $arg2
is
NaN
.
Either operand (and therefore the result) may be negative.
The expression op:dividedayTimeDuration(xs:dayTimeDuration("P1DT2H30M10.5S"),
1.5)
returns xs:duration("PT17H40M7S")
.
Returns the ratio of two xs:dayTimeDuration
values, as a decimal
number.
Defines the semantics of the
"div" operator when applied to two xs:dayTimeDuration
values.
op:dividedayTimeDurationbydayTimeDuration (

$arg1 
as xs:dayTimeDuration ,

$arg2 
as xs:dayTimeDuration ) as xs:decimal 
The function returns the result of dividing $arg1
by
$arg2
. The result is the xs:dayTimeDuration
whose length in
seconds is equal to the length in seconds of $arg1
divided by the length in
seconds of $arg2
. The calculation is performed by applying
op:numericdivide
to the two xs:decimal
operands.
For handling of overflow and underflow, see 9.7.1 Limits and precision.
Either operand (and therefore the result) may be negative.
The expression fn:roundhalftoeven( op:dividedayTimeDurationbydayTimeDuration(
xs:dayTimeDuration("P2DT53M11S"), xs:dayTimeDuration("P1DT10H")),
4)
returns 1.4378
.
This examples shows how to determine the number of seconds in a duration.
The expression op:dividedayTimeDurationbydayTimeDuration(xs:dayTimeDuration("P2DT53M11S"),
xs:dayTimeDuration("PT1S"))
returns 175991.0
.
This section defines operations on the [XML Schema Part 2: Datatypes Second Edition] date and time types.
See [Working With Timezones] for a disquisition on working with date and time values with and without timezones.
The operators described in this section are defined on the following date and time types:
xs:dateTime
xs:date
xs:time
xs:gYearMonth
xs:gYear
xs:gMonthDay
xs:gMonth
xs:gDay
The only operation defined on
xs:gYearMonth
, xs:gYear
,
xs:gMonthDay
, xs:gMonth
and xs:gDay
values is
equality comparison.
For other types, further operations are provided, including component extraction,
order comparisons, arithmetic, formatted display, and timezone
adjustment.
All minimally conforming processors must support positive year values with a minimum of 4 digits (i.e., YYYY) and a minimum fractional second precision of 1 millisecond or three digits (i.e., s.sss). However, conforming processors may set larger ·implementationdefined· limits on the maximum number of digits they support in these two situations. Processors may also choose to support the year 0000 and years with negative values. The results of operations on dates that cross the year 0000 are ·implementationdefined·.
A processor that limits the number of digits in date and time datatype representations may encounter overflow and underflow conditions when it tries to execute the functions in 9.7 Arithmetic operators on durations, dates and times. In these situations, the processor must return 00:00:00 in case of time underflow. It must raise a dynamic error [err:FODT0001] in case of overflow.
As defined in Section
3.3.2 Dates and Times
^{DM31}, xs:dateTime
,
xs:date
, xs:time
, xs:gYearMonth
, xs:gYear
,
xs:gMonthDay
, xs:gMonth
, xs:gDay
values,
referred to collectively as date/time values, are represented as seven components
or properties:
year
, month
, day
, hour
, minute
,
second
and timezone
. The first five components are
xs:integer
values. The value of the second
component is an xs:decimal
and the value of the timezone
component is an xs:dayTimeDuration
.
For all the primitive date/time datatypes, the timezone
property is optional and may or may not
be present. Depending on the datatype, some of the remaining six properties must
be present and
some must be absent^{DM31}.
Absent, or missing, properties are represented by the empty sequence.
This value is referred to as the local value in that the value retains its original timezone.
Before comparing or subtracting xs:dateTime
values, this local value must
be translated or normalized to UTC.
For xs:time
, 00:00:00
and 24:00:00
are alternate lexical forms
for the same value, whose canonical representation is 00:00:00
. For xs:dateTime
,
a time component 24:00:00
translates to 00:00:00
of the following day.
An xs:dateTime
with lexical
representation 19990531T05:00:00
is represented in the datamodel by {1999, 5, 31, 5, 0, 0.0, ()}
.
An xs:dateTime
with lexical
representation 19990531T13:20:0005:00
is represented by {1999, 5, 31, 13, 20, 0.0, PT5H}
.
An xs:dateTime
with lexical
representation 19991231T24:00:00
is represented by {2000, 1, 1, 0, 0, 0.0, ()}
.
An xs:date
with lexical
representation 20050228+8:00
is represented by {2005, 2, 28, (), (), (), PT8H}
.
An xs:time
with lexical
representation 24:00:00
is represented by {(), (), (), 0, 0, 0, ()}
.
A function is provided for constructing a
xs:dateTime
value from a xs:date
value and a
xs:time
value.
Function  Meaning 

fn:dateTime 
Returns an xs:dateTime value created by combining an xs:date
and an xs:time .

Returns an xs:dateTime
value created by combining an xs:date
and an xs:time
.
fn:dateTime
($date
as
xs:date?
, $time
as
xs:time?
) as
xs:dateTime?
This function is ·deterministic·, ·contextindependent·, and ·focusindependent·.
If either $date
or $time
is the empty sequence the function
returns the empty sequence.
Otherwise, the function returns an xs:dateTime
whose date component is
equal to $date
and whose time component is equal to $time
.
The timezone of the result is computed as follows:
If neither argument has a timezone, the result has no timezone.
If exactly one of the arguments has a timezone, or if both arguments have the same timezone, the result has this timezone.
A dynamic error is raised [err:FORG0008] if the two arguments both have timezones and the timezones are different.
The expression fn:dateTime(xs:date("19991231"),
xs:time("12:00:00"))
returns xs:dateTime("19991231T12:00:00")
.
The expression fn:dateTime(xs:date("19991231"),
xs:time("24:00:00"))
returns xs:dateTime("19991231T00:00:00")
. (This is because "24:00:00"
is an alternate lexical form
for "00:00:00"
).
Function  Meaning 

op:dateTimeequal 
Returns true if the two supplied xs:dateTime values refer to the same
instant in time.

op:dateTimelessthan 
Returns true if the first argument represents an earlier instant in time
than the second argument.

op:dateequal 
Returns true if and only if the starting instants of the two supplied
xs:date values are the same.

op:datelessthan 
Returns true if and only if the starting instant of $arg1 is
less than the starting instant of $arg2 . Returns false
otherwise.

op:timeequal 
Returns true if the two xs:time values represent the same
instant in time, when treated as being times on the same date, before adjusting the
timezone.

op:timelessthan 
Returns true if the first xs:time value represents an earlier
instant in time than the second, when both are treated as being times on the same
date,
before adjusting the timezone.

op:gYearMonthequal 
Returns true if the two xs:gYearMonth values have the same starting
instant.

op:gYearequal 
Returns true if the two xs:gYear values have the same starting instant.

op:gMonthDayequal 
Returns true if the two xs:gMonthDay values have the same starting instant,
when considered as days in the same year.

op:gMonthequal 
Returns true if the two xs:gMonth values have the same starting instant,
when considered as months in the same year.

op:gDayequal 
Returns true if the two xs:gDay values have the same starting instant, when
considered as days in the same month of the same year.

The following comparison operators are defined on the [XML Schema Part 2: Datatypes Second Edition]
date/time datatypes. Each operator takes two operands of the same
type and returns an xs:boolean
result.
[XML Schema Part 2: Datatypes Second Edition] also states that the order relation on date and time datatypes is not a total order but a partial order because these datatypes may or may not have a timezone. This is handled as follows. If either operand to a comparison function on date or time values does not have an (explicit) timezone then, for the purpose of the operation, an implicit timezone, provided by the dynamic context Section C.2 Dynamic Context Components ^{XP31}, is assumed to be present as part of the value. This creates a total order for all date and time values.
An xs:dateTime
can be considered to consist of seven components:
year
, month
, day
, hour
, minute
,
second
and timezone
. For xs:dateTime
six components (year
,
month
, day
, hour
, minute
and second
) are required
and timezone
is optional. For other date/time values, of the first six components, some are
required
and others must be absent^{DM31}.
Timezone
is always optional. For example, for xs:date
,
the year
, month
and day
components are required and hour
,
minute
and second
components must be absent; for xs:time
the hour
,
minute
and second
components are required and year
, month
and
day
are missing; for xs:gDay
, day
is required and year
,
month
, hour
, minute
and second
are missing.
Note:
In [Schema 1.1 Part 2], a new explicitTimezone
facet is available with values
optional
, required
, or prohibited
to
enable the timezone to be defined as mandatory or disallowed.
Values of the date/time datatypes xs:time
, xs:gMonthDay
, xs:gMonth
,
and xs:gDay
, can be considered to represent a sequence of recurring time instants or time periods.
An xs:time
occurs every day. An xs:gMonth
occurs every year. Comparison operators
on these datatypes compare the starting instants of equivalent occurrences in the
recurring series.
These xs:dateTime
values are calculated as described below.
Comparison operators on xs:date
, xs:gYearMonth
and xs:gYear
compare
their starting instants. These xs:dateTime
values are calculated as described below.
The starting instant of an occurrence of a date/time value is an xs:dateTime
calculated by filling
in the missing components of the local value from a reference xs:dateTime
. An example of a suitable
reference xs:dateTime
is 19720101T00:00:00
. Then, for example, the starting
instant corresponding to the xs:date
value 20090312
is
20090312T00:00:00
; the starting instant corresponding to the xs:time
value
13:30:02
is 19720101T13:30:02
; and the starting instant corresponding to the
gMonthDay
value 0229
is 19720229T00:00:00
(which explains
why a leap year was chosen for the reference).
Note:
In the previous version of this specification, the reference date/time chosen was
19721231T00:00:00
. While this gives the same results, it produces a "starting instant" for
a gMonth
or gMonthDay
that bears no
relation to the ordinary meaning of the term, and it also required special handling
of short months.
The original choice was made to allow for leap seconds; but since leap seconds are
not recognized
in date/time arithmetic, this is not actually necessary.
If the xs:time
value written as
24:00:00
is to be compared, filling in the missing components gives 19720101T00:00:00
,
because 24:00:00
is an alternative representation of 00:00:00
(the lexical value
"24:00:00"
is
converted to the time components {0,0,0} before the missing components are filled
in). This has the consequence that when ordering xs:time
values,
24:00:00
is
considered to be earlier than 23:59:59
. However, when ordering
xs:dateTime
values, a time component of 24:00:00
is considered equivalent to 00:00:00
on the
following day.
Note that the reference xs:dateTime
does not have a timezone. The timezone
component
is never filled in from the reference xs:dateTime
. In some cases, if the date/time value does not
have a timezone, the implicit timezone from the dynamic context is used as the
timezone.
Note:
This specification uses the reference xs:dateTime 19720101T00:00:00
in the description of the
comparison operators. Implementations may use other reference xs:dateTime
values
as long as they yield the same results. The reference xs:dateTime
used must meet the following
constraints: when it is used to supply components into xs:gMonthDay
values, the year must allow
for February 29 and so must be a leap year; when it is used to supply missing
components into xs:gDay
values, the month must allow for 31 days. Different reference xs:dateTime
values may be used for
different operators.
Returns true if the two supplied xs:dateTime
values refer to the same
instant in time.
Defines the
semantics of the "eq" operator when applied to two xs:dateTime
values. Also
used in the definition of the "ne", "le" and "ge" operators.
op:dateTimeequal
($arg1
as
xs:dateTime
, $arg2
as
xs:dateTime
) as
xs:boolean
This function is ·deterministic·, ·contextdependent·, and ·focusindependent·. It depends on implicit timezone.
If either $arg1
or $arg2
has no timezone component, the
effective value of the argument is obtained by substituting the implicit timezone
from
the dynamic evaluation context.
The function then returns true
if and only if the effective value of
$arg1
is equal to the effective value of $arg2
according to
the algorithm defined in section 3.2.7.4 of [XML Schema Part 2: Datatypes Second Edition]
"Order relation on dateTime" for xs:dateTime
values with
timezones. Otherwise the function returns false
.
Assume that the dynamic context provides an implicit timezone value of
05:00
The expression op:dateTimeequal(xs:dateTime("20020402T12:00:0001:00"),
xs:dateTime("20020402T17:00:00+04:00"))
returns true()
.
The expression op:dateTimeequal(xs:dateTime("20020402T12:00:00"),
xs:dateTime("20020402T23:00:00+06:00"))
returns true()
.
The expression op:dateTimeequal(xs:dateTime("20020402T12:00:00"),
xs:dateTime("20020402T17:00:00"))
returns false()
.
The expression op:dateTimeequal(xs:dateTime("20020402T12:00:00"),
xs:dateTime("20020402T12:00:00"))
returns true()
.
The expression op:dateTimeequal(xs:dateTime("20020402T23:00:0004:00"),
xs:dateTime("20020403T02:00:0001:00"))
returns true()
.
The expression op:dateTimeequal(xs:dateTime("19991231T24:00:00"),
xs:dateTime("20000101T00:00:00"))
returns true()
.
The expression op:dateTimeequal(xs:dateTime("20050404T24:00:00"),
xs:dateTime("20050404T00:00:00"))
returns false()
.
Returns true
if the first argument represents an earlier instant in time
than the second argument.
Defines the
semantics of the "lt" operator when applied to two xs:dateTime
values. Also
used in the definition of the "ge" operator.
op:dateTimelessthan
($arg1
as
xs:dateTime
, $arg2
as
xs:dateTime
) as
xs:boolean
This function is ·deterministic·, ·contextdependent·, and ·focusindependent·. It depends on implicit timezone.
If either $arg1
or $arg2
has no timezone component, the
effective value of the argument is obtained by substituting the implicit timezone
from
the dynamic evaluation context.
The function then returns true
if and only if the effective value of
$arg1
is less than the effective value of $arg2
according
to the algorithm defined in section 3.2.7.4 of [XML Schema Part 2: Datatypes Second Edition]
"Order relation on dateTime" for xs:dateTime
values with
timezones. Otherwise the function returns false
.
Returns true
if and only if the starting instants of the two supplied
xs:date
values are the same.
Defines the
semantics of the "eq" operator when applied to two xs:date
values. Also used
in the definition of the "ne", "le" and "ge" operators.
op:dateequal
($arg1
as
xs:date
, $arg2
as
xs:date
) as
xs:boolean
This function is ·deterministic·, ·contextdependent·, and ·focusindependent·. It depends on implicit timezone.
The starting instant of an xs:date
is the xs:dateTime
at time
00:00:00
on that date.
The function returns the result of the expression:
op:dateTimeequal(xs:dateTime($arg1), xs:dateTime($arg2))
The expression op:dateequal(xs:date("20041225Z"),
xs:date("20041225+07:00"))
returns false()
. (The starting instants are
xs:dateTime("20041225T00:00:00Z")
and
xs:dateTime("20041225T00:00:00+07:00")
. These are normalized to
xs:dateTime("20041225T00:00:00Z")
and
xs:dateTime("20041224T17:00:00Z")
. ).
The expression op:dateequal(xs:date("2004122512:00"),
xs:date("20041226+12:00"))
returns true()
.
Returns true
if and only if the starting instant of $arg1
is
less than the starting instant of $arg2
. Returns false
otherwise.
Defines the semantics
of the "lt" operator when applied to two xs:date
values. Also used in the
definition of the "ge" operator.
op:datelessthan
($arg1
as
xs:date
, $arg2
as
xs:date
) as
xs:boolean
The starting instant of an xs:date
is the xs:dateTime
at time
00:00:00
on that date.
The function returns the result of the expression:
op:dateTimelessthan(xs:dateTime($arg1), xs:dateTime($arg2))
The expression op:datelessthan(xs:date("20041225Z"),
xs:date("2004122505:00"))
returns true()
.
The expression op:datelessthan(xs:date("2004122512:00"),
xs:date("20041226+12:00"))
returns false()
.
Returns true
if the two xs:time
values represent the same
instant in time, when treated as being times on the same date, before adjusting the
timezone.
Defines the
semantics of the "eq" operator when applied to two xs:time
values. Also used
in the definition of the "ne", "le" and "ge" operators.
op:timeequal
($arg1
as
xs:time
, $arg2
as
xs:time
) as
xs:boolean
This function is ·deterministic·, ·contextdependent·, and ·focusindependent·. It depends on implicit timezone.
Each of the supplied xs:time
values is expanded to an
xs:dateTime
value by associating the time with an arbitrary date. The
function returns the result of comparing these two xs:dateTime
values using
op:dateTimeequal
.
The result of the function is thus the same as the value of the expression:
op:dateTimeequal( fn:dateTime(xs:date('19721231'), $arg1), fn:dateTime(xs:date('19721231'), $arg2))
Assume that the date components from the reference xs:dateTime
correspond to 19721231
.
The expression op:timeequal(xs:time("08:00:00+09:00"),
xs:time("17:00:0006:00"))
returns false()
. (The xs:dateTime
s calculated using the reference date
components are 19721231T08:00:00+09:00
and
19721231T17:00:0006:00
. These normalize to
19721230T23:00:00Z
and 19721231T23:00:00Z
.
).
The expression op:timeequal(xs:time("21:30:00+10:30"),
xs:time("06:00:0005:00"))
returns true()
.
The expression op:timeequal(xs:time("24:00:00+01:00"),
xs:time("00:00:00+01:00"))
returns true()
. (This not the result one might expect. For xs:dateTime
values, a time of 24:00:00
is equivalent to 00:00:00
on
the following day. For xs:time
, the normalization from
24:00:00
to 00:00:00
happens before the
xs:time
is converted into an xs:dateTime
for the
purpose of the equality comparison. For xs:time
, any operation on
24:00:00
produces the same result as the same operation on
00:00:00
because these are two different lexical representations
of the same value. ).
Returns true
if the first xs:time
value represents an earlier
instant in time than the second, when both are treated as being times on the same
date,
before adjusting the timezone.
Defines the semantics
of the "lt" operator when applied to two xs:time
values. Also used in the
definition of the "ge" operator.
op:timelessthan
($arg1
as
xs:time
, $arg2
as
xs:time
) as
xs:boolean
This function is ·deterministic·, ·contextdependent·, and ·focusindependent·. It depends on implicit timezone.
Each of the supplied xs:time
values is expanded to an
xs:dateTime
value by associating the time with an arbitrary date. The
function returns the result of comparing these two xs:dateTime
values using
op:dateTimelessthan
.
The result of the function is thus the same as the value of the expression:
op:dateTimelessthan( fn:dateTime(xs:date('19721231'), $arg1), fn:dateTime(xs:date('19721231'), $arg2))
Assume that the dynamic context provides an implicit timezone value of
05:00
.
The expression op:timelessthan(xs:time("12:00:00"),
xs:time("23:00:00+06:00"))
returns false()
.
The expression op:timelessthan(xs:time("11:00:00"),
xs:time("17:00:00Z"))
returns true()
.
The expression op:timelessthan(xs:time("23:59:59"),
xs:time("24:00:00"))
returns false()
.
Returns true if the two xs:gYearMonth
values have the same starting
instant.
Defines the
semantics of the "eq" operator when applied to two xs:gYearMonth
values. Also
used in the definition of the "ne" operator.
op:gYearMonthequal (

$arg1 
as xs:gYearMonth ,

$arg2 
as xs:gYearMonth ) as xs:boolean 
This function is ·deterministic·, ·contextdependent·, and ·focusindependent·. It depends on implicit timezone.
The starting instants of $arg1
and $arg2
are calculated by
supplying the missing components of $arg1
and $arg2
from the
xs:dateTime
template xxxxxx01T00:00:00
. The function
returns the result of comparing these two starting instants using
op:dateTimeequal
.
Assume that the dynamic context provides an implicit timezone value of
05:00
.
op:gYearMonthequal(xs:gYearMonth("198602"), xs:gYearMonth("198603"))
returns false()
. The starting instants are
19860201T00:00:0005:00
and 19860301T00:00:00
,
respectively.
op:gYearMonthequal(xs:gYearMonth("197803"), xs:gYearMonth("198603Z"))
returns false()
. The starting instants are
19780301T00:00:0005:00
and 19860301T00:00:00Z
,
respectively.
Returns true if the two xs:gYear
values have the same starting instant.
Defines the semantics
of the "eq" operator when applied to two xs:gYear
values. Also used in the
definition of the "ne" operator.
op:gYearequal
($arg1
as
xs:gYear
, $arg2
as
xs:gYear
) as
xs:boolean
This function is ·deterministic·, ·contextdependent·, and ·focusindependent·. It depends on implicit timezone.
The starting instants of $arg1
and $arg2
are calculated by
supplying the missing components of $arg1
and $arg2
from the
xs:dateTime
template xxxx0101T00:00:00
. The function
returns the result of comparing these two starting instants using
op:dateTimeequal
.
Assume that the dynamic context provides an implicit timezone value of
05:00
. Assume, also, that the xs:dateTime
template is
xxxx0101T00:00:00
.
op:gYearequal(xs:gYear("200512:00"), xs:gYear("2005+12:00"))
returns
false()
. The starting instants are
20050101T00:00:0012:00
and 20050101T00:00:00+12:00
,
respectively, and normalize to 20050101T12:00:00Z
and
20041231T12:00:00Z
.
The expression op:gYearequal(xs:gYear("197605:00"),
xs:gYear("1976"))
returns true()
.
Returns true if the two xs:gMonthDay
values have the same starting instant,
when considered as days in the same year.
Defines the
semantics of the "eq" operator when applied to two xs:gMonthDay
values. Also
used in the definition of the "ne" operator.
op:gMonthDayequal
($arg1
as
xs:gMonthDay
, $arg2
as
xs:gMonthDay
) as
xs:boolean
This function is ·deterministic·, ·contextdependent·, and ·focusindependent·. It depends on implicit timezone.
The starting instants of $arg1
and $arg2
are calculated by
supplying the missing components of $arg1
and $arg2
from the
xs:dateTime
template 1972xxxxT00:00:00
or an equivalent.
The function returns the result of comparing these two starting instants using
op:dateTimeequal
.
Assume that the dynamic context provides an implicit timezone value of
05:00
. Assume for the purposes of illustration that the
xs:dateTime
template used is 1972xxxxT00:00:00
(this
does not affect the result).
The expression op:gMonthDayequal(xs:gMonthDay("122514:00"),
xs:gMonthDay("1226+10:00"))
returns true()
. ( The starting instants are 19721225T00:00:0014:00
and
19721226T00:00:00+10:00
, respectively, and normalize to
19721225T14:00:00Z
and 19721225T14:00:00Z
.
).
The expression op:gMonthDayequal(xs:gMonthDay("1225"),
xs:gMonthDay("1226Z"))
returns false()
.
Returns true if the two xs:gMonth
values have the same starting instant,
when considered as months in the same year.
Defines the
semantics of the "eq" operator when applied to two xs:gMonth
values. Also used
in the definition of the "ne" operator.
op:gMonthequal
($arg1
as
xs:gMonth
, $arg2
as
xs:gMonth
) as
xs:boolean
This function is ·deterministic·, ·contextdependent·, and ·focusindependent·. It depends on implicit timezone.
The starting instants of $arg1
and $arg2
are calculated by
supplying the missing components of $arg1
and $arg2
from the
xs:dateTime
template 1972xx01T00:00:00
or an equivalent.
The function returns the result of comparing these two starting instants using
op:dateTimeequal
.
Assume that the dynamic context provides an implicit timezone value of
05:00
. Assume, also, that the xs:dateTime
template
chosen is 1972xx01T00:00:00
.
The expression op:gMonthequal(xs:gMonth("1214:00"),
xs:gMonth("12+10:00"))
returns false()
. ( The starting instants are 19721201T00:00:0014:00
and
19721201T00:00:00+10:00
, respectively, and normalize to
19721130T14:00:00Z
and 19721201T14:00:00Z
.