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W3C XML Schema Definition Language (XSD) 1.1 Part 2: Datatypes

This section describes the status of this document at the time of its publication. Other documents may supersede this document. A list of current W3C publications and the latest revision of this technical report can be found in the W3C technical reports index at http://www.w3.org/TR/.

This W3C Recommendation specifies the W3C XML Schema Definition Language (XSD) 1.1 Part 2: Datatypes. It is here made available for review by W3C members and the public.

Changes since the previous public Working Draft include the following:

• Some minor errors, typographic and otherwise, have been corrected.

For those primarily interested in the changes since version 1.0, the appendix Changes since version 1.0 (§I) is the recommended starting point. An accompanying version of this document displays in color all changes to normative text since version 1.0; another shows changes since the previous Working Draft.

Comments on this document should be made in W3C's public installation of Bugzilla, specifying "XML Schema" as the product. Instructions can be found at http://www.w3.org/XML/2006/01/public-bugzilla. If access to Bugzilla is not feasible, please send your comments to the W3C XML Schema comments mailing list, www-xml-schema-comments@w3.org (archive) and note explicitly that you have not made a Bugzilla entry for the comment. Each Bugzilla entry and email message should contain only one comment.

This document has been reviewed by W3C Members, by software developers, and by other W3C groups and interested parties, and is endorsed by the Director as a W3C Recommendation. It is a stable document and may be used as reference material or cited from another document. W3C's role in making the Recommendation is to draw attention to the specification and to promote its widespread deployment. This enhances the functionality and interoperability of the Web.

An implementation report for XSD 1.1 was prepared and used in the Director's decision to publish the previous version of this specification as a Proposed Recommendation. The Director's decision to publish this document as a W3C Recommendation is based on consideration of reviews of the Proposed Recommendation by the public and by the members of the W3C Advisory committee.

The W3C XML Schema Working Group intends to process comments made about this recommendation, with any approved changes being handled as errata to be published separately.

This document has been produced by the W3C XML Schema Working Group as part of the W3C XML Activity. The goals of the XML Schema language version 1.1 are discussed in the Requirements for XML Schema 1.1 document. The authors of this document are the members of the XML Schema Working Group. Different parts of this specification have different editors.

This document was produced by a group operating under the 5 February 2004 W3C Patent Policy. W3C maintains a public list of any patent disclosures made in connection with the deliverables of the group; that page also includes instructions for disclosing a patent. An individual who has actual knowledge of a patent which the individual believes contains Essential Claim(s) must disclose the information in accordance with section 6 of the W3C Patent Policy.

The English version of this specification is the only normative version. Information about translations of this document is available at http://www.w3.org/2003/03/Translations/byTechnology?technology=xmlschema.

The Working Group has two main goals for this version of W3C XML Schema:

• Significant improvements in simplicity of design and clarity of exposition without loss of backward or forward compatibility;

• Provision of support for versioning of XML languages defined using the XML Schema specification, including the XML transfer syntax for schemas itself.

These goals are slightly in tension with one another -- the following summarizes the Working Group's strategic guidelines for changes between versions 1.0 and 1.1:

1. Add support for versioning (acknowledging that this may be slightly disruptive to the XML transfer syntax at the margins)

2. Allow bug fixes (unless in specific cases we decide that the fix is too disruptive for a point release)

3. Allow editorial changes

4. Allow design cleanup to change behavior in edge cases

5. Allow relatively non-disruptive changes to type hierarchy (to better support current and forthcoming international standards and W3C recommendations)

6. Allow design cleanup to change component structure (changes to functionality restricted to edge cases)

7. Do not allow any significant changes in functionality

8. Do not allow any changes to XML transfer syntax except those required by version control hooks and bug fixes

The overall aim as regards compatibility is that

• All schema documents conformant to version 1.0 of this specification should also conform to version 1.1, and should have the same validation behavior across 1.0 and 1.1 implementations (except possibly in edge cases and in the details of the resulting PSVI);

• The vast majority of schema documents conformant to version 1.1 of this specification should also conform to version 1.0, leaving aside any incompatibilities arising from support for versioning, and when they are conformant to version 1.0 (or are made conformant by the removal of versioning information), should have the same validation behavior across 1.0 and 1.1 implementations (again except possibly in edge cases and in the details of the resulting PSVI);

The [XML] specification defines limited facilities for applying datatypes to document content in that documents may contain or refer to DTDs that assign types to elements and attributes. However, document authors, including authors of traditional documents and those transporting data in XML, often require a higher degree of type checking to ensure robustness in document understanding and data interchange.

The table below offers two typical examples of XML instances in which datatypes are implicit: the instance on the left represents a billing invoice, the instance on the right a memo or perhaps an email message in XML.

<invoice>
  <orderDate>1999-01-21</orderDate>
  <shipDate>1999-01-25</shipDate>
  <billingAddress>
   <name>Ashok Malhotra</name>
   <street>123 Microsoft Ave.</street>
   <city>Hawthorne</city>
   <state>NY</state>
   <zip>10532-0000</zip>
  </billingAddress>
  <voice>555-1234</voice>
  <fax>555-4321</fax>
</invoice>

<memo importance='high'
      date='1999-03-23'>
  <from>Paul V. Biron</from>
  <to>Ashok Malhotra</to>
  <subject>Latest draft</subject>
  <body>
    We need to discuss the latest
    draft <emph>immediately</emph>.
    Either email me at <email>
    mailto:paul.v.biron@kp.org</email>
    or call <phone>555-9876</phone>
  </body>
</memo>

The invoice contains several dates and telephone numbers, the postal abbreviation for a state (which comes from an enumerated list of sanctioned values), and a ZIP code (which takes a definable regular form).  The memo contains many of the same types of information: a date, telephone number, email address and an "importance" value (from an enumerated list, such as "low", "medium" or "high").  Applications which process invoices and memos need to raise exceptions if something that was supposed to be a date or telephone number does not conform to the rules for valid dates or telephone numbers.

In both cases, validity constraints exist on the content of the instances that are not expressible in XML DTDs.  The limited datatyping facilities in XML have prevented validating XML processors from supplying the rigorous type checking required in these situations.  The result has been that individual applications writers have had to implement type checking in an ad hoc manner.  This specification addresses the need of both document authors and applications writers for a robust, extensible datatype system for XML which could be incorporated into XML processors.  As discussed below, these datatypes could be used in other XML-related standards as well.

Other specifications on which this one depends are listed in References (§K).

This specification defines some datatypes which depend on definitions in [XML] and [Namespaces in XML]; those definitions, and therefore the datatypes based on them, vary between version 1.0 ([XML 1.0], [Namespaces in XML 1.0]) and version 1.1 ([XML], [Namespaces in XML]) of those specifications. In any given use of this specification, the choice of the 1.0 or the 1.1 definition of those datatypes is ·implementation-defined·.

Conforming implementations of this specification may provide either the 1.1-based datatypes or the 1.0-based datatypes, or both. If both are supported, the choice of which datatypes to use in a particular assessment episode should be under user control.

Note: When this specification is used to check the datatype validity of XML input, implementations may provide the heuristic of using the 1.1 datatypes if the input is labeled as XML 1.1, and using the 1.0 datatypes if the input is labeled 1.0, but this heuristic should be subject to override by users, to support cases where users wish to accept XML 1.1 input but validate it using the 1.0 datatypes, or accept XML 1.0 input and validate it using the 1.1 datatypes.

This specification makes use of the EBNF notation used in the [XML] specification. Note that some constructs of the EBNF notation used here resemble the regular-expression syntax defined in this specification (Regular Expressions (§G)), but that they are not identical: there are differences. For a fuller description of the EBNF notation, see Section 6. Notation of the [XML] specification.

The [XML Schema Requirements] document spells out concrete requirements to be fulfilled by this specification, which state that the XML Schema Language must:

1. provide for primitive data typing, including byte, date, integer, sequence, SQL and Java primitive datatypes, etc.;

2. define a type system that is adequate for import/export from database systems (e.g., relational, object, OLAP);

3. distinguish requirements relating to lexical data representation vs. those governing an underlying information set;

4. allow creation of user-defined datatypes, such as datatypes that are derived from existing datatypes and which may constrain certain of its properties (e.g., range, precision, length, format).

This specification defines datatypes that can be used in an XML Schema.  These datatypes can be specified for element content that would be specified as #PCDATA and attribute values of various types in a DTD.  It is the intention of this specification that it be usable outside of the context of XML Schemas for a wide range of other XML-related activities such as [XSL] and [RDF Schema].

The terminology used to describe XML Schema Datatypes is defined in the body of this specification. The terms defined in the following list are used in building those definitions and in describing the actions of a datatype processor:

A feature of this specification included solely to ensure that schemas which use this feature remain compatible with

.

(Of strings or names:) Two strings or names being compared must be identical. Characters with multiple possible representations in ISO/IEC 10646 (e.g. characters with both precomposed and base+diacritic forms) match only if they have the same representation in both strings. No case folding is performed.

(Of strings and rules in the grammar:) A string matches a grammatical production if and only if it belongs to the language generated by that production.

Schemas, schema documents, and processors are permitted to but need not behave as described.

It is recommended that schemas, schema documents, and processors behave as described, but there can be valid reasons for them not to; it is important that the full implications be understood and carefully weighed before adopting behavior at variance with the recommendation.

Schemas and documents are required to behave as described; otherwise they are in

.

(Of processors:) Processors are required to behave as described.

Schemas, schema documents and processors are forbidden to behave as described; schemas and documents which nevertheless do so are in

.

A failure of a schema or schema document to conform to the rules of this specification.

Except as otherwise specified, processors

distinguish error-free (conforming) schemas and schema documents from those with errors; if a schema used in type-validation or a schema document used in constructing a schema is in error, processors

report the fact; if more than one is in error, it is

whether more than one is reported as being in error. If more than one of the constraints given in this specification is violated, it is

how many of the violations, and which, are reported.

Note: Failure of an XML element or attribute to be datatype-valid against a particular datatype in a particular schema is not in itself a failure to conform to this specification and thus, for purposes of this specification, not an error.

A choice left under the control of the user of a processor, rather than being fixed for all users or uses of the processor.

Statements in this specification that "Processors may at user option" behave in a certain way mean that processors may provide mechanisms to allow users (i.e. invokers of the processor) to enable or disable the behavior indicated. Processors which do not provide such user-operable controls must not behave in the way indicated. Processors which do provide such user-operable controls must make it possible for the user to disable the optional behavior.

Note: The normal expectation is that the default setting for such options will be to disable the optional behavior in question, enabling it only when the user explicitly requests it. This is not, however, a requirement of conformance: if the processor's documentation makes clear that the user can disable the optional behavior, then invoking the processor without requesting that it be disabled can be taken as equivalent to a request that it be enabled. It is required, however, that it in fact be possible for the user to disable the optional behavior.

Note: Nothing in this specification constrains the manner in which processors allow users to control user options. Command-line options, menu choices in a graphical user interface, environment variables, alternative call patterns in an application programming interface, and other mechanisms may all be taken as providing user options.

This specification provides three different kinds of normative statements about schema components, their representations in XML and their contribution to the schema-validation of information items:

Constraints on the schema components themselves, i.e. conditions components

satisfy to be components at all. Largely to be found in

.

Constraints expressed by schema components which information items

satisfy to be schema-valid. Largely to be found in

.

This section describes the conceptual framework behind the datatype system defined in this specification.  The framework has been influenced by the [ISO 11404] standard on language-independent datatypes as well as the datatypes for [SQL] and for programming languages such as Java.

The datatypes discussed in this specification are for the most part well known abstract concepts such as integer and date. It is not the place of this specification to thoroughly define these abstract concepts; many other publications provide excellent definitions. However, this specification will attempt to describe the abstract concepts well enough that they can be readily recognized and distinguished from other abstractions with which they may be confused.

Only those operations and relations needed for schema processing are defined in this specification. Applications using these datatypes are generally expected to implement appropriate additional functions and/or relations to make the datatype generally useful. For example, the description herein of the

datatype does not define addition or multiplication, much less all of the operations defined for that datatype in

on which it is based. For some datatypes (e.g.

or

) defined in part by reference to other specifications which impose constraints not part of the datatypes as defined here, applications may also wish to check that values conform to the requirements given in the current version of the relevant external specification.

In this specification, a

has three properties:

Note: This specification only defines the operations and relations needed for schema processing.  The choice of terminology for describing/naming the datatypes is selected to guide users and implementers in how to expand the datatype to be generally useful—i.e., how to recognize the "real world" datatypes and their variants for which the datatypes defined herein are meant to be used for data interchange.

Along with the ·lexical mapping· it is often useful to have an inverse which provides a standard ·lexical representation· for each value.  Such a ·canonical mapping· is not required for schema processing, but is described herein for the benefit of users of this specification, and other specifications which might find it useful to reference these descriptions normatively. For some datatypes, notably QName and NOTATION, the mapping from lexical representations to values is context-dependent; for these types, no ·canonical mapping· is defined.

Note: This specification sometimes uses the shorter form "type" where one might strictly speaking expect the longer form "datatype" (e.g. in the phrases "union type", "list type", "base type", "item type", etc. No systematic distinction is intended between the forms of these phrase with "type" and those with "datatype"; the two forms are used interchangeably.

The distinction between "datatype" and "simple type definition", by contrast, carries more information: the datatype is characterized by its

,

,

, etc., as just described, independently of the specific facets or other definitional mechanisms used in the simple type definition to describe that particular

or

. Different simple type definitions with different selections of facets can describe the same datatype.

[Definition:]  The value space of a datatype is the set of values for that datatype.  Associated with each value space are selected operations and relations necessary to permit proper schema processing.  Each value in the value space of a ·primitive· or ·ordinary· datatype is denoted by one or more character strings in its ·lexical space·, according to ·the lexical mapping·; ·special· datatypes, by contrast, may include "ineffable" values not mapped to by any lexical representation. (If the mapping is restricted during a derivation in such a way that a value has no denotation, that value is dropped from the value space.)

The value spaces of datatypes are abstractions, and are defined in Built-in Datatypes and Their Definitions (§3) to the extent needed to clarify them for readers.  For example, in defining the numerical datatypes, we assume some general numerical concepts such as number and integer are known.  In many cases we provide references to other documents providing more complete definitions.

Note: The value spaces and the values therein are abstractions.  This specification does not prescribe any particular internal representations that must be used when implementing these datatypes.  In some cases, there are references to other specifications which do prescribe specific internal representations; these specific internal representations must be used to comply with those other specifications, but need not be used to comply with this specification.

In addition, other applications are expected to define additional appropriate operations and/or relations on these value spaces (e.g., addition and multiplication on the various numerical datatypes' value spaces), and are permitted where appropriate to even redefine the operations and relations defined within this specification, provided that for schema processing the relations and operations used are those defined herein.

The

of a datatype can be defined in one of the following ways:

• defined elsewhere axiomatically from fundamental notions (intensional definition) [see

  ·primitive·

  ]

• enumerated outright from values of an already defined datatype (extensional definition) [see

  ·enumeration·

  ]

• defined by restricting the

  ·value space·

  of an already defined datatype to a particular subset with a given set of properties [see

  ·derived·

  ]

• defined as a combination of values from one or more already defined

  ·value space·

  (s) by a specific construction procedure [see

  ·list·

  and

  ·union·

  ]

The relations of identity and equality are required for each value space. An order relation is specified for some value spaces, but not all. A very few datatypes have other relations or operations prescribed for the purposes of this specification.

The identity relation is always defined. Every value space inherently has an identity relation. Two things are identical if and only if they are actually the same thing: i.e., if there is no way whatever to tell them apart. 

Note: This does not preclude implementing datatypes by using more than one internal representation for a given value, provided no mechanism inherent in the datatype implementation (i.e., other than bit-string-preserving "casting" of the datum to a different datatype) will distinguish between the two representations.

In the identity relation defined herein, values from different ·primitive· datatypes' ·value spaces· are made artificially distinct if they might otherwise be considered identical.  For example, there is a number two in the decimal datatype and a number two in the float datatype.  In the identity relation defined herein, these two values are considered distinct.  Other applications making use of these datatypes may choose to consider values such as these identical, but for the view of ·primitive· datatypes' ·value spaces· used herein, they are distinct.

WARNING:  Care must be taken when identifying values across distinct primitive datatypes.  The ·literals· '0.1' and '0.10000000009' map to the same value in float (neither 0.1 nor 0.10000000009 is in the value space, and each literal is mapped to the nearest value, namely 0.100000001490116119384765625), but map to distinct values in decimal.

Given a list A and a list B, A and B are the same list if they are the same sequence of atomic values. The necessary and sufficient conditions for this identity are that A and B have the same length and that the items of A are pairwise identical to the items of B.

It is a consequence of the rule just given for list identity that there is only one empty list. An empty list declared as having

and an empty list declared as having

are not only equal but identical.

Each ·primitive· datatype has prescribed an equality relation for its value space.  The equality relation for most datatypes is the identity relation.  In the few cases where it is not, equality has been carefully defined so that for most operations of interest to the datatype, if two values are equal and one is substituted for the other as an argument to any of the operations, the results will always also be equal.

On the other hand, equality need not cover the entire value space of the datatype (though it usually does). In particular, NaN is not equal to itself in the float and double datatypes.

This equality relation is used in conjunction with identity when making ·facet-based restrictions· by enumeration, when checking identity constraints (in the context of [XSD 1.1 Part 1: Structures]) and when checking value constraints. It is used in conjunction with order when making ·facet-based restrictions· involving order. The equality relation used in the evaluation of XPath expressions may differ.  When processing XPath expressions as part of XML schema-validity assessment or otherwise testing membership in the ·value space· of a datatype whose derivation involves ·assertions·, equality (like all other relations) within those expressions is interpreted using the rules of XPath ([XPath 2.0]).  All comparisons for "sameness" prescribed by this specification test for either equality or identity, not for identity alone.

Note: In the prior version of this specification (1.0), equality was always identity.  This has been changed to permit the datatypes defined herein to more closely match the "real world" datatypes for which they are intended to be used as transmission formats.

For example, the

datatype has an equality which is not the identity ( −0 = +0 , but they are not identical—although they

identical in the 1.0 version of this specification), and whose domain excludes one value, NaN, so that NaN ≠ NaN .

For another example, the

datatype previously lost any time-zone offset information in the

as the value was converted to

; now the time zone offset is retained and two values representing the same "moment in time" but with different remembered time zone offsets are now

but not

.

In the equality relation defined herein, values from different primitive data spaces are made artificially unequal even if they might otherwise be considered equal.  For example, there is a number two in the decimal datatype and a number two in the float datatype.  In the equality relation defined herein, these two values are considered unequal.  Other applications making use of these datatypes may choose to consider values such as these equal; nonetheless, in the equality relation defined herein, they are unequal.

Two lists A and B are equal if and only if they have the same length and their items are pairwise equal. A list of length one containing a value V1 and an atomic value V2 are equal if and only if V1 is equal to V2.

For the purposes of this specification, there is one equality relation for all values of all datatypes (the union of the various datatype's individual equalities, if one consider relations to be sets of ordered pairs).  The equality relation is denoted by '=' and its negation by '≠', each used as a binary infix predicate:  x = y  and  x ≠ y .  On the other hand, identity relationships are always described in words.

For some datatypes, an order relation is prescribed for use in checking upper and lower bounds of the ·value space·.  This order may be a partial order, which means that there may be values in the ·value space· which are neither equal, less-than, nor greater-than.  Such value pairs are incomparable.  In many cases, no order is prescribed; each pair of values is either equal or ·incomparable·. [Definition:]  Two values that are neither equal, less-than, nor greater-than are incomparable. Two values that are not ·incomparable· are comparable.

The order relation is used in conjunction with equality when making ·facet-based restrictions· involving order.  This is the only use of this order relation for schema processing.  Of course, when processing XPath expressions as part of XML schema-validity assessment or otherwise testing membership in the ·value space· of a datatype whose derivation involves ·assertions·, order (like all other relations) within those expressions is interpreted using the rules of XPath ([XPath 2.0]).

In this specification, this less-than order relation is denoted by '<' (and its inverse by '>'), the weak order by '≤' (and its inverse by '≥'), and the resulting ·incomparable· relation by '<>', each used as a binary infix predicate:  x < y ,  x ≤ y ,  x > y ,  x ≥ y , and  x <> y .

The weak order "less-than-or-equal" means "less-than" or "equal"

. For example, the

P1M (one month) is

less-than-or-equal P31D (thirty-one days) because P1M is not less than P31D, nor is P1M equal to P31D. Instead, P1M is

with P31D.) The formal definition of order for

(

) ensures that this is true.

For purposes of this specification, the value spaces of primitive datatypes are disjoint, even in cases where the abstractions they represent might be thought of as having values in common.  In the order relations defined in this specification, values from different value spaces are ·incomparable·.  For example, the numbers two and three are values in both the decimal datatype and the float datatype.  In the order relation defined here, the two in the decimal datatype is not less than the three in the float datatype; the two values are incomparable.  Other applications making use of these datatypes may choose to consider values such as these comparable.

Comparison of values from different

datatypes can sometimes be an error and sometimes not, depending on context.

When made for purposes of checking an enumeration constraint, such a comparison is not in itself an error, but since no two values from different

are equal, any comparison of

values will invariably be false.

Specifying an upper or lower bound which is of the wrong primitive datatype (and therefore

with the values of the datatype it is supposed to restrict) is, by contrast, always an error. It is a consequence of the rules for

that in conforming simple type definitions, the values of upper and lower bounds, and enumerated values,

be drawn from the value space of the

, which necessarily means from the same

datatype.

[Definition:]  The lexical mapping for a datatype is a prescribed relation which maps from the ·lexical space· of the datatype into its ·value space·.

[Definition:]  The lexical space of a datatype is the prescribed set of strings which ·the lexical mapping· for that datatype maps to values of that datatype.

[Definition:]  The members of the ·lexical space· are lexical representations of the values to which they are mapped.

[Definition:]  A sequence of zero or more characters in the Universal Character Set (UCS) which may or may not prove upon inspection to be a member of the ·lexical space· of a given datatype and thus a ·lexical representation· of a given value in that datatype's ·value space·, is referred to as a literal. The term is used indifferently both for character sequences which are members of a particular ·lexical space· and for those which are not.

If a derivation introduces a ·pre-lexical· facet value (a new value for whiteSpace or an implementation-defined ·pre-lexical· facet), the corresponding ·pre-lexical· transformation of a character string, if indeed it changed that string, could prevent that string from ever having the ·lexical mapping· of the derived datatype applied to it.  Character strings that a ·pre-lexical· transformation blocks in this way (i.e., they are not in the range of the ·pre-lexical· facet's transformation) are always dropped from the derived datatype's ·lexical space·.

One should be aware that in the context of XML schema-validity

, there are

transformations of the input character string (controlled by the

facet and any implementation-defined

facets) which result in the intended

. Systems other than XML schema-validity

utilizing this specification may or may not implement these transformations. If they do not, then input character strings that would have been transformed into correct

, when taken "raw", may not be correct

.

Should a derivation be made using a derivation mechanism that removes ·lexical representations· from the·lexical space· to the extent that one or more values cease to have any ·lexical representation·, then those values are dropped from the ·value space·.

Conversely, should a derivation remove values then their ·lexical representations· are dropped from the ·lexical space· unless there is a facet value whose impact is defined to cause the otherwise-dropped ·lexical representation· to be mapped to another value instead.

Note: There are currently no facets with such an impact.  There may be in the future.

For example, '100' and '1.0E2' are two different ·lexical representations· from the float datatype which both denote the same value.  The datatype system defined in this specification provides mechanisms for schema designers to control the ·value space· and the corresponding set of acceptable ·lexical representations· of those values for a datatype.

It is useful to categorize the datatypes defined in this specification along various dimensions, defining terms which can be used to characterize datatypes and the Simple Type Definitions which define them.

First, we distinguish ·atomic·, ·list·, and ·union· datatypes.

[Definition:]  An atomic value is an elementary value, not constructed from simpler values by any user-accessible means defined by this specification.

For example, a single token which ·matches· Nmtoken from [XML] is in the value space of the ·atomic· datatype NMTOKEN, while a sequence of such tokens is in the value space of the ·list· datatype NMTOKENS.

·List· datatypes are always ·constructed· from some other type; they are never ·primitive·. The ·value space· of a ·list· datatype is the set of finite-length sequences of zero or more ·atomic· values where each ·atomic· value is drawn from the ·value space· of the lists's ·item type· and has a ·lexical representation· containing no whitespace. The ·lexical space· of a ·list· datatype is a set of ·literals· each of which is a space-separated sequence of ·literals· of the ·item type·.

[Definition:]   The ·atomic· or ·union· datatype that participates in the definition of a ·list· datatype is the item type of that ·list· datatype.  If the ·item type· is a ·union·, each of its ·basic members· must be ·atomic·.

<simpleType name='sizes'>
  <list itemType='decimal'/>
</simpleType>

<cerealSizes xsi:type='sizes'> 8 10.5 12 </cerealSizes>

A ·list· datatype can be ·constructed· from an ordinary or ·primitive· ·atomic· datatype whose ·lexical space· allows whitespace (such as string or anyURI) or a ·union· datatype any of whose {member type definitions}'s ·lexical space· allows space. Since ·list· items are separated at whitespace before the ·lexical representations· of the items are mapped to values, no whitespace will ever occur in the ·lexical representation· of a ·list· item, even when the item type would in principle allow it.  For the same reason, when every possible ·lexical representation· of a given value in the ·value space· of the ·item type· includes whitespace, that value can never occur as an item in any value of the ·list· datatype.

<simpleType name='listOfString'>
  <list itemType='string'/>
</simpleType>

<someElement xsi:type='listOfString'>
this is not list item 1
this is not list item 2
this is not list item 3
</someElement>

For each of ·length·, ·maxLength· and ·minLength·, the length is measured in number of list items.  The value of ·whiteSpace· is fixed to the value collapse.

For ·list· datatypes the ·lexical space· is composed of space-separated ·literals· of the ·item type·.  Any ·pattern· specified when a new datatype is ·derived· from a ·list· datatype applies to the members of the ·list· datatype's ·lexical space·, not to the members of the ·lexical space· of the ·item type·.  Similarly, enumerated values are compared to the entire ·list·, not to individual list items, and assertions apply to the entire ·list· too. Lists are identical if and only if they have the same length and their items are pairwise identical; they are equal if and only if they have the same length and their items are pairwise equal. And a list of length one whose item is an atomic value V1 is equal or identical to an atomic value V2 if and only if V1 is equal or identical to V2.

<xs:simpleType name='myList'>
	<xs:list itemType='xs:integer'/>
</xs:simpleType>
<xs:simpleType name='myRestrictedList'>
	<xs:restriction base='myList'>
		<xs:pattern value='123 (\d+\s)*456'/>
	</xs:restriction>
</xs:simpleType>
<someElement xsi:type='myRestrictedList'>123 456</someElement>
<someElement xsi:type='myRestrictedList'>123 987 456</someElement>
<someElement xsi:type='myRestrictedList'>123 987 567 456</someElement>

The ·canonical mapping· of a ·list· datatype maps each value onto the space-separated concatenation of the ·canonical representations· of all the items in the value (in order), using the ·canonical mapping· of the ·item type·.

Union types may be defined in either of two ways. When a union type is ·constructed· by ·union·, its ·value space·, ·lexical space·, and ·lexical mapping· are the "ordered unions" of the ·value spaces·, ·lexical spaces·, and ·lexical mappings· of its ·member types·.

It will be observed that the ·lexical mapping· of a union, so defined, is not necessarily a function: a given ·literal· may map to one value or to several values of different ·primitive· datatypes, and it may be indeterminate which value is to be preferred in a particular context. When the datatypes defined here are used in the context of [XSD 1.1 Part 1: Structures], the xsi:type attribute defined by that specification in section xsi:type can be used to indicate which value a ·literal· which is the content of an element should map to. In other contexts, other rules (such as type coercion rules) may be employed to determine which value is to be used.

When a union type is defined by ·restricting· another ·union·, its ·value space·, ·lexical space·, and ·lexical mapping· are subsets of the ·value spaces·, ·lexical spaces·, and ·lexical mappings· of its ·base type·.

·Union· datatypes are always ·constructed· from other datatypes; they are never ·primitive·. Currently, there are no ·built-in· ·union· datatypes.

A prototypical example of a

type is the

on the

in XML Schema itself: it is a union of nonNegativeInteger and an enumeration with the single member, the string "unbounded", as shown below.

  <attributeGroup name="occurs">
    <attribute name="minOccurs" type="nonNegativeInteger"
    	use="optional" default="1"/>
    <attribute name="maxOccurs"use="optional" default="1">
      <simpleType>
        <union>
          <simpleType>
            <restriction base='nonNegativeInteger'/>
          </simpleType>
          <simpleType>
            <restriction base='string'>
              <enumeration value='unbounded'/>
            </restriction>
          </simpleType>
        </union>
      </simpleType>
    </attribute>
  </attributeGroup>

Any number (zero or more) of ordinary or ·primitive· ·datatypes· can participate in a ·union· type.

[Definition:]   The datatypes that participate in the definition of a ·union· datatype are known as the member types of that ·union· datatype.

[Definition:]  The transitive membership of a ·union· is the set of its own ·member types·, and the ·member types· of its members, and so on. More formally, if U is a ·union·, then (a) its ·member types· are in the transitive membership of U, and (b) for any datatypes T1 and T2, if T1 is in the transitive membership of U and T2 is one of the ·member types· of T1, then T2 is also in the transitive membership of U.

The ·transitive membership· of a ·union· must not contain the ·union· itself, nor any datatype ·derived· or ·constructed· from the ·union·.

[Definition:]  Those members of the ·transitive membership· of a ·union· datatype U which are themselves not ·union· datatypes are the basic members of U.

[Definition:]  If a datatype M is in the ·transitive membership· of a ·union· datatype U, but not one of U's ·member types·, then a sequence of one or more ·union· datatypes necessarily exists, such that the first is one of the ·member types· of U, each is one of the ·member types· of its predecessor in the sequence, and M is one of the ·member types· of the last in the sequence. The ·union· datatypes in this sequence are said to intervene between M and U. When U and M are given by the context, the datatypes in the sequence are referred to as the intervening unions. When M is one of the ·member types· of U, the set of intervening unions is the empty set.

[Definition:]  In a valid instance of any ·union·, the first of its members in order which accepts the instance as valid is the active member type. [Definition:]  If the ·active member type· is itself a ·union·, one of its members will be its ·active member type·, and so on, until finally a ·basic (non-union) member· is reached. That ·basic member· is the active basic member of the union.

The order in which the ·member types· are specified in the definition (that is, in the case of datatypes defined in a schema document, the order of the <simpleType> children of the <union> element, or the order of the QNames in the memberTypes attribute) is significant. During validation, an element or attribute's value is validated against the ·member types· in the order in which they appear in the definition until a match is found.  As noted above, the evaluation order can be overridden with the use of xsi:type.

For example, given the definition below, the first instance of the <size> element validates correctly as an

, the second and third as

.

  <xs:element name='size'>
    <xs:simpleType>
      <xs:union>
        <xs:simpleType>
          <xs:restriction base='integer'/>
        </xs:simpleType>
        <xs:simpleType>
          <xs:restriction base='string'/>
        </xs:simpleType>
      </xs:union>
    </xs:simpleType>
  </xs:element>

  <size>1</size>
  <size>large</size>
  <size xsi:type='xs:string'>1</size>

The ·canonical mapping· of a ·union· datatype maps each value onto the ·canonical representation· of that value obtained using the ·canonical mapping· of the first ·member type· in whose value space it lies.

Next, we distinguish ·special·, ·primitive·, and ·ordinary· (or ·constructed·) datatypes.  Each datatype defined by or in accordance with this specification falls into exactly one of these categories.

• Note:

  As normatively specified elsewhere, conforming processors

  must

  support all the primitive datatypes defined in this specification; it is

  ·implementation-defined·

  whether other primitive datatypes are supported.

  Processors

  may

  , for example, support the floating-point decimal datatype specified in

  [Precision Decimal]

  .

For example, in this specification, float is a ·primitive· datatype based on a well-defined mathematical concept and not defined in terms of other datatypes, while integer is ·constructed· from the more general datatype decimal.

Definition, derivation, restriction, and construction are conceptually distinct, although in practice they are frequently performed by the same mechanisms.

By 'definition' is meant the explicit identification of the relevant properties of a datatype, in particular its ·value space·, ·lexical space·, and ·lexical mapping·.

The properties of the ·special· and the standard ·primitive· datatypes are defined by this specification. A Simple Type Definition is present for each of these datatypes in every valid schema; it serves as a representation of the datatype, but by itself it does not capture all the relevant information and does not suffice (without knowledge of this specification) to define the datatype.

The properties of any

datatypes are given not here but in the documentation for the implementation in question. Alternatively, a primitive datatype not specified in this document can be specified in a document of its own not tied to a particular implementation;

is an example of such a document.

For all other datatypes, a Simple Type Definition does suffice. The properties of an ·ordinary· datatype can be inferred from the datatype's Simple Type Definition and the properties of the ·base type·, ·item type· if any, and ·member types· if any. All ·ordinary· datatypes can be defined in this way.

By 'derivation' is meant the relation of a datatype to its ·base type·, or to the ·base type· of its ·base type·, and so on.

Every datatype other than anySimpleType is associated with another datatype, its base type. Base types can be ·special·, ·primitive·, or ·ordinary·.

[Definition:]  A datatype T is immediately derived from another datatype X if and only if X is the ·base type· of T.

More generally,

A datatype

is

from another datatype

if and only if one of the following is true:

• There is some datatype

  X

  such that

  X

  is the

  ·base type·

  of

  R

  , and

  X

  is derived from

  B

  .

A datatype must not be ·derived· from itself. That is, the base type relation must be acyclic.

It is a consequence of the above that every datatype other than anySimpleType is ·derived· from anySimpleType.

Since each datatype has exactly one ·base type·, and every datatype other than anySimpleType is ·derived· directly or indirectly from anySimpleType, it follows that the ·base type· relation arranges all simple types into a tree structure, which is conventionally referred to as the derivation hierarchy.

By 'restriction' is meant the definition of a datatype whose ·value space· and ·lexical space· are subsets of those of its ·base type·.

Formally,

Note that all three forms of datatype ·construction· produce ·restrictions· of the ·base type·: ·facet-based restriction· does so by means of ·constraining facets·, while ·construction· by ·list· or ·union· does so because those ·constructions· take anySimpleType as the ·base type·. It follows that all datatypes are ·restrictions· of anySimpleType. This specification provides no means by which a datatype may be defined so as to have a larger ·lexical space· or ·value space· than its ·base type·.

By 'construction' is meant the creation of a datatype by defining it in terms of another.

[Definition:]  All ·ordinary· datatypes are defined in terms of, or constructed from, other datatypes, either by ·restricting· the ·value space· or ·lexical space· of a ·base type· using zero or more ·constraining facets· or by specifying the new datatype as a ·list· of items of some ·item type·, or by defining it as a ·union· of some specified sequence of ·member types·. These three forms of ·construction· are often called "·facet-based restriction·", "·construction· by ·list·", and "·construction· by ·union·", respectively. Datatypes so constructed may be understood fully (for purposes of a type system) in terms of (a) the properties of the datatype(s) from which they are constructed, and (b) their Simple Type Definition. This distinguishes ·ordinary· datatypes from the ·special· and ·primitive· datatypes, which can be understood only in the light of documentation (namely, their descriptions elsewhere in this specification, or, for ·implementation-defined· ·primitives·, in the appropriate implementation-specific documentation). All ·ordinary· datatypes are ·constructed·, and all ·constructed· datatypes are ·ordinary·.

• [Definition:]   User-defined datatypes are those datatypes that are defined by individual schema designers.

The ·built-in· datatypes are intended to be available automatically whenever this specification is implemented or used, whether by itself or embedded in a host language. In the language defined by [XSD 1.1 Part 1: Structures], the ·built-in· datatypes are automatically included in every valid schema. Other host languages should specify that all of the datatypes decribed here as built-ins are automatically available; they may specify that additional datatypes are also made available automatically.

datatypes, whether

or

, may sometimes be included automatically in any schemas processed by that implementation; nevertheless, they are not built in to

schema, and are thus not included in the term 'built-in', as that term is used in this specification.

The mechanism for making ·user-defined· datatypes available for use is not defined in this specification; if ·user-defined· datatypes are to be available, some such mechanism must be specified by the host language.

[Definition:]  A datatype which is not available for use is said to be unknown.

From the schema author's perspective, a reference to a datatype which proves to be

might reflect any of the following causes, or others:

1

2

4

From the point of view of the implementation, these cases are likely to be indistinguishable.

Conceptually there is no difference between the ·ordinary· ·built-in· datatypes included in this specification and the ·user-defined· datatypes which will be created by individual schema designers. The ·built-in· ·constructed· datatypes are those which are believed to be so common that if they were not defined in this specification many schema designers would end up reinventing them.  Furthermore, including these ·constructed· datatypes in this specification serves to demonstrate the mechanics and utility of the datatype generation facilities of this specification.

Each built-in datatype defined in this specification can be uniquely addressed via a URI Reference constructed as follows:

1. the base URI is the URI of the XML Schema namespace

2. the fragment identifier is the name of the datatype

For example, to address the

datatype, the URI is:

• http://www.w3.org/2001/XMLSchema#int

Additionally, each facet definition element can be uniquely addressed via a URI constructed as follows:

1. the base URI is the URI of the XML Schema namespace

2. the fragment identifier is the name of the facet

For example, to address the maxInclusive facet, the URI is:

• http://www.w3.org/2001/XMLSchema#maxInclusive

Additionally, each facet usage in a built-in

can be uniquely addressed via a URI constructed as follows:

1. the base URI is the URI of the XML Schema namespace

2. the fragment identifier is the name of the

   Simple Type Definition

   , followed by a period ('

   .

   ') followed by the name of the facet

For example, to address the usage of the maxInclusive facet in the definition of int, the URI is:

• http://www.w3.org/2001/XMLSchema#int.maxInclusive

The ·built-in· datatypes defined by this specification are designed to be used with the XML Schema definition language as well as other XML specifications. To facilitate usage within the XML Schema definition language, the ·built-in· datatypes in this specification have the namespace name:

• http://www.w3.org/2001/XMLSchema

To facilitate usage in specifications other than the XML Schema definition language, such as those that do not want to know anything about aspects of the XML Schema definition language other than the datatypes, each ·built-in· datatype is also defined in the namespace whose URI is:

• http://www.w3.org/2001/XMLSchema-datatypes

Each ·user-defined· datatype may also be associated with a target namespace.  If it is constructed from a schema document, then its namespace is typically the target namespace of that schema document. (See XML Representation of Schemas in [XSD 1.1 Part 1: Structures].)

The two datatypes at the root of the hierarchy of simple types are anySimpleType and anyAtomicType.

The ·primitive· datatypes defined by this specification are described below.  For each datatype, the ·value space· is described; the ·lexical space· is defined using an extended Backus Naur Format grammar (and in most cases also a regular expression using the regular expression language of Regular Expressions (§G)); ·constraining facets· which apply to the datatype are listed; and any datatypes ·constructed· from this datatype are specified.

Conforming processors must support the ·primitive· datatypes defined in this specification; it is ·implementation-defined· whether they support others. ·Primitive· datatypes may be added by revisions to this specification.

Processors

, for example, support the floating-point decimal datatype specified in

.

[Definition:]  The string datatype represents character strings in XML.

[Definition:]  boolean represents the values of two-valued logic.

[Definition:]  decimal represents a subset of the real numbers, which can be represented by decimal numerals. The ·value space· of decimal is the set of numbers that can be obtained by dividing an integer by a non-negative power of ten, i.e., expressible as i / 10ⁿ where i and n are integers and n ≥ 0. Precision is not reflected in this value space; the number 2.0 is not distinct from the number 2.00. The order relation on decimal is the order relation on real numbers, restricted to this subset.

decimal has a lexical representation consisting of a non-empty finite-length sequence of decimal digits (#x30–#x39) separated by a period as a decimal indicator.  An optional leading sign is allowed.  If the sign is omitted, "+" is assumed.  Leading and trailing zeroes are optional.  If the fractional part is zero, the period and following zero(es) can be omitted. For example:  '-1.23', '12678967.543233', '+100000.00', '210'.

The lexical space of decimal is the set of lexical representations which match the grammar given above, or (equivalently) the regular expression

(\+|-)?([0-9]+(\.[0-9]*)?|\.[0-9]+)

The mapping from lexical representations to values is the usual one for decimal numerals; it is given formally in ·decimalLexicalMap·.

The definition of the ·canonical representation· has the effect of prohibiting certain options from the Lexical Mapping (§3.3.3.1).  Specifically, for integers, the decimal point and fractional part are prohibited. For other values, the preceding optional "+" sign is prohibited.  The decimal point is required.  In all cases, leading and trailing zeroes are prohibited subject to the following:  there must be at least one digit to the right and to the left of the decimal point which may be a zero.

The mapping from values to ·canonical representations· is given formally in ·decimalCanonicalMap·.

[Definition:]  The float datatype is patterned after the IEEE single-precision 32-bit floating point datatype [IEEE 754-2008].  Its value space is a subset of the rational numbers.  Floating point numbers are often used to approximate arbitrary real numbers.

The ·value space· of float contains the non-zero numbers  m × 2^e , where m is an integer whose absolute value is less than 2²⁴, and e is an integer between −149 and 104, inclusive.  In addition to these values, the ·value space· of float also contains the following ·special values·:  positiveZero, negativeZero, positiveInfinity, negativeInfinity, and notANumber.

As explained below, the

of the

value

is '

'. Accordingly, in English text we generally use 'NaN' to refer to that value. Similarly, we use 'INF' and '−INF' to refer to the two values

and

, and '0' and '−0' to refer to

and

.

Equality and order for

are defined as follows:

• Equality is identity, except that  0 = −0  (although they are not identical) and  NaN ≠ NaN  (although NaN is of course identical to itself).

  0 and −0 are thus equivalent for purposes of enumerations and identity constraints, as well as for minimum and maximum values.

• For the basic values, the order relation on float is the order relation for rational numbers. INF is greater than all other non-NaN values; −INF is less than all other non-NaN values. NaN is

  ·incomparable·

  with any value in the

  ·value space·

  including itself. 0 and −0 are greater than all the negative numbers and less than all the positive numbers.

The Schema 1.0 version of this datatype did not differentiate between 0 and −0 and NaN was equal to itself. The changes were made to make the datatype more closely mirror

.

The

of

is the set of all decimal numerals with or without a decimal point, numerals in scientific (exponential) notation, and the

'

', '

', '

', and '

'

The

production is equivalent to this regular expression (after whitespace is removed from the regular expression):

(\+|-)?([0-9]+(\.[0-9]*)?|\.[0-9]+)([Ee](\+|-)?[0-9]+)?
|(\+|-)?INF|NaN

The float datatype is designed to implement for schema processing the single-precision floating-point datatype of [IEEE 754-2008].  That specification does not specify specific ·lexical representations·, but does prescribe requirements on any ·lexical mapping· used.  Any ·lexical mapping· that maps the ·lexical space· just described onto the ·value space·, is a function, satisfies the requirements of [IEEE 754-2008], and correctly handles the mapping of the literals 'INF', 'NaN', etc., to the ·special values·, satisfies the conformance requirements of this specification.

Since IEEE allows some variation in rounding of values, processors conforming to this specification may exhibit some variation in their ·lexical mappings·.

The ·lexical mapping· ·floatLexicalMap· is provided as an example of a simple algorithm that yields a conformant mapping, and that provides the most accurate rounding possible—and is thus useful for insuring inter-implementation reproducibility and inter-implementation round-tripping.  The simple rounding algorithm used in ·floatLexicalMap· may be more efficiently implemented using the algorithms of [Clinger, WD (1990)].

The Schema 1.0 version of this datatype did not permit rounding algorithms whose results differed from

.

The ·canonical mapping· ·floatCanonicalMap· is provided as an example of a mapping that does not produce unnecessarily long ·canonical representations·.  Other algorithms which do not yield identical results for mapping from float values to character strings are permitted by [IEEE 754-2008].

[Definition:]  The double datatype is patterned after the IEEE double-precision 64-bit floating point datatype [IEEE 754-2008].  Each floating point datatype has a value space that is a subset of the rational numbers.  Floating point numbers are often used to approximate arbitrary real numbers.

Note: The only significant differences between float and double are the three defining constants 53 (vs 24), −1074 (vs −149), and 971 (vs 104).

The ·value space· of double contains the non-zero numbers  m × 2^e , where m is an integer whose absolute value is less than 2⁵³, and e is an integer between −1074 and 971, inclusive.  In addition to these values, the ·value space· of double also contains the following ·special values·:  positiveZero, negativeZero, positiveInfinity, negativeInfinity, and notANumber.

As explained below, the

of the

value

is '

'. Accordingly, in English text we generally use 'NaN' to refer to that value. Similarly, we use 'INF' and '−INF' to refer to the two values

and

, and '0' and '−0' to refer to

and

.

Equality and order for

are defined as follows:

• Equality is identity, except that  0 = −0  (although they are not identical) and  NaN ≠ NaN  (although NaN is of course identical to itself).

  0 and −0 are thus equivalent for purposes of enumerations, identity constraints, and minimum and maximum values.

• For the basic values, the order relation on double is the order relation for rational numbers. INF is greater than all other non-NaN values; −INF is less than all other non-NaN values. NaN is

  ·incomparable·

  with any value in the

  ·value space·

  including itself. 0 and −0 are greater than all the negative numbers and less than all the positive numbers.

The Schema 1.0 version of this datatype did not differentiate between 0 and −0 and NaN was equal to itself. The changes were made to make the datatype more closely mirror

.

The

of

is the set of all decimal numerals with or without a decimal point, numerals in scientific (exponential) notation, and the

'

', '

', '

', and '

'

The

production is equivalent to this regular expression (after whitespace is eliminated from the expression):

(\+|-)?([0-9]+(\.[0-9]*)?|\.[0-9]+)([Ee](\+|-)?[0-9]+)? |(\+|-)?INF|NaN

The double datatype is designed to implement for schema processing the double-precision floating-point datatype of [IEEE 754-2008].  That specification does not specify specific ·lexical representations·, but does prescribe requirements on any ·lexical mapping· used.  Any ·lexical mapping· that maps the ·lexical space· just described onto the ·value space·, is a function, satisfies the requirements of [IEEE 754-2008], and correctly handles the mapping of the literals 'INF', 'NaN', etc., to the ·special values·, satisfies the conformance requirements of this specification.

Since IEEE allows some variation in rounding of values, processors conforming to this specification may exhibit some variation in their ·lexical mappings·.

The ·lexical mapping· ·doubleLexicalMap· is provided as an example of a simple algorithm that yields a conformant mapping, and that provides the most accurate rounding possible—and is thus useful for insuring inter-implementation reproducibility and inter-implementation round-tripping.  The simple rounding algorithm used in ·doubleLexicalMap· may be more efficiently implemented using the algorithms of [Clinger, WD (1990)].

The Schema 1.0 version of this datatype did not permit rounding algorithms whose results differed from

.

The ·canonical mapping· ·doubleCanonicalMap· is provided as an example of a mapping that does not produce unnecessarily long ·canonical representations·.  Other algorithms which do not yield identical results for mapping from float values to character strings are permitted by [IEEE 754-2008].

[Definition:]  duration is a datatype that represents durations of time.  The concept of duration being captured is drawn from those of [ISO 8601], specifically durations without fixed endpoints.  For example, "15 days" (whose most common lexical representation in duration is "'P15D'") is a duration value; "15 days beginning 12 July 1995" and "15 days ending 12 July 1995" are not duration values.  duration can provide addition and subtraction operations between duration values and between duration/dateTime value pairs, and can be the result of subtracting dateTime values.  However, only addition to dateTime is required for XML Schema processing and is defined in the function ·dateTimePlusDuration·.

Duration values can be modelled as two-property tuples. Each value consists of an integer number of months and a decimal number of seconds. The

value

be negative if the

value is positive and

be positive if the

is negative.

is partially ordered. Equality of

is defined in terms of equality of

; order for

is defined in terms of the order of

. Specifically, the equality or order of two

values is determined by adding each

in the pair to each of the following four

values:

• 1696-09-01T00:00:00Z

• 1697-02-01T00:00:00Z

• 1903-03-01T00:00:00Z

• 1903-07-01T00:00:00Z

If all four resulting

value pairs are ordered the same way (less than, equal, or greater than), then the original pair of

values is ordered the same way; otherwise the original pair is

.

These four values are chosen so as to maximize the possible differences in results that could occur, such as the difference when adding P1M and P30D: 1697-02-01T00:00:00Z + P1M < 1697-02-01T00:00:00Z + P30D , but 1903-03-01T00:00:00Z + P1M > 1903-03-01T00:00:00Z + P30D , so that P1M <> P30D . If two

values are ordered the same way when added to each of these four

values, they will retain the same order when added to

other

values. Therefore, two

values are incomparable if and only if they can

result in different orders when added to

value.

Under the definition just given, two duration values are equal if and only if they are identical.

There are many ways to implement

, some of which do not base the implementation on the two-component model. This specification does not prescribe any particular implementation, as long as the visible results are isomorphic to those described herein.

Thus, a durationLexicalRep consists of one or more of a duYearFrag, duMonthFrag, duDayFrag, duHourFrag, duMinuteFrag, and/or duSecondFrag, in order, with letters 'P' and 'T' (and perhaps a '-') where appropriate.

The language accepted by the

production is the set of strings which satisfy all of the following three regular expressions:

• The expression

  -?P[0-9]+Y?([0-9]+M)?([0-9]+D)?(T([0-9]+H)?([0-9]+M)?([0-9]+(\.[0-9]+)?S)?)?

  matches only strings in which the fields occur in the proper order.

• The expression '.*[YMDHS].*' matches only strings in which at least one field occurs.

• The expression '.*[^T]' matches only strings in which 'T' is not the final character, so that if 'T' appears, something follows it. The first rule ensures that what follows 'T' will be an hour, minute, or second field.

The intersection of these three regular expressions is equivalent to the following (after removal of the white space inserted here for legibility):

-?P( ( ( [0-9]+Y([0-9]+M)?([0-9]+D)?
       | ([0-9]+M)([0-9]+D)?
       | ([0-9]+D)
       )
       (T ( ([0-9]+H)([0-9]+M)?([0-9]+(\.[0-9]+)?S)?
          | ([0-9]+M)([0-9]+(\.[0-9]+)?S)?
          | ([0-9]+(\.[0-9]+)?S)
          )
       )?
    )
  | (T ( ([0-9]+H)([0-9]+M)?([0-9]+(\.[0-9]+)?S)?
       | ([0-9]+M)([0-9]+(\.[0-9]+)?S)?
       | ([0-9]+(\.[0-9]+)?S)
       )
    )
  )

The ·lexical mapping· for duration is ·durationMap·.

·The canonical mapping· for duration is ·durationCanonicalMap·.

dateTime represents instants of time, optionally marked with a particular time zone offset.  Values representing the same instant but having different time zone offsets are equal but not identical.

dateTime uses the date/timeSevenPropertyModel, with no properties except ·timezoneOffset· permitted to be absent. The ·timezoneOffset· property remains ·optional·.

In version 1.0 of this specification, the

property was not permitted to have the value zero. The year before the year 1 in the proleptic Gregorian calendar, traditionally referred to as 1 BC or as 1 BCE, was represented by a

value of −1, 2 BCE by −2, and so forth. Of course, many, perhaps most, references to 1 BCE (or 1 BC) actually refer not to a year in the proleptic Gregorian calendar but to a year in the Julian or "old style" calendar; the two correspond approximately but not exactly to each other.

In this version of this specification, two changes are made in order to agree with existing usage. First,

is permitted to have the value zero. Second, the interpretation of

values is changed accordingly: a

value of zero represents 1 BCE, −1 represents 2 BCE, etc. This representation simplifies interval arithmetic and leap-year calculation for dates before the common era (which may be why astronomers and others interested in such calculations with the proleptic Gregorian calendar have adopted it), and is consistent with the current edition of

.

Note that 1 BCE, 5 BCE, and so on (years 0000, -0004, etc. in the lexical representation defined here) are leap years in the proleptic Gregorian calendar used for the date/time datatypes defined here. Version 1.0 of this specification was unclear about the treatment of leap years before the common era. If existing schemas or data specify dates of 29 February for any years before the common era, then some values giving a date of 29 February which were valid under a plausible interpretation of XSD 1.0 will be invalid under this specification, and some which were invalid will be valid. With that possible exception, schemas and data valid under the old interpretation remain valid under the new.

The

value

be no more than 30 if

is one of 4, 6, 9, or 11; no more than 28 if

is 2 and

is not divisible by 4, or is divisible by 100 but not by 400; and no more than 29 if

is 2 and

is divisible by 400, or by 4 but not by 100.

Equality and order are as prescribed in The Seven-property Model (§D.2.1).  dateTime values are ordered by their ·timeOnTimeline· value.

Since the order of a

value having a

relative to another value whose

is

is determined by imputing time zone offsets of both +14:00 and −14:00 to the value with no time zone offset, many such combinations will be

because the two imputed time zone offsets yield different orders.

Although

and other types related to dates and times have only a partial order, it is possible for datatypes derived from

to have total orders, if they are restricted (e.g. using the

facet) to the subset of values with, or the subset of values without, time zone offsets. Similar restrictions on other date- and time-related types will similarly produce totally ordered subtypes. Note, however, that such restrictions do not affect the value shown, for a given

, in the

facet.

Order and equality are essentially the same for

in this version of this specification as they were in version 1.0. However, since values now distinguish time zone offsets, equal values with different

s are not

, and values with extreme

s may no longer be equal to any value with a smaller

.

The lexical representations for

are as follows:

Within a

, a

begin with the digit '

' or be '

' unless the value to which it would map would satisfy the value constraint on

values ("Constraint: Day-of-month Values") given above.

In such representations:

• yearFrag

  is a numeral consisting of at least four decimal digits, optionally preceded by a minus sign; leading '

  0

  ' digits are prohibited except to bring the digit count up to four. It represents the

  ·year·

  value.

• Subsequent '-', 'T', and ':', separate the various numerals.

• secondFrag

  is a numeral consisting of exactly two decimal digits, or two decimal digits, a decimal point, and one or more trailing digits. It represents the

  ·second·

  value.

• timezoneFrag

  , if present, specifies an offset between UTC and local time. Time zone offsets are a count of minutes (expressed in

  timezoneFrag

  as a count of hours and minutes) that are added or subtracted from UTC time to get the "local" time. '

  Z

  ' is an alternative representation of the time zone offset '

  00:00

  ', which is, of course, zero minutes from UTC.

  For example, 2002-10-10T12:00:00−05:00 (noon on 10 October 2002, Central Daylight Savings Time as well as Eastern Standard Time in the U.S.) is equal to 2002-10-10T17:00:00Z, five hours later than 2002-10-10T12:00:00Z.

  Note:

  For the most part, this specification adopts the distinction between 'timezone' and 'timezone offset' laid out in

  [Timezones]

  . Version 1.0 of this specification did not make this distinction, but used the term 'timezone' for the time zone offset information associated with date- and time-related datatypes. Some traces of the earlier usage remain visible in this and other specifications. The names

  timezoneFrag

  and

  explicitTimezone

  are such traces ; others will be found in the names of functions defined in

  [XQuery 1.0 and XPath 2.0 Functions and Operators]

  , or in references in this specification to "timezoned" and "non-timezoned" values.

The

production is equivalent to this regular expression once whitespace is removed.

-?([1-9][0-9]{3,}|0[0-9]{3})
-(0[1-9]|1[0-2])
-(0[1-9]|[12][0-9]|3[01])
T(([01][0-9]|2[0-3]):[0-5][0-9]:[0-5][0-9](\.[0-9]+)?|(24:00:00(\.0+)?))
(Z|(\+|-)((0[0-9]|1[0-3]):[0-5][0-9]|14:00))?

Note that neither the

production nor this regular expression alone enforce the constraint on

given above.

The ·lexical mapping· for dateTime is ·dateTimeLexicalMap·. The ·canonical mapping· is ·dateTimeCanonicalMap·.

time represents instants of time that recur at the same point in each calendar day, or that occur in some arbitrary calendar day.

time uses the date/timeSevenPropertyModel, with ·year·, ·month·, and ·day· required to be absent.  ·timezoneOffset· remains ·optional·.

Equality and order are as prescribed in The Seven-property Model (§D.2.1).  time values (points in time in an "arbitrary" day) are ordered taking into account their ·timezoneOffset·.

A calendar (or "local time") day with a larger positive time zone offset begins earlier than the same calendar day with a smaller (or negative) time zone offset. Since the time zone offsets allowed spread over 28 hours, it is possible for the period denoted by a given calendar day with one time zone offset to be completely disjoint from the period denoted by the same calendar day with a different offset — the earlier day ends before the later one starts.  The moments in time represented by a single calendar day are spread over a 52-hour interval, from the beginning of the day in the +14:00 time zone offset to the end of that day in the −14:00 time zone offset.

The relative order of two

values, one of which has a

of

is determined by imputing time zone offsets of both +14:00 and −14:00 to the value without an offset. Many such combinations will be

because the two imputed time zone offsets yield different orders. However, for a given non-timezoned value, there will always be timezoned values at one or both ends of the 52-hour interval that are

(because the interval of

is only 28 hours wide).

Some pairs of

literals which in the 1.0 version of this specification denoted the same value now (in this version) denote distinct values instead, because values now include time zone offset information. Some such pairs, such as '

' and '

', now denote equal though distinct values (because they identify the same points on the time line); others, such as '

' and '

', now denote unequal values (23:00:00−03:00 > 02:00:00Z because 23:00:00−03:00 on any given day is equal to 02:00:00Z on

).

[Definition:]   date represents top-open intervals of exactly one day in length on the timelines of dateTime, beginning on the beginning moment of each day, up to but not including the beginning moment of the next day).  For non-timezoned values, the top-open intervals disjointly cover the non-timezoned timeline, one per day.  For timezoned values, the intervals begin at every minute and therefore overlap.

date uses the date/timeSevenPropertyModel, with ·hour·, ·minute·, and ·second· required to be absent.  ·timezoneOffset· remains ·optional·.

The

value

be no more than 30 if

is one of 4, 6, 9, or 11, no more than 28 if

is 2 and

is not divisible by 4, or is divisible by 100 but not by 400, and no more than 29 if

is 2 and

is divisible by 400, or by 4 but not by 100.

Equality and order are as prescribed in The Seven-property Model (§D.2.1).

In version 1.0 of this specification,

values did not retain a time zone offset explicitly, but for offsets not too far from zero their time zone offset could be recovered based on their value's first moment on the timeline. The

retains all time zone offsets.

Some

values with different time zone offsets that were identical in the 1.0 version of this specification, such as 2000-01-01+13:00 and 1999-12-31−11:00, are in this version of this specification equal (because they begin at the same moment on the time line) but are not identical (because they have and retain different time zone offsets). This situation will arise for dates only if one has a far-from-zero time zone offset and hence in 1.0 its "recoverable time zone offset" was different from the the time zone offset which is retained in the

used in this version of this specification.

The lexical representations for

are "projections" of those of

, as follows:

Within a

, a

begin with the digit '

' or be '

' unless the value to which it would map would satisfy the value constraint on

values ("Constraint: Day-of-month Values") given above.

The

production is equivalent to this regular expression:

-?([1-9][0-9]{3,}|0[0-9]{3})-(0[1-9]|1[0-2])-(0[1-9]|[12][0-9]|3[01])(Z|(\+|-)((0[0-9]|1[0-3]):[0-5][0-9]|14:00))?

Note that neither the

production nor this regular expression alone enforce the constraint on

given above.

The ·lexical mapping· for date is ·dateLexicalMap·. The ·canonical mapping· is ·dateCanonicalMap·.

gYearMonth represents specific whole Gregorian months in specific Gregorian years.

Note: Because month/year combinations in one calendar only rarely correspond to month/year combinations in other calendars, values of this type are not, in general, convertible to simple values corresponding to month/year combinations in other calendars.  This type should therefore be used with caution in contexts where conversion to other calendars is desired.

gYear represents Gregorian calendar years.

Note: Because years in one calendar only rarely correspond to years in other calendars, values of this type are not, in general, convertible to simple values corresponding to years in other calendars.  This type should therefore be used with caution in contexts where conversion to other calendars is desired.

gMonthDay represents whole calendar days that recur at the same point in each calendar year, or that occur in some arbitrary calendar year.  (Obviously, days beyond 28 cannot occur in all Februaries; 29 is nonetheless permitted.)

This datatype can be used, for example, to record birthdays; an instance of the datatype could be used to say that someone's birthday occurs on the 14th of September every year.

Note: Because day/month combinations in one calendar only rarely correspond to day/month combinations in other calendars, values of this type do not, in general, have any straightforward or intuitive representation in terms of most other calendars. This type should therefore be used with caution in contexts where conversion to other calendars is desired.

gMonthDay uses the date/timeSevenPropertyModel, with ·year·, ·hour·, ·minute·, and ·second· required to be absent.  ·timezoneOffset· remains ·optional·.

The

value

be no more than 30 if

is one of 4, 6, 9, or 11, and no more than 29 if

is 2.

Equality and order are as prescribed in The Seven-property Model (§D.2.1).

In version 1.0 of this specification,

values did not retain a time zone offset explicitly, but for time zone offsets not too far from

their time zone offset could be recovered based on their value's first moment on the timeline. The

retains all time zone offsets.

An example that shows the difference from version 1.0 (see

for the notations):

• A day is a calendar (or "local time") day offset from

  ·UTC·

  by the appropriate interval; this is now true for all

  ·day·

  values, including those with time zone offsets outside the range +12:00 through -11:59 inclusive:

  --12-12+13:00 < --12-12+11:00  (just as --12-12+12:00 has always been less than --12-12+11:00, but in version 1.0  --12-12+13:00 > --12-12+11:00 , since --12-12+13:00's "recoverable time zone offset" was −11:00)

[Definition:]  gDay represents whole days within an arbitrary month—days that recur at the same point in each (Gregorian) month. This datatype is used to represent a specific day of the month. To indicate, for example, that an employee gets a paycheck on the 15th of each month.  (Obviously, days beyond 28 cannot occur in all months; they are nonetheless permitted, up to 31.)

Because days in one calendar only rarely correspond to days in other calendars,

values do not, in general, have any straightforward or intuitive representation in terms of most non-Gregorian calendars.

should therefore be used with caution in contexts where conversion to other calendars is desired.

gDay uses the date/timeSevenPropertyModel, with ·year·, ·month·, ·hour·, ·minute·, and ·second· required to be absent.  ·timezoneOffset· remains ·optional· and ·day· must be between 1 and 31 inclusive.

Equality and order are as prescribed in The Seven-property Model (§D.2.1).  Since gDay values (days) are ordered by their first moments, it is possible for apparent anomalies to appear in the order when ·timezoneOffset· values differ by at least 24 hours.  (It is possible for ·timezoneOffset· values to differ by up to 28 hours.)

Examples that may appear anomalous (see

for the notations):

• ---15 < ---16 , but  ---15−13:00 > ---16+13:00

• ---15−11:00 = ---16+13:00

• ---15−13:00 <> ---16 , because  ---15−13:00 > ---16+14:00  and ---15−13:00 < 16−14:00

Note: Time zone offsets do not cause wrap-around at the end of the month:  the last day of a given month with a time zone offset of −13:00 may start after the first day of the next month with offset +13:00, as measured on the global timeline, but nonetheless  ---01+13:00 < ---31−13:00 .

gMonth represents whole (Gregorian) months within an arbitrary year—months that recur at the same point in each year.  It might be used, for example, to say what month annual Thanksgiving celebrations fall in different countries (--11 in the United States, --10 in Canada, and possibly other months in other countries).

Note: Because months in one calendar only rarely correspond to months in other calendars, values of this type do not, in general, have any straightforward or intuitive representation in terms of most other calendars. This type should therefore be used with caution in contexts where conversion to other calendars is desired.

[Definition:]  hexBinary represents arbitrary hex-encoded binary data. 

The ·value space· of hexBinary is the set of finite-length sequences of zero or more binary octets.  The length of a value is the number of octets.

[Definition:]   base64Binary represents arbitrary Base64-encoded binary data.  For base64Binary data the entire binary stream is encoded using the Base64 Encoding defined in [RFC 3548], which is derived from the encoding described in [RFC 2045].

The ·value space· of base64Binary is the set of finite-length sequences of zero or more binary octets.  The length of a value is the number of octets.

The ·lexical representations· of base64Binary values are limited to the 65 characters of the Base64 Alphabet defined in [RFC 3548], i.e., a-z, A-Z, 0-9, the plus sign (+), the forward slash (/) and the equal sign (=), together with the space character (#x20). No other characters are allowed.

For compatibility with older mail gateways, [RFC 2045] suggests that Base64 data should have lines limited to at most 76 characters in length.  This line-length limitation is not required by [RFC 3548] and is not mandated in the ·lexical representations· of base64Binary data.  It must not be enforced by XML Schema processors.

The ·lexical space· of base64Binary is the set of literals which ·match· the base64Binaryproduction.

Lexical space of base64Binary

::=

'

' #x20? '

'

::= [A-Za-z0-9+/]

::= [AEIMQUYcgkosw048]

The

production is equivalent to the following regular expression.

((([A-Za-z0-9+/] ?){4})*(([A-Za-z0-9+/] ?){3}[A-Za-z0-9+/]|([A-Za-z0-9+/] ?){2}[AEIMQUYcgkosw048] ?=|[A-Za-z0-9+/] ?[AQgw] ?= ?=))?

Note that each '

' except the last is preceded by a single space character.

Note that this grammar requires the number of non-whitespace characters in the ·lexical representation· to be a multiple of four, and for equals signs to appear only at the end of the ·lexical representation·; literals which do not meet these constraints are not legal ·lexical representations· of base64Binary.

The ·lexical mapping· for base64Binary is as given in [RFC 2045] and [RFC 3548].

The above definition of the

is more restrictive than that given in

as regards whitespace — and less restrictive than

. This is not an issue in practice. Any string compatible with either RFC can occur in an element or attribute validated by this type, because the

facet of this type is fixed to

, which means that all leading and trailing whitespace will be stripped, and all internal whitespace collapsed to single space characters,

the above grammar is enforced. The possibility of ignoring whitespace in Base64 data is foreseen in clause 2.3 of

, but for the reasons given there this specification does not allow implementations to ignore non-whitespace characters which are not in the Base64 Alphabet.

The canonical ·lexical representation· of a base64Binary data value is the Base64 encoding of the value which matches the Canonical-base64Binary production in the following grammar:

Canonical representation of base64Binary

That is, the ·canonical representation· of a base64Binary value is the ·lexical representation· which maps to that value and contains no whitespace. The ·canonical mapping· for base64Binary is thus the encoding algorithm for Base64 data given in [RFC 2045] and [RFC 3548], with the proviso that no characters except those in the Base64 Alphabet are to be written out.

The length of a base64Binary value may be calculated from the ·lexical representation· by removing whitespace and padding characters and performing the calculation shown in the pseudo-code below:

lex2   := killwhitespace(lexform)    -- remove whitespace characters
lex3   := strip_equals(lex2)         -- strip padding characters at end
length := floor (length(lex3) * 3 / 4)         -- calculate length

Note on encoding:  [RFC 2045] and [RFC 3548] explicitly reference US-ASCII encoding.  However, decoding of base64Binary data in an XML entity is to be performed on the Unicode characters obtained after character encoding processing as specified by [XML].

[Definition:]   anyURI represents an Internationalized Resource Identifier Reference (IRI).  An anyURI value can be absolute or relative, and may have an optional fragment identifier (i.e., it may be an IRI Reference).  This type should be used when the value fulfills the role of an IRI, as defined in [RFC 3987] or its successor(s) in the IETF Standards Track.

IRIs may be used to locate resources or simply to identify them. In the case where they are used to locate resources using a URI, applications should use the mapping from

values to URIs given by the reference escaping procedure defined in

and in Section 3.1

of

or its successor(s) in the IETF Standards Track. This means that a wide range of internationalized resource identifiers can be specified when an

is called for, and still be understood as URIs per

and its successor(s).

The ·lexical space· of anyURI is the set of finite-length sequences of zero or more characters (as defined in [XML]) that ·match· the Char production from [XML].

For an

value to be usable in practice as an IRI, the result of applying to it the algorithm defined in Section 3.1 of

should be a string which is a legal URI according to

. (This is true at the time this document is published; if in the future

and

are replaced by other specifications in the IETF Standards Track, the relevant constraints will be those imposed by those successor specifications.)

Each URI scheme imposes specialized syntax rules for URIs in that scheme, including restrictions on the syntax of allowed fragment identifiers. Because it is impractical for processors to check that a value is a context-appropriate URI reference, neither the syntactic constraints defined by the definitions of individual schemes nor the generic syntactic constraints defined by

and

and their successors are part of this datatype as defined here. Applications which depend on

values being legal according to the rules of the relevant specifications should make arrangements to check values against the appropriate definitions of IRI, URI, and specific schemes.

Spaces are, in principle, allowed in the

of

, however, their use is highly discouraged (unless they are encoded by '

').

The ·lexical mapping· for anyURI is the identity mapping.

Note: The definitions of URI in the current IETF specifications define certain URIs as equivalent to each other. Those equivalences are not part of this datatype as defined here: if two "equivalent" URIs or IRIs are different character sequences, they map to different values in this datatype.

[Definition:]  NOTATION represents the NOTATION attribute type from [XML]. The ·value space· of NOTATION is the set of QNames of notations declared in the current schema. The ·lexical space· of NOTATION is the set of all names of notations declared in the current schema (in the form of QNames).

The lexical mapping rules for NOTATION are as given for QName in QName (§3.3.18).

The exception is that in the

of a new type the

used to enumerate the allowed values

be (and in the context of [XSD 1.1 Part 1: Structures] will be) validated directly against

; this amounts to verifying that the value is a

and that the

is the name of a

declared in the current schema.

For compatibility (see Terminology (§1.6)) NOTATION should be used only on attributes and should only be used in schemas with no target namespace.

This section gives conceptual definitions for all ·built-in· ·ordinary· datatypes defined by this specification. The XML representation used to define ·ordinary· datatypes (whether ·built-in· or ·user-defined·) is given in XML Representation of Simple Type Definition Schema Components (§4.1.2) and the complete definitions of the ·built-in· ·ordinary· datatypes are provided in the appendix Schema for Schema Documents (Datatypes) (normative) (§A).

[Definition:]   normalizedString represents white space normalized strings.  The ·value space· of normalizedString is the set of strings that do not contain the carriage return (#xD), line feed (#xA) nor tab (#x9) characters.  The ·lexical space· of normalizedString is the set of strings that do not contain the carriage return (#xD), line feed (#xA) nor tab (#x9) characters.  The ·base type· of normalizedString is string.

[Definition:]   token represents tokenized strings. The ·value space· of token is the set of strings that do not contain the carriage return (#xD), line feed (#xA) nor tab (#x9) characters, that have no leading or trailing spaces (#x20) and that have no internal sequences of two or more spaces. The ·lexical space· of token is the set of strings that do not contain the carriage return (#xD), line feed (#xA) nor tab (#x9) characters, that have no leading or trailing spaces (#x20) and that have no internal sequences of two or more spaces. The ·base type· of token is normalizedString.

The regular expression above provides the only normative constraint on the lexical and value spaces of this type. The additional constraints imposed on language identifiers by

and its successor(s), and in particular their requirement that language codes be registered with IANA or ISO if not given in ISO 639, are not part of this datatype as defined here.

specifies that language codes "are to be treated as case insensitive; there exist conventions for capitalization of some of the subtags, but these MUST NOT be taken to carry meaning." Since the

datatype is derived from

, it inherits from

a one-to-one mapping from lexical representations to values. The literals '

' and '

' (for Mongolian) therefore correspond to distinct values and have distinct canonical forms. Users of this specification should be aware of this fact, the consequence of which is that the case-insensitive treatment of language values prescribed by

does not follow from the definition of this datatype given here; applications which require case-insensitivity should make appropriate adjustments.

The empty string is not a member of the

of

. Some constructs which normally take language codes as their values, however, also allow the empty string. The attribute

defined by

is one example; there, the empty string overrides a value which would otherwise be inherited, but without specifying a new value.

One way to define the desired set of possible values is illustrated by the schema document for the XML namespace at

, which defines the attribute

as having a type which is a union of

and an anonymous type whose only value is the empty string:

 <xs:attribute name="lang">
   <xs:annotation>
     <xs:documentation>
       See RFC 3066 at http://www.ietf.org/rfc/rfc3066.txt 
       and the IANA registry at 
       http://www.iana.org/assignments/lang-tag-apps.htm for
       further information.

       The union allows for the 'un-declaration' of xml:lang with
       the empty string.
     </xs:documentation>
   </xs:annotation>
   <xs:simpleType>
     <xs:union memberTypes="xs:language">
       <xs:simpleType>    
         <xs:restriction base="xs:string">
           <xs:enumeration value=""/>
         </xs:restriction>
       </xs:simpleType>
     </xs:union>
   </xs:simpleType>
 </xs:attribute>

[Definition:]   integer is ·derived· from decimal by fixing the value of ·fractionDigits· to be 0 and disallowing the trailing decimal point.  This results in the standard mathematical concept of the integer numbers.  The ·value space· of integer is the infinite set {...,-2,-1,0,1,2,...}.  The ·base type· of integer is decimal.

integer has a lexical representation consisting of a finite-length sequence of one or more decimal digits (#x30-#x39) with an optional leading sign.  If the sign is omitted, "+" is assumed.  For example: -1, 0, 12678967543233, +100000.

[Definition:]   nonPositiveInteger is ·derived· from integer by setting the value of ·maxInclusive· to be 0.  This results in the standard mathematical concept of the non-positive integers. The ·value space· of nonPositiveInteger is the infinite set {...,-2,-1,0}.  The ·base type· of nonPositiveInteger is integer.

nonPositiveInteger has a lexical representation consisting of an optional preceding sign followed by a non-empty finite-length sequence of decimal digits (#x30-#x39).  The sign may be "+" or may be omitted only for lexical forms denoting zero; in all other lexical forms, the negative sign ('-') must be present.  For example: -1, 0, -12678967543233, -100000.

[Definition:]   negativeInteger is ·derived· from nonPositiveInteger by setting the value of ·maxInclusive· to be -1.  This results in the standard mathematical concept of the negative integers.  The ·value space· of negativeInteger is the infinite set {...,-2,-1}.  The ·base type· of negativeInteger is nonPositiveInteger.

negativeInteger has a lexical representation consisting of a negative sign ('-') followed by a non-empty finite-length sequence of decimal digits (#x30-#x39), at least one of which must be a digit other than '0'.  For example: -1, -12678967543233, -100000.

[Definition:]   long is ·derived· from integer by setting the value of ·maxInclusive· to be 9223372036854775807 and ·minInclusive· to be -9223372036854775808. The ·base type· of long is integer.

long has a lexical representation consisting of an optional sign followed by a non-empty finite-length sequence of decimal digits (#x30-#x39).  If the sign is omitted, "+" is assumed.  For example: -1, 0, 12678967543233, +100000.

[Definition:]   int is ·derived· from long by setting the value of ·maxInclusive· to be 2147483647 and ·minInclusive· to be -2147483648.  The ·base type· of int is long.

int has a lexical representation consisting of an optional sign followed by a non-empty finite-length sequence of decimal digits (#x30-#x39).  If the sign is omitted, "+" is assumed. For example: -1, 0, 126789675, +100000.

[Definition:]   short is ·derived· from int by setting the value of ·maxInclusive· to be 32767 and ·minInclusive· to be -32768.  The ·base type· of short is int.

short has a lexical representation consisting of an optional sign followed by a non-empty finite-length sequence of decimal digits (#x30-#x39).  If the sign is omitted, "+" is assumed. For example: -1, 0, 12678, +10000.

[Definition:]   byte is ·derived· from short by setting the value of ·maxInclusive· to be 127 and ·minInclusive· to be -128. The ·base type· of byte is short.

byte has a lexical representation consisting of an optional sign followed by a non-empty finite-length sequence of decimal digits (#x30-#x39).  If the sign is omitted, "+" is assumed. For example: -1, 0, 126, +100.

[Definition:]   nonNegativeInteger is ·derived· from integer by setting the value of ·minInclusive· to be 0.  This results in the standard mathematical concept of the non-negative integers. The ·value space· of nonNegativeInteger is the infinite set {0,1,2,...}.  The ·base type· of nonNegativeInteger is integer.

nonNegativeInteger has a lexical representation consisting of an optional sign followed by a non-empty finite-length sequence of decimal digits (#x30-#x39).  If the sign is omitted, the positive sign ('+') is assumed. If the sign is present, it must be "+" except for lexical forms denoting zero, which may be preceded by a positive ('+') or a negative ('-') sign. For example: 1, 0, 12678967543233, +100000.

[Definition:]   unsignedLong is ·derived· from nonNegativeInteger by setting the value of ·maxInclusive· to be 18446744073709551615.  The ·base type· of unsignedLong is nonNegativeInteger.

unsignedLong has a lexical representation consisting of an optional sign followed by a non-empty finite-length sequence of decimal digits (#x30-#x39).  If the sign is omitted, the positive sign ('+') is assumed.  If the sign is present, it must be '+' except for lexical forms denoting zero, which may be preceded by a positive ('+') or a negative ('-') sign. For example: 0, 12678967543233, 100000.

[Definition:]   unsignedInt is ·derived· from unsignedLong by setting the value of ·maxInclusive· to be 4294967295.  The ·base type· of unsignedInt is unsignedLong.

unsignedInt has a lexical representation consisting of an optional sign followed by a non-empty finite-length sequence of decimal digits (#x30-#x39).  If the sign is omitted, the positive sign ('+') is assumed.  If the sign is present, it must be '+' except for lexical forms denoting zero, which may be preceded by a positive ('+') or a negative ('-') sign. For example: 0, 1267896754, 100000.

[Definition:]   unsignedShort is ·derived· from unsignedInt by setting the value of ·maxInclusive· to be 65535.  The ·base type· of unsignedShort is unsignedInt.

unsignedShort has a lexical representation consisting of an optional sign followed by a non-empty finite-length sequence of decimal digits (#x30-#x39). If the sign is omitted, the positive sign ('+') is assumed.  If the sign is present, it must be '+' except for lexical forms denoting zero, which may be preceded by a positive ('+') or a negative ('-') sign.  For example: 0, 12678, 10000.

[Definition:]   unsignedByte is ·derived· from unsignedShort by setting the value of ·maxInclusive· to be 255.  The ·base type· of unsignedByte is unsignedShort.

unsignedByte has a lexical representation consisting of an optional sign followed by a non-empty finite-length sequence of decimal digits (#x30-#x39). If the sign is omitted, the positive sign ('+') is assumed.  If the sign is present, it must be '+' except for lexical forms denoting zero, which may be preceded by a positive ('+') or a negative ('-') sign.  For example: 0, 126, 100.

[Definition:]   positiveInteger is ·derived· from nonNegativeInteger by setting the value of ·minInclusive· to be 1.  This results in the standard mathematical concept of the positive integer numbers.  The ·value space· of positiveInteger is the infinite set {1,2,...}.  The ·base type· of positiveInteger is nonNegativeInteger.

positiveInteger has a lexical representation consisting of an optional positive sign ('+') followed by a non-empty finite-length sequence of decimal digits (#x30-#x39), at least one of which must be a digit other than '0'.  For example: 1, 12678967543233, +100000.

The preceding sections of this specification have described datatypes in a way largely independent of their use in the particular context of schema-aware processing as defined in [XSD 1.1 Part 1: Structures].

This section presents the mechanisms necessary to integrate datatypes into the context of [XSD 1.1 Part 1: Structures], mostly in terms of the schema component abstraction introduced there. The account of datatypes given in this specification is also intended to be useful in other contexts. Any specification or other formal system intending to use datatypes as defined above, particularly if definition of new datatypes via facet-based restriction is envisaged, will need to provide analogous mechanisms for some, but not necessarily all, of what follows below. For example, the {target namespace} and {final} properties are required because of particular aspects of [XSD 1.1 Part 1: Structures] which are not in principle necessary for the use of datatypes as defined here.

The following sections provide full details on the properties and significance of each kind of schema component involved in datatype definitions. For each property, the kinds of values it is allowed to have is specified.  Any property not identified as optional is required to be present; optional properties which are not present have absent as their value. Any property identified as a having a set, subset or ·list· value may have an empty value unless this is explicitly ruled out: this is not the same as absent. Any property value identified as a superset or a subset of some set may be equal to that set, unless a proper superset or subset is explicitly called for.

For more information on the notion of schema components, see Schema Component Details of [XSD 1.1 Part 1: Structures].

[Definition:]  A component may be referred to as the owner of its properties, and of the values of those properties.

Simple Type Definitions provide for:

• In the case of

  ·primitive·

  datatypes, identifying a datatype with its definition in this specification.

• In the case of

  ·constructed·

  datatypes, defining the datatype in terms of other datatypes.

• Attaching a

  QName

  to the datatype.

The Simple Type Definition schema component has the following properties:

{name}

An xs:NCName value. Optional.

{target namespace}

An xs:anyURI value. Optional.

{final}

A subset of {restriction, extension, list, union}

{primitive type definition}

{item type definition}

A

component. Required if

is

, otherwise

be

.

The value of this property must be a primitive or ordinary simple type definition with {variety} = atomic, or an ordinary simple type definition with {variety} = union whose basic members are all atomic; the value must not itself be a list type (have {variety} = list) or have any basic members which are list types.

{member type definitions}

A sequence of primitive or ordinary

components.

Must be present (but may be empty) if {variety} is union, otherwise must be absent.

The sequence may contain any primitive or ordinary simple type definition, but must not contain any special type definitions.

Simple type definitions are identified by their {name} and {target namespace}.  Except for anonymous Simple Type Definitions (those with no {name}), Simple Type Definitions must be uniquely identified within a schema. Within a valid schema, each Simple Type Definition uniquely determines one datatype. The ·value space·, ·lexical space·, ·lexical mapping·, etc., of a Simple Type Definition are the ·value space·, ·lexical space·, etc., of the datatype uniquely determined (or "defined") by that Simple Type Definition.

If {variety} is ·atomic· then the ·value space· of the datatype defined will be a subset of the ·value space· of {base type definition} (which is a subset of the ·value space· of {primitive type definition}). If {variety} is ·list· then the ·value space· of the datatype defined will be the set of (possibly empty) finite-length sequences of values from the ·value space· of {item type definition}. If {variety} is ·union· then the ·value space· of the datatype defined will be a subset (possibly an improper subset) of the union of the ·value spaces· of each Simple Type Definition in {member type definitions}.

If {variety} is ·atomic· then the {variety} of {base type definition} must be ·atomic·, unless the {base type definition} is anySimpleType. If {variety} is ·list· then the {variety} of {item type definition} must be either ·atomic· or ·union·, and if {item type definition} is ·union· then all its ·basic members· must be ·atomic·. If {variety} is ·union· then {member type definitions} must be a list of Simple Type Definitions.

The {facets} property determines the ·value space· and ·lexical space· of the datatype being defined by imposing constraints which are to be satisfied by all valid values and ·lexical representations·.

The {fundamental facets} property provides some basic information about the datatype being defined: its cardinality, whether an ordering is defined for it by this specification, whether it has upper and lower bounds, and whether it is numeric.

If {final} is the empty set then the type can be used in deriving other types; the explicit values restriction, list and union prevent further derivations of Simple Type Definitions by ·facet-based restriction·, ·list· and ·union· respectively; the explicit value extension prevents any derivation of Complex Type Definitions by extension.

The {context} property is only relevant for anonymous type definitions, for which its value is the component in which this type definition appears as the value of a property, e.g. {item type definition} or {base type definition}.

The XML representation for a Simple Type Definition schema component is a <simpleType> element information item. The correspondences between the properties of the information item and properties of the component are as follows:

Property

Representation

The appropriate

among the following:

A subset of

,

,

,

, determined as follows.

Then the property value is the appropriate

among the following:

1

is the empty string,

the empty set;

2

is '

',

,

,

,

;

3

Consider

as a space-separated list, and include

if '

' is in that list, and similarly for

,

and

.

The appropriate

among the following:

2

the appropriate

among the following:

2.4

(the parent element information item is

), the appropriate

among the following:

The appropriate

among the following:

3 otherwise the empty set

If the

is

, the following additional property mapping also applies:

Property

Representation

An electronic commerce schema might define a datatype called '

' (the barcode number that appears on products) from the

datatype

by supplying a value for the

facet.

<simpleType name='SKU'>
    <restriction base='string'>
      <pattern value='\d{3}-[A-Z]{2}'/>
    </restriction>
</simpleType>

If the

is

, the following additional property mappings also apply:

Property

Representation

The appropriate

among the following:

A system might want to store lists of floating point values.

<simpleType name='listOfFloat'>
  <list itemType='float'/>
</simpleType>

If the

is

, the following additional property mappings also apply:

Property

Representation

The appropriate

among the following:

As an example, taken from a typical display oriented text markup language, one might want to express font sizes as an integer between 8 and 72, or with one of the tokens "small", "medium" or "large". The

below would accomplish that.

<xs:attribute name="size">
  <xs:simpleType>
    <xs:union>
      <xs:simpleType>
        <xs:restriction base="xs:positiveInteger">
          <xs:minInclusive value="8"/>
          <xs:maxInclusive value="72"/>
        </xs:restriction>
      </xs:simpleType>
      <xs:simpleType>
        <xs:restriction base="xs:NMTOKEN">
          <xs:enumeration value="small"/>
          <xs:enumeration value="medium"/>
          <xs:enumeration value="large"/>
        </xs:restriction>
      </xs:simpleType>
    </xs:union>
  </xs:simpleType>
</xs:attribute>

<p>
<font size='large'>A header</font>
</p>
<p>
<font size='12'>this is a test</font>
</p>

A datatype can be ·constructed· from a ·primitive· datatype or an ·ordinary· datatype by one of three means: by ·facet-based restriction·, by ·list· or by ·union·.

Either the

of the

element

be non-empty or there

be at least one

.

Since every value in the

is denoted by some

, and every

in the

maps to some value, the requirement that the

be in the

entails the requirement that the value it maps to should fulfill all of the constraints imposed by the

of the datatype. If the datatype is a

, the Datatype Valid constraint also entails that each whitespace-delimited token in the list be datatype-valid against the

of the list. If the datatype is a

, the Datatype Valid constraint entails that the

be datatype-valid against at least one of the

.

That is, the constraints on

s and on datatype

defined in this specification have as a consequence that a

is datatype-valid with respect to a

if and only if either

corresponds to a

datatype or

of the following are true:

2

The appropriate case among the following is true:

2.2

Note that

facets and other

facets do not take part in checking Datatype Valid. In cases where this specification is used in conjunction with schema-validation of XML documents, such facets are used to normalize infoset values

the normalized results are checked for datatype validity. In the case of unions the

facets to use are those associated with

in clause

above. When more than one

facet applies, the

facet is applied first; the order in which

facets are applied is

.

If {variety} is absent, then no facets are applicable. (This is true for anySimpleType.)

If {variety} is list, then the applicable facets are assertions, length, minLength, maxLength, pattern, enumeration, and whiteSpace.

If {variety} is union, then the applicable facets are pattern, enumeration, and assertions.

If {variety} is atomic, and {primitive type definition} is absent then no facets are applicable. (This is true for anyAtomicType.)

In all other cases ({variety} is atomic and {primitive type definition} is not absent), then the applicable facets are shown in the table below.

The Simple Type Definition of anySimpleType is present in every schema.  It has the following properties:

'http://www.w3.org/2001/XMLSchema'

The definition of anySimpleType is the root of the Simple Type Definition hierarchy; as such it mediates between the other simple type definitions, which all eventually trace back to it via their {base type definition} properties, and the definition of anyType, which is its {base type definition}.

The Simple Type Definition of anyAtomicType is present in every schema.  It has the following properties:

'http://www.w3.org/2001/XMLSchema'

Simple type definitions for all the built-in primitive datatypes, namely string, boolean, float, double, decimal, dateTime, duration, time, date, gMonth, gMonthDay, gDay, gYear, gYearMonth, hexBinary, base64Binary, anyURI are present by definition in every schema.  All have a very similar structure, with only the {name}, the {primitive type definition} (which is self-referential), the {fundamental facets}, and in one case the {facets} varying from one to the next:

'http://www.w3.org/2001/XMLSchema'

datatypes will normally have a value other than '

' for the

property. That namespace is controlled by the W3C and datatypes will be added to it only by W3C or its designees.

Similarly, Simple Type Definitions for all the built-in ·ordinary· datatypes are present by definition in every schema, with properties as specified in Other Built-in Datatypes (§3.4) and as represented in XML in Illustrative XML representations for the built-in ordinary type definitions (§C.2).

'http://www.w3.org/2001/XMLSchema'

[Definition:]   Each fundamental facet is a schema component that provides a limited piece of information about some aspect of each datatype.  All ·fundamental facet· components are defined in this section.  For example, cardinality is a ·fundamental facet·.  Most ·fundamental facets· are given a value fixed with each primitive datatype's definition, and this value is not changed by subsequent ·derivations· (even when it would perhaps be reasonable to expect an application to give a more accurate value based on the constraining facets used to define the ·derivation·).  The cardinality and bounded facets are exceptions to this rule; their values may change as a result of certain ·derivations·.

Schema components are identified by kind. "Fundamental" is not a kind of component. Each kind of

("ordered", "bounded", etc.) is a separate kind of schema component.

A ·fundamental facet· can occur only in the {fundamental facets} of a Simple Type Definition, and this is the only place where ·fundamental facet· components occur.    Each kind of ·fundamental facet· component occurs (once) in each Simple Type Definition's {fundamental facets} set.

The value of any

component can always be calculated from other properties of its

. Fundamental facets are not required for schema processing, but some applications use them.

For some datatypes, this document specifies an order relation for their value spaces (see Order (§2.2.3)); the ordered facet reflects this. It takes the values total, partial, and false, with the meanings described below. For the ·primitive· datatypes, the value of the ordered facet is specified in Fundamental Facets (§F.1). For ·ordinary· datatypes, the value is inherited without change from the ·base type·. For a ·list·, the value is always false; for a ·union·, the value is computed as described below.

A false value means no order is prescribed; a total value assures that the prescribed order is a total order; a partial value means that the prescribed order is a partial order, but not (for the primitive type in question) a total order.

Note: The value false in the ordered facet does not mean no partial or total ordering exists for the value space, only that none is specified by this document for use in checking upper and lower bounds. Mathematically, any set of values possesses at least one trivial partial ordering, in which every value pair that is not equal is incomparable.

When new datatypes are derived from datatypes with partial orders, the constraints imposed can sometimes result in a value space for which the ordering is total, or trivial. The value of the

facet is not, however, changed to reflect this. The value

should therefore be interpreted with appropriate caution.

[Definition:]  A ·value space·, and hence a datatype, is said to be ordered if some members of the ·value space· are drawn from a ·primitive· datatype for which the table in Fundamental Facets (§F.1) specifies the value total or partial for the ordered facet.

Some of the "real-world" datatypes which are the basis for those defined herein are ordered in some applications, even though no order is prescribed for schema-processing purposes. For example,

is sometimes ordered, and

and

datatypes

from ordered

datatypes are sometimes given "lexical" orderings. They are

ordered for schema-processing purposes.

{value}

One of {false, partial, total}. Required.

Some ordered datatypes have the property that there is one value greater than or equal to every other value, and another that is less than or equal to every other value.  (In the case of ·ordinary· datatypes, these two values are not necessarily in the value space of the derived datatype, but they will always be in the value space of the primitive datatype from which they have been derived.) The bounded facet value is boolean and is generally true for such bounded datatypes.  However, it will remain false when the mechanism for imposing such a bound is difficult to detect, as, for example, when the boundedness occurs because of derivation using a pattern component.

Every value space has a specific number of members.  This number can be characterized as finite or infinite.  (Currently there are no datatypes with infinite value spaces larger than countable.)  The cardinality facet value is either finite or countably infinite and is generally finite for datatypes with finite value spaces.  However, it will remain countably infinite when the mechanism for causing finiteness is difficult to detect, as, for example, when finiteness occurs because of a derivation using a pattern component.

Some value spaces are made up of things that are conceptually numeric, others are not. The numeric facet value indicates which are considered numeric.

[Definition:]  Constraining facets are schema components whose values may be set or changed during ·derivation· (subject to facet-specific controls) to control various aspects of the derived datatype.  All ·constraining facet· components defined by this specification are defined in this section.  For example, whiteSpace is a ·constraining facet·.  ·Constraining Facets· are given a value as part of the ·derivation· when an ·ordinary· datatype is defined by ·restricting· a ·primitive· or ·ordinary· datatype; a few ·constraining facets· have default values that are also provided for ·primitive· datatypes.

Schema components are identified by kind. "Constraining" is not a kind of component. Each kind of

("whiteSpace", "length", etc.) is a separate kind of schema component.

This specification distinguishes three kinds of constraining facets:

• [Definition:]  A constraining facet which is used to normalize an initial ·literal· before checking to see whether the resulting character sequence is a member of a datatype's ·lexical space· is a pre-lexical facet.

• Most of the constraining facets defined by this specification are

  ·value-based·

  facets.

Conforming processors must support all the facets defined in this section. It is ·implementation-defined· whether a processor supports other constraining facets. [Definition:]  An ·constraining facet· which is not supported by the processor in use is unknown.

A reference to an

facet might be a reference to an

facet supported by some other processor, or might be the result of a typographic error, or might have some other explanation.

The descriptions of individual facets given below include both constraints on Simple Type Definition components and rules for checking the datatype validity of a given literal against a given datatype. The validation rules typically depend upon having a full knowledge of the datatype; full knowledge of the datatype, in turn, depends on having a fully instantiated Simple Type Definition. A full instantiation of the Simple Type Definition, and the checking of the component constraints, require knowledge of the ·base type·. It follows that if a datatype's ·base type· is ·unknown·, the Simple Type Definition defining the datatype will be incompletely instantiated, and the datatype itself will be ·unknown·. Similarly, any datatype defined using an ·unknown· ·constraining facet· will be ·unknown·. It is not possible to perform datatype validation as defined here using ·unknown· datatypes.

The preceding paragraph does not forbid implementations from attempting to make use of such partial information as they have about

datatypes. But the exploitation of such partial knowledge is not datatype validity checking as defined here and is to be distinguished from it in the implementation's documentation and interface.

[Definition:]   length is the number of units of length, where units of length varies depending on the type that is being ·derived· from. The value of length must be a nonNegativeInteger.

For string and datatypes ·derived· from string, length is measured in units of characters as defined in [XML]. For anyURI, length is measured in units of characters (as for string). For hexBinary and base64Binary and datatypes ·derived· from them, length is measured in octets (8 bits) of binary data. For datatypes ·constructed· by ·list·, length is measured in number of list items.

For

and datatypes

from

,

will not always coincide with "string length" as perceived by some users or with the number of storage units in some digital representation. Therefore, care should be taken when specifying a value for

and in attempting to infer storage requirements from a given value for

.

·length· provides for:

The following is the definition of a

datatype to represent product codes which must be exactly 8 characters in length. By fixing the value of the

facet we ensure that types derived from productCode can change or set the values of other facets, such as

, but cannot change the length.

<simpleType name='productCode'>
   <restriction base='string'>
     <length value='8' fixed='true'/>
   </restriction>
</simpleType>

{value}

An xs:nonNegativeInteger value. Required.

{fixed}

An xs:boolean value. Required.

If {fixed} is true, then types for which the current type is the {base type definition} cannot specify a value for length other than {value}.

The

property is defined for parallelism with other facets and for compatibility with version 1.0 of this specification. But it is a consequence of

that the value of the

facet cannot be changed, regardless of whether

is

or

.

The XML representation for a length schema component is a <length> element information item. The correspondences between the properties of the information item and properties of the component are as follows:

The use of ·length· on QName, NOTATION, and datatypes ·derived· from them is deprecated.  Future versions of this specification may remove this facet for these datatypes.

If

is a member of

then

2

It is an error for

to be a member of

unless

2.2

[Definition:]   minLength is the minimum number of units of length, where units of length varies depending on the type that is being ·derived· from. The value of minLength  must be a nonNegativeInteger.

For string and datatypes ·derived· from string, minLength is measured in units of characters as defined in [XML]. For hexBinary and base64Binary and datatypes ·derived· from them, minLength is measured in octets (8 bits) of binary data. For datatypes ·constructed· by ·list·, minLength is measured in number of list items.

For

and datatypes

from

,

will not always coincide with "string length" as perceived by some users or with the number of storage units in some digital representation. Therefore, care should be taken when specifying a value for

and in attempting to infer storage requirements from a given value for

.

·minLength· provides for:

The following is the definition of a

datatype which requires strings to have at least one character (i.e., the empty string is not in the

of this datatype).

<simpleType name='non-empty-string'>
  <restriction base='string'>
    <minLength value='1'/>
  </restriction>
</simpleType>

{value}

An xs:nonNegativeInteger value. Required.

{fixed}

An xs:boolean value. Required.

If {fixed} is true, then types for which the current type is the {base type definition} cannot specify a value for minLength other than {value}.

The XML representation for a minLength schema component is a <minLength> element information item. The correspondences between the properties of the information item and properties of the component are as follows:

The use of ·minLength· on QName, NOTATION, and datatypes ·derived· from them is deprecated.  Future versions of this specification may remove this facet for these datatypes.

[Definition:]   maxLength is the maximum number of units of length, where units of length varies depending on the type that is being ·derived· from. The value of maxLength  must be a nonNegativeInteger.

For string and datatypes ·derived· from string, maxLength is measured in units of characters as defined in [XML]. For hexBinary and base64Binary and datatypes ·derived· from them, maxLength is measured in octets (8 bits) of binary data. For datatypes ·constructed· by ·list·, maxLength is measured in number of list items.

For

and datatypes

from

,

will not always coincide with "string length" as perceived by some users or with the number of storage units in some digital representation. Therefore, care should be taken when specifying a value for

and in attempting to infer storage requirements from a given value for

.

·maxLength· provides for:

The following is the definition of a

datatype which might be used to accept form input with an upper limit to the number of characters that are acceptable.

<simpleType name='form-input'>
  <restriction base='string'>
    <maxLength value='50'/>
  </restriction>
</simpleType>

{value}

An xs:nonNegativeInteger value. Required.

{fixed}

An xs:boolean value. Required.

If {fixed} is true, then types for which the current type is the {base type definition} cannot specify a value for maxLength other than {value}.

The XML representation for a maxLength schema component is a <maxLength> element information item. The correspondences between the properties of the information item and properties of the component are as follows:

The use of ·maxLength· on QName, NOTATION, and datatypes ·derived· from them is deprecated.  Future versions of this specification may remove this facet for these datatypes.

[Definition:]   pattern is a constraint on the ·value space· of a datatype which is achieved by constraining the ·lexical space· to ·literals· which match each member of a set of ·regular expressions·.  The value of pattern  must be a set of ·regular expressions·.

·pattern· provides for:

The following is the definition of a

datatype which is a better representation of postal codes in the United States, by limiting strings to those which are matched by a specific

.

<simpleType name='better-us-zipcode'>
  <restriction base='string'>
    <pattern value='[0-9]{5}(-[0-9]{4})?'/>
  </restriction>
</simpleType>

The XML representation for a pattern schema component is one or more <pattern> element information items. The correspondences between the properties of the information item and properties of the component are as follows:

Property

Representation

the appropriate

among the following:

The value is then given by the appropriate

among the following:

The

property will only have more than one member when

involves a

facet at more than one step in a type derivation. During validation, lexical forms will be checked against every member of the resulting

, effectively creating a conjunction of patterns.

In summary,

facets specified on the

step in a type derivation are

ed together, while

facets specified on

steps of a type derivation are

ed together.

Thus, to impose two

constraints simultaneously, schema authors may either write a single

which expresses the intersection of the two

s they wish to impose, or define each

on a separate type derivation step.

As noted in

, certain uses of the

facet may eliminate from the lexical space the canonical forms of some values in the value space; this can be inconvenient for applications which write out the canonical form of a value and rely on being able to read it in again as a legal lexical form. This specification provides no recourse in such situations; applications are free to deal with it as they see fit. Caution is advised.

For components constructed from XML representations in schema documents, the satisfaction of this constraint is a consequence of the XML mapping rules: any pattern imposed by a simple type definition

will always also be imposed by any type derived from

by

. This constraint ensures that components constructed by other means (so-called "born-binary" components) similarly preserve

facets across

.

[Definition:]   enumeration constrains the ·value space· to a specified set of values.

enumeration does not impose an order relation on the ·value space· it creates; the value of the ·ordered· property of the ·derived· datatype remains that of the datatype from which it is ·derived·.

·enumeration· provides for:

<simpleType name='holidays'>
    <annotation>
        <documentation>some US holidays</documentation>
    </annotation>
    <restriction base='gMonthDay'>
      <enumeration value='--01-01'>
        <annotation>
            <documentation>New Year's day</documentation>
        </annotation>
      </enumeration>
      <enumeration value='--07-04'>
        <annotation>
            <documentation>4th of July</documentation>
        </annotation>
      </enumeration>
      <enumeration value='--12-25'>
        <annotation>
            <documentation>Christmas</documentation>
        </annotation>
      </enumeration>
    </restriction>
</simpleType>

The XML representation for an enumeration schema component is one or more <enumeration> element information items. The correspondences between the properties of the information item and properties of the component are as follows:

Property

Representation

The appropriate

among the following:

Note: As specified normatively elsewhere, for purposes of checking enumerations, no distinction is made between an atomic value V and a list of length one containing V as its only item.

[Definition:]   whiteSpace constrains the ·value space· of types ·derived· from string such that the various behaviors specified in Attribute Value Normalization in [XML] are realized.  The value of whiteSpace must be one of {preserve, replace, collapse}.

preserve

No normalization is done, the value is not changed (this is the behavior required by

for element content)

replace

All occurrences of #x9 (tab), #xA (line feed) and #xD (carriage return) are replaced with #x20 (space)

collapse

After the processing implied by replace, contiguous sequences of #x20's are collapsed to a single #x20, and any #x20 at the start or end of the string is then removed.

The notation #xA used here (and elsewhere in this specification) represents the Universal Character Set (UCS) code point

(line feed), which is denoted by U+000A. This notation is to be distinguished from

, which is the XML

to that same UCS code point.

whiteSpace is applicable to all ·atomic· and ·list· datatypes.  For all ·atomic· datatypes other than string (and types ·derived· by ·facet-based restriction· from it) the value of whiteSpace is collapse and cannot be changed by a schema author; for string the value of whiteSpace is preserve; for any type ·derived· by ·facet-based restriction· from string the value of whiteSpace can be any of the three legal values (as long as the value is at least as restrictive as the value of the ·base type·; see Constraints on whiteSpace Schema Components (§4.3.6.4)).  For all datatypes ·constructed· by ·list· the value of whiteSpace is collapse and cannot be changed by a schema author.  For all datatypes ·constructed· by ·union·  whiteSpace does not apply directly; however, the normalization behavior of ·union· types is controlled by the value of whiteSpace on that one of the ·basic members· against which the ·union· is successfully validated.

·whiteSpace· provides for:

• Constraining a

  ·value space·

  according to the white space normalization rules.

<simpleType name='token'>
    <restriction base='normalizedString'>
      <whiteSpace value='collapse'/>
    </restriction>
</simpleType>

Note: The values "replace" and "collapse" may appear to provide a convenient way to "unwrap" text (i.e. undo the effects of pretty-printing and word-wrapping). In some cases, especially highly constrained data consisting of lists of artificial tokens such as part numbers or other identifiers, this appearance is correct. For natural-language data, however, the whitespace processing prescribed for these values is not only unreliable but will systematically remove the information needed to perform unwrapping correctly. For Asian scripts, for example, a correct unwrapping process will replace line boundaries not with blanks but with zero-width separators or nothing. In consequence, it is normally unwise to use these values for natural-language data, or for any data other than lists of highly constrained tokens.

{value}

One of {preserve, replace, collapse}. Required.

{fixed}

An xs:boolean value. Required.

If {fixed} is true, then types for which the current type is the {base type definition} cannot specify a value for whiteSpace other than {value}.

The XML representation for a whiteSpace schema component is a <whiteSpace> element information item. The correspondences between the properties of the information item and properties of the component are as follows:

fixed =

: false

id =

= (

|

|

)

>

(

?)

</whiteSpace>

Property

Representation

In order of increasing restrictiveness, the legal values for the

facet are

,

, and

. The more restrictive keywords are more restrictive not in the sense of accepting progressively fewer instance documents but in the sense that each corresponds to a progressively smaller, more tightly restricted value space.

[Definition:]   maxInclusive is the inclusive upper bound of the ·value space· for a datatype with the ·ordered· property.  The value of maxInclusive must be equal to some value in the ·value space· of the ·base type·.

·maxInclusive· provides for:

• Constraining a

  ·value space·

  to values with a specific inclusive upper bound.

The following is the definition of a

datatype which limits values to integers less than or equal to 100, using

.

<simpleType name='one-hundred-or-less'>
  <restriction base='integer'>
    <maxInclusive value='100'/>
  </restriction>
</simpleType>

The XML representation for a maxInclusive schema component is a <maxInclusive> element information item. The correspondences between the properties of the information item and properties of the component are as follows:

It is an

if any of the following conditions is true:

[Definition:]   maxExclusive is the exclusive upper bound of the ·value space· for a datatype with the ·ordered· property.  The value of maxExclusive  must be equal to some value in the ·value space· of the ·base type· or be equal to {value} in {base type definition}.

·maxExclusive· provides for:

• Constraining a

  ·value space·

  to values with a specific exclusive upper bound.

The following is the definition of a

datatype which limits values to integers less than or equal to 100, using

.

<simpleType name='less-than-one-hundred-and-one'>
  <restriction base='integer'>
    <maxExclusive value='101'/>
  </restriction>
</simpleType>

Note that the

of this datatype is identical to the previous one (named 'one-hundred-or-less').

The XML representation for a maxExclusive schema component is a <maxExclusive> element information item. The correspondences between the properties of the information item and properties of the component are as follows:

It is an

if any of the following conditions is true:

[Definition:]   minExclusive is the exclusive lower bound of the ·value space· for a datatype with the ·ordered· property. The value of minExclusive must be equal to some value in the ·value space· of the ·base type· or be equal to {value} in {base type definition}.

·minExclusive· provides for:

• Constraining a

  ·value space·

  to values with a specific exclusive lower bound.

The following is the definition of a

datatype which limits values to integers greater than or equal to 100, using

.

<simpleType name='more-than-ninety-nine'>
  <restriction base='integer'>
    <minExclusive value='99'/>
  </restriction>
</simpleType>

Note that the

of this datatype is identical to the following one (named 'one-hundred-or-more').

The XML representation for a minExclusive schema component is a <minExclusive> element information item. The correspondences between the properties of the information item and properties of the component are as follows:

It is an

if any of the following conditions is true:

[Definition:]   minInclusive is the inclusive lower bound of the ·value space· for a datatype with the ·ordered· property.  The value of minInclusive  must be equal to some value in the ·value space· of the ·base type·.

·minInclusive· provides for:

• Constraining a

  ·value space·

  to values with a specific inclusive lower bound.

The following is the definition of a

datatype which limits values to integers greater than or equal to 100, using

.

<simpleType name='one-hundred-or-more'>
  <restriction base='integer'>
    <minInclusive value='100'/>
  </restriction>
</simpleType>

The XML representation for a minInclusive schema component is a <minInclusive> element information item. The correspondences between the properties of the information item and properties of the component are as follows:

It is an

if any of the following conditions is true:

[Definition:]   totalDigits restricts the magnitude and arithmetic precision of values in the ·value spaces· of decimal and datatypes derived from it.

For decimal, if the {value} of totalDigits is t, the effect is to require that values be equal to i / 10ⁿ, for some integers i and n, with | i | < 10^t and 0 ≤ n ≤ t. This has as a consequence that the values are expressible using at most t digits in decimal notation.

The {value} of totalDigits must be a positiveInteger.

The term 'totalDigits' is chosen to reflect the fact that it restricts the ·value space· to those values that can be represented lexically using at most totalDigits digits in decimal notation, or at most totalDigits digits for the coefficient, in scientific notation.  Note that it does not restrict the ·lexical space· directly; a lexical representation that adds non-significant leading or trailing zero digits is still permitted. It also has no effect on the values NaN, INF, and -INF.

{value}

An xs:positiveInteger value. Required.

{fixed}

An xs:boolean value. Required.

If {fixed} is true, then types for which the current type is the {base type definition} must not specify a value for totalDigits other than {value}.

The XML representation for a totalDigits schema component is a <totalDigits> element information item. The correspondences between the properties of the information item and properties of the component are as follows:

A value

is facet-valid with respect to a

facet with a

of

if and only if

is a

value equal to

/ 10

, for some integers

and

, with |

| < 10

and 0 ≤

≤

.

[Definition:]   fractionDigits places an upper limit on the arithmetic precision of decimal values: if the {value} of fractionDigits = f, then the value space is restricted to values equal to i / 10ⁿ for some integers i and n and 0 ≤ n ≤ f. The value of fractionDigits must be a nonNegativeInteger

The term fractionDigits is chosen to reflect the fact that it restricts the ·value space· to those values that can be represented lexically in decimal notation using at most fractionDigits to the right of the decimal point. Note that it does not restrict the ·lexical space· directly; a lexical representation that adds non-significant leading or trailing zero digits is still permitted.

The following is the definition of a

datatype which could be used to represent the magnitude of a person's body temperature on the Celsius scale. This definition would appear in a schema authored by an "end-user" and shows how to define a datatype by specifying facet values which constrain the range of the

.

<simpleType name='celsiusBodyTemp'>
  <restriction base='decimal'>
    <fractionDigits value='1'/>
    <minInclusive value='32'/>
	 <maxInclusive value='41.7'/>
  </restriction>
</simpleType>

{value}

An xs:nonNegativeInteger value. Required.

{fixed}

An xs:boolean value. Required.

If {fixed} is true, then types for which the current type is the {base type definition} must not specify a value for fractionDigits other than {value}.

The XML representation for a fractionDigits schema component is a <fractionDigits> element information item. The correspondences between the properties of the information item and properties of the component are as follows:

A value is facet-valid with respect to

if and only if that value is equal to

/ 10

for integer

and

, with 0 ≤

≤

.

[Definition:]   Assertions constrain the ·value space· by requiring the values to satisfy specified XPath ([XPath 2.0]) expressions. The value of the assertions facet is a sequence of Assertion components as defined in [XSD 1.1 Part 1: Structures].

The following is the definition of a ·user-defined· datatype which allows all integers but 0 by using an assertion to disallow the value 0.

<simpleType name='nonZeroInteger'>
  <restriction base='integer'>
    <assertion test='$value ne 0'/>
  </restriction>
</simpleType>

The following example defines the datatype "triple", whose ·value space· is the set of integers evenly divisible by three.

<simpleType name='triple'>
  <restriction base='integer'>
    <assertion test='$value mod 3 eq 0'/>
  </restriction>
</simpleType>

The same datatype can be defined without the use of assertions, but the pattern necessary to represent the set of triples is long and error-prone:

<simpleType name='triple'>
  <restriction base='integer'>
    <pattern value=
    "([0369]|[147][0369]*[258]|(([258]|[147][0369]*[147])([0369]|[258][0369]*[147])*([147]|[258][0369]*[258]))*"/>
  </restriction>
</simpleType>

The assertion used in the first version of "triple" is likely to be clearer for many readers of the schema document.

The XML representation for an assertions schema component is one or more <assertion> element information items. The correspondences between the properties of the information item and properties of the component are as follows:

id =

=

xpathDefaultNamespace = (

| (

|

|

))

>

(

?)

</assertion>

Property

Representation

A sequence whose members are

s drawn from the following sources, in order:

The empty sequence.

Annotations specified within an

element are captured by the individual

component to which it maps.

The following rule refers to "the nearest built-in" datatype and to the "XDM representation" of a value under a datatype. [Definition:]  For any datatype T, the nearest built-in datatype to T is the first ·built-in· datatype encountered in following the chain of links connecting each datatype to its ·base type·. If T is a ·built-in· datatype, then the nearest built-in datatype of T is T itself; otherwise, it is the nearest built-in datatype of T's ·base type·.

For any value

and any datatype

, the

is defined recursively as follows. Call the XDM representation

. Then

A value

is facet-valid with respect to an

facet belonging to a simple type

if and only if the {test} property of each

in its

evaluates to

under the conditions laid out below, without raising any

or

.

Evaluation of {test} is performed as defined in

, with the following conditions:

1

The XPath expression {test} is evaluated, following the rules given in

of

, with the following modifications.

1.1

Note: The XDM type label anyAtomicType* simply says that for static typing purposes the variable $value will have a value consisting of a sequence of zero or more atomic values.

1.2

As a consequence the expression '

', or any implicit or explicit reference to the context item, will raise a dynamic error, which will cause the assertion to be treated as false. If an error is detected statically, then the assertion violates the schema component constraint

and causes an error to be flagged in the schema.

The variable "$value" can be used to refer to the value being checked.

1.5

2

For components constructed from XML representations in schema documents, the satisfaction of this constraint is a consequence of the XML mapping rules: any assertion imposed by a simple type definition

will always also be imposed by any type derived from

by

. This constraint ensures that components constructed by other means (so-called "born-binary" components) similarly preserve

facets across

.

[Definition:]   explicitTimezone is a three-valued facet which can can be used to require or prohibit the time zone offset in date/time datatypes.

<simpleType name='bare-date'>
  <restriction base='date'>
    <explicitTimezone value='prohibited'/>
  </restriction>
</simpleType>

The same effect could also be achieved using the

facet, as shown below, but it is somewhat less clear what is going on in this derivation, and it is better practice to use the more straightforward

for this purpose.

<simpleType name='bare-date'>
  <restriction base='date'>
    <pattern value='[^:Z]*'/>
  </restriction>
</simpleType>

{value}

One of {required, prohibited, optional}. Required.

{fixed}

An xs:boolean value. Required.

If {fixed} is true, then datatypes for which the current type is the {base type definition} cannot specify a value for explicitTimezone other than {value}.

The XML representation for an explicitTimezone schema component is an <explicitTimezone> element information item. The correspondences between the properties of the information item and properties of the component are as follows:

The effect of this rule is to allow datatypes with a

value of

to be restricted by specifying a value of

or

, and to forbid any other derivations using this facet.

XSD 1.1: Datatypes is intended to be usable in a variety of contexts.

In the usual case, it will embedded in a host language such as [XSD 1.1 Part 1: Structures], which refers to this specification normatively to define some part of the host language. In some cases, XSD 1.1: Datatypes may be implemented independently of any host language.

When XSD 1.1: Datatypes is embedded in a host language, the definition of conformance is specified by the host language, not by this specification. That is, when this specification is implemented in the context of an implementation of a host language, the question of conformance to this specification (separate from the host language) does not arise.

This specification imposes certain constraints on the embedding of XSD 1.1: Datatypes by a host language; these are indicated in the normative text by the use of the verbs 'must', etc., with the phrase "host language" as the subject of the verb.

For convenience, the most important of these constraints are noted here:

• Host languages should specify that all of the datatypes described here as built-ins are automatically available.

• Host languages may specify that additional datatypes are also made available automatically.

• If user-defined datatypes are to be supported in the host language, then the host language must specify how user-defined datatypes are defined and made available for use.

In addition, host languages must require conforming implementations of the host language to obey all of the constraints and rules specified here.

Implementations claiming

to this specification independent of any host language

do

of the following:

1

3

Implementations claiming

to this specification, independent of any host language

be minimally conforming. In addition, they must do

of the following:

2

3

The term

is used here for parallelism with the corresponding term in

. The reference to schema documents may be taken as referring to the fact that schema-document-aware implementations accept the XML representation of simple type definitions found in XSD schema documents. It does

mean that the simple type definitions must themselves be free-standing XML documents, nor that they typically will be.

Abstract representations of simple type definitions conform to this specification if and only if they obey all of the ·constraints on schemas· defined in this specification.

XML representations of simple type definitions conform to this specification if they obey all of the applicable rules defined in this specification.

Because the conformance of the resulting simple type definition component depends not only on the XML representation of a given simple type definition, but on the properties of its

, the conformance of an XML representation of a simple type definition does not guarantee that, in the context of other schema components, it will map to a conforming component.

Some ·primitive· datatypes defined in this specification have infinite ·value spaces·; no finite implementation can completely handle all their possible values. For some such datatypes, minimum implementation limits are specified below. For other infinite types such as string, hexBinary, and base64Binary, no minimum implementation limits are specified.

When this specification is used in the context of other languages (as it is, for example, by [XSD 1.1 Part 1: Structures]), the host language may specify other minimum implementation limits.

When presented with a literal or value exceeding the capacity of its partial implementation of a datatype, a minimally conforming implementation of this specification will sometimes be unable to determine with certainty whether the value is datatype-valid or not. Sometimes it will be unable to represent the value correctly through its interface to any downstream application.

When either of these is so, a conforming processor must indicate to the user and/or downstream application that it cannot process the input data with assured correctness (much as it would indicate if it ran out of memory). When the datatype validity of a value or literal is uncertain because it exceeds the capacity of a partial implementation, the literal or value must not be treated as invalid, and the unsupported value must not be quietly changed to a supported value.

This specification does not constrain the method used to indicate that a literal or value in the input data has exceeded the capacity of the implementation, or the form such indications take.

·Minimally conforming· processors which set an application- or ·implementation-defined· limit on the size of the values supported must clearly document that limit.

These are the partial-implementation

requirements:

• All

  ·minimally conforming·

  processors

  must

  support

  decimal

  values whose absolute value can be expressed as

  i

  / 10

  ^k

  , where

  i

  and

  k

  are nonnegative integers such that

  i

  < 10

  ¹⁶

  and

  k

  ≤ 16 (i.e., those expressible with sixteen total digits).

• All

  ·minimally conforming·

  processors

  must

  support fractional-second

  duration

  values to milliseconds (i.e. those expressible with three fraction digits).

The XML representation of the datatypes-relevant part of the schema for schema documents is presented here as a normative part of the specification. Independent copies of this material are available in an undated (mutable) version at http://www.w3.org/2009/XMLSchema/datatypes.xsd and in a dated (immutable) version at http://www.w3.org/2012/04/datatypes.xsd — the mutable version will be updated with future revisions of this specification, and the immutable one will not.

Like any other XML document, schema documents may carry XML and document type declarations. An XML declaration and a document type declaration are provided here for convenience. Since this schema document describes the XML Schema language, the targetNamespace attribute on the schema element refers to the XML Schema namespace itself.

Schema documents conforming to this specification may be in XML 1.0 or XML 1.1. Conforming implementations may accept input in XML 1.0 or XML 1.1 or both. See Dependencies on Other Specifications (§1.3).

Schema for Schema Documents (Datatypes)

<?xml version='1.0'?>
<!DOCTYPE xs:schema PUBLIC "-//W3C//DTD XSD 1.1//EN" "XMLSchema.dtd" [

<!--
        Make sure that processors that do not read the external
        subset will know about the various IDs we declare
  -->
        <!ATTLIST xs:simpleType id ID #IMPLIED>
        <!ATTLIST xs:maxExclusive id ID #IMPLIED>
        <!ATTLIST xs:minExclusive id ID #IMPLIED>
        <!ATTLIST xs:maxInclusive id ID #IMPLIED>
        <!ATTLIST xs:minInclusive id ID #IMPLIED>
        <!ATTLIST xs:totalDigits id ID #IMPLIED>
        <!ATTLIST xs:fractionDigits id ID #IMPLIED>
        <!ATTLIST xs:length id ID #IMPLIED>
        <!ATTLIST xs:minLength id ID #IMPLIED>
        <!ATTLIST xs:maxLength id ID #IMPLIED>
        <!ATTLIST xs:enumeration id ID #IMPLIED>
        <!ATTLIST xs:pattern id ID #IMPLIED>
        <!ATTLIST xs:assertion id ID #IMPLIED>
        <!ATTLIST xs:explicitTimezone id ID #IMPLIED>
        <!ATTLIST xs:appinfo id ID #IMPLIED>
        <!ATTLIST xs:documentation id ID #IMPLIED>
        <!ATTLIST xs:list id ID #IMPLIED>
        <!ATTLIST xs:union id ID #IMPLIED>
        ]>

<xs:schema xmlns:xs="http://www.w3.org/2001/XMLSchema"
           elementFormDefault="qualified" 
           xml:lang="en"
           targetNamespace="http://www.w3.org/2001/XMLSchema"
           version="datatypes.xsd (rec-20120405)">
  <xs:annotation>
    <xs:documentation source="../datatypes/datatypes.html">
      The schema corresponding to this document is normative,
      with respect to the syntactic constraints it expresses in the
      XML Schema language.  The documentation (within 'documentation'
      elements) below, is not normative, but rather highlights important
      aspects of the W3C Recommendation of which this is a part.

      See below (at the bottom of this document) for information about
      the revision and namespace-versioning policy governing this
      schema document.
    </xs:documentation>
  </xs:annotation>


  <xs:simpleType name="derivationControl">
    <xs:annotation>
      <xs:documentation>
   A utility type, not for public use</xs:documentation>
    </xs:annotation>
    <xs:restriction base="xs:NMTOKEN">
      <xs:enumeration value="substitution"/>
      <xs:enumeration value="extension"/>
      <xs:enumeration value="restriction"/>
      <xs:enumeration value="list"/>
      <xs:enumeration value="union"/>
    </xs:restriction>
  </xs:simpleType>
  <xs:group name="simpleDerivation">
    <xs:choice>
      <xs:element ref="xs:restriction"/>
      <xs:element ref="xs:list"/>
      <xs:element ref="xs:union"/>
    </xs:choice>
  </xs:group>
  <xs:simpleType name="simpleDerivationSet">
    <xs:annotation>
      <xs:documentation>
   #all or (possibly empty) subset of {restriction, extension, union, list}
   </xs:documentation>
      <xs:documentation>
   A utility type, not for public use</xs:documentation>
    </xs:annotation>
    <xs:union>
      <xs:simpleType>
        <xs:restriction base="xs:token">
          <xs:enumeration value="#all"/>
        </xs:restriction>
      </xs:simpleType>
      <xs:simpleType>
        <xs:list>
          <xs:simpleType>
            <xs:restriction base="xs:derivationControl">
              <xs:enumeration value="list"/>
              <xs:enumeration value="union"/>
              <xs:enumeration value="restriction"/>
              <xs:enumeration value="extension"/>
            </xs:restriction>
          </xs:simpleType>
        </xs:list>
      </xs:simpleType>
    </xs:union>
  </xs:simpleType>
  <xs:complexType name="simpleType" abstract="true">
    <xs:complexContent>
      <xs:extension base="xs:annotated">
        <xs:group ref="xs:simpleDerivation"/>
        <xs:attribute name="final" type="xs:simpleDerivationSet"/>
        <xs:attribute name="name" type="xs:NCName">
          <xs:annotation>
            <xs:documentation>
              Can be restricted to required or forbidden
            </xs:documentation>
          </xs:annotation>
        </xs:attribute>
      </xs:extension>
    </xs:complexContent>
  </xs:complexType>
  <xs:complexType name="topLevelSimpleType">
    <xs:complexContent>
      <xs:restriction base="xs:simpleType">
        <xs:sequence>
          <xs:element ref="xs:annotation" minOccurs="0"/>
          <xs:group ref="xs:simpleDerivation"/>
        </xs:sequence>
        <xs:attribute name="name" type="xs:NCName" use="required">
          <xs:annotation>
            <xs:documentation>
              Required at the top level
            </xs:documentation>
          </xs:annotation>
        </xs:attribute>
        <xs:anyAttribute namespace="##other" processContents="lax"/>
      </xs:restriction>
    </xs:complexContent>
  </xs:complexType>
  <xs:complexType name="localSimpleType">
    <xs:complexContent>
      <xs:restriction base="xs:simpleType">
        <xs:sequence>
          <xs:element ref="xs:annotation" minOccurs="0"/>
          <xs:group ref="xs:simpleDerivation"/>
        </xs:sequence>
        <xs:attribute name="name" use="prohibited">
          <xs:annotation>
            <xs:documentation>
              Forbidden when nested
            </xs:documentation>
          </xs:annotation>
        </xs:attribute>
        <xs:attribute name="final" use="prohibited"/>
        <xs:anyAttribute namespace="##other" processContents="lax"/>
      </xs:restriction>
    </xs:complexContent>
  </xs:complexType>
  <xs:element name="simpleType" type="xs:topLevelSimpleType" id="simpleType">
    <xs:annotation>
      <xs:documentation
           source="http://www.w3.org/TR/xmlschema11-2/#element-simpleType"/>
    </xs:annotation>
  </xs:element>
  <xs:element name="facet" abstract="true">
    <xs:annotation>
      <xs:documentation>
        An abstract element, representing facets in general.
        The facets defined by this spec are substitutable for
        this element, and implementation-defined facets should
        also name this as a substitution-group head.
      </xs:documentation>
    </xs:annotation>
  </xs:element>
  <xs:group name="simpleRestrictionModel">
    <xs:sequence>
      <xs:element name="simpleType" type="xs:localSimpleType" minOccurs="0"/>
      <xs:choice minOccurs="0" 
          maxOccurs="unbounded">
        <xs:element ref="xs:facet"/>
        <xs:any processContents="lax"
            namespace="##other"/>
      </xs:choice>
    </xs:sequence>
  </xs:group>
  <xs:element name="restriction" id="restriction">
    <xs:complexType>
      <xs:annotation>
        <xs:documentation
             source="http://www.w3.org/TR/xmlschema11-2/#element-restriction">
          base attribute and simpleType child are mutually
          exclusive, but one or other is required
        </xs:documentation>
      </xs:annotation>
      <xs:complexContent>
        <xs:extension base="xs:annotated">
          <xs:group ref="xs:simpleRestrictionModel"/>
          <xs:attribute name="base" type="xs:QName" use="optional"/>
        </xs:extension>
      </xs:complexContent>
    </xs:complexType>
  </xs:element>
  <xs:element name="list" id="list">
    <xs:complexType>
      <xs:annotation>
        <xs:documentation
             source="http://www.w3.org/TR/xmlschema11-2/#element-list">
          itemType attribute and simpleType child are mutually
          exclusive, but one or other is required
        </xs:documentation>
      </xs:annotation>
      <xs:complexContent>
        <xs:extension base="xs:annotated">
          <xs:sequence>
            <xs:element name="simpleType" type="xs:localSimpleType"
                        minOccurs="0"/>
          </xs:sequence>
          <xs:attribute name="itemType" type="xs:QName" use="optional"/>
        </xs:extension>
      </xs:complexContent>
    </xs:complexType>
  </xs:element>
  <xs:element name="union" id="union">
    <xs:complexType>
      <xs:annotation>
        <xs:documentation
             source="http://www.w3.org/TR/xmlschema11-2/#element-union">
          memberTypes attribute must be non-empty or there must be
          at least one simpleType child
        </xs:documentation>
      </xs:annotation>
      <xs:complexContent>
        <xs:extension base="xs:annotated">
          <xs:sequence>
            <xs:element name="simpleType" type="xs:localSimpleType"
                        minOccurs="0" maxOccurs="unbounded"/>
          </xs:sequence>
          <xs:attribute name="memberTypes" use="optional">
            <xs:simpleType>
              <xs:list itemType="xs:QName"/>
            </xs:simpleType>
          </xs:attribute>
        </xs:extension>
      </xs:complexContent>
    </xs:complexType>
  </xs:element>
  <xs:complexType name="facet">
    <xs:complexContent>
      <xs:extension base="xs:annotated">
        <xs:attribute name="value" use="required"/>
        <xs:attribute name="fixed" type="xs:boolean" default="false"
                      use="optional"/>
      </xs:extension>
    </xs:complexContent>
  </xs:complexType>
  <xs:complexType name="noFixedFacet">
    <xs:complexContent>
      <xs:restriction base="xs:facet">
        <xs:sequence>
          <xs:element ref="xs:annotation" minOccurs="0"/>
        </xs:sequence>
        <xs:attribute name="fixed" use="prohibited"/>
        <xs:anyAttribute namespace="##other" processContents="lax"/>
      </xs:restriction>
    </xs:complexContent>
  </xs:complexType>
  <xs:element name="minExclusive" type="xs:facet"  
    id="minExclusive"
    substitutionGroup="xs:facet">
    <xs:annotation>
      <xs:documentation
           source="http://www.w3.org/TR/xmlschema11-2/#element-minExclusive"/>
    </xs:annotation>
  </xs:element>
  <xs:element name="minInclusive" type="xs:facet" 
    id="minInclusive"
    substitutionGroup="xs:facet">
    <xs:annotation>
      <xs:documentation
           source="http://www.w3.org/TR/xmlschema11-2/#element-minInclusive"/>
    </xs:annotation>
  </xs:element>
  <xs:element name="maxExclusive" type="xs:facet" 
    id="maxExclusive"
    substitutionGroup="xs:facet">
    <xs:annotation>
      <xs:documentation
           source="http://www.w3.org/TR/xmlschema11-2/#element-maxExclusive"/>
    </xs:annotation>
  </xs:element>
  <xs:element name="maxInclusive" type="xs:facet"  
    id="maxInclusive"
    substitutionGroup="xs:facet">
    <xs:annotation>
      <xs:documentation
           source="http://www.w3.org/TR/xmlschema11-2/#element-maxInclusive"/>
    </xs:annotation>
  </xs:element>
  <xs:complexType name="numFacet">
    <xs:complexContent>
      <xs:restriction base="xs:facet">
        <xs:sequence>
          <xs:element ref="xs:annotation" minOccurs="0"/>
        </xs:sequence>
        <xs:attribute name="value"  
            type="xs:nonNegativeInteger" use="required"/>
        <xs:anyAttribute namespace="##other" processContents="lax"/>
      </xs:restriction>
    </xs:complexContent>
  </xs:complexType>

  <xs:complexType name="intFacet">
    <xs:complexContent>
      <xs:restriction base="xs:facet">
        <xs:sequence>
          <xs:element ref="xs:annotation" minOccurs="0"/>
        </xs:sequence>
        <xs:attribute name="value" type="xs:integer" use="required"/>
        <xs:anyAttribute namespace="##other" processContents="lax"/>
      </xs:restriction>
    </xs:complexContent>
  </xs:complexType>

  <xs:element name="totalDigits" id="totalDigits"
    substitutionGroup="xs:facet">
    <xs:annotation>
      <xs:documentation
           source="http://www.w3.org/TR/xmlschema11-2/#element-totalDigits"/>
    </xs:annotation>
    <xs:complexType>
      <xs:complexContent>
        <xs:restriction base="xs:numFacet">
          <xs:sequence>
            <xs:element ref="xs:annotation" minOccurs="0"/>
          </xs:sequence>
          <xs:attribute name="value" type="xs:positiveInteger" use="required"/>
          <xs:anyAttribute namespace="##other" processContents="lax"/>
        </xs:restriction>
      </xs:complexContent>
    </xs:complexType>
  </xs:element>
  <xs:element name="fractionDigits" type="xs:numFacet"  
    id="fractionDigits"
    substitutionGroup="xs:facet">
    <xs:annotation>
      <xs:documentation
           source="http://www.w3.org/TR/xmlschema11-2/#element-fractionDigits"/>
    </xs:annotation>
  </xs:element>

  <xs:element name="length" type="xs:numFacet" id="length"
    substitutionGroup="xs:facet">
    <xs:annotation>
      <xs:documentation
           source="http://www.w3.org/TR/xmlschema11-2/#element-length"/>
    </xs:annotation>
  </xs:element>
  <xs:element name="minLength" type="xs:numFacet"  
    id="minLength"
    substitutionGroup="xs:facet">
    <xs:annotation>
      <xs:documentation
           source="http://www.w3.org/TR/xmlschema11-2/#element-minLength"/>
    </xs:annotation>
  </xs:element>
  <xs:element name="maxLength" type="xs:numFacet"  
    id="maxLength"
    substitutionGroup="xs:facet">
    <xs:annotation>
      <xs:documentation
           source="http://www.w3.org/TR/xmlschema11-2/#element-maxLength"/>
    </xs:annotation>
  </xs:element>
  <xs:element name="enumeration" type="xs:noFixedFacet"  
    id="enumeration"
    substitutionGroup="xs:facet">
    <xs:annotation>
      <xs:documentation
           source="http://www.w3.org/TR/xmlschema11-2/#element-enumeration"/>
    </xs:annotation>
  </xs:element>
  <xs:element name="whiteSpace" id="whiteSpace"
    substitutionGroup="xs:facet">
    <xs:annotation>
      <xs:documentation
           source="http://www.w3.org/TR/xmlschema11-2/#element-whiteSpace"/>
    </xs:annotation>
    <xs:complexType>
      <xs:complexContent>
        <xs:restriction base="xs:facet">
          <xs:sequence>
            <xs:element ref="xs:annotation" minOccurs="0"/>
          </xs:sequence>
          <xs:attribute name="value" use="required">
            <xs:simpleType>
              <xs:restriction base="xs:NMTOKEN">
                <xs:enumeration value="preserve"/>
                <xs:enumeration value="replace"/>
                <xs:enumeration value="collapse"/>
              </xs:restriction>
            </xs:simpleType>
          </xs:attribute>
          <xs:anyAttribute namespace="##other" processContents="lax"/>
        </xs:restriction>
      </xs:complexContent>
    </xs:complexType>
  </xs:element>
  <xs:element name="pattern" id="pattern"
    substitutionGroup="xs:facet">
    <xs:annotation>
      <xs:documentation
           source="http://www.w3.org/TR/xmlschema11-2/#element-pattern"/>
    </xs:annotation>
    <xs:complexType>
      <xs:complexContent>
        <xs:restriction base="xs:noFixedFacet">
          <xs:sequence>
            <xs:element ref="xs:annotation" minOccurs="0"/>
          </xs:sequence>
          <xs:attribute name="value" type="xs:string"  
              use="required"/>
          <xs:anyAttribute namespace="##other"  
              processContents="lax"/>
        </xs:restriction>
      </xs:complexContent>
    </xs:complexType>
  </xs:element>
  <xs:element name="assertion" type="xs:assertion"
              id="assertion" substitutionGroup="xs:facet">
    <xs:annotation>
      <xs:documentation
           source="http://www.w3.org/TR/xmlschema11-2/#element-assertion"/>
    </xs:annotation>
  </xs:element>
  <xs:element name="explicitTimezone" id="explicitTimezone"
    substitutionGroup="xs:facet">
    <xs:annotation>
      <xs:documentation
           source="http://www.w3.org/TR/xmlschema11-2/#element-explicitTimezone"/>
    </xs:annotation>
    <xs:complexType>
      <xs:complexContent>
        <xs:restriction base="xs:facet">
          <xs:sequence>
            <xs:element ref="xs:annotation" minOccurs="0"/>
          </xs:sequence>
          <xs:attribute name="value" use="required">
            <xs:simpleType>
              <xs:restriction base="xs:NMTOKEN">
                <xs:enumeration value="optional"/>
                <xs:enumeration value="required"/>
                <xs:enumeration value="prohibited"/>
              </xs:restriction>
            </xs:simpleType>
          </xs:attribute>
          <xs:anyAttribute namespace="##other" processContents="lax"/>
        </xs:restriction>
      </xs:complexContent>
    </xs:complexType>
  </xs:element>

  <xs:annotation>
    <xs:documentation>
      In keeping with the XML Schema WG's standard versioning policy, 
      this schema document will persist at the URI
      http://www.w3.org/2012/04/datatypes.xsd.

      At the date of issue it can also be found at the URI
      http://www.w3.org/2009/XMLSchema/datatypes.xsd.

      The schema document at that URI may however change in the future, 
      in order to remain compatible with the latest version of XSD 
      and its namespace.  In other words, if XSD or the XML Schema 
      namespace change, the version of this document at 
      http://www.w3.org/2009/XMLSchema/datatypes.xsd will change accordingly; 
      the version at http://www.w3.org/2012/04/datatypes.xsd will not change.

      Previous dated (and unchanging) versions of this schema document 
      include:

        http://www.w3.org/2012/01/datatypes.xsd
          (XSD 1.1 Proposed Recommendation)

        http://www.w3.org/2011/07/datatypes.xsd
          (XSD 1.1 Candidate Recommendation)

        http://www.w3.org/2009/04/datatypes.xsd
          (XSD 1.1 Candidate Recommendation)

        http://www.w3.org/2004/10/datatypes.xsd
          (XSD 1.0 Recommendation, Second Edition)

        http://www.w3.org/2001/05/datatypes.xsd
          (XSD 1.0 Recommendation, First Edition)

    </xs:documentation>
  </xs:annotation>



</xs:schema>

The DTD for the datatypes-specific aspects of schema documents is given below. Note there is no implication here that schema must be the root element of a document.

DTD for datatype definitions

<!--
        DTD for XML Schemas: Part 2: Datatypes
        
        Id: datatypes.dtd,v 1.1.2.4 2005/01/31 18:40:42 cmsmcq Exp 
        Note this DTD is NOT normative, or even definitive.
  -->

<!--
        This DTD cannot be used on its own, it is intended
        only for incorporation in XMLSchema.dtd, q.v.
  -->

<!-- Define all the element names, with optional prefix -->
<!ENTITY % simpleType "%p;simpleType">
<!ENTITY % restriction "%p;restriction">
<!ENTITY % list "%p;list">
<!ENTITY % union "%p;union">
<!ENTITY % maxExclusive "%p;maxExclusive">
<!ENTITY % minExclusive "%p;minExclusive">
<!ENTITY % maxInclusive "%p;maxInclusive">
<!ENTITY % minInclusive "%p;minInclusive">
<!ENTITY % totalDigits "%p;totalDigits">
<!ENTITY % fractionDigits "%p;fractionDigits">

<!ENTITY % length "%p;length">
<!ENTITY % minLength "%p;minLength">
<!ENTITY % maxLength "%p;maxLength">
<!ENTITY % enumeration "%p;enumeration">
<!ENTITY % whiteSpace "%p;whiteSpace">
<!ENTITY % pattern "%p;pattern">

<!ENTITY % assertion "%p;assertion">

<!ENTITY % explicitTimezone "%p;explicitTimezone">


<!--
        Customization entities for the ATTLIST of each element
        type. Define one of these if your schema takes advantage
        of the anyAttribute='##other' in the schema for schemas
  -->

<!ENTITY % simpleTypeAttrs "">
<!ENTITY % restrictionAttrs "">
<!ENTITY % listAttrs "">
<!ENTITY % unionAttrs "">
<!ENTITY % maxExclusiveAttrs "">
<!ENTITY % minExclusiveAttrs "">
<!ENTITY % maxInclusiveAttrs "">
<!ENTITY % minInclusiveAttrs "">
<!ENTITY % totalDigitsAttrs "">
<!ENTITY % fractionDigitsAttrs "">
<!ENTITY % lengthAttrs "">
<!ENTITY % minLengthAttrs "">
<!ENTITY % maxLengthAttrs "">

<!ENTITY % enumerationAttrs "">
<!ENTITY % whiteSpaceAttrs "">
<!ENTITY % patternAttrs "">
<!ENTITY % assertionAttrs "">
<!ENTITY % explicitTimezoneAttrs "">

<!-- Define some entities for informative use as attribute
        types -->
<!ENTITY % URIref "CDATA">
<!ENTITY % XPathExpr "CDATA">
<!ENTITY % QName "NMTOKEN">
<!ENTITY % QNames "NMTOKENS">
<!ENTITY % NCName "NMTOKEN">
<!ENTITY % nonNegativeInteger "NMTOKEN">
<!ENTITY % boolean "(true|false)">
<!ENTITY % simpleDerivationSet "CDATA">
<!--
        #all or space-separated list drawn from derivationChoice
  -->

<!--
        Note that the use of 'facet' below is less restrictive
        than is really intended:  There should in fact be no
        more than one of each of minInclusive, minExclusive,
        maxInclusive, maxExclusive, totalDigits, fractionDigits,
        length, maxLength, minLength within datatype,
        and the min- and max- variants of Inclusive and Exclusive
        are mutually exclusive. On the other hand,  pattern and
        enumeration and assertion may repeat.
  -->
<!ENTITY % minBound "(%minInclusive; | %minExclusive;)">
<!ENTITY % maxBound "(%maxInclusive; | %maxExclusive;)">
<!ENTITY % bounds "%minBound; | %maxBound;">
<!ENTITY % numeric "%totalDigits; | %fractionDigits;"> 
<!ENTITY % ordered "%bounds; | %numeric;">
<!ENTITY % unordered
   "%pattern; | %enumeration; | %whiteSpace; | %length; |
   %maxLength; | %minLength; | %assertion;
   | %explicitTimezone;">
<!ENTITY % implementation-defined-facets "">
<!ENTITY % facet "%ordered; | %unordered; %implementation-defined-facets;">
<!ENTITY % facetAttr 
        "value CDATA #REQUIRED
        id ID #IMPLIED">
<!ENTITY % fixedAttr "fixed %boolean; #IMPLIED">
<!ENTITY % facetModel "(%annotation;)?">
<!ELEMENT %simpleType;
        ((%annotation;)?, (%restriction; | %list; | %union;))>
<!ATTLIST %simpleType;
    name      %NCName; #IMPLIED
    final     %simpleDerivationSet; #IMPLIED
    id        ID       #IMPLIED
    %simpleTypeAttrs;>
<!-- name is required at top level -->
<!ELEMENT %restriction; ((%annotation;)?,
                         (%restriction1; |
                          ((%simpleType;)?,(%facet;)*)),
                         (%attrDecls;))>
<!ATTLIST %restriction;
    base      %QName;                  #IMPLIED
    id        ID       #IMPLIED
    %restrictionAttrs;>
<!--
        base and simpleType child are mutually exclusive,
        one is required.

        restriction is shared between simpleType and
        simpleContent and complexContent (in XMLSchema.xsd).
        restriction1 is for the latter cases, when this
        is restricting a complex type, as is attrDecls.
  -->
<!ELEMENT %list; ((%annotation;)?,(%simpleType;)?)>
<!ATTLIST %list;
    itemType      %QName;             #IMPLIED
    id        ID       #IMPLIED
    %listAttrs;>
<!--
        itemType and simpleType child are mutually exclusive,
        one is required
  -->
<!ELEMENT %union; ((%annotation;)?,(%simpleType;)*)>
<!ATTLIST %union;
    id            ID       #IMPLIED
    memberTypes   %QNames;            #IMPLIED
    %unionAttrs;>
<!--
        At least one item in memberTypes or one simpleType
        child is required
  -->

<!ELEMENT %maxExclusive; %facetModel;>
<!ATTLIST %maxExclusive;
        %facetAttr;
        %fixedAttr;
        %maxExclusiveAttrs;>
<!ELEMENT %minExclusive; %facetModel;>
<!ATTLIST %minExclusive;
        %facetAttr;
        %fixedAttr;
        %minExclusiveAttrs;>

<!ELEMENT %maxInclusive; %facetModel;>
<!ATTLIST %maxInclusive;
        %facetAttr;
        %fixedAttr;
        %maxInclusiveAttrs;>
<!ELEMENT %minInclusive; %facetModel;>
<!ATTLIST %minInclusive;
        %facetAttr;
        %fixedAttr;
        %minInclusiveAttrs;>

<!ELEMENT %totalDigits; %facetModel;>
<!ATTLIST %totalDigits;
        %facetAttr;
        %fixedAttr;
        %totalDigitsAttrs;>
<!ELEMENT %fractionDigits; %facetModel;>
<!ATTLIST %fractionDigits;
        %facetAttr;
        %fixedAttr;
        %fractionDigitsAttrs;>

<!ELEMENT %length; %facetModel;>
<!ATTLIST %length;
        %facetAttr;
        %fixedAttr;
        %lengthAttrs;>
<!ELEMENT %minLength; %facetModel;>
<!ATTLIST %minLength;
        %facetAttr;
        %fixedAttr;
        %minLengthAttrs;>
<!ELEMENT %maxLength; %facetModel;>
<!ATTLIST %maxLength;
        %facetAttr;
        %fixedAttr;
        %maxLengthAttrs;>

<!-- This one can be repeated -->
<!ELEMENT %enumeration; %facetModel;>
<!ATTLIST %enumeration;
        %facetAttr;
        %enumerationAttrs;>

<!ELEMENT %whiteSpace; %facetModel;>
<!ATTLIST %whiteSpace;
        %facetAttr;
        %fixedAttr;
        %whiteSpaceAttrs;>

<!-- This one can be repeated -->
<!ELEMENT %pattern; %facetModel;>
<!ATTLIST %pattern;
        %facetAttr;
        %patternAttrs;>

<!ELEMENT %assertion; %facetModel;>
<!ATTLIST %assertion;
        %facetAttr;
        %assertionAttrs;>

<!ELEMENT %explicitTimezone; %facetModel;>
<!ATTLIST %explicitTimezone;
        %facetAttr;
        %explicitTimezoneAttrs;>

The following, although in the form of a schema document, does not conform to the rules for schema documents defined in this specification. It contains explicit XML representations of the primitive datatypes which need not be declared in a schema document, since they are automatically included in every schema, and indeed must not be declared in a schema document, since it is forbidden to try to derive types with anyAtomicType as the base type definition. It is included here as a form of documentation.

The (not a) schema document for primitive built-in type definitions

<?xml version='1.0'?>
<!DOCTYPE xs:schema SYSTEM "../namespace/XMLSchema.dtd" [

<!--
     keep this schema XML1.0 DTD valid
  -->
        <!ENTITY % schemaAttrs 'xmlns:hfp CDATA #IMPLIED'>

        <!ELEMENT hfp:hasFacet EMPTY>
        <!ATTLIST hfp:hasFacet
                name NMTOKEN #REQUIRED>

        <!ELEMENT hfp:hasProperty EMPTY>
        <!ATTLIST hfp:hasProperty
                name NMTOKEN #REQUIRED
                value CDATA #REQUIRED>
]>
<xs:schema
  xmlns:hfp="http://www.w3.org/2001/XMLSchema-hasFacetAndProperty" 
  xmlns:xs="http://www.w3.org/2001/XMLSchema"
  elementFormDefault="qualified" 
  xml:lang="en" 
  targetNamespace="http://www.w3.org/2001/XMLSchema">

  <xs:annotation>
    <xs:documentation>
      This document contains XML elements which look like 
      definitions for the primitive datatypes.  These definitions are for
      information only; the real built-in definitions are magic.
    </xs:documentation>
    <xs:documentation>
      For each built-in datatype in this schema (both primitive and
      derived) can be uniquely addressed via a URI constructed
      as follows:
        1) the base URI is the URI of the XML Schema namespace
        2) the fragment identifier is the name of the datatype

      For example, to address the int datatype, the URI is:

        http://www.w3.org/2001/XMLSchema#int

      Additionally, each facet definition element can be uniquely
      addressed via a URI constructed as follows:
        1) the base URI is the URI of the XML Schema namespace
        2) the fragment identifier is the name of the facet

      For example, to address the maxInclusive facet, the URI is:

        http://www.w3.org/2001/XMLSchema#maxInclusive

      Additionally, each facet usage in a built-in datatype definition
      can be uniquely addressed via a URI constructed as follows:
        1) the base URI is the URI of the XML Schema namespace
        2) the fragment identifier is the name of the datatype, followed
           by a period (".") followed by the name of the facet

      For example, to address the usage of the maxInclusive facet in
      the definition of int, the URI is:

        http://www.w3.org/2001/XMLSchema#int.maxInclusive

    </xs:documentation>
  </xs:annotation>
  <xs:simpleType name="string" id="string">
    <xs:annotation>
      <xs:appinfo>
        <hfp:hasFacet name="length"/>
        <hfp:hasFacet name="minLength"/>
        <hfp:hasFacet name="maxLength"/>
        <hfp:hasFacet name="pattern"/>
        <hfp:hasFacet name="enumeration"/>
        <hfp:hasFacet name="whiteSpace"/>
        <hfp:hasFacet name="assertions"/>
        <hfp:hasProperty name="ordered" value="false"/>
        <hfp:hasProperty name="bounded" value="false"/>
        <hfp:hasProperty name="cardinality" value="countably infinite"/>
        <hfp:hasProperty name="numeric" value="false"/>
      </xs:appinfo>
      <xs:documentation source="http://www.w3.org/TR/xmlschema11-2/#string"/>
    </xs:annotation>
    <xs:restriction base="xs:anyAtomicType">
      <xs:whiteSpace value="preserve" id="string.whiteSpace"/>
    </xs:restriction>
  </xs:simpleType>
  <xs:simpleType name="boolean" id="boolean">
    <xs:annotation>
      <xs:appinfo>
        <hfp:hasFacet name="pattern"/>
        <hfp:hasFacet name="whiteSpace"/>
        <hfp:hasFacet name="assertions"/>
        <hfp:hasProperty name="ordered" value="false"/>
        <hfp:hasProperty name="bounded" value="false"/>
        <hfp:hasProperty name="cardinality" value="finite"/>
        <hfp:hasProperty name="numeric" value="false"/>
      </xs:appinfo>
      <xs:documentation source="http://www.w3.org/TR/xmlschema11-2/#boolean"/>
    </xs:annotation>
    <xs:restriction base="xs:anyAtomicType">
      <xs:whiteSpace fixed="true" value="collapse" id="boolean.whiteSpace"/>
    </xs:restriction>
  </xs:simpleType>
  <xs:simpleType name="float" id="float">
    <xs:annotation>
      <xs:appinfo>
        <hfp:hasFacet name="pattern"/>
        <hfp:hasFacet name="enumeration"/>
        <hfp:hasFacet name="whiteSpace"/>
        <hfp:hasFacet name="maxInclusive"/>
        <hfp:hasFacet name="maxExclusive"/>
        <hfp:hasFacet name="minInclusive"/>
        <hfp:hasFacet name="minExclusive"/>
        <hfp:hasFacet name="assertions"/>
        <hfp:hasProperty name="ordered" value="partial"/>
        <hfp:hasProperty name="bounded" value="true"/>
        <hfp:hasProperty name="cardinality" value="finite"/>
        <hfp:hasProperty name="numeric" value="true"/>
      </xs:appinfo>
      <xs:documentation source="http://www.w3.org/TR/xmlschema11-2/#float"/>
    </xs:annotation>
    <xs:restriction base="xs:anyAtomicType">
      <xs:whiteSpace fixed="true" value="collapse" id="float.whiteSpace"/>
    </xs:restriction>
  </xs:simpleType>
  <xs:simpleType name="double" id="double">
    <xs:annotation>
      <xs:appinfo>
        <hfp:hasFacet name="pattern"/>
        <hfp:hasFacet name="enumeration"/>
        <hfp:hasFacet name="whiteSpace"/>
        <hfp:hasFacet name="maxInclusive"/>
        <hfp:hasFacet name="maxExclusive"/>
        <hfp:hasFacet name="minInclusive"/>
        <hfp:hasFacet name="minExclusive"/>
        <hfp:hasFacet name="assertions"/>
        <hfp:hasProperty name="ordered" value="partial"/>
        <hfp:hasProperty name="bounded" value="true"/>
        <hfp:hasProperty name="cardinality" value="finite"/>
        <hfp:hasProperty name="numeric" value="true"/>
      </xs:appinfo>
      <xs:documentation source="http://www.w3.org/TR/xmlschema11-2/#double"/>
    </xs:annotation>
    <xs:restriction base="xs:anyAtomicType">
      <xs:whiteSpace fixed="true" value="collapse" id="double.whiteSpace"/>
    </xs:restriction>
  </xs:simpleType>
  <xs:simpleType name="decimal" id="decimal">
    <xs:annotation>
      <xs:appinfo>
        <hfp:hasFacet name="totalDigits"/>
        <hfp:hasFacet name="fractionDigits"/>
        <hfp:hasFacet name="pattern"/>
        <hfp:hasFacet name="whiteSpace"/>
        <hfp:hasFacet name="enumeration"/>
        <hfp:hasFacet name="maxInclusive"/>
        <hfp:hasFacet name="maxExclusive"/>
        <hfp:hasFacet name="minInclusive"/>
        <hfp:hasFacet name="minExclusive"/>
        <hfp:hasFacet name="assertions"/>
        <hfp:hasProperty name="ordered" value="total"/>
        <hfp:hasProperty name="bounded" value="false"/>
        <hfp:hasProperty name="cardinality" value="countably infinite"/>
        <hfp:hasProperty name="numeric" value="true"/>
      </xs:appinfo>
      <xs:documentation source="http://www.w3.org/TR/xmlschema11-2/#decimal"/>
    </xs:annotation>
    <xs:restriction base="xs:anyAtomicType">
      <xs:whiteSpace fixed="true" value="collapse" id="decimal.whiteSpace"/>
    </xs:restriction>
  </xs:simpleType>

  <xs:simpleType name="duration" id="duration">
    <xs:annotation>
      <xs:appinfo>
        <hfp:hasFacet name="pattern"/>
        <hfp:hasFacet name="enumeration"/>
        <hfp:hasFacet name="whiteSpace"/>
        <hfp:hasFacet name="maxInclusive"/>
        <hfp:hasFacet name="maxExclusive"/>
        <hfp:hasFacet name="minInclusive"/>
        <hfp:hasFacet name="minExclusive"/>
        <hfp:hasFacet name="assertions"/>
        <hfp:hasProperty name="ordered" value="partial"/>
        <hfp:hasProperty name="bounded" value="false"/>
        <hfp:hasProperty name="cardinality" value="countably infinite"/>
        <hfp:hasProperty name="numeric" value="false"/>
      </xs:appinfo>
      <xs:documentation source="http://www.w3.org/TR/xmlschema11-2/#duration"/>
    </xs:annotation>
    <xs:restriction base="xs:anyAtomicType">
      <xs:whiteSpace fixed="true" value="collapse" id="duration.whiteSpace"/>
    </xs:restriction>
  </xs:simpleType>
  <xs:simpleType name="dateTime" id="dateTime">
    <xs:annotation>
      <xs:appinfo>
        <hfp:hasFacet name="pattern"/>
        <hfp:hasFacet name="enumeration"/>
        <hfp:hasFacet name="whiteSpace"/>
        <hfp:hasFacet name="maxInclusive"/>
        <hfp:hasFacet name="maxExclusive"/>
        <hfp:hasFacet name="minInclusive"/>
        <hfp:hasFacet name="minExclusive"/>
        <hfp:hasFacet name="assertions"/>
        <hfp:hasFacet name="explicitTimezone"/>
        <hfp:hasProperty name="ordered" value="partial"/>
        <hfp:hasProperty name="bounded" value="false"/>
        <hfp:hasProperty name="cardinality" value="countably infinite"/>
        <hfp:hasProperty name="numeric" value="false"/>
      </xs:appinfo>
      <xs:documentation source="http://www.w3.org/TR/xmlschema11-2/#dateTime"/>
    </xs:annotation>
    <xs:restriction base="xs:anyAtomicType">
      <xs:whiteSpace fixed="true" value="collapse" id="dateTime.whiteSpace"/>
      <xs:explicitTimezone value="optional" id="dateTime.explicitTimezone"/>
    </xs:restriction>
  </xs:simpleType>
  <xs:simpleType name="time" id="time">
    <xs:annotation>
      <xs:appinfo>
        <hfp:hasFacet name="pattern"/>
        <hfp:hasFacet name="enumeration"/>
        <hfp:hasFacet name="whiteSpace"/>
        <hfp:hasFacet name="maxInclusive"/>
        <hfp:hasFacet name="maxExclusive"/>
        <hfp:hasFacet name="minInclusive"/>
        <hfp:hasFacet name="minExclusive"/>
        <hfp:hasFacet name="assertions"/>
        <hfp:hasFacet name="explicitTimezone"/>
        <hfp:hasProperty name="ordered" value="partial"/>
        <hfp:hasProperty name="bounded" value="false"/>
        <hfp:hasProperty name="cardinality" value="countably infinite"/>
        <hfp:hasProperty name="numeric" value="false"/>
      </xs:appinfo>
      <xs:documentation source="http://www.w3.org/TR/xmlschema11-2/#time"/>
    </xs:annotation>
    <xs:restriction base="xs:anyAtomicType">
      <xs:whiteSpace fixed="true" value="collapse" id="time.whiteSpace"/>
      <xs:explicitTimezone value="optional" id="time.explicitTimezone"/>
    </xs:restriction>
  </xs:simpleType>
  <xs:simpleType name="date" id="date">
    <xs:annotation>
      <xs:appinfo>
        <hfp:hasFacet name="pattern"/>
        <hfp:hasFacet name="enumeration"/>
        <hfp:hasFacet name="whiteSpace"/>
        <hfp:hasFacet name="maxInclusive"/>
        <hfp:hasFacet name="maxExclusive"/>
        <hfp:hasFacet name="minInclusive"/>
        <hfp:hasFacet name="minExclusive"/>
        <hfp:hasFacet name="assertions"/>
        <hfp:hasFacet name="explicitTimezone"/>
        <hfp:hasProperty name="ordered" value="partial"/>
        <hfp:hasProperty name="bounded" value="false"/>
        <hfp:hasProperty name="cardinality" value="countably infinite"/>
        <hfp:hasProperty name="numeric" value="false"/>
      </xs:appinfo>
      <xs:documentation source="http://www.w3.org/TR/xmlschema11-2/#date"/>
    </xs:annotation>
    <xs:restriction base="xs:anyAtomicType">
      <xs:whiteSpace fixed="true" value="collapse" id="date.whiteSpace"/>
      <xs:explicitTimezone value="optional" id="date.explicitTimezone"/>
    </xs:restriction>
  </xs:simpleType>
  <xs:simpleType name="gYearMonth" id="gYearMonth">
    <xs:annotation>
      <xs:appinfo>
        <hfp:hasFacet name="pattern"/>
        <hfp:hasFacet name="enumeration"/>
        <hfp:hasFacet name="whiteSpace"/>
        <hfp:hasFacet name="maxInclusive"/>
        <hfp:hasFacet name="maxExclusive"/>
        <hfp:hasFacet name="minInclusive"/>
        <hfp:hasFacet name="minExclusive"/>
        <hfp:hasFacet name="assertions"/>
        <hfp:hasFacet name="explicitTimezone"/>
        <hfp:hasProperty name="ordered" value="partial"/>
        <hfp:hasProperty name="bounded" value="false"/>
        <hfp:hasProperty name="cardinality" value="countably infinite"/>
        <hfp:hasProperty name="numeric" value="false"/>
      </xs:appinfo>
      <xs:documentation source="http://www.w3.org/TR/xmlschema11-2/#gYearMonth"/>
    </xs:annotation>
    <xs:restriction base="xs:anyAtomicType">
      <xs:whiteSpace fixed="true" value="collapse" id="gYearMonth.whiteSpace"/>
      <xs:explicitTimezone value="optional" id="gYearMonth.explicitTimezone"/>
    </xs:restriction>
  </xs:simpleType>
  <xs:simpleType name="gYear" id="gYear">
    <xs:annotation>
      <xs:appinfo>
        <hfp:hasFacet name="pattern"/>
        <hfp:hasFacet name="enumeration"/>
        <hfp:hasFacet name="whiteSpace"/>
        <hfp:hasFacet name="maxInclusive"/>
        <hfp:hasFacet name="maxExclusive"/>
        <hfp:hasFacet name="minInclusive"/>
        <hfp:hasFacet name="minExclusive"/>
        <hfp:hasFacet name="assertions"/>
        <hfp:hasFacet name="explicitTimezone"/>
        <hfp:hasProperty name="ordered" value="partial"/>
        <hfp:hasProperty name="bounded" value="false"/>
        <hfp:hasProperty name="cardinality" value="countably infinite"/>
        <hfp:hasProperty name="numeric" value="false"/>
      </xs:appinfo>
      <xs:documentation source="http://www.w3.org/TR/xmlschema11-2/#gYear"/>
    </xs:annotation>
    <xs:restriction base="xs:anyAtomicType">
      <xs:whiteSpace fixed="true" value="collapse" id="gYear.whiteSpace"/>
      <xs:explicitTimezone value="optional" id="gYear.explicitTimezone"/>
    </xs:restriction>
  </xs:simpleType>
  <xs:simpleType name="gMonthDay" id="gMonthDay">
    <xs:annotation>
      <xs:appinfo>
        <hfp:hasFacet name="pattern"/>
        <hfp:hasFacet name="enumeration"/>
        <hfp:hasFacet name="whiteSpace"/>
        <hfp:hasFacet name="maxInclusive"/>
        <hfp:hasFacet name="maxExclusive"/>
        <hfp:hasFacet name="minInclusive"/>
        <hfp:hasFacet name="minExclusive"/>
        <hfp:hasFacet name="assertions"/>
        <hfp:hasFacet name="explicitTimezone"/>
        <hfp:hasProperty name="ordered" value="partial"/>
        <hfp:hasProperty name="bounded" value="false"/>
        <hfp:hasProperty name="cardinality" value="countably infinite"/>
        <hfp:hasProperty name="numeric" value="false"/>
      </xs:appinfo>
      <xs:documentation source="http://www.w3.org/TR/xmlschema11-2/#gMonthDay"/>
    </xs:annotation>
    <xs:restriction base="xs:anyAtomicType">
      <xs:whiteSpace fixed="true" value="collapse" id="gMonthDay.whiteSpace"/>
      <xs:explicitTimezone value="optional" id="gMonthDay.explicitTimezone"/>
    </xs:restriction>
  </xs:simpleType>
  <xs:simpleType name="gDay" id="gDay">
    <xs:annotation>
      <xs:appinfo>
        <hfp:hasFacet name="pattern"/>
        <hfp:hasFacet name="enumeration"/>
        <hfp:hasFacet name="whiteSpace"/>
        <hfp:hasFacet name="maxInclusive"/>
        <hfp:hasFacet name="maxExclusive"/>
        <hfp:hasFacet name="minInclusive"/>
        <hfp:hasFacet name="minExclusive"/>
        <hfp:hasFacet name="assertions"/>
        <hfp:hasFacet name="explicitTimezone"/>
        <hfp:hasProperty name="ordered" value="partial"/>
        <hfp:hasProperty name="bounded" value="false"/>
        <hfp:hasProperty name="cardinality" value="countably infinite"/>
        <hfp:hasProperty name="numeric" value="false"/>
      </xs:appinfo>
      <xs:documentation source="http://www.w3.org/TR/xmlschema11-2/#gDay"/>
    </xs:annotation>
    <xs:restriction base="xs:anyAtomicType">
      <xs:whiteSpace fixed="true" value="collapse" id="gDay.whiteSpace"/>
      <xs:explicitTimezone value="optional" id="gDay.explicitTimezone"/>
    </xs:restriction>
  </xs:simpleType>
  <xs:simpleType name="gMonth" id="gMonth">
    <xs:annotation>
      <xs:appinfo>
        <hfp:hasFacet name="pattern"/>
        <hfp:hasFacet name="enumeration"/>
        <hfp:hasFacet name="whiteSpace"/>
        <hfp:hasFacet name="maxInclusive"/>
        <hfp:hasFacet name="maxExclusive"/>
        <hfp:hasFacet name="minInclusive"/>
        <hfp:hasFacet name="minExclusive"/>
        <hfp:hasFacet name="assertions"/>
        <hfp:hasFacet name="explicitTimezone"/>
        <hfp:hasProperty name="ordered" value="partial"/>
        <hfp:hasProperty name="bounded" value="false"/>
        <hfp:hasProperty name="cardinality" value="countably infinite"/>
        <hfp:hasProperty name="numeric" value="false"/>
      </xs:appinfo>
      <xs:documentation source="http://www.w3.org/TR/xmlschema11-2/#gMonth"/>
    </xs:annotation>
    <xs:restriction base="xs:anyAtomicType">
      <xs:whiteSpace fixed="true" value="collapse" id="gMonth.whiteSpace"/>
      <xs:explicitTimezone value="optional" id="gMonth.explicitTimezone"/>
    </xs:restriction>
  </xs:simpleType>
  <xs:simpleType name="hexBinary" id="hexBinary">
    <xs:annotation>
      <xs:appinfo>
        <hfp:hasFacet name="length"/>
        <hfp:hasFacet name="minLength"/>
        <hfp:hasFacet name="maxLength"/>
        <hfp:hasFacet name="pattern"/>
        <hfp:hasFacet name="enumeration"/>
        <hfp:hasFacet name="whiteSpace"/>
        <hfp:hasFacet name="assertions"/>
        <hfp:hasProperty name="ordered" value="false"/>
        <hfp:hasProperty name="bounded" value="false"/>
        <hfp:hasProperty name="cardinality" value="countably infinite"/>
        <hfp:hasProperty name="numeric" value="false"/>
      </xs:appinfo>
      <xs:documentation source="http://www.w3.org/TR/xmlschema11-2/#hexBinary"/>
    </xs:annotation>
    <xs:restriction base="xs:anyAtomicType">
      <xs:whiteSpace fixed="true" value="collapse" id="hexBinary.whiteSpace"/>
    </xs:restriction>
  </xs:simpleType>
  <xs:simpleType name="base64Binary" id="base64Binary">
    <xs:annotation>
      <xs:appinfo>
        <hfp:hasFacet name="length"/>
        <hfp:hasFacet name="minLength"/>
        <hfp:hasFacet name="maxLength"/>
        <hfp:hasFacet name="pattern"/>
        <hfp:hasFacet name="enumeration"/>
        <hfp:hasFacet name="whiteSpace"/>
        <hfp:hasFacet name="assertions"/>
        <hfp:hasProperty name="ordered" value="false"/>
        <hfp:hasProperty name="bounded" value="false"/>
        <hfp:hasProperty name="cardinality" value="countably infinite"/>
        <hfp:hasProperty name="numeric" value="false"/>
      </xs:appinfo>
      <xs:documentation source="http://www.w3.org/TR/xmlschema11-2/#base64Binary"/>
    </xs:annotation>
    <xs:restriction base="xs:anyAtomicType">
      <xs:whiteSpace fixed="true" value="collapse" id="base64Binary.whiteSpace"/>
    </xs:restriction>
  </xs:simpleType>
  <xs:simpleType name="anyURI" id="anyURI">
    <xs:annotation>
      <xs:appinfo>
        <hfp:hasFacet name="length"/>
        <hfp:hasFacet name="minLength"/>
        <hfp:hasFacet name="maxLength"/>
        <hfp:hasFacet name="pattern"/>
        <hfp:hasFacet name="enumeration"/>
        <hfp:hasFacet name="whiteSpace"/>
        <hfp:hasFacet name="assertions"/>
        <hfp:hasProperty name="ordered" value="false"/>
        <hfp:hasProperty name="bounded" value="false"/>
        <hfp:hasProperty name="cardinality" value="countably infinite"/>
        <hfp:hasProperty name="numeric" value="false"/>
      </xs:appinfo>
      <xs:documentation source="http://www.w3.org/TR/xmlschema11-2/#anyURI"/>
    </xs:annotation>
    <xs:restriction base="xs:anyAtomicType">
      <xs:whiteSpace fixed="true" value="collapse" id="anyURI.whiteSpace"/>
    </xs:restriction>
  </xs:simpleType>
  <xs:simpleType name="QName" id="QName">
    <xs:annotation>
      <xs:appinfo>
        <hfp:hasFacet name="length"/>
        <hfp:hasFacet name="minLength"/>
        <hfp:hasFacet name="maxLength"/>
        <hfp:hasFacet name="pattern"/>
        <hfp:hasFacet name="enumeration"/>
        <hfp:hasFacet name="whiteSpace"/>
        <hfp:hasFacet name="assertions"/>
        <hfp:hasProperty name="ordered" value="false"/>
        <hfp:hasProperty name="bounded" value="false"/>
        <hfp:hasProperty name="cardinality" value="countably infinite"/>
        <hfp:hasProperty name="numeric" value="false"/>
      </xs:appinfo>
      <xs:documentation source="http://www.w3.org/TR/xmlschema11-2/#QName"/>
    </xs:annotation>
    <xs:restriction base="xs:anyAtomicType">
      <xs:whiteSpace fixed="true" value="collapse" id="QName.whiteSpace"/>
    </xs:restriction>
  </xs:simpleType>
  <xs:simpleType name="NOTATION" id="NOTATION">
    <xs:annotation>
      <xs:appinfo>
        <hfp:hasFacet name="length"/>
        <hfp:hasFacet name="minLength"/>
        <hfp:hasFacet name="maxLength"/>
        <hfp:hasFacet name="pattern"/>
        <hfp:hasFacet name="enumeration"/>
        <hfp:hasFacet name="whiteSpace"/>
        <hfp:hasFacet name="assertions"/>
        <hfp:hasProperty name="ordered" value="false"/>
        <hfp:hasProperty name="bounded" value="false"/>
        <hfp:hasProperty name="cardinality" value="countably infinite"/>
        <hfp:hasProperty name="numeric" value="false"/>
      </xs:appinfo>
      <xs:documentation source="http://www.w3.org/TR/xmlschema11-2/#NOTATION"/>
      <xs:documentation>
        NOTATION cannot be used directly in a schema; rather a type
        must be derived from it by specifying at least one enumeration
        facet whose value is the name of a NOTATION declared in the
        schema.
      </xs:documentation>
    </xs:annotation>
    <xs:restriction base="xs:anyAtomicType">
      <xs:whiteSpace fixed="true" value="collapse" id="NOTATION.whiteSpace"/>
    </xs:restriction>
  </xs:simpleType>
</xs:schema>

The following, although in the form of a schema document, contains XML representations of components already present in all schemas by definition. It is included here as a form of documentation.

Note: These datatypes do not need to be declared in a schema document, since they are automatically included in every schema.

Issue (B-1933):

It is an open question whether this and similar XML documents should be accepted or rejected by software conforming to this specification. The XML Schema Working Group expects to resolve this question in connection with its work on issues relating to schema composition.

In the meantime, some existing schema processors will accept declarations for them; other existing processors will reject such declarations as duplicates.

Illustrative schema document for derived built-in type definitions

<?xml version='1.0'?>
<!DOCTYPE xs:schema SYSTEM "../namespace/XMLSchema.dtd" [

<!--
     keep this schema XML1.0 DTD valid
  -->
        <!ENTITY % schemaAttrs 'xmlns:hfp CDATA #IMPLIED'>

        <!ELEMENT hfp:hasFacet EMPTY>
        <!ATTLIST hfp:hasFacet
                name NMTOKEN #REQUIRED>

        <!ELEMENT hfp:hasProperty EMPTY>
        <!ATTLIST hfp:hasProperty
                name NMTOKEN #REQUIRED
                value CDATA #REQUIRED>

]>
<xs:schema
  xmlns:hfp="http://www.w3.org/2001/XMLSchema-hasFacetAndProperty"
  xmlns:xs="http://www.w3.org/2001/XMLSchema"
  elementFormDefault="qualified" 
  xml:lang="en" 
  targetNamespace="http://www.w3.org/2001/XMLSchema">
 <xs:annotation>
    <xs:documentation>
      This document contains XML representations for the 
     ordinary non-primitive built-in datatypes
    </xs:documentation>
  </xs:annotation>
  <xs:simpleType name="normalizedString" id="normalizedString">
    <xs:annotation>
      <xs:documentation source="http://www.w3.org/TR/xmlschema11-2/#normalizedString"/>
    </xs:annotation>
    <xs:restriction base="xs:string">
      <xs:whiteSpace value="replace" id="normalizedString.whiteSpace"/>
    </xs:restriction>
  </xs:simpleType>
  <xs:simpleType name="token" id="token">
    <xs:annotation>
      <xs:documentation source="http://www.w3.org/TR/xmlschema11-2/#token"/>
    </xs:annotation>
    <xs:restriction base="xs:normalizedString">
      <xs:whiteSpace value="collapse" id="token.whiteSpace"/>
    </xs:restriction>
  </xs:simpleType>
  <xs:simpleType name="language" id="language">
    <xs:annotation>
      <xs:documentation source="http://www.w3.org/TR/xmlschema11-2/#language"/>
    </xs:annotation>
    <xs:restriction base="xs:token">
      <xs:pattern value="[a-zA-Z]{1,8}(-[a-zA-Z0-9]{1,8})*" id="language.pattern">
        <xs:annotation>
          <xs:documentation source="http://www.ietf.org/rfc/bcp/bcp47.txt">
            pattern specifies the content of section 2.12 of XML 1.0e2
            and RFC 3066 (Revised version of RFC 1766).  N.B. RFC 3066 is now
            obsolete; the grammar of RFC4646 is more restrictive.  So strict
            conformance to the rules for language codes requires extra checking
            beyond validation against this type.
          </xs:documentation>
        </xs:annotation>
      </xs:pattern>
    </xs:restriction>
  </xs:simpleType>
  <xs:simpleType name="IDREFS" id="IDREFS">
    <xs:annotation>
      <xs:appinfo>
        <hfp:hasFacet name="length"/>
        <hfp:hasFacet name="minLength"/>
        <hfp:hasFacet name="maxLength"/>
        <hfp:hasFacet name="enumeration"/>
        <hfp:hasFacet name="whiteSpace"/>
        <hfp:hasFacet name="pattern"/>
        <hfp:hasFacet name="assertions"/>
        <hfp:hasProperty name="ordered" value="false"/>
        <hfp:hasProperty name="bounded" value="false"/>
        <hfp:hasProperty name="cardinality" value="countably infinite"/>
        <hfp:hasProperty name="numeric" value="false"/>
      </xs:appinfo>
      <xs:documentation source="http://www.w3.org/TR/xmlschema11-2/#IDREFS"/>
    </xs:annotation>
    <xs:restriction>
      <xs:simpleType>
        <xs:list itemType="xs:IDREF"/>
      </xs:simpleType>
      <xs:minLength value="1" id="IDREFS.minLength"/>
    </xs:restriction>
  </xs:simpleType>
  <xs:simpleType name="ENTITIES" id="ENTITIES">
    <xs:annotation>
      <xs:appinfo>
        <hfp:hasFacet name="length"/>
        <hfp:hasFacet name="minLength"/>
        <hfp:hasFacet name="maxLength"/>
        <hfp:hasFacet name="enumeration"/>
        <hfp:hasFacet name="whiteSpace"/>
        <hfp:hasFacet name="pattern"/>
        <hfp:hasFacet name="assertions"/>
        <hfp:hasProperty name="ordered" value="false"/>
        <hfp:hasProperty name="bounded" value="false"/>
        <hfp:hasProperty name="cardinality" value="countably infinite"/>
        <hfp:hasProperty name="numeric" value="false"/>
      </xs:appinfo>
      <xs:documentation source="http://www.w3.org/TR/xmlschema11-2/#ENTITIES"/>
    </xs:annotation>
    <xs:restriction>
      <xs:simpleType>
        <xs:list itemType="xs:ENTITY"/>
      </xs:simpleType>
      <xs:minLength value="1" id="ENTITIES.minLength"/>
    </xs:restriction>
  </xs:simpleType>
  <xs:simpleType name="NMTOKEN" id="NMTOKEN">
    <xs:annotation>
      <xs:documentation source="http://www.w3.org/TR/xmlschema11-2/#NMTOKEN"/>
    </xs:annotation>
    <xs:restriction base="xs:token">
      <xs:pattern value="\c+" id="NMTOKEN.pattern">
        <xs:annotation>
          <xs:documentation source="http://www.w3.org/TR/REC-xml#NT-Nmtoken">
            pattern matches production 7 from the XML spec
          </xs:documentation>
        </xs:annotation>
      </xs:pattern>
    </xs:restriction>
  </xs:simpleType>
  <xs:simpleType name="NMTOKENS" id="NMTOKENS">
    <xs:annotation>
      <xs:appinfo>
        <hfp:hasFacet name="length"/>
        <hfp:hasFacet name="minLength"/>
        <hfp:hasFacet name="maxLength"/>
        <hfp:hasFacet name="enumeration"/>
        <hfp:hasFacet name="whiteSpace"/>
        <hfp:hasFacet name="pattern"/>
        <hfp:hasFacet name="assertions"/>
        <hfp:hasProperty name="ordered" value="false"/>
        <hfp:hasProperty name="bounded" value="false"/>
        <hfp:hasProperty name="cardinality" value="countably infinite"/>
        <hfp:hasProperty name="numeric" value="false"/>
      </xs:appinfo>
      <xs:documentation source="http://www.w3.org/TR/xmlschema11-2/#NMTOKENS"/>
    </xs:annotation>
    <xs:restriction>
      <xs:simpleType>
        <xs:list itemType="xs:NMTOKEN"/>
      </xs:simpleType>
      <xs:minLength value="1" id="NMTOKENS.minLength"/>
    </xs:restriction>
  </xs:simpleType>
  <xs:simpleType name="Name" id="Name">
    <xs:annotation>
      <xs:documentation source="http://www.w3.org/TR/xmlschema11-2/#Name"/>
    </xs:annotation>
    <xs:restriction base="xs:token">
      <xs:pattern value="\i\c*" id="Name.pattern">
        <xs:annotation>
          <xs:documentation source="http://www.w3.org/TR/REC-xml#NT-Name">
            pattern matches production 5 from the XML spec
          </xs:documentation>
        </xs:annotation>
      </xs:pattern>
    </xs:restriction>
  </xs:simpleType>
  <xs:simpleType name="NCName" id="NCName">
    <xs:annotation>
      <xs:documentation source="http://www.w3.org/TR/xmlschema11-2/#NCName"/>
    </xs:annotation>
    <xs:restriction base="xs:Name">
      <xs:pattern value="[\i-[:]][\c-[:]]*" id="NCName.pattern">
        <xs:annotation>
          <xs:documentation source="http://www.w3.org/TR/REC-xml-names/#NT-NCName">
            pattern matches production 4 from the Namespaces in XML spec
          </xs:documentation>
        </xs:annotation>
      </xs:pattern>
    </xs:restriction>
  </xs:simpleType>
  <xs:simpleType name="ID" id="ID">
    <xs:annotation>
      <xs:documentation source="http://www.w3.org/TR/xmlschema11-2/#ID"/>
    </xs:annotation>
    <xs:restriction base="xs:NCName"/>
  </xs:simpleType>
  <xs:simpleType name="IDREF" id="IDREF">
    <xs:annotation>
      <xs:documentation source="http://www.w3.org/TR/xmlschema11-2/#IDREF"/>
    </xs:annotation>
    <xs:restriction base="xs:NCName"/>
  </xs:simpleType>
  <xs:simpleType name="ENTITY" id="ENTITY">
    <xs:annotation>
      <xs:documentation source="http://www.w3.org/TR/xmlschema11-2/#ENTITY"/>
    </xs:annotation>
    <xs:restriction base="xs:NCName"/>
  </xs:simpleType>
  <xs:simpleType name="integer" id="integer">
    <xs:annotation>
      <xs:documentation source="http://www.w3.org/TR/xmlschema11-2/#integer"/>
    </xs:annotation>
    <xs:restriction base="xs:decimal">
      <xs:fractionDigits fixed="true" value="0" id="integer.fractionDigits"/>
      <xs:pattern value="[\-+]?[0-9]+" id="integer.pattern"/>
      
    </xs:restriction>
  </xs:simpleType>
  <xs:simpleType name="nonPositiveInteger" id="nonPositiveInteger">
    <xs:annotation>
      <xs:documentation source="http://www.w3.org/TR/xmlschema11-2/#nonPositiveInteger"/>
    </xs:annotation>
    <xs:restriction base="xs:integer">
      <xs:maxInclusive value="0" id="nonPositiveInteger.maxInclusive"/>
    </xs:restriction>
  </xs:simpleType>
  <xs:simpleType name="negativeInteger" id="negativeInteger">
    <xs:annotation>
      <xs:documentation source="http://www.w3.org/TR/xmlschema11-2/#negativeInteger"/>
    </xs:annotation>
    <xs:restriction base="xs:nonPositiveInteger">
      <xs:maxInclusive value="-1" id="negativeInteger.maxInclusive"/>
    </xs:restriction>
  </xs:simpleType>
  <xs:simpleType name="long" id="long">
    <xs:annotation>
      <xs:appinfo>
        <hfp:hasProperty name="bounded" value="true"/>
        <hfp:hasProperty name="cardinality" value="finite"/>
      </xs:appinfo>
      <xs:documentation source="http://www.w3.org/TR/xmlschema11-2/#long"/>
    </xs:annotation>
    <xs:restriction base="xs:integer">
      <xs:minInclusive value="-9223372036854775808" id="long.minInclusive"/>
      <xs:maxInclusive value="9223372036854775807" id="long.maxInclusive"/>
    </xs:restriction>
  </xs:simpleType>
  <xs:simpleType name="int" id="int">
    <xs:annotation>
      <xs:documentation source="http://www.w3.org/TR/xmlschema11-2/#int"/>
    </xs:annotation>
    <xs:restriction base="xs:long">
      <xs:minInclusive value="-2147483648" id="int.minInclusive"/>
      <xs:maxInclusive value="2147483647" id="int.maxInclusive"/>
    </xs:restriction>
  </xs:simpleType>
  <xs:simpleType name="short" id="short">
    <xs:annotation>
      <xs:documentation source="http://www.w3.org/TR/xmlschema11-2/#short"/>
    </xs:annotation>
    <xs:restriction base="xs:int">
      <xs:minInclusive value="-32768" id="short.minInclusive"/>
      <xs:maxInclusive value="32767" id="short.maxInclusive"/>
    </xs:restriction>
  </xs:simpleType>
  <xs:simpleType name="byte" id="byte">
    <xs:annotation>
      <xs:documentation source="http://www.w3.org/TR/xmlschema11-2/#byte"/>
    </xs:annotation>
    <xs:restriction base="xs:short">
      <xs:minInclusive value="-128" id="byte.minInclusive"/>
      <xs:maxInclusive value="127" id="byte.maxInclusive"/>
    </xs:restriction>
  </xs:simpleType>
  <xs:simpleType name="nonNegativeInteger" id="nonNegativeInteger">
    <xs:annotation>
      <xs:documentation source="http://www.w3.org/TR/xmlschema11-2/#nonNegativeInteger"/>
    </xs:annotation>
    <xs:restriction base="xs:integer">
      <xs:minInclusive value="0" id="nonNegativeInteger.minInclusive"/>
    </xs:restriction>
  </xs:simpleType>
  <xs:simpleType name="unsignedLong" id="unsignedLong">
    <xs:annotation>
      <xs:appinfo>
        <hfp:hasProperty name="bounded" value="true"/>
        <hfp:hasProperty name="cardinality" value="finite"/>
      </xs:appinfo>
      <xs:documentation source="http://www.w3.org/TR/xmlschema11-2/#unsignedLong"/>
    </xs:annotation>
    <xs:restriction base="xs:nonNegativeInteger">
      <xs:maxInclusive value="18446744073709551615" id="unsignedLong.maxInclusive"/>
    </xs:restriction>
  </xs:simpleType>
  <xs:simpleType name="unsignedInt" id="unsignedInt">
    <xs:annotation>
      <xs:documentation source="http://www.w3.org/TR/xmlschema11-2/#unsignedInt"/>
    </xs:annotation>
    <xs:restriction base="xs:unsignedLong">
      <xs:maxInclusive value="4294967295" id="unsignedInt.maxInclusive"/>
    </xs:restriction>
  </xs:simpleType>
  <xs:simpleType name="unsignedShort" id="unsignedShort">
    <xs:annotation>
      <xs:documentation source="http://www.w3.org/TR/xmlschema11-2/#unsignedShort"/>
    </xs:annotation>
    <xs:restriction base="xs:unsignedInt">
      <xs:maxInclusive value="65535" id="unsignedShort.maxInclusive"/>
    </xs:restriction>
  </xs:simpleType>
  <xs:simpleType name="unsignedByte" id="unsignedByte">
    <xs:annotation>
      <xs:documentation source="http://www.w3.org/TR/xmlschema11-2/#unsignedByte"/>
    </xs:annotation>
    <xs:restriction base="xs:unsignedShort">
      <xs:maxInclusive value="255" id="unsignedByte.maxInclusive"/>
    </xs:restriction>
  </xs:simpleType>
  <xs:simpleType name="positiveInteger" id="positiveInteger">
    <xs:annotation>
      <xs:documentation source="http://www.w3.org/TR/xmlschema11-2/#positiveInteger"/>
    </xs:annotation>
    <xs:restriction base="xs:nonNegativeInteger">
      <xs:minInclusive value="1" id="positiveInteger.minInclusive"/>
    </xs:restriction>
  </xs:simpleType>

  <xs:simpleType name="yearMonthDuration">
    <xs:annotation>
      <xs:documentation source="http://www.w3.org/TR/xmlschema11-2/#yearMonthDuration">
        This type includes just those durations expressed in years and months.
        Since the pattern given excludes days, hours, minutes, and seconds,
        the values of this type have a seconds property of zero.  They are
        totally ordered.
      </xs:documentation>
    </xs:annotation>
    <xs:restriction base="xs:duration">
      <xs:pattern id="yearMonthDuration.pattern" value="[^DT]*"/>
    </xs:restriction>
  </xs:simpleType>
  <xs:simpleType name="dayTimeDuration">
    <xs:annotation>
      <xs:documentation source="http://www.w3.org/TR/xmlschema11-2/#dayTimeDuration">
        This type includes just those durations expressed in days, hours, minutes, and seconds.
        The pattern given excludes years and months, so the values of this type 
        have a months property of zero.  They are totally ordered.
      </xs:documentation>
    </xs:annotation>
    <xs:restriction base="xs:duration">
      <xs:pattern id="dayTimeDuration.pattern" value="[^YM]*(T.*)?"/>
     </xs:restriction>
  </xs:simpleType>
    <xs:simpleType name="dateTimeStamp" id="dateTimeStamp">
    <xs:annotation>
      <xs:documentation source="http://www.w3.org/TR/xmlschema11-2/#dateTimeStamp">
        This datatype includes just those dateTime values Whose explicitTimezone
        is present.  They are totally ordered.
      </xs:documentation>
    </xs:annotation>
    <xs:restriction base="xs:dateTime">
      <xs:explicitTimezone fixed="true"
        id="dateTimeStamp.explicitTimezone" value="required"/>
     </xs:restriction>
  </xs:simpleType>

</xs:schema>

Some datatypes, such as integer, describe well-known mathematically abstract systems.  Others, such as the date/time datatypes, describe "real-life", "applied" systems.  Certain of the systems described by datatypes, both abstract and applied, have values in their value spaces most easily described as things having several properties, which in turn have values which are in some sense "primitive" or are from the value spaces of simpler datatypes.

In this document, the arguments to functions are assumed to be "call by value" unless explicitly noted to the contrary, meaning that if the argument is modified during the processing of the algorithm, that modification is not reflected in the "outside world".  On the other hand, the arguments to procedures are assumed to be "call by location", meaning that modifications are so reflected, since that is the only way the processing of the algorithm can have any effect.

Properties always have values.  [Definition:]  An optional property is permitted but not required to have the distinguished value absent.

[Definition:]  Throughout this specification, the value absent is used as a distinguished value to indicate that a given instance of a property "has no value" or "is absent".  This should not be interpreted as constraining implementations, as for instance between using a null value for such properties or not representing them at all.

Those values that are more primitive, and are used (among other things) herein to construct object value spaces but which we do not explicitly define are described here:

• A

  number (without precision)

  is an ordinary mathematical number; 1, 1.0, and 1.000000000000 are the same number. The decimal numbers and integers generally used in the algorithms of appendix

  Function Definitions (§E)

  are such ordinary numbers, not carrying precision.

• [Definition:]  A special value is an object whose only relevant properties for purposes of this specification are that it is distinct from, and unequal to, any other values (special or otherwise).

  A few special values in different value spaces (e.g.

  positiveInfinity

  ,

  negativeInfinity

  , and

  notANumber

  in

  float

  and

  double

  ) share names. Thus, special values can be distinguished from each other in the general case by considering both the name and the primitive datatype of the value; in some cases, of course, the name alone suffices to identify the value uniquely.

The following standard operators are defined here in case the reader is unsure of their definition:

• [Definition:]  If m and n are numbers, then m div n is the greatest integer less than or equal to m / n .

1 is a convenient and short way of expressing "the greatest integer less than or equal to

".

Numerals and Fragments Thereof

::=

+

::=

+

Generic Numeral-to-Number Lexical Mappings

Generic Number to Numeral Canonical Mappings

Some numerical datatypes include some or all of three non-numerical

:

,

, and

. Their lexical spaces include non-numeral lexical representations for these non-numeric values:

Special Non-numerical Lexical Representations Used With Numerical Datatypes

::= '

' | '

' | '

'

Lexical Mapping for Non-numerical

Used With Numerical Datatypes

Canonical Mapping for Non-numerical

Used with Numerical Datatypes

There are several different primitive but related datatypes defined in the specification which pertain to various combinations of dates and times, and parts thereof.  They all use related value-space models, which are described in detail in this section.  It is not difficult for a casual reader of the descriptions of the individual datatypes elsewhere in this specification to misunderstand some of the details of just what the datatypes are intended to represent, so more detail is presented here in this section.

All of the value spaces for dates and times described here represent moments or periods of time in Universal Coordinated Time (UTC).  [Definition:]  Universal Coordinated Time (UTC) is an adaptation of TAI which closely approximates UT1 by adding ·leap-seconds· to selected ·UTC· days.

[Definition:]  A leap-second is an additional second added to the last day of December, June, October, or March, when such an adjustment is deemed necessary by the International Earth Rotation and Reference Systems Service in order to keep ·UTC· within 0.9 seconds of observed astronomical time.  When leap seconds are introduced, the last minute in the day has more than sixty seconds.  In theory leap seconds can also be removed from a day, but this has not yet occurred. (See [International Earth Rotation Service (IERS)], [ITU-R TF.460-6].) Leap seconds are not supported by the types defined here.

Because the dateTime type and other date- and time-related types defined in this specification do not support leap seconds, there are portions of the ·UTC· timeline which cannot be represented by values of these types. Users whose applications require that leap seconds be represented and that date/time arithmetic take historically occurring leap seconds into account will wish to make appropriate adjustments at the application level, or to use other types.

There are two distinct ways to model moments in time:  either by tracking their year, month, day, hour, minute and second (with fractional seconds as needed), or by tracking their time (measured generally in seconds or days) from some starting moment.  Each has its advantages.  The two are isomorphic.  For definiteness, we choose to model the first using five integer and one decimal number properties.  We superimpose the second by providing one decimal number-valued function which gives the corresponding count of seconds from zero (the "time on the time line").

There is also a seventh

property which specifies the time zone offset as the number of minutes of offset from UTC. Values for the six primary properties are always stored in their "local" values (the values shown in the lexical representations), rather than converted to

.

an integer

an integer between 1 and 12 inclusive

an integer between 1 and 31 inclusive, possibly restricted further depending on

and

an integer between 0 and 23 inclusive

an integer between 0 and 59 inclusive

a decimal number greater than or equal to 0 and less than 60.

an

integer between −840 and 840 inclusive

Non-negative values of the properties map to the years, months, days of month, etc. of the Gregorian calendar in the obvious way. Values less than 1582 in the ·year· property represent years in the "proleptic Gregorian calendar". A value of zero in the ·year· property represents the year 1 BCE; a value of −1 represents the year 2 BCE, −2 is 3 BCE, etc.

In version 1.0 of this specification, the

property was not permitted to have the value zero. The year before the year 1 in the proleptic Gregorian calendar, traditionally referred to as 1 BC or as 1 BCE, was represented by a

value of −1, 2 BCE by −2, and so forth. Of course, many, perhaps most, references to 1 BCE (or 1 BC) actually refer not to a year in the proleptic Gregorian calendar but to a year in the Julian or "old style" calendar; the two correspond approximately but not exactly to each other.

In this version of this specification, two changes are made in order to agree with existing usage. First,

is permitted to have the value zero. Second, the interpretation of

values is changed accordingly: a

value of zero represents 1 BCE, −1 represents 2 BCE, etc. This representation simplifies interval arithmetic and leap-year calculation for dates before the common era (which may be why astronomers and others interested in such calculations with the proleptic Gregorian calendar have adopted it), and is consistent with the current edition of

.

Note that 1 BCE, 5 BCE, and so on (years 0000, −0004, etc. in the lexical representation defined here) are leap years in the proleptic Gregorian calendar used for the date/time datatypes defined here. Version 1.0 of this specification was unclear about the treatment of leap years before the common era. If existing schemas or data specify dates of 29 February for any years before the common era, then some values giving a date of 29 February which were valid under a plausible interpretation of XSD 1.0 will be invalid under this specification, and some which were invalid will be valid. With that possible exception, schemas and data valid under the old interpretation remain valid under the new.

The model just described is called herein the "seven-property" model for date/time datatypes.  It is used "as is" for dateTime; all other date/time datatypes except duration use the same model except that some of the six primary properties are required to have the value absent, instead of being required to have a numerical value.  (An ·optional· property, like ·timezoneOffset·, is always permitted to have the value absent.)

·timezoneOffset· values are limited to 14 hours, which is 840 (= 60 × 14) minutes.

Note: Leap-seconds are not permitted

Readers interested in when leap-seconds have been introduced should consult [USNO Historical List], which includes a list of times when the difference between TAI and ·UTC· has changed.  Because the simple types defined here do not support leap seconds, they cannot be used to represent the final second, in ·UTC·, of any of the days containing one.  If it is important, at the application level, to track the occurrence of leap seconds, then users will need to make special arrangements for special handling of them and of time intervals crossing them.

While calculating, property values from the dateTime 1972-12-31T00:00:00 are used to fill in for those that are absent, except that if ·day· is absent but ·month· is not, the largest permitted day for that month is used.

Time on Timeline for Date/time Seven-property Model Datatypes

Values from any one date/time datatype using the seven-component model (all except

) are ordered the same as their

values, except that if one value's

is

and the other's is not, and using maximum and minimum

values for the one whose

is actually

changes the resulting (strict) inequality, the original two values are incomparable.

They are defined by the following productions.

Date/time Lexical Representation Fragments

::= ('

' [

]) | ('

' [

])

::= ('

' [

]) | ([

]

) | ('

' [

])

::= ([

]

) | ('

' [

])

::= [

]

::= ([

]

) ('

'

+)?

::= '

' ('

' '

'+)?

::= '

' | ('

' | '

') (('

'

| '

' [

]) '

'

| '

')

The more important functions and procedures defined here are summarized in the text  When there is a text summary, the name of the function in each is a "hot-link" to the same name in the other.  All other links to these functions link to the complete definition in this section.

The following functions are used with various numeric and date/time datatypes.

Auxiliary Functions for Operating on Numeral Fragments

(

) → integer

Maps each digit to its numerical value.

a nonnegative integer less than ten

Return

• 0   when  d = '0' ,

• 1   when  d = '1' ,

• 2   when  d = '2' ,

• etc.

(

) → integer

Maps a sequence of digits to the position-weighted sum of the terms numerical values.

a nonnegative integer

Return the sum of

(

) × 10

where

runs over the domain of

.

(

) → integer

Maps a sequence of digits to the position-weighted sum of the terms numerical values, weighted appropriately for fractional digits.

a nonnegative integer

Return the sum of

(

) − 10

where

runs over the domain of

.

a nonnegative decimal number

is necessarily the left-to-right concatenation of a finite sequence

of

, each term matching

.

Generic Numeral-to-Number Lexical Mappings

a nonnegative integer

is the left-to-right concatenation of a finite sequence

of

, each term matching

.

an integer

a nonnegative decimal number

a decimal number

a decimal number

Auxiliary Functions for Producing Numeral Fragments

Return

• '0'   when  i = 0 ,

• '1'   when  i = 1 ,

• '2'   when  i = 2 ,

• etc.

sequence of nonnegative integers

Return that sequence

for which

• s₀ = i  and

sequence of integers where each term is between 0 and 9 inclusive

(

) → integer

Maps a sequence of nonnegative integers to the index of the first zero term.

a nonnegative integer

Return the smallest nonnegative integer j such that s(i)_j+1 is 0.

a sequence of nonnegative decimal numbers

Return that sequence

for which

• s₀ = f − 10 , and

• s_j+1

  = (

  s_j ·mod·

  1) − 10 .

a sequence of integer;s where each term is between 0 and 9 inclusive

Generic Number to Numeral Canonical Mappings

For example:

• 123.4567

  ·mod·

  1 = 0.4567 and 123.4567

  ·div·

  1 = 123 .

Lexical Mapping for Non-numerical

Used With Numerical Datatypes

one of positiveInfinity, negativeInfinity, or notANumber.

Return

• positiveInfinity   when S is 'INF' or '+INF',

• negativeInfinity   when S is '-INF', and

• notANumber   when S is 'NaN'

Canonical Mapping for Non-numerical

Used with Numerical Datatypes

Return

• 'INF'   when c is positiveInfinity

• '-INF'   when c is negativeInfinity

• 'NaN'   when c is notANumber

Lexical Mapping

Canonical Mapping

Auxiliary Functions for Binary Floating-point Lexical/Canonical Mappings

• s be an integer initially 1,

• c be a nonnegative integer, and

• e be an integer.

1. Set s to −1   when  nV < 0 .

2. So select e that 2^cWidth × 2^(e−1) ≤ |nV| < 2^cWidth × 2^e .

3. So select c that  (c − 1) × 2^e ≤ |nV | <c × 2^e   .

4. • when

     eMax

     <

     e  (overflow)

     return:

     • positiveInfinity   when s is positive, and

     • negativeInfinity   otherwise.

   • otherwise:

     1. When

        e

        <

        eMin  (underflow):

        • Set  e = eMin

        • So select c that  (c − 1) × 2^e ≤ |nV | <c × 2^e .

     2. Set

        nV

        to

        • c × 2^e   when  |nV | > c × 2^e − 2^(e−1) ;

        • (c − 1) × 2^e   when  |nV | < c × 2^e − 2^(e−1) ;

        • c × 2^e or (c − 1) × 2^e   according to whether c is even or  c − 1  is even, otherwise (i.e.,  |nV | = c × 2^e − 2^(e−1) , the midpoint between the two values).

     3. Return

        • s × nV   when nV < 2^cWidth × 2^eMax,

        • positiveInfinity   when s is positive, and

        • negativeInfinity   otherwise.

Implementers will find the algorithms of

more efficient in memory than the simple abstract algorithm employed above.

(

,

) → decimal number

Maps a decimal number to that value rounded by some power of 10.

a decimal number

Return ((

/ 10

+ 0.5)

1) × 10

.

(

,

,

) → decimal number

Maps a decimal number ( c × 10^e ) to successive approximations.

a decimal number

Lexical Mapping

• otherwise (

  LEX

  is a numeral):

  3. Return:

     • When

       nV

       is zero:

       • negativeZero   when the first character of LEX is '-', and

       • positiveZero   otherwise.

     • nV   otherwise.

This specification permits the substitution of any other rounding algorithm which conforms to the requirements of

.

Lexical Mapping

• otherwise (

  LEX

  is a numeral):

  3. Return:

     • When

       nV

       is zero:

       • negativeZero   when the first character of LEX is '-', and

       • positiveZero   otherwise.

     • nV   otherwise.

This specification permits the substitution of any other rounding algorithm which conforms to the requirements of

.

Canonical Mapping

• l be a nonnegative integer

• s be an integer intially 1,

• c be a positive integer, and

• e be an integer.

• return '0.0E0'   when f is positiveZero;

• return '-0.0E0'   when f is negativeZero;

• otherwise (

  f

  is numeric and non-zero):

  1. Set s to −1   when  f < 0 .

  2. Let c be the smallest integer for which there exists an integer e for which  |f | = c × 10^e .

  3. Let e be log₁₀(|f | / c)   (so that  |f | = c × 10^e ).

Canonical Mapping

• l be a nonnegative integer

• s be an integer intially 1,

• c be a positive integer, and

• e be an integer.

• return '0.0E0'   when f is positiveZero;

• return '-0.0E0'   when f is negativeZero;

• otherwise (

  f

  is numeric and non-zero):

  1. Set s to −1   when  f < 0 .

  2. Let c be the smallest integer for which there exists an integer e for which  |f | = c × 10^e .

  3. Let e be log₁₀(|f | / c)   (so that  |f | = c × 10^e ).

The following functions are primarily used with the

datatype and its derivatives.

Auxiliary

-related Functions Operating on Representation Fragments

a nonnegative integer

Y is necessarily the letter 'Y' followed by a numeral N:

a nonnegative integer

M is necessarily the letter 'M' followed by a numeral N:

a nonnegative integer

D is necessarily the letter 'D' followed by a numeral N:

a nonnegative integer

D is necessarily the letter 'D' followed by a numeral N:

a nonnegative integer

M is necessarily the letter 'M' followed by a numeral N:

a nonnegative decimal number

S is necessarily 'S' followed by a numeral N:

a nonnegative integer

Return  12 × y + m .

a nonnegative decimal number

Return  3600 × h + 60 × m + s .

a nonnegative decimal number

Return  86400 × d + t .

consists of possibly a leading '

', followed by '

' and then an instance

of

and/or an instance

of

:

necessarily consists of an optional leading '

', followed by '

' and then an instance

of

:

necessarily consists of possibly a leading '

', followed by '

' and then an instance

of

:

Auxiliary

-related Functions Producing Representation Fragments

Return

• the empty string ('')   when d is zero.

Return

• the empty string ('')   when h is zero.

Return

• the empty string ('')   when m is zero.

Return

• the empty string ('') when s is zero.

Return

• the empty string ('') when all arguments are zero.

Return

• 'T0S'   when ss is zero.

• sgn be '-' if m or s is negative and the empty string ('') otherwise.

• sgn be '-' if m is negative and the empty string ('') otherwise.

• sgn be '-' if s is negative and the empty string ('') otherwise.

When adding and subtracting numbers from date/time properties, the immediate results may not conform to the limits specified. Accordingly, the following procedures are used to "normalize" potential property values to corresponding values that do conform to the appropriate limits. Normalization is required when dealing with time zone offset changes (as when converting to

from "local" values) and when adding

values to or subtracting them from

values.

Date/time Datatype Normalizing Procedures

(

,

)

If month (mo) is out of range, adjust month and year (yr) accordingly; otherwise, make no change.

1. Add (

   mo

   − 1)

   ·div·

   12 to

   yr

   .

2. Set

   mo

   to (

   mo

   − 1)

   ·mod·

   12 + 1 .

(

,

,

)

If month (mo) is out of range, or day (da) is out of range for the appropriate month, then adjust values accordingly, otherwise make no change.

2. Repeat until

   da

   is positive and not greater than

   ·daysInMonth·

   (

   yr

   ,

   mo

   ):

   1. If

      da

      exceeds

      ·daysInMonth·

      (

      yr

      ,

      mo

      ) then:

      1. Subtract that limit from da.

      2. Add 1 to mo.

   2. If

      da

      is not positive then:

      1. Subtract 1 from mo.

      3. Add the new upper limit from the table to da.

(

,

,

,

,

)

Normalizes minute, hour, month, and year values to values that obey the appropriate constraints.

(

,

,

,

,

,

)

Normalizes second, minute, hour, month, and year values to values that obey the appropriate constraints.  (This algorithm ignores leap seconds.)

Date/time Auxiliary Functions

(

,

) → integer

Returns the number of the last day of the month for any combination of year and month.

between 28 and 31 inclusive

Return:

• 28   when m is 2 and y is not evenly divisible by 4, or is evenly divisible by 100 but not by 400, or is absent,

• 29   when m is 2 and y is evenly divisible by 400, or is evenly divisible by 4 but not by 100,

• 30   when m is 4, 6, 9, or 11,

• 31   otherwise (m is 1, 3, 5, 7, 8, 10, or 12)

• yr be Yr when Yr is not absent, otherwise 1

• mo be Mowhen Mo is not absent, otherwise 1

• da be Dawhen Da is not absent, otherwise 1

• hr be Hrwhen Hr is not absent, otherwise 0

• mi be Miwhen Mi is not absent, otherwise 0

• se be Sewhen Se is not absent, otherwise 0

2. Set the

   ·year·

   property of

   dt

   to

   absent

   when

   Yr

   is

   absent

   , otherwise

   yr

   .

3. Set the

   ·month·

   property of

   dt

   to

   absent

   when

   Mo

   is

   absent

   , otherwise

   mo

   .

4. Set the

   ·day·

   property of

   dt

   to

   absent

   when

   Da

   is

   absent

   , otherwise

   da

   .

5. Set the

   ·hour·

   property of

   dt

   to

   absent

   when

   Hr

   is

   absent

   , otherwise

   hr

   .

6. Set the

   ·minute·

   property of

   dt

   to

   absent

   when

   Mi

   is

   absent

   , otherwise

   mi

   .

7. Set the

   ·second·

   property of

   dt

   to

   absent

   when

   Se

   is

   absent

   , otherwise

   se

   .

9. Return dt.

Given a dateTime S and a duration D, function ·dateTimePlusDuration· specifies how to compute a dateTime E, where E is the end of the time period with start S and duration D i.e. E = S + D.  Such computations are used, for example, to determine whether a dateTime is within a specific time period.  This algorithm can also be applied, when applications need the operation, to the addition of durations to the datatypes date, gYearMonth, gYear, gDay and gMonth, each of which can be viewed as denoting a set of dateTimes. In such cases, the addition is made to the first or starting dateTime in the set.  Note that the extension of this algorithm to types other than dateTime is not needed for schema-validity assessment.

Essentially, this calculation adds the ·months· and ·seconds· properties of the duration value separately to the dateTime value. The ·months· value is added to the starting dateTime value first. If the day is out of range for the new month value, it is pinned to be within range. Thus April 31 turns into April 30. Then the ·seconds· value is added. This latter addition can cause the year, month, day, hour, and minute to change.

Leap seconds are ignored by the computation. All calculations use 60 seconds per minute.

Thus the addition of either PT1M or PT60S to any dateTime will always produce the same result. This is a special definition of addition which is designed to match common practice, and—most importantly—be stable over time.

A definition that attempted to take leap-seconds into account would need to be constantly updated, and could not predict the results of future implementation's additions. The decision to introduce a leap second in ·UTC· is the responsibility of the [International Earth Rotation Service (IERS)]. They make periodic announcements as to when leap seconds are to be added, but this is not known more than a year in advance. For more information on leap seconds, see [U.S. Naval Observatory Time Service Department].

2. ·normalizeMonth·

   (

   yr

   ,

   mo

   ). (I.e., carry any over- or underflow, adjust month.)

3. Set

   da

   to min(

   da

   ,

   ·daysInMonth·

   (

   yr

   ,

   mo

   )). (I.e.,

   pin

   the value if necessary.)

5. ·normalizeSecond·

   (

   yr

   ,

   mo

   ,

   da

   ,

   hr

   ,

   mi

   ,

   se

   ). (I.e., carry over- or underflow of seconds up to minutes, hours, etc.)

This algorithm may be applied to date/time types other than dateTime, by

1. For each absent property, supply the minimum legal value for that property (1 for years, months, days, 0 for hours, minutes, seconds).

2. Call the function.

3. For each property absent in the initial value, set the corresponding property in the result value to absent.

Examples:

Note that the addition defined by

differs from addition on integers or real numbers in not being commutative. The order of addition of durations to instants

significant. For example, there are cases where:

((dateTime + duration1) + duration2) != ((dateTime + duration2) + duration1)

Example:

• (2000-03-30 + P1D) + P1M = 2000-03-31 + P1M = 2000-04-30

• (2000-03-30 + P1M) + P1D = 2000-04-30 + P1D = 2000-05-01

Time on Timeline for Date/time Seven-property Model Datatypes

a decimal number

• yr

  be 1971 when

  dt

  's

  ·year·

  is

  absent

  , and

  dt

  's

  ·year·

  − 1 otherwise,

• mo

  be 12 or

  dt

  's

  ·month·

  , similarly,

• hr

  be 0 or

  dt

  's

  ·hour·

  , similarly,

• mi

  be 0 or

  dt

  's

  ·minute·

  , similarly, and

2. (

   ·year·

   )

   1. Set ToTl to  31536000 × yr .

3. (Leap-year Days,

   ·month·

   , and

   ·day·

   )

   3. Add   86400 × da  to ToTl.

5. Return ToTl.

Partial Date/time Lexical Mappings

an integer

an integer