XML Schema 1.1 Part 2: Datatypes

wd-20040716

W3C Working Draft

16 July 2004 http://www.w3.org/TR/2004/WD-xmlschema11-2-20040716/ XML XHTML with visible change markup Independent copy of the schema for schema documents A schema for built-in datatypes only, in a separate namespace Independent copy of the DTD for schema documents http://www.w3.org/TR/xmlschema-2/http://www.w3.org/TR/xmlschema11-2/ David Peterson invited expert (SGMLWorks!) davep@iit.edu Paul V. Biron Kaiser Permanente, for Health Level Seven Paul.V.Biron@kp.org Ashok Malhotra invited expert (formerly of Microsoft) ashokmalhotra@alum.mit.edu

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 is the First Public Working Draft of XML Schema 1.1. It is here made available for review by W3C members and the public. It is intended to give an indication of the W3C XML Schema Working Group's intentions for this new version of the XML Schema language. It attempts to be complete in indicating what will change from version 1.0, but is not complete in terms of fully specifying how things will change.

For those primarily interested in the changes since version 1.0, the appendix, which summarizes both changes already made and also those in prospect, with links to the relevant sections of this draft, is the recommended starting point.

Please send comments on this Working Draft to www-xml-schema-comments@w3.org (archive).

Publication as a Working Draft does not imply endorsement by the W3C Membership. This is a draft document and may be updated, replaced or obsoleted by other documents at any time. It is inappropriate to cite this document as other than work in progress.

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.

Patent disclosures relevant to this specification may be found on the Working Group's Patent disclosure page in conformance with the W3C Patent Policy of 5 February 2004. An individual who has actual knowledge of a patent which the individual believes contains Essential Claim(s) with respect to this specification should disclose the information in accordance with section 6 of the W3C Patent Policy.

Per section 4 of the W3C Patent Policy, Working Group participants have 150 days from the title page date of this document to exclude essential claims from the W3C RF licensing requirements with respect to this document series. Exclusions are with respect to the exclusion reference document, defined by the W3C Patent Policy to be the latest version of a document in this series that is published no later than 90 days after the title page date of this document.

The English version of this specification is the only normative version. Information about translations of this document is available at http://www.w3.org/2001/05/xmlschema-translations.

XML Schema: Datatypes is part 2 of the specification of the XML Schema language. It defines facilities for defining datatypes to be used in XML Schemas as well as other XML specifications. The datatype language, which is itself represented in XML 1.0, provides a superset of the capabilities found in XML 1.0 document type definitions (DTDs) for specifying datatypes on elements and attributes.

RQ-152 (xml1.1)

How should this specification be aligned with XML 1.1? The changes in character set and name characters, and the question of what determines which ones to use, must be addressed.

English Extended Backus-Naur Form (formal grammar)

Introduction

RQ-21 (regex/BNF for all primitive types)

Current plan is that all datatypes defined herein will have EBNF productions at least approximately defining their lexical space, and will include a nonnormative regex derived from the EBNF if a user wishes to copy it directly.

RQ-24 (systematic facets: canonical representations for all datatypes)

It is not possible for all datatypes to have canonical representations of all values without violating the rules of derivation or adding special-purpose &cfacet;s which the WG does not deem appropriate. The WG has not yet decided how to deal with datatypes whose lexical and/or canonical mappings are context sensitive.

RQ-148 (clarify use of "truncation)

The word will probably be removed.

RQ-120 (consistent use of "derived)

"Derivations" other than "derivations by restriction" will be renamed "constructions".

RQ-24 (systematic facets: assignment of datatype to nodes without components)

Introduction to Version 1.1

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:

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

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

Allow editorial changes

Allow design cleanup to change behavior in edge cases

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

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

Do not allow any significant changes in functionality

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 behaviour 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 behaviour across 1.0 and 1.1 implementations (again except possibly in edge cases and in the details of the resulting PSVI);

Purpose

The 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.

Data oriented	Document oriented
1999-01-21 1999-01-25 Ashok Malhotra 123 Microsoft Ave. Hawthorne NY 10532-0000 555-1234 555-4321 ]]>	Paul V. Biron Ashok Malhotra Latest draft We need to discuss the latest draft immediately. Either email me at mailto:paul.v.biron@kp.org or call 555-9876 ]]>

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.

Requirements

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

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

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

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

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).

Scope

This portion of the XML Schema Language discusses 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 and .

Terminology

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:

for compatibility

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

may

Conforming documents and processors are permitted to but need not behave as described.

match

(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 it belongs to the language generated by that production.

must

Conforming documents and processors are required to behave as described; otherwise they are in error.

error

A violation of the rules of this specification; results are undefined. Conforming software detect and report an error and recover from it.

Constraints and Contributions

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:

Constraint on Schemas

Constraints on the schema components themselves, i.e. conditions components satisfy to be components at all. Largely to be found in .

Schema Representation Constraint

Constraints on the representation of schema components in XML. Some but not all of these are expressed in and .

Validation Rule

Constraints expressed by schema components which information items satisfy to be schema-valid. Largely to be found in .

Datatype System

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

The datatypes discussed in this specification are computer representations offor 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.

Datatype

In this specification, a datatype is a 3-tuple, consisting of a) a set of distinct values, called its , b) a set of lexical representations, called its , and c) a set of s that characterize properties of the , individual values or lexical items.

In this specification, a datatype is a thing with four properties:

A , which is simply a set. What the members of this set are called (beyond being generically called values) is influenced by the set of value-space operations and relations used therewith.

A , which is the domain of the . Some lexical mappings are context sensitive, so that the depends on the context in which the lexical representation occurs.

A small collection of functions, relations, and procedures associated with the datatype. Included are equality and order relations on the , and a , which is a function on the onto the .

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.

A , which serves to define and/or identify the datatype.

Along with the it is often useful to have an inverse which provides a standard for each value. Such a 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.

Value space

A value space is the set of values for a given datatype. Each value in the value space of a datatype is denoted by one or more literals in its .

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 datatype is denoted by one or more character strings in its , according to the lexical mapping. (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 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.

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

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

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

defined by restricting the of an already defined datatype to a particular subset with a given set of properties [see ]

defined as a combination of values from one or more already defined (s) by a specific construction procedure [see and ]

s have certain properties. For example, they always have the property of , some definition of equality and might be , by which individual values within the can be compared to one another. The properties of s that are recognized by this specification are defined in .

The relations of identity, equality, and order are required for each value space. A very few datatypes have other relations or operations prescribed for the purposes of this specification.

Identity

The identity relation is always defined. Every value space inherently has an identity relation. Two things are identical if they are actually the same thing: i.e., if there is no way whatever to tell them apart. The identity relation is used when making restrictions by enumeration, and when checking identity constraints. These are the only uses of identity for schema processing.

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 datatypes' value spaces are made artificially distinct if they might otherwise be considered identical. For example, there is a number two in the datatype and a number two in the 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 datatypes' value spaces used herein, they are distinct.

WARNING: Care must be taken when identifying values across distinct primitive datatypes. It turns out that, for example, 0.1 and 0.10000000009 are effectively identical in but not in . (Neither 0.1 nor 0.10000000009 are in the value space, but the lexical mapping of maps both 0.1 and 0.10000000009 to the same number (0.100000001490116119384765625) that is in the value space.)

Equality

Each 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, it has been carefully defined so as to be a congruence relation for most other operations of interest to the datatype. (This means simply that 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. For example, identity is by definition a congruence relation for all other operations of interest.) Equality is always a congruence for the order relation.

On the other hand, equality need not cover the entire value space of the datatype (though it usually does).

The equality relation is used in conjunction with order when making restrictions involving order. This is the only use of equality for schema processing.

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 were 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 timezone information in the as the value was converted to timezone Z; now the timezone is retained and two values representing the same moment in time but with different remembered timezones are now equal but not identical.

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 datatype and a number two in the 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 (and must do so if they choose to consider them identical); nonetheless, in the equality relation defined herein, they are unequal.

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 an binary infix predicate: x = y and x ≠ y . On the other hand, identity relationships are always described in words.

Order

Each datatype has an order relation prescribed. This order may be a partial order, which means that there may be values in the which are neither equal, less-than, nor greater-than. Such value pairs are incomparable. In many cases, the prescribed order is the null order: the ultimate partial order, in which no pairs are less-than or greater-than; they are all equal or incomparable. The order relation is used in conjunction with equality when making restrictions involving order. This is the only use of order for schema processing.

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 an binary infix predicate: x < y , x ≤ y , x > y , x ≥ y , and x &inc; y .

The weak order less-than-or-equal means less-than or equal and one can tell which. For example, the P1M (one month) is not less-than-or-equal P31D (thirty-one days) because P1M is not less than P31D, nor is P1M equal to P31D. Instead, P1M is incomparable with P31D.) The formal definition of order for () insures that this is true.

The value spaces of primitive datatypes are abstractions, which may have values in common. In the order relation defined herein, these value spaces are made artificially incomparable. For example, the numbers two and three are values in both the decimal datatype and the float datatype. In the order relation defined herein, two in the decimal datatype and three in the float datatype are incomparable values. Other applications making use of these datatypes may choose to consider values such as these comparable.

While it is not an error to attempt to compare values from the value spaces of two different primitive datatypes, they will alway be incomparable and therefore unequal: If x and y are in the value spaces of different primitive datatypes then x &inc; y (and hence x ≠ y ).

Lexical space

In addition to its , each datatype also has a lexical space.

A lexical space is the set of valid literals for a datatype.

For example, "100" and "1.0E2" are two different literals from the of which both denote the same value. The type system defined in this specification provides a mechanism for schema designers to control the set of values and the corresponding set of acceptable literals of those values for a datatype.

The literals in the s defined in this specification have the following characteristics:

Interoperability:

The number of literals for each value has been kept small; for many datatypes there is a one-to-one mapping between literals and values. This makes it easy to exchange the values between different systems. In many cases, conversion from locale-dependent representations will be required on both the originator and the recipient side, both for computer processing and for interaction with humans.

Basic readability:

Textual, rather than binary, literals are used. This makes hand editing, debugging, and similar activities possible.

Ease of parsing and serializing:

Where possible, literals correspond to those found in common programming languages and libraries.

Canonical Lexical Representation

While the datatypes defined in this specification have, for the most part, a single lexical representation i.e. each value in the datatype's is denoted by a single literal in its , this is not always the case. The example in the previous section showed two literals for the datatype which denote the same value. Similarly, there be several literals for one of the date or time datatypes that denote the same value using different timezone indicators.

A canonical lexical representation is a set of literals from among the valid set of literals for a datatype such that there is a one-to-one mapping between literals in the canonical lexical representation and values in the .

The Lexical Space and Lexical Mapping Some things in this section and elsewhere will need to be rewritten once we decide just how to deal with context-dependent lexical mappings and lexical spaces.

The lexical mapping for a datatype is a prescribed function whose domain is a prescribed set of character strings (the ) and whose range is the of that datatype.

The lexical space of a datatype is the prescribed domain of the lexical mapping for that datatype.

The members of the are lexical representations of the values to which they are mapped.

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

This could happen by means of a facet.

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

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 datatype which both denote the same value. The datatype system defined in this specification provides mechanisms for schema designers to control the and the corresponding set of acceptable lexical representations of those values for a datatype.

Canonical Mapping

RQ-129 (remove dependency on canonical representations)

The dependencies are in Part 1; they will be resolved there. Text in this Part will reflect that canonical representation are provided for the benefit of other users, including other specifications that might want to reference these datatypes.

RQ-126 (restricting away canonical representations)

Given the "pattern" &cfacet;, restricting away canonical representations cannot be prohibited without undue processing expense. A warning will be inserted, and RQ-129 will insure that loss of canonical representations will not affect schema processing.

While the datatypes defined in this specification generally have a single for each value (i.e., each value in the datatype's is denoted by a single representation in its ), this is not always the case. The example in the previous section shows two lexical representations from the datatype which denote the same value.

The canonical mapping is a prescribed subset of the inverse of a which is one-to-one and whose domain (where possible) is the entire range of the (the ). Thus a selects one for each value in the .

The canonical representation of a value in the of a datatype is the associated with that value by the datatype's .

Canonical mappings are not available for datatypes whose lexical mappings are context dependent (i.e., mappings for which the value of a depends on the context in which it occurs, or for which a character string may or may not be a valid similarly depending on its context)

Canonical representations are provided where feasible for the use of other appilications; they are not required for schema processing itself. A conforming schema processor implementation is not required to implement canonical mappings.

Datatype dichotomies

It is useful to categorize the datatypes defined in this specification along various dimensions, forming a set of characterization dichotomies.

Atomic vs. list vs. union datatypes

The first distinction to be made is that between , and datatypes.

Atomic datatypes are those having values which are regarded by this specification as being indivisible.

List datatypes are those having values each of which consists of a finite-length (possibly empty) sequence of values of an datatype.

Union datatypes are those whose s and s are the union of the s and s of one or more other datatypes.

For example, a single token which es Nmtoken from could be the value of an datatype (); while a sequence of such tokens could be the value of a datatype ().

Atomic datatypes

datatypes can be either or . The of an datatype is a set of "atomic" values, which for the purposes of this specification, are not further decomposable. The of an datatype is a set of literals whose internal structure is specific to the datatype in question.

List datatypes

Several type systems (such as the one described in ) treat datatypes as special cases of the more general notions of aggregate or collection datatypes.

datatypes are always . The of a datatype is a set of finite-length sequences of values. The of a datatype is a set of literals whose internal structure is a space-separated sequence of literals of the datatype of the items in the .

The or datatype that participates in the definition of a datatype is known as the itemType of that datatype.

]]> 8 10.5 12 ]]>

A datatype can be from an datatype whose allows space (such as or )or a datatype any of whose 's allows space. In such a case, regardless of the input, list items will be separated at space boundaries.

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

In the above example, the value of the someElement element is not a of 3; rather, it is a of 18.

When a datatype is from a datatype, the following s apply:

For each of , and , the unit of length is measured in number of list items. The value of is fixed to the value collapse.

For datatypes the is composed of space-separated literals of its . Hence, any specified when a new datatype is from a datatype is matched against each literal of the datatype and not against the literals of the datatype that serves as its .

123 456 123 987 456 123 987 567 456 ]]>

The for the datatype is defined as the lexical form in which each item in the has the canonical lexical representation of its .

Union datatypes

The and of a datatype are the union of the s and s of its . datatypes are always . Currently, there are no datatypes.

A prototypical example of a type is the maxOccurs attribute on the element element in XML Schema itself: it is a union of nonNegativeInteger and an enumeration with the single member, the string "unbounded", as shown below.

use="optional" use="optional" default="1" ]]>

Any number (greater than 1) of or s can participate in a type.

The datatypes that participate in the definition of a datatype are known as the memberTypes of that datatype.

The order in which the are specified in the definition (that is, the order of the <simpleType> children of the <union> element, or the order of the s in the memberTypes attribute) is significant. During validation, an element or attribute's value is validated against the in the order in which they appear in the definition until a match is found. 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 .

]]> 1 large 1 ]]>

The for a datatype is defined as the lexical form in which the values have the canonical lexical representation of the appropriate .

A datatype which is in this specification need not be an "atomic" datatype in any programming language used to implement this specification. Likewise, a datatype which is a in this specification need not be a "list" datatype in any programming language used to implement this specification. Furthermore, a datatype which is a in this specification need not be a "union" datatype in any programming language used to implement this specification.

Primitive vs. derived datatypes

Next, we distinguish between and datatypes.

Primitive datatypes are those that are not defined in terms of other datatypes; they exist ab initio.

Derived datatypes are those that are defined in terms of other datatypes.

For example, in this specification, is a well-defined mathematical concept that cannot be defined in terms of other datatypes, while a is a special case of the more general datatype .

RQ-141 (add abstract anyAtomicType) RQ-24 (systematic facets: status and value space of anySimpleType)

A new "magic" datatype will be introduced as a child of anySimpleType and the parent of all primitive atomic datatypes.

The simple ur-type definition is a special restriction of the ur-type definition whose name is anySimpleType in the XML Schema namespace. anySimpleType can be considered as the of all datatypes. anySimpleType is considered to have an unconstrained lexical space and a consisting of the union of the s of all the datatypes and the set of all lists of all members of the s of all the datatypes.

The datatypes defined by this specification fall into both the and categories. It is felt that a judiciously chosen set of datatypes will serve the widest possible audience by providing a set of convenient datatypes that can be used as is, as well as providing a rich enough base from which the variety of datatypes needed by schema designers can be .

In the example above, is from .

A datatype which is in this specification need not be a "primitive" datatype in any programming language used to implement this specification. Likewise, a datatype which is in this specification need not be a "derived" datatype in any programming language used to implement this specification.

As described in more detail in , each datatype be defined in terms of another datatype in one of three ways: 1) by assigning s which serve to restrict the of the datatype to a subset of that of the ; 2) by creating a datatype whose consists of finite-length sequences of values of its ; or 3) by creating a datatype whose consists of the union of the s of its .

Derived by restriction

A datatype is said to be by restriction from another datatype when values for zero or more s are specified that serve to constrain its and/or its to a subset of those of its .

Every datatype that is by restriction is defined in terms of an existing datatype, referred to as its base type. base types can be either or .

Derived by list

A datatype can be from another datatype (its ) by creating a that consists of a finite-length sequence of values of its .

Derived by union

One datatype can be from one or more datatypes by ing their s and, consequently, their s.

Built-in vs. user-derived datatypes

Built-in datatypes are those which are defined in this specification, and can be either or ;

User-derived datatypes are those datatypes that are defined by individual schema designers.

Conceptually there is no difference between the datatypes included in this specification and the datatypes which will be created by individual schema designers. The 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 datatypes in this specification serves to demonstrate the mechanics and utility of the datatype generation facilities of this specification.

A datatype which is in this specification need not be a "built-in" datatype in any programming language used to implement this specification. Likewise, a datatype which is in this specification need not be a "user-derived" datatype in any programming language used to implement this specification.

Built-in datatypes

Each built-in datatype in this specification (both and ) can be uniquely addressed via a URI Reference constructed as follows:

the base URI is the URI of the XML Schema namespace

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:

the base URI is the URI of the XML Schema namespace

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:

the base URI is the URI of the XML Schema namespace

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

Namespace considerations

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

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

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

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

This applies to both and datatypes.

Each datatype is also associated with a unique namespace. However, datatypes do not come from the namespace defined by this specification; rather, they come from the namespace of the schema in which they are defined (see XML Representation of Schemas in ).

Primitive datatypes

The datatypes defined by this specification are described below. For each datatype, the and are defined, s which apply to the datatype are listed and any datatypes from this datatype are specified.

datatypes can only be added by revisions to this specification.

string

The string datatype represents character strings in XML. The of string is the set of finite-length sequences of characters (as defined in ) that the Char production from . A character is an atomic unit of communication; it is not further specified except to note that every character has a corresponding Universal Character Set code point, which is an integer.

Many human languages have writing systems that require child elements for control of aspects such as bidirectional formating or ruby annotation (see and Section 8.2.4 Overriding the bidirectional algorithm: the BDO element of ). Thus, string, as a simple type that can contain only characters but not child elements, is often not suitable for representing text. In such situations, a complex type that allows mixed content should be considered. For more information, see Section 5.5 Any Element, Any Attribute of .

As noted in , the fact that this specification does not specify an for does not preclude other applications from treating strings as being ordered.

Derived datatypes boolean

boolean has the required to support the mathematical concept of binary-valued logic: {true, false}.

Lexical representation

An instance of a datatype that is defined as can have the following legal literals {true, false, 1, 0}.

Canonical representation

The canonical representation for boolean is the set of literals {true, false}.

decimal

RQ-150 (minimum nbr of digits for decimal)

The minimum will be lowered to 16 digits; a health warning will be added to indicate that optimized implementations of derived datatypes may exceed the limits of the base, but are not required to.

decimal represents a subset of the real numbers, which can be represented by decimal numerals. The of decimal is the set of numbers that can be obtained by multiplying an integer by a non-positive power of ten, i.e., expressible as i × 10^-n 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 on decimal is the order relation on real numbers, restricted to this subset.

All processors support decimal numbers with a minimum of 18 decimal digits (i.e., with a of 18). However, processors set an application-defined limit on the maximum number of decimal digits they are prepared to support, in which case that application-defined maximum number be clearly documented.

Lexical representation

decimal has a lexical representation consisting of a 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.

Canonical representation

The canonical representation for decimal is defined by prohibiting certain options from the . Specifically, the preceding optional "+" sign is prohibited. The decimal point is required. 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.

Derived datatypes float

RQ-1 (canonical representation of float, double)

The description of canonical representations for float and double needs to be cleaned up.

RQ-140 (positive and negative zero in float and double)

Two zeros will be provided similar to those in precisionDecimal

float is patterned after the IEEE single-precision 32-bit floating point type . The basic of float consists of the values m × 2^e, where m is an integer whose absolute value is less than 2^24, and e is an integer between -149 and 104, inclusive. In addition to the basic described above, the of float also contains the following three special values: positive and negative infinity and not-a-number (NaN). The on float is: x < y iff y - x is positive for x and y in the value space. Positive infinity is greater than all other non-NaN values. NaN equals itself but is incomparable with (neither greater than nor less than) any other value in the .

"Equality" in this Recommendation is defined to be "identity" (i.e., values that are identical in the are equal and vice versa). Identity must be used for the few operations that are defined in this Recommendation. Applications using any of the datatypes defined in this Recommendation may use different definitions of equality for computational purposes; -based computation systems are examples. Nothing in this Recommendation should be construed as requiring that such applications use identity as their equality relationship when computing.

Any value incomparable with the value used for the four bounding facets (, , , and ) will be excluded from the resulting restricted . In particular, when "NaN" is used as a facet value for a bounding facet, since no other float values are with it, the result is a either having NaN as its only member (the inclusive cases) or that is empty (the exclusive cases). If any other value is used for a bounding facet, NaN will be excluded from the resulting restricted ; to add NaN back in requires union with the NaN-only space.

This datatype differs from that of in that there is only one NaN and only one zero. This makes the equality and ordering of values in the data space differ from that of only in that for schema purposes NaN = NaN.

A literal in the representing a decimal number d maps to the normalized value in the of float that is closest to d in the sense defined by ; if d is exactly halfway between two such values then the even value is chosen.

Lexical representation

float values have a lexical representation consisting of a mantissa followed, optionally, by the character "E" or "e", followed by an exponent. The exponent be an . The mantissa must be a number. The representations for exponent and mantissa must follow the lexical rules for and . If the "E" or "e" and the following exponent are omitted, an exponent value of 0 is assumed.

The special values positive and negative infinity and not-a-number have lexical representations INF, -INF and NaN, respectively. Lexical representations for zero may take a positive or negative sign.

For example, -1E4, 1267.43233E12, 12.78e-2, 12 , -0, 0 and INF are all legal literals for float.

Canonical representation

The canonical representation for float is defined by prohibiting certain options from the . Specifically, the exponent must be indicated by "E". Leading zeroes and the preceding optional "+" sign are prohibited in the exponent. If the exponent is zero, it must be indicated by "E0". For the mantissa, the preceding optional "+" sign is prohibited and the decimal point is required. Leading and trailing zeroes are prohibited subject to the following: number representations must be normalized such that there is a single digit which is non-zero to the left of the decimal point and at least a single digit to the right of the decimal point unless the value being represented is zero. The canonical representation for zero is 0.0E0.

double

The double datatype is patterned after the IEEE double-precision 64-bit floating point type . The basic of double consists of the values m × 2^e, where m is an integer whose absolute value is less than 2^53, and e is an integer between -1075 and 970, inclusive. In addition to the basic described above, the of double also contains the following three special values: positive and negative infinity and not-a-number (NaN). The on double is: x < y iff y - x is positive for x and y in the value space. Positive infinity is greater than all other non-NaN values. NaN equals itself but is incomparable with (neither greater than nor less than) any other value in the .

Any value incomparable with the value used for the four bounding facets (, , , and ) will be excluded from the resulting restricted . In particular, when "NaN" is used as a facet value for a bounding facet, since no other double values are with it, the result is a either having NaN as its only member (the inclusive cases) or that is empty (the exclusive cases). If any other value is used for a bounding facet, NaN will be excluded from the resulting restricted ; to add NaN back in requires union with the NaN-only space.

A literal in the representing a decimal number d maps to the normalized value in the of double that is closest to d; if d is exactly halfway between two such values then the even value is chosen. This is the best approximation of d (, ), which is more accurate than the mapping required by .

Lexical representation

double values have a lexical representation consisting of a mantissa followed, optionally, by the character "E" or "e", followed by an exponent. The exponent be an integer. The mantissa must be a decimal number. The representations for exponent and mantissa must follow the lexical rules for and . If the "E" or "e" and the following exponent are omitted, an exponent value of 0 is assumed.

For example, -1E4, 1267.43233E12, 12.78e-2, 12 , -0, 0 and INF are all legal literals for double.

Canonical representation

The canonical representation for double is defined by prohibiting certain options from the . Specifically, the exponent must be indicated by "E". Leading zeroes and the preceding optional "+" sign are prohibited in the exponent. If the exponent is zero, it must be indicated by "E0". For the mantissa, the preceding optional "+" sign is prohibited and the decimal point is required. Leading and trailing zeroes are prohibited subject to the following: number representations must be normalized such that there is a single digit which is non-zero to the left of the decimal point and at least a single digit to the right of the decimal point unless the value being represented is zero. The canonical representation for zero is 0.0E0.

precisionDecimal

RQ-31 (precisionDecimal)

precisionDecimal has been added. It is possible that precisionDecimal will replace decimal.

RQ-30 (negative fractionDigits for decimal)

The WG feels that having this capability for precisionDecimal will be adequate.

RQ-28 (scientific notation for decimal)

The WG feels that having this capability for precisionDecimal will be adequate.

The precisionDecimal datatype is similar to , except that each value carries with it a precision as well as a numeric value; it also includes special values for positive and negative infinity and not a number, and differentiates between positive zero and negative zero. Precision is explained in . The special values are introduced to make the datatype correspond closely to decimal datatypes whose definition is planned for the next revision of IEEE/ANSI 754.

Value Space Properties of Values numericalValue a &decimal;, positiveInfinity, negativeInfinity or notANumber arthmeticPrecision an &integer; or absent; absent if and only if is a . sign positive, negative, or absent; must be positive if is positive or positiveInfinity, must be negative if is negative or negativeInfinity, must be absent if and only if is notANumber

The property is redundant except when is zero; in other cases, the value is fully determined by the value. Code optimization may well make it desirable to separate out the and the absolute value of the , which will make implementation easier, but the verbal descriptions of such things as equality and order somewhat more complicated.

As explained below, the lexical representation of the value object whose is notANumber is NaN. Accordingly, in English text we use NaN to refer to that value. Similarly we use INF and −INF to refer to the two value objects whose is positiveInfinity and negativeInfinity. These three value objects are also informally called not-a-number, positive infinity, and negative infinity.

Equality and order for are defined as follows:

Two numerical values are ordered (or equal) as their values are ordered (or equal). (This means the two zeros with a given but different are equal; negative zeros are not ordered less than positive zeros.)

INF is equal only to itself, and is greater than −INF and all numerical values.

−INF is equal only to itself, and is less than INF and all numerical values.

NaN is incomparable with all values, including itself.

Lexical Mapping The notation constraining facet has not yet been written up. Its effect will be to remove some portions of the lexical mapping.

's lexical space is the set of all no-decimal-point, decimal, and scientific numerals, plus the character strings INF, +INF, -INF, and NaN. (Lexical representations of numbers are traditionally called numerals.) The notation constraining facet can remove any one or two of the three subsets of numerals, with corresponding reductions in the value space. Using this facet rather than will change the canonical mapping to insure that the resulting datatype will still have canonical representations of all its values. Lexical Space precisionDecimalRep | | |

Canonical mappings are not used during schema processing. They are provided in this specification for the benefit of other users of these datatype definitions who may find them useful, and for other specifications which might find it useful to reference them normatively.

&CFacet;s The notation constraining facet has not yet been written up. It's effect will be to remove some portions of the lexical mapping.

precisionDecimal has the following &cfacet;s:

fractionDigits

minFractionDigits

totalDigits

specials

notation constraining

maxInclusive

maxExclusive

minInclusive

minExclusive

pattern

whitespace

eunmeration

duration

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

Value Space

Durations can be modeled in at least two ways: as six-property tuples (similar to the seven-property model used for other date/time datatypes) or as two-property tuples (somewhat similar to the alternative one-property timeOnTimeline model especially useful for order). For durations, it is useful to use the latter: values are two-property tuples. (Note, however, that the six-property model was implicitly used in Schema 1.0. The only effective difference to the user caused by this change is in the canonical representations.) See for more information on the seven-property model. Properties of Values month second Must not be negative if is positive, and not be positive if is negative. is partially ordered. Equality and order are defined in terms of that of , and are determined by adding each value pair in turn to 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 incomparable.

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 any other values, unless one is within a leap-second and either the other is also or is the beginning moment of the next second—in which case, the two results will be equal even though the original values were not. Therefore, two values are incomparable if and only if they can ever result in different orders when added to any value not within a leap-second.

This minor anomaly is the result of having unaware of leap-seconds while the other date/time primitive datatypes are leap-second aware.

It turns out that under the definition just given, two values are equal if and only if they are identical.

Two totally ordered datatypes ( and ) are derived from in .

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.

Lexical Space

The lexical representations of are more or less based on the pattern: PnYnMnDTnHnMnS

More precisely, the of is the set of character strings that satisfy as defined by the following productions: Lexical Representation Fragments duYearFrag Y duMonthFrag M duDayFrag D duHourFrag H duMinuteFrag M duSecondFrag ( | ) S duYearMonthFrag ( ?) | duTimeFrag T (( ? ?) | ( ?) | ) duDayTimeFrag ( ?) | Lexical Representation durationLexicalRep -? P (( ?) | )

Thus, a consists of one or more of a , , , , , and/or , in order, with letters P and T (and perhaps a -) where appropriate.

The production is equivalent to this regular expression -?P(((([0-9]+Y([0-9]+M)?)| ( ([0-9]+M) ) )(([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) ) )) ) )?)| ( (([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) ) )) ) ) ) ) once you delete the whitespace. Redundant parehtheses are shown as ghosts; some find them helpful in reading the expression.)

The for is called herein, is defined as follows:.

The canonical mapping for is called herein, is defined as follows:.

dateTime

dateTime values may be viewed as objects with integer-valued year, month, day, hour and minute properties, a decimal-valued second property, and a boolean timezoned property. Each such object also has one decimal-valued method or computed property, timeOnTimeline, whose value is always a decimal number; the values are dimensioned in seconds, the integer 0 is 0001-01-01T00:00:00 and the value of timeOnTimeline for other dateTime values is computed using the Gregorian algorithm as modified for leap-seconds. The timeOnTimeline values form two related "timelines", one for timezoned values and one for non-timezoned values. Each timeline is a copy of the of , with integers given units of seconds.

The of dateTime is closely related to the dates and times described in ISO 8601. For clarity, the text above specifies a particular origin point for the timeline. It should be noted, however, that schema processors need not expose the timeOnTimeline value to schema users, and there is no requirement that a timeline-based implementation use the particular origin described here in its internal representation. Other interpretations of the which lead to the same results (i.e., are isomorphic) are of course acceptable.

All timezoned times are Coordinated Universal Time (, sometimes called "Greenwich Mean Time"). Other timezones indicated in lexical representations are converted to during conversion of literals to values. "Local" or untimezoned times are presumed to be the time in the timezone of some unspecified locality as prescribed by the appropriate legal authority; currently there are no legally prescribed timezones which are durations whose magnitude is greater than 14 hours. The value of each numeric-valued property (other than timeOnTimeline) is limited to the maximum value within the interval determined by the next-higher property. For example, the day value can never be 32, and cannot even be 29 for month 02 and year 2002 (February 2002).

The date and time datatypes described in this recommendation were inspired by . '0001' is the lexical representation of the year 1 of the Common Era (1 CE, sometimes written "AD 1" or "1 AD"). There is no year 0, and '0000' is not a valid lexical representation. '-0001' is the lexical representation of the year 1 Before Common Era (1 BCE, sometimes written "1 BC").

Those using this (1.0) version of this Recommendation to represent negative years should be aware that the interpretation of lexical representations beginning with a '-' is likely to change in subsequent versions.

makes no mention of the year 0; in the form '0000' was disallowed and this recommendation disallows it as well. However, , which became available just as we were completing version 1.0, allows the form '0000', representing the year 1 BCE. A number of external commentators have also suggested that '0000' be allowed, as the lexical representation for 1 BCE, which is the normal usage in astronomical contexts. It is the intention of the XML Schema Working Group to allow '0000' as a lexical representation in the dateTime, date, gYear, and gYearMonth datatypes in a subsequent version of this Recommendation. '0000' will be the lexical representation of 1 BCE (which is a leap year), '-0001' will become the lexical representation of 2 BCE (not 1 BCE as in this (1.0) version), '-0002' of 3 BCE, etc.

See the conformance note in which applies to this datatype as well.

Lexical representation

The of dateTime consists of finite-length sequences of characters of the form: '-'? yyyy '-' mm '-' dd 'T' hh ':' mm ':' ss ('.' s+)? (zzzzzz)?, where

'-'? yyyy is a four-or-more digit optionally negative-signed numeral that represents the year; if more than four digits, leading zeros are prohibited, and '0000' is prohibited (see the Note above ; also note that a plus sign is not permitted);

the remaining '-'s are separators between parts of the date portion;

the first mm is a two-digit numeral that represents the month;

dd is a two-digit numeral that represents the day;

'T' is a separator indicating that time-of-day follows;

hh is a two-digit numeral that represents the hour; '24' is permitted if the minutes and seconds represented are zero, and the dateTime value so represented is the first instant of the following day (the hour property of a dateTime object in the cannot have a value greater than 23);

':' is a separator between parts of the time-of-day portion;

the second mm is a two-digit numeral that represents the minute;

ss is a two-integer-digit numeral that represents the whole seconds;

'.' s+ (if present) represents the fractional seconds;

zzzzzz (if present) represents the timezone (as described below).

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 2002-10-10T17:00:00Z, five hours later than 2002-10-10T12:00:00Z.

For further guidance on arithmetic with dateTimes and durations, see .

Canonical representation

Except for trailing fractional zero digits in the seconds representation, '24:00:00' time representations, and timezone (for timezoned values), the mapping from literals to values is one-to-one. Where there is more than one possible representation, the canonical representation is as follows:

The 2-digit numeral representing the hour must not be '24';

The fractional second string, if present, must not end in '0';

for timezoned values, the timezone must be represented with 'Z' (All timezoned dateTime values are .).

Timezones

Timezones are durations with (integer-valued) hour and minute properties (with the hour magnitude limited to at most 14, and the minute magnitude limited to at most 59, except that if the hour magnitude is 14, the minute value must be 0); they may be both positive or both negative.

The lexical representation of a timezone is a string of the form: (('+' | '-') hh ':' mm) | 'Z', where

hh is a two-digit numeral (with leading zeros as required) that represents the hours,

mm is a two-digit numeral that represents the minutes,

'+' indicates a nonnegative duration,

'-' indicates a nonpositive duration.

The mapping so defined is one-to-one, except that '+00:00', '-00:00', and 'Z' all represent the same zero-length duration timezone, ; 'Z' is its canonical representation.

When a timezone is added to a dateTime, the result is the date and time "in that timezone". For example, 2002-10-10T12:00:00+05:00 is 2002-10-10T07:00:00Z and 2002-10-10T00:00:00+05:00 is 2002-10-09T19:00:00Z.

Order relation on dateTime

dateTime value objects on either timeline are totally ordered by their timeOnTimeline values; between the two timelines, dateTime value objects are ordered by their timeOnTimeline values when their timeOnTimeline values differ by more than fourteen hours, with those whose difference is a duration of 14 hours or less being incomparable.

In general, the on dateTime is a partial order since there is no determinate relationship between certain instants. For example, there is no determinate ordering between (a) 2000-01-20T12:00:00 and (b) 2000-01-20T12:00:00Z. Based on timezones currently in use, (c) could vary from 2000-01-20T12:00:00+12:00 to 2000-01-20T12:00:00-13:00. It is, however, possible for this range to expand or contract in the future, based on local laws. Because of this, the following definition uses a somewhat broader range of indeterminate values: +14:00..-14:00.

The following definition uses the notation S[year] to represent the year field of S, S[month] to represent the month field, and so on. The notation (Q & "-14:00") means adding the timezone -14:00 to Q, where Q did not already have a timezone. This is a logical explanation of the process. Actual implementations are free to optimize as long as they produce the same results.

The ordering between two dateTimes P and Q is defined by the following algorithm:

A.Normalize P and Q. That is, if there is a timezone present, but it is not Z, convert it to Z using the addition operation defined in

Thus 2000-03-04T23:00:00+03:00 normalizes to 2000-03-04T20:00:00Z

B. If P and Q either both have a time zone or both do not have a time zone, compare P and Q field by field from the year field down to the second field, and return a result as soon as it can be determined. That is:

For each i in {year, month, day, hour, minute, second}

If P[i] and Q[i] are both not specified, continue to the next i

If P[i] is not specified and Q[i] is, or vice versa, stop and return P <> Q

If P[i] < Q[i], stop and return P < Q

If P[i] > Q[i], stop and return P > Q

Stop and return P = Q

C.Otherwise, if P contains a time zone and Q does not, compare as follows:

P < Q if P < (Q with time zone +14:00)

P > Q if P > (Q with time zone -14:00)

P <> Q otherwise, that is, if (Q with time zone +14:00) < P < (Q with time zone -14:00)

D. Otherwise, if P does not contain a time zone and Q does, compare as follows:

P < Q if (P with time zone -14:00) < Q.

P > Q if (P with time zone +14:00) > Q.

P <> Q otherwise, that is, if (P with time zone +14:00) < Q < (P with time zone -14:00)

Examples:

Determinate	Indeterminate
2000-01-15T00:00:00 < 2000-02-15T00:00:00	2000-01-01T12:00:00 <> 1999-12-31T23:00:00Z
2000-01-15T12:00:00 < 2000-01-16T12:00:00Z	2000-01-16T12:00:00 <> 2000-01-16T12:00:00Z
	2000-01-16T00:00:00 <> 2000-01-16T12:00:00Z

Totally ordered dateTimes

Certain derived types from dateTime can be guaranteed have a total order. To do so, they must require that a specific set of fields are always specified, and that remaining fields (if any) are always unspecified. For example, the date datatype without time zone is defined to contain exactly year, month, and day. Thus dates without time zone have a total order among themselves.

time

time represents an instant of time that recurs every day. The of time is the space of time of day values as defined in § 5.3 of . Specifically, it is a set of zero-duration daily time instances.

Since the lexical representation allows an optional time zone indicator, time values are partially ordered because it may not be able to determine the order of two values one of which has a time zone and the other does not. The order relation on time values is the using an arbitrary date. See also . Pairs of time values with or without time zone indicators are totally ordered.

See the conformance note in which applies to the seconds part of this datatype as well.

Lexical representation

The lexical representation for time is the left truncated lexical representation for : hh:mm:ss.sss with optional following time zone indicator. For example, to indicate 1:20 pm for Eastern Standard Time which is 5 hours behind Coordinated Universal Time (), one would write: 13:20:00-05:00. See also .

Canonical representation

The canonical representation for time is defined by prohibiting certain options from the . Specifically, either the time zone must be omitted or, if present, the time zone must be Coordinated Universal Time () indicated by a "Z". Additionally, the canonical representation for midnight is 00:00:00.

date

The of date consists of top-open intervals of exactly one day in length on the timelines of , beginning on the beginning moment of each day (in each timezone), i.e. '00:00:00', up to but not including '24:00:00' (which is identical with '00:00:00' of the next day). For nontimezoned values, the top-open intervals disjointly cover the nontimezoned timeline, one per day. For timezoned values, the intervals begin at every minute and therefore overlap.

A "date object" is an object with year, month, and day properties just like those of objects, plus an optional timezone-valued timezone property. (As with values of timezones are a special case of durations.) Just as a object corresponds to a point on one of the timelines, a date object corresponds to an interval on one of the two timelines as just described.

Timezoned date values track the starting moment of their day, as determined by their timezone; said timezone is generally recoverable for canonical representations. The recoverable timezone is that duration which is the result of subtracting the first moment (or any moment) of the timezoned date from the first moment (or the corresponding moment) on the same date. s are always durations between '+12:00' and '-11:59'. This "timezone normalization" (which follows automatically from the definition of the date ) is explained more in .

For example: the first moment of 2002-10-10+13:00 is 2002-10-10T00:00:00+13, which is 2002-10-09T11:00:00Z, which is also the first moment of 2002-10-09-11:00. Therefore 2002-10-10+13:00 is 2002-10-09-11:00; they are the same interval.

For most timezones, either the first moment or last moment of the day (a value, always ) will have a date portion different from that of the date itself! However, noon of that date (the midpoint of the interval) in that (normalized) timezone will always have the same date portion as the date itself, even when that noon point in time is normalized to . For example, 2002-10-10-05:00 begins during 2002-10-09Z and 2002-10-10+05:00 ends during 2002-10-11Z, but noon of both 2002-10-10-05:00 and 2002-10-10+05:00 falls in the interval which is 2002-10-10Z.

See the conformance note in which applies to the year part of this datatype as well.

Lexical representation

For the following discussion, let the "date portion" of a or date object be an object similar to a or date object, with similar year, month, and day properties, but no others, having the same value for these properties as the original or date object.

The of date consists of finite-length sequences of characters of the form: '-'? yyyy '-' mm '-' dd zzzzzz? where the date and optional timezone are represented exactly the same way as they are for . The first moment of the interval is that represented by: '-' yyyy '-' mm '-' dd 'T00:00:00' zzzzzz? and the least upper bound of the interval is the timeline point represented (noncanonically) by: '-' yyyy '-' mm '-' dd 'T24:00:00' zzzzzz?.

The of a date will always be a duration between '+12:00' and '11:59'. Timezone lexical representations, as explained for , can range from '+14:00' to '-14:00'. The result is that literals of dates with very large or very negative timezones will map to a "normalized" date value with a different from that represented in the original representation, and a matching difference of +/- 1 day in the date itself.

Canonical representation

Given a member of the date , the date portion of the canonical representation (the entire representation for nontimezoned values, and all but the timezone representation for timezoned values) is always the date portion of the canonical representation of the interval midpoint (the representation, truncated on the right to eliminate 'T' and all following characters). For timezoned values, append the canonical representation of the .

gYearMonth

gYearMonth represents a specific gregorian month in a specific gregorian year. The of gYearMonth is the set of Gregorian calendar months as defined in § 5.2.1 of . Specifically, it is a set of one-month long, non-periodic instances e.g. 1999-10 to represent the whole month of 1999-10, independent of how many days this month has.

Since the lexical representation allows an optional time zone indicator, gYearMonth values are partially ordered because it may not be possible to unequivocally determine the order of two values one of which has a time zone and the other does not. If gYearMonth values are considered as periods of time, the order relation on gYearMonth values is the order relation on their starting instants. This is discussed in . See also . Pairs of gYearMonth values with or without time zone indicators are totally ordered.

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.

See the conformance note in which applies to the year part of this datatype as well.

Lexical representation

The lexical representation for gYearMonth is the reduced (right truncated) lexical representation for : CCYY-MM. No left truncation is allowed. An optional following time zone qualifier is allowed. To accommodate year values outside the range from 0001 to 9999, additional digits can be added to the left of this representation and a preceding "-" sign is allowed.

For example, to indicate the month of May 1999, one would write: 1999-05. See also .

gYear

gYear represents a gregorian calendar year. The of gYear is the set of Gregorian calendar years as defined in § 5.2.1 of . Specifically, it is a set of one-year long, non-periodic instances e.g. lexical 1999 to represent the whole year 1999, independent of how many months and days this year has.

Since the lexical representation allows an optional time zone indicator, gYear values are partially ordered because it may not be possible to unequivocally determine the order of two values one of which has a time zone and the other does not. If gYear values are considered as periods of time, the order relation on gYear values is the order relation on their starting instants. This is discussed in . See also . Pairs of gYear values with or without time zone indicators are totally ordered.

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.

See the conformance note in which applies to the year part of this datatype as well.

Lexical representation

The lexical representation for gYear is the reduced (right truncated) lexical representation for : CCYY. No left truncation is allowed. An optional following time zone qualifier is allowed as for . To accommodate year values outside the range from 0001 to 9999, additional digits can be added to the left of this representation and a preceding "-" sign is allowed.

For example, to indicate 1999, one would write: 1999. See also .

gMonthDay

gMonthDay is a gregorian date that recurs, specifically a day of the year such as the third of May. Arbitrary recurring dates are not supported by this datatype. The of gMonthDay is the set of calendar dates, as defined in § 3 of . Specifically, it is a set of one-day long, annually periodic instances.

Since the lexical representation allows an optional time zone indicator, gMonthDay values are partially ordered because it may not be possible to unequivocally determine the order of two values one of which has a time zone and the other does not. If gMonthDay values are considered as periods of time, in an arbitrary leap year, the order relation on gMonthDay values is the order relation on their starting instants. This is discussed in . See also . Pairs of gMonthDay values with or without time zone indicators are totally ordered.

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.

Lexical representation

The lexical representation for gMonthDay is the left truncated lexical representation for : --MM-DD. An optional following time zone qualifier is allowed as for . No preceding sign is allowed. No other formats are allowed. See also .

This datatype can be used to represent a specific day in a month. To say, for example, that my birthday occurs on the 14th of September ever year.

gDay

gDay is a gregorian day that recurs, specifically a day of the month such as the 5th of the month. Arbitrary recurring days are not supported by this datatype. The of gDay is the space of a set of calendar dates as defined in § 3 of . Specifically, it is a set of one-day long, monthly periodic instances.

gDay is a datatype that represents whole days within an arbitrary month—days that recur at the same point in each (Gregorian) month. This datatype can beis used to represent a specific day of the month. To say, for example, that I get my paycheckindicate, 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.)

Since the lexical representation allows an optional time zone indicator, gDay values are partially ordered because it may not be possible to unequivocally determine the order of two values one of which has a time zone and the other does not. If gDay values are considered as periods of time, in an arbitrary month that has 31 days, the order relation on gDay values is the order relation on their starting instants. This is discussed in . See also . Pairs of gDay values with or without time zone indicators are totally ordered.

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

Value Space

uses the , with , , , , and required to be absent. remains and must be between 1 and 31 inclusive.

RQ-13 (time zone crosses date line)

The "seven property model" rewrite of date/time datatype descriptions includes a carefully crafted definition of order that insures that for repeating datatypes (time, gDay, etc.), timezoned values will be compared as though they are on the same "calendar day" ("raw" property values) so that in any given timezone, the days start at "raw" 00:00:00 and end not quite including "raw" 24:00:00. Days are not 00:00:00Z to 24:00:00Z in timezones other than Z.

Equality and order are as prescribed in . Since values (days) are ordered by their first moments, it is possible for apparent anomalies to appear in the order when values are differ by at least 24 hours. (It is possible for 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

Timezones do not cause wrap-around at the end of the month: ---31−13:00 in one month may start after ---01+13:00 in the next month, but nonetheless ---01+13:00 < ---31−13:00 .

Lexical representation

The lexical representation for gDay is the left truncated lexical representation for : ---DD . An optional following time zone qualifier is allowed as for . No preceding sign is allowed. No other formats are allowed. See also .

Lexical Mappings

The lexical representations for are restrictions of those of , as follows: Lexical Space gDayLexicalRep --- ? The is equivalent to this regular expression: ---([0-2][0-9]|3[01])((+|-)(0[0-9]|1[0-4]):[0-5][0-9])?

The lexical mapping and canonical mapping for are defined as follows:

gMonth

gMonth is a gregorian month that recurs every year. The of gMonth is the space of a set of calendar months as defined in § 3 of . Specifically, it is a set of one-month long, yearly periodic instances.

This datatype can be used to represent a specific month. To say, for example, that Thanksgiving falls in the month of November.

Since the lexical representation allows an optional time zone indicator, gMonth values are partially ordered because it may not be possible to unequivocally determine the order of two values one of which has a time zone and the other does not. If gMonth values are considered as periods of time, the order relation on gMonth is the order relation on their starting instants. This is discussed in . See also . Pairs of gMonth values with or without time zone indicators are totally ordered.

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.

Lexical representation

The lexical representation for gMonth is the left and right truncated lexical representation for : --MM. An optional following time zone qualifier is allowed as for . No preceding sign is allowed. No other formats are allowed. See also .

hexBinary

hexBinary represents arbitrary hex-encoded binary data. The of hexBinary is the set of finite-length sequences of binary octets.

Lexical Representation

hexBinary has a lexical representation where each binary octet is encoded as a character tuple, consisting of two hexadecimal digits ([0-9a-fA-F]) representing the octet code. For example, "0FB7" is a hex encoding for the 16-bit integer 4023 (whose binary representation is 111110110111).

Canonical Representation

The canonical representation for hexBinary is defined by prohibiting certain options from the . Specifically, the lower case hexadecimal digits ([a-f]) are not allowed.

base64Binary

base64Binary represents Base64-encoded arbitrary binary data. The of base64Binary is the set of finite-length sequences of binary octets. For base64Binary data the entire binary stream is encoded using the Base64 Alphabet in .

The lexical forms of base64Binary values are limited to the 65 characters of the Base64 Alphabet defined in , i.e., a-z, A-Z, 0-9, the plus sign (+), the forward slash (/) and the equal sign (=), together with the characters defined in as white space. No other characters are allowed.

For compatibility with older mail gateways, suggests that base64 data should have lines limited to at most 76 characters in length. This line-length limitation is not mandated in the lexical forms of base64Binary data and must not be enforced by XML Schema processors.

The lexical space of base64Binary is given by the following grammar (the notation is that used in ); legal lexical forms must match the Base64Binary production.

Base64Binary ::= ((B64S B64S B64S B64S)* ((B64S B64S B64S B64) | (B64S B64S B16S '=') | (B64S B04S '=' #x20? '=')))? B64S ::= B64 #x20? B16S ::= B16 #x20? B04S ::= B04 #x20? B04 ::= [AQgw] B16 ::= [AEIMQUYcgkosw048] B64 ::= [A-Za-z0-9+/]

Note that this grammar requires the number of non-whitespace characters in the lexical form to be a multiple of four, and for equals signs to appear only at the end of the lexical form; strings which do not meet these constraints are not legal lexical forms of base64Binary because they cannot successfully be decoded by base64 decoders.

The above definition of the lexical space is more restrictive than that given in as regards whitespace -- this is not an issue in practice. Any string compatible with the RFC can occur in an element or attribute validated by this type, because the facet of this type is fixed to collapse, which means that all leading and trailing whitespace will be stripped, and all internal whitespace collapsed to single space characters, before the above grammar is enforced.

The canonical lexical form of a base64Binary data value is the base64 encoding of the value which matches the Canonical-base64Binary production in the following grammar:

Canonical-base64Binary ::= (B64 B64 B64 B64)* ((B64 B64 B16 '=') | (B64 B04 '=='))?

For some values the canonical form defined above does not conform to , which requires breaking with linefeeds at appropriate intervals.

The length of a base64Binary value is the number of octets it contains. This may be calculated from the lexical form 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: explicitly references 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

anyURI

anyURI represents a Uniform Resource Identifier Reference (URI). An anyURI value can be absolute or relative, and may have an optional fragment identifier (i.e., it may be a URI Reference). This type should be used to specify the intention that the value fulfills the role of a URI as defined by , as amended by .

The mapping from anyURI values to URIs is as defined by the URI reference escaping procedure defined in Section 5.4 Locator Attribute of (see also Section 7 Character Encoding in URI References of ). This means that a wide range of internationalized resource identifiers can be specified when an anyURI is called for, and still be understood as URIs per , as amended by , where appropriate to identify resources.

Section 5.4 Locator Attribute of requires that relative URI references be absolutized as defined in before use. This is an XLink-specific requirement and is not appropriate for XML Schema, since neither the nor the of the type are restricted to absolute URIs. Accordingly absolutization must not be performed by schema processors as part of schema validation.

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, this specification follows the lead of (as amended by ) in this matter: such rules and restrictions are not part of type validity and are not checked by processors. Thus in practice the above definition imposes only very modest obligations on processors.

Lexical representation

The of anyURI is finite-length character sequences which, when the algorithm defined in Section 5.4 of is applied to them, result in strings which are legal URIs according to , as amended by .

Spaces are, in principle, allowed in the of anyURI, however, their use is highly discouraged (unless they are encoded by %20).

QName

QName represents XML qualified names. The of QName is the set of tuples {namespace name, local part}, where namespace name is an and local part is an . The of QName is the set of strings that the QName production of .

The mapping between literals in the and values in the of QName requires a namespace declaration to be in scope for the context in which QName is used.

NOTATION

NOTATION represents the NOTATION attribute type from . The of NOTATION is the set of s of notations declared in the current schema. The of NOTATION is the set of all names of notations declared in the current schema (in the form of s).

enumeration facet value required for NOTATION

It is an for NOTATION to be used directly in a schema. Only datatypes that are from NOTATION by specifying a value for can be used in a schema.

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

Derived datatypes

This section gives conceptual definitions for all datatypes defined by this specification. The XML representation used to define datatypes (whether or ) is given in section and the complete definitions of the datatypes are provided in Appendix A .

normalizedString

normalizedString represents white space normalized strings. The of normalizedString is the set of strings that do not contain the carriage return (#xD), line feed (#xA) nor tab (#x9) characters. The of normalizedString is the set of strings that do not contain the carriage return (#xD), line feed (#xA) nor tab (#x9) characters. The of normalizedString is .

Derived datatypes token

token represents tokenized strings. The 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 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 of token is .

Derived datatypes language

language represents natural language identifiers as defined by by . The of language is the set of all strings that are valid language identifiers as defined . The of language is the set of all strings that conform to the pattern [a-zA-Z]{1,8}(-[a-zA-Z0-9]{1,8})* . The of language is .

NMTOKEN

NMTOKEN represents the NMTOKEN attribute type from . The of NMTOKEN is the set of tokens that the Nmtoken production in . The of NMTOKEN is the set of strings that the Nmtoken production in . The of NMTOKEN is .

For compatibility (see ) NMTOKEN should be used only on attributes.

Derived datatypes NMTOKENS

NMTOKENS represents the NMTOKENS attribute type from . The of NMTOKENS is the set of finite, non-zero-length sequences of s. The of NMTOKENS is the set of space-separated lists of tokens, of which each token is in the of . The of NMTOKENS is .

For compatibility (see ) NMTOKENS should be used only on attributes.

Name

Name represents XML Names. The of Name is the set of all strings which the Name production of . The of Name is the set of all strings which the Name production of . The of Name is .

Derived datatypes NCName

NCName represents XML "non-colonized" Names. The of NCName is the set of all strings which the NCName production of . The of NCName is the set of all strings which the NCName production of . The of NCName is .

Derived datatypes ID

ID represents the ID attribute type from . The of ID is the set of all strings that the NCName production in . The of ID is the set of all strings that the NCName production in . The of ID is .

For compatibility (see ) ID should be used only on attributes.

IDREF

IDREF represents the IDREF attribute type from . The of IDREF is the set of all strings that the NCName production in . The of IDREF is the set of strings that the NCName production in . The of IDREF is .

For compatibility (see ) this datatype should be used only on attributes.

Derived datatypes IDREFS

IDREFS represents the IDREFS attribute type from . The of IDREFS is the set of finite, non-zero-length sequences of s. The of IDREFS is the set of space-separated lists of tokens, of which each token is in the of . The of IDREFS is .

For compatibility (see ) IDREFS should be used only on attributes.

ENTITY

ENTITY represents the ENTITY attribute type from . The of ENTITY is the set of all strings that the NCName production in and have been declared as an unparsed entity in a document type definition. The of ENTITY is the set of all strings that the NCName production in . The of ENTITY is .

The of ENTITY is scoped to a specific instance document.

For compatibility (see ) ENTITY should be used only on attributes.

Derived datatypes ENTITIES

ENTITIES represents the ENTITIES attribute type from . The of ENTITIES is the set of finite, non-zero-length sequences of s that have been declared as unparsed entities in a document type definition. The of ENTITIES is the set of space-separated lists of tokens, of which each token is in the of . The of ENTITIES is .

The of ENTITIES is scoped to a specific instance document.

For compatibility (see ) ENTITIES should be used only on attributes.

integer

integer is from by fixing the value of to be 0and disallowing the trailing decimal point. This results in the standard mathematical concept of the integer numbers. The of integer is the infinite set {...,-2,-1,0,1,2,...}. The of integer is .

Lexical representation

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

Canonical representation

The canonical representation for integer is defined by prohibiting certain options from the . Specifically, the preceding optional "+" sign is prohibited and leading zeroes are prohibited.

Derived datatypes nonPositiveInteger

nonPositiveInteger is from by setting the value of to be 0. This results in the standard mathematical concept of the non-positive integers. The of nonPositiveInteger is the infinite set {...,-2,-1,0}. The of nonPositiveInteger is .

Lexical representation

nonPositiveInteger has a lexical representation consisting of an optional preceding sign followed by a 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.

Canonical representation

The canonical representation for nonPositiveInteger is defined by prohibiting certain options from the . In the canonical form for zero, the sign must be omitted. Leading zeroes are prohibited.

Derived datatypes negativeInteger

negativeInteger is from by setting the value of to be -1. This results in the standard mathematical concept of the negative integers. The of negativeInteger is the infinite set {...,-2,-1}. The of negativeInteger is .

Lexical representation

negativeInteger has a lexical representation consisting of a negative sign ("-") followed by a finite-length sequence of decimal digits (#x30-#x39). For example: -1, -12678967543233, -100000.

Canonical representation

The canonical representation for negativeInteger is defined by prohibiting certain options from the . Specifically, leading zeroes are prohibited.

long

long is from by setting the value of to be 9223372036854775807 and to be -9223372036854775808. The of long is .

Lexical representation

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

Canonical representation

The canonical representation for long is defined by prohibiting certain options from the . Specifically, the the optional "+" sign is prohibited and leading zeroes are prohibited.

Derived datatypes int

int is from by setting the value of to be 2147483647 and to be -2147483648. The of int is .

Lexical representation

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

Canonical representation

The canonical representation for int is defined by prohibiting certain options from the . Specifically, the the optional "+" sign is prohibited and leading zeroes are prohibited.

Derived datatypes short

short is from by setting the value of to be 32767 and to be -32768. The of short is .

Lexical representation

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

Canonical representation

The canonical representation for short is defined by prohibiting certain options from the . Specifically, the the optional "+" sign is prohibited and leading zeroes are prohibited.

Derived datatypes byte

byte is from by setting the value of to be 127 and to be -128. The of byte is .

Lexical representation

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

Canonical representation

The canonical representation for byte is defined by prohibiting certain options from the . Specifically, the the optional "+" sign is prohibited and leading zeroes are prohibited.

nonNegativeInteger

nonNegativeInteger is from by setting the value of to be 0. This results in the standard mathematical concept of the non-negative integers. The of nonNegativeInteger is the infinite set {0,1,2,...}. The of nonNegativeInteger is .

Lexical representation

nonNegativeInteger has a lexical representation consisting of an optional sign followed by a 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.

Canonical representation

The canonical representation for nonNegativeInteger is defined by prohibiting certain options from the . Specifically, the the optional "+" sign is prohibited and leading zeroes are prohibited.

Derived datatypes unsignedLong

unsignedLong is from by setting the value of to be 18446744073709551615. The of unsignedLong is .

Lexical representation

unsignedLong has a lexical representation consisting of a finite-length sequence of decimal digits (#x30-#x39). For example: 0, 12678967543233, 100000.

Canonical representation

The canonical representation for unsignedLong is defined by prohibiting certain options from the . Specifically, leading zeroes are prohibited.

Derived datatypes unsignedInt

unsignedInt is from by setting the value of to be 4294967295. The of unsignedInt is .

Lexical representation

unsignedInt has a lexical representation consisting of a finite-length sequence of decimal digits (#x30-#x39). For example: 0, 1267896754, 100000.

Canonical representation

The canonical representation for unsignedInt is defined by prohibiting certain options from the . Specifically, leading zeroes are prohibited.

Derived datatypes unsignedShort

unsignedShort is from by setting the value of to be 65535. The of unsignedShort is .

Lexical representation

unsignedShort has a lexical representation consisting of a finite-length sequence of decimal digits (#x30-#x39). For example: 0, 12678, 10000.

Canonical representation

The canonical representation for unsignedShort is defined by prohibiting certain options from the . Specifically, the leading zeroes are prohibited.

Derived datatypes unsignedByte

unsignedByte is from by setting the value of to be 255. The of unsignedByte is .

Lexical representation

unsignedByte has a lexical representation consisting of a finite-length sequence of decimal digits (#x30-#x39). For example: 0, 126, 100.

Canonical representation

The canonical representation for unsignedByte is defined by prohibiting certain options from the . Specifically, leading zeroes are prohibited.

positiveInteger

positiveInteger is from by setting the value of to be 1. This results in the standard mathematical concept of the positive integer numbers. The of positiveInteger is the infinite set {1,2,...}. The of positiveInteger is .

Lexical representation

positiveInteger has a lexical representation consisting of an optional positive sign ("+") followed by a finite-length sequence of decimal digits (#x30-#x39). For example: 1, 12678967543233, +100000.

Canonical representation

The canonical representation for positiveInteger is defined by prohibiting certain options from the . Specifically, the optional "+" sign is prohibited and leading zeroes are prohibited.

yearMonthDuration

yearMonthDuration is a datatype from by restricting its lexical representations to instances of . The of yearMonthDuration is therefore that of restricted to those whose property is 0. This results in a duration datatype which is totally ordered.

The always-zero is formally retained in order that 's (abstract) value space truly be a subset of that of An obvious implementation optimization is to ignore the zero and implement values simply as values.

The Lexical Mapping

The lexical space is reduced from that of by disallowing and fragments in the lexical representations. The , called herein, is that of restricted to the lexical space. The Lexical Representation yearMonthDurationLexicalRep -? P

The regular expression -?P([0-9]+Y)?([0-9]+M)? has instances that are not in the lexical space—but they are not in the lexical space of either, so it serves as a relatively simple regular expression that extracts from the of those representations that are instances of .

The is that of restricted in its range to the (which reduces its domain to omit any values not in the value space).

The value whose and are both zero has no in this datatype since its in (PT0S) is not in the of .

dayTimeDuration

dayTimeDuration is a datatype from by restricting its lexical representations to instances of . The of dayTimeDuration is therefore that of restricted to those whose property is 0. This results in a duration datatype which is totally ordered.

The Lexical Space

The lexical space is reduced from that of by disallowing and fragments in the lexical representations. The , called herein, is that of restricted to the lexical space.

The Lexical Representation dayTimeDurationLexicalRep -? P

The regular expression -?P([0-9]+D)?(T([0-9]+H)?([0-9]+M)?([0-9]+(.[0-9]+)?S)?)? has several instances that are not in the lexical space—but they are not in the lexical space of either, so it serves as a relatively simple regular expression that extracts from the of those representations that are instances of .

The is that of restricted to the The is that of restricted in its range to the (which reduces its domain to omit any values not into the value space).

Datatype components

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 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 datatype (schema) components, see Schema Component Details of .

Simple Type Definition

Simple Type definitions provide for:

Establishing the and of a datatype, through the combined set of s specified in the definition;

Attaching a unique name (actually a ) to the and .

The Simple Type Definition Schema Component

The Simple Type Definition schema component has the following properties:

Optional. An NCName as defined by . Either absent or a namespace name, as defined in . One of {atomic, list, union}. Depending on the value of , further properties are defined as follows: atomic A datatype definition). list An or simple type definition. union A non-empty sequence of simple type definitions. If the datatype has been by then the component from which it is , otherwise the . A subset of {restriction, list, union}. Optional. An annotation.

Datatypes are identified by their and . Except for anonymous datatypes (those with no ), datatype definitions be uniquely identified within a schema.

If is then the of the datatype defined will be a subset of the of (which is a subset of the of ). If is then the of the datatype defined will be the set of finite-length sequence of values from the of . If is then the of the datatype defined will be the union of the s of each datatype in .

If is then the of must be . If is then the of must be either or . If is then must be a list of datatype definitions.

The value of consists of the set of s specified directly in the datatype definition unioned with the possibly empty set of of .

The value of consists of the set of s and their values.

If is the empty set then the type can be used in deriving other types; the explicit values restriction, list and union prevent further derivations by , and respectively.

XML Representation of Simple Type Definition Schema Components

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

The &v-value; of the name &i-attribute;, if present, otherwise null A set corresponding to the &v-value; of the final &i-attribute;, if present, otherwise the &v-value; of the finalDefault &i-attribute; of the ancestor schema element information item, if present, otherwise the empty string, as follows: the empty string

the empty set;

#all

{restriction, list, union};

otherwise

a set with members drawn from the set above, each being present or absent depending on whether the string contains an equivalently named space-delimited substring.

Although the finalDefault &i-attribute; of schema may include values other than restriction, list or union, those values are ignored in the determination of

The &v-value; of the targetNamespace &i-attribute; of the parent schema element information item. The annotation corresponding to the element information item in the &i-children;, if present, otherwise null

A datatype can be from a datatype or another datatype by one of three means: by restriction, by list or by union.

Derivation by restriction The &v-value; of of The union of the set of components resolved to by the facet &i-children; merged with from , subject to the Facet Restriction Valid constraints specified in . The component resolved to by the &v-value; of the base &i-attribute; or the &i-children;, whichever is present.

An electronic commerce schema might define a datatype called Sku (the barcode number that appears on products) from the datatype by supplying a value for the facet.

]]>

In this case, Sku is the name of the new datatype, is its and is the facet.

Derivation by list list The component resolved to by the &v-value; of the itemType &i-attribute; or the &i-children;, whichever is present.

A datatype must be from an or a datatype, known as the of the datatype. This yields a datatype whose is composed of finite-length sequences of values from the of the and whose is composed of space-separated lists of literals of the .

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

]]>

In this case, listOfFloat is the name of the new datatype, is its and is the derivation method.

As mentioned in , when a datatype is from a datatype, the following s can be used:

regardless of the s that are applicable to the datatype that serves as the of the .

For each of , and , the unit of length is measured in number of list items. The value of is fixed to the value collapse.

Derivation by union union The sequence of components resolved to by the items in the &v-value; of the memberTypes &i-attribute;, if any, in order, followed by the components resolved to by the &i-children;, if any, in order. If is union for any components resolved to above, then the is replaced by its .

A datatype can be from one or more , or other datatypes, known as the of that datatype.

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 type definition below would accomplish that.

]]> A header

this is a test

]]>

As mentioned in , when a datatype is from a datatype, the only following s can be used:

regardless of the s that are applicable to the datatypes that participate in the

Constraints on XML Representation of Simple Type Definition itemType attribute or simpleType child

Either the itemType &i-attribute; or the &i-child; of the element must be present, but not both.

base attribute or simpleType child

Either the base &i-attribute; or the simpleType &i-child; of the element must be present, but not both.

memberTypes attribute or simpleType children

Either the memberTypes &i-attribute; of the element must be non-empty or there must be at least one simpleType &i-child;.

Simple Type Definition Validation Rules Datatype Valid

A string is datatype-valid with respect to a datatype definition if:

it es a literal in the of the datatype, determined as follows:

if is a member of , then the string must be ;

if is not a member of , then

if is then the string must a literal in the of

if is then the string must be a sequence of space-separated tokens, each of which es a literal in the of

if is then the string must a literal in the of at least one member of

the value denoted by the literal ed in the previous step is a member of the of the datatype, as determined by it being with respect to each member of (except for ).

Constraints on Simple Type Definition Schema Components list of atomic

If is , then the of be or .

no circular unions

If is , then it is an if and and of any member of .

Simple Type Definition for anySimpleType

There is a simple type definition nearly equivalent to the simple version of the ur-type definition present in every schema by definition. It has the following properties:

anySimpleType http://www.w3.org/2001/XMLSchema the ur-type definition the empty set absent Information Facets

(Information facets were called "fundamental facets" in the 1.0 version of this specification.) The purpose of an is to provide a limited piece of information about some aspect of a datatype. Most information 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 &cfacet;s used to define the derivation). The and facets are exceptions to this rule; their values may change as a result of certain derivations.

Schema components are identified by kind. Information is not a kind of component. Each kind of (ordered, bounded, etc.) is realized as a separate kind of schema component.

An component can occur only in the of a , and this is the only place where components occur. The in whose an component occurs is that component's parent. Each kind of component occurs (once) in each 's set.

The value of any component can always be calculated from other properties of its .

ordered

An order relation on a is a mathematical relation that imposes a or a on the members of the .

A , and hence a datatype, is said to be ordered if there exists an defined for that .

A partial order is an that is irreflexive, asymmetric and transitive.

A has the following properties:

for no a in the , a < a (irreflexivity)

for all a and b in the , a < b implies not(b < a) (asymmetry)

for all a, b and c in the , a < b and b < c implies a < c (transitivity)

The notation a <> b is used to indicate the case when a != b and neither a < b nor b < a. For any values a and b from different s, a <> b.

When a <> b, a and b are incomparable,otherwise they are comparable.

A total order is an such that for no a and b is it the case that a <> b.

A has all of the properties specified above for , plus the following property:

for all a and b in the , either a < b or b < a or a = b

The fact that this specification does not define an for some datatype does not mean that some other application cannot treat that datatype as being ordered by imposing its own order relation.

provides for:

indicating whether an is defined on a , and if so, whether that is a or a

Some datatypes have a nontrivial order relation associated with their value spaces (see ). (There is always a trivial partial ordering wherein every value pair that is not equal is incomparable, which could be associated with any value space.) The ordered facet value is a "near-boolean": one of false, partial, and total, as prescribed in for datatypes; all datatypes inherit this value without change. The vale for a and is always false and the value for a 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 there is no simple means prescribed to be sure the prescribed order is either tivial or total based on the derivation mechanism.

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 not ordered for schema-processing purposes.

The ordered Schema Component One of {false, partial, total}. The writeup here has been changed to look more like the way logic is currently presented in Part 1. Some find it harder to understand. The editors are trying to harmonize the two. Until this is sorted out in "editors' committee", the other facet writeups are not going to change. This will not occur before second working draft.

depends on , and in the component in which a component appears as a member of .

When is , is inherited from of . For all types is as specified in the table in .

When is , is false.

When is , is partial unless one of the following:

If every member of is derived from a common ancestor other than the simple ur-type, then is the same as that ancestor's ordered facet

If every member of has a of false for the ordered facet, then is false

depends on the parent's , and .

the parent's is atomic

the is

is as specified in the table in .

is the parent's 's .

the parent's is list

is false.

the parent's is union;

every member of the parent's is derived from a common ancestor other than the simple ur-type

is the same as the component's in that common ancestor's .

each member of the parent's has an component in its whose is false

is false.

is partial.

bounded

A value u in an U is said to be an inclusive upper bound of a V (where V is a subset of U) if for all v in V, u >= v.

A value u in an U is said to be an exclusive upper bound of a V (where V is a subset of U) if for all v in V, u > v.

A value l in an L is said to be an inclusive lower bound of a V (where V is a subset of L) if for all v in V, l <= v.

A value l in an L is said to be an exclusive lower bound of a V (where V is a subset of L) if for all v in V, l < v.

A datatype is bounded if its has either an or an and either an or an .

provides for:

indicating whether a is

Some ordered datatypes have the property that there is one value greater than or equal to every other value, and another that less than or equal to every other value. (In the case of derived datatypes, these two values may not be in the value space of the derived datatype, but must be in the value space of the primitive datatype from which they have been derived.) The bounded facet value is 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 component.

The bounded Schema Component A .

depends on the parent's , and in the component in which a component appears as a member of .

When the is , is as specified in the table in . Otherwise, when the parent's is atomic, if one of or and one of or are among members of the parent's set, then is true; elseotherwise is false.

When the parent's is list, is false.

When the parent's is union, if is true for every member of and all members of the parent's set and all of these share a common ancestor, then is true; elseotherwise is false.

cardinality

Every has associated with it the concept of cardinality. Some s are finite, some are countably infinite while still others could conceivably be uncountably infinite (although no defined by this specification is uncountable infinite). A datatype is said to have the cardinality of its .

It is sometimes useful to categorize s (and hence, datatypes) as to their cardinality. There are two significant cases:

s that are finite

s that are countably infinite

provides for:

indicating whether the of a is finite or countably infinite

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 component.

The cardinality Schema Component One of {finite, countably infinite}.

depends on the parent's , , and in the component in which a component appears as a member of .

When is and of is finite, then is finite.

When is and of is countably infinite and either of the following conditions are true, then is finite; else is countably infinite:

one of , , is among ,

all of the following are true:

one of or is among

either of the following are true:

is among

is one of , , , , or or any type from them

When the is , is as specified in the table in . Otherwise, when the parent's is atomic, is countably infinite unless any of the following conditions are true, in which case is finite:

the parent's 's is finite,

at least one of , , or is a member of the parent's set,

all of the following are true:

one of or is a member of the parent's set

either of the following are true:

is a member of the parent's set

is one of , , , , or

When the parent's is list, if or both of and are among members of the parent's set and the parent's 's is finite then is finite; elseotherwise is countably infinite.

When the parent's is union, if 's is finite for every member of the parent's set then is finite, elseotherwise is countably infinite.

numeric

A datatype is said to be numeric if its values are conceptually quantities (in some mathematical number system).

A datatype whose values are not is said to be non-numeric.

provides for:

indicating whether a is

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

The numeric Schema Component A

depends on the parent's , , and in the component in which a component appears as a member of .

When the is , is as specified in the table in . Otherwise, when the parent's is atomic, is inherited from the parent's 's of . For all types is as specified in the table in .

When the parent's is list, is false.

When the parent's is union, if 's is true for every member of the parent's set then is true, elseotherwise is false.

Constraining Facets length

RQ-147b (phase out length facet)

The WG is considering the ramifications of removing the length &cfacet;, letting the schema document elements that currently set that facet set both minLength and maxLength instead.

length is the number of units of length, where units of length varies depending on the type that is being from. The value of length be a .

For and datatypes from , length is measured in units of characters as defined in . For , length is measured in units of characters (as for ). For and and datatypes from them, length is measured in octets (8 bits) of binary data. For datatypes by , length is measured in number of list items.

For and datatypes from , length 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 length and in attempting to infer storage requirements from a given value for length.

provides for:

Constraining a to values with a specific number of units of length, where units of length varies depending on .

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 length facet we ensure that types derived from productCode can change or set the values of other facets, such as pattern, but cannot change the length.

]]> The length Schema Component A . A . Optional. An annotation.

If is true, then types for which the current type is the cannot specify a value for other than .

XML Representation of length Schema Components

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

The &v-value; of the value &i-attribute; The &v-value; of the fixed &i-attribute;, if present, otherwise false The annotations corresponding to all the element information items in the &i-children;, if any. length Validation Rules Length Valid

A value in a is facet-valid with respect to , determined as follows:

if the is then

if is or , then the length of the value, as measured in characters be equal to ;

if is or , then the length of the value, as measured in octets of the binary data, be equal to ;

if is or , then any is facet-valid.

if the is , then the length of the value, as measured in list items, be equal to

The use of on datatypes from and is deprecated. Future versions of this specification may remove this facet for these datatypes.

Constraints on length Schema Components length and minLength or maxLength

If is a member of then

It is an error for to be a member of unless

the of <= the of and

there is type definition from which this one is derived by one or more restriction steps in which has the same and is not specified.

It is an error for to be a member of unless

the of <= the of and

there is type definition from which this one is derived by one or more restriction steps in which has the same and is not specified.

length valid restriction

It is an if is among the members of of and is not equal to the of the parent .

minLength

minLength is the minimum number of units of length, where units of length varies depending on the type that is being from. The value of minLength be a .

For and datatypes from , minLength is measured in units of characters as defined in . For and and datatypes from them, minLength is measured in octets (8 bits) of binary data. For datatypes by , minLength is measured in number of list items.

For and datatypes from , minLength 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 minLength and in attempting to infer storage requirements from a given value for minLength.

provides for:

Constraining a to values with at least a specific number of units of length, where units of length varies depending on .

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).

]]> The minLength Schema Component A . A . Optional. An annotation.

If is true, then types for which the current type is the cannot specify a value for other than .

XML Representation of minLength Schema Component

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

A value in a is facet-valid with respect to , determined as follows:

if the is then

if is or , then the length of the value, as measured in characters be greater than or equal to ;

if is or , then the length of the value, as measured in octets of the binary data, be greater than or equal to ;

if is or , then any is facet-valid.

if the is , then the length of the value, as measured in list items, be greater than or equal to

The use of on datatypes from and is deprecated. Future versions of this specification may remove this facet for these datatypes.

Constraints on minLength Schema Components minLength <= maxLength

If both and are members of , then the of be less than or equal to the of .

minLength valid restriction

It is an if is among the members of of and is less than the of the parent .

maxLength

maxLength is the maximum number of units of length, where units of length varies depending on the type that is being from. The value of maxLength be a .

For and datatypes from , maxLength is measured in units of characters as defined in . For and and datatypes from them, maxLength is measured in octets (8 bits) of binary data. For datatypes by , maxLength is measured in number of list items.

For and datatypes from , maxLength 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 maxLength and in attempting to infer storage requirements from a given value for maxLength.

provides for:

Constraining a to values with at most a specific number of units of length, where units of length varies depending on .

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.

]]> The maxLength Schema Component A . A . Optional. An annotation.

If is true, then types for which the current type is the cannot specify a value for other than .

XML Representation of maxLength Schema Components

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

A value in a is facet-valid with respect to , determined as follows:

if the is then

if is or , then the length of the value, as measured in characters be less than or equal to ;

if is or , then the length of the value, as measured in octets of the binary data, be less than or equal to ;

if is or , then any is facet-valid.

if the is , then the length of the value, as measured in list items, be less than or equal to

The use of on datatypes from and is deprecated. Future versions of this specification may remove this facet for these datatypes.

Constraints on maxLength Schema Components maxLength valid restriction

It is an if is among the members of of and is greater than the of the parent .

pattern

pattern is a constraint on the of a datatype which is achieved by constraining the to literals which match a specific pattern. The value of pattern be a .

provides for:

Constraining a to values that are denoted by literals which match a specific .

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 .

]]> The pattern Schema Component A . Optional. An annotation. XML Representation of pattern Schema Components

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

be a valid . The &v-value; of the value &i-attribute; The annotations corresponding to all the element information items in the &i-children;, if any. Constraints on XML Representation of pattern Multiple patterns

If multiple element information items appear as &i-children; of a , the &i-value;s should be combined as if they appeared in a single as separate es.

It is a consequence of the schema representation constraint and of the rules for that facets specified on the same step in a type derivation are ORed together, while facets specified on different steps of a type derivation are ANDed 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.

pattern Validation Rules pattern valid

A literal in a is facet-valid with respect to if:

the literal is among the set of character sequences denoted by the specified in .

enumeration

enumeration constrains the to a specified set of values.

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

provides for:

Constraining a to a specified set of values.

The following example is a datatype definition for a datatype which limits the values of dates to the three US holidays enumerated. This datatype definition would appear in a schema authored by an "end-user" and shows how to define a datatype by enumerating the values in its . The enumerated values must be type-valid literals for the .

some US holidays New Year's day 4th of July Christmas ]]> The enumeration Schema Component A set of values from the of the . Optional. An annotation. XML Representation of enumeration Schema Components

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

be in the of . The &v-value; of the value &i-attribute; The annotations corresponding to all the element information items in the &i-children;, if any. Constraints on XML Representation of enumeration Multiple enumerations

If multiple element information items appear as &i-children; of a the of the component should be the set of all such &i-value;s.

enumeration Validation Rules enumeration valid

A value in a is facet-valid with respect to if the value is one of the values specified in

Constraints on enumeration Schema Components enumeration valid restriction

It is an if any member of is not in the of .

whiteSpace

whiteSpace constrains the of types from such that the various behaviors specified in Attribute Value Normalization in 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 leading and trailing #x20's are removed.

The notation #xA used here (and elsewhere in this specification) represents the Universal Character Set (UCS) code point hexadecimal A (line feed), which is denoted by U+000A. This notation is to be distinguished from 
, which is the XML character reference to that same UCS code point.

whiteSpace is applicable to all and datatypes. For all datatypes other than (and types by from it) the value of whiteSpace is collapse and cannot be changed by a schema author; for the value of whiteSpace is preserve; for any type by from the value of whiteSpace can be any of the three legal values. For all datatypes by the value of whiteSpace is collapse and cannot be changed by a schema author. For all datatypes by whiteSpace does not apply directly; however, the normalization behavior of types is controlled by the value of whiteSpace on that one of the against which the is successfully validated.

For more information on whiteSpace, see the discussion on white space normalization in Schema Component Details in .

provides for:

Constraining a according to the white space normalization rules.

The following example is the datatype definition for the datatype.

]]> The whiteSpace Schema Component One of {preserve, replace, collapse}. A . Optional. An annotation.

If is true, then types for which the current type is the cannot specify a value for other than .

XML Representation of whiteSpace Schema Components

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

There are no s associated . For more information, see the discussion on white space normalization in Schema Component Details in .

Constraints on whiteSpace Schema Components whiteSpace valid restriction

It is an if is among the members of of and any of the following conditions is true:

is replace or preserve and the of the parent is collapse

is preserve and the of the parent is replace

maxInclusive

maxInclusive is the of the for a datatype with the property. The value of maxInclusive be in the of the .

provides for:

Constraining a to values with a specific .

The following is the definition of a datatype which limits values to integers less than or equal to 100, using .

]]> The maxInclusive Schema Component A value from the of the . A . Optional. An annotation.

If is true, then types for which the current type is the cannot specify a value for other than .

XML Representation of maxInclusive Schema Components

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

be in the of . The &v-value; of the value &i-attribute; The &v-value; of the fixed &i-attribute;, if present, otherwise false, if present, otherwise false The annotations corresponding to all the element information items in the &i-children;, if any. maxInclusive Validation Rules maxInclusive Valid

A value in an is facet-valid with respect to , determined as follows:

if the property in is true, then the value be numerically less than or equal to ;

if the property in is false (i.e., is one of the date and time related datatypes), then the value be chronologically less than or equal to ;

Constraints on maxInclusive Schema Components minInclusive <= maxInclusive

It is an for the value specified for to be greater than the value specified for for the same datatype.

maxInclusive valid restriction

It is an if any of the following conditions is true:

is among the members of of and is greater than the of the parent

is among the members of of and is greater than or equal to the of the parent

is among the members of of and is less than the of the parent

is among the members of of and is less than or equal to the of the parent

maxExclusive

maxExclusive is the of the for a datatype with the property. The value of maxExclusive be in the of the or be equal to in .

provides for:

Constraining a to values with a specific .

The following is the definition of a datatype which limits values to integers less than or equal to 100, using .

]]>

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

The maxExclusive Schema Component A value from the of the . A . Optional. An annotation.

If is true, then types for which the current type is the cannot specify a value for other than .

XML Representation of maxExclusive Schema Components

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

be in the of . The &v-value; of the value &i-attribute; The &v-value; of the fixed &i-attribute;, if present, otherwise false The annotations corresponding to all the element information items in the &i-children;, if any. maxExclusive Validation Rules maxExclusive Valid

A value in an is facet-valid with respect to , determined as follows:

if the property in is true, then the value be numerically less than ;

if the property in is false (i.e., is one of the date and time related datatypes), then the value be chronologically less than ;

Constraints on maxExclusive Schema Components maxInclusive and maxExclusive

It is an for both and to be specified in the same derivation step of a datatype definition.

minExclusive <= maxExclusive

It is an for the value specified for to be greater than the value specified for for the same datatype.

maxExclusive valid restriction

It is an if any of the following conditions is true:

is among the members of of and is greater than the of the parent

is among the members of of and is less than or equal to the of the parent

minExclusive

minExclusive is the of the for a datatype with the property. The value of minExclusive be in the of the or be equal to in .

provides for:

Constraining a to values with a specific .

The following is the definition of a datatype which limits values to integers greater than or equal to 100, using .

]]>

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

The minExclusive Schema Component A value from the of the . A . Optional. An annotation.

If is true, then types for which the current type is the cannot specify a value for other than .

XML Representation of minExclusive Schema Components

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

A value in an is facet-valid with respect to if:

if the property in is true, then the value be numerically greater than ;

if the property in is false (i.e., is one of the date and time related datatypes), then the value be chronologically greater than ;

Constraints on minExclusive Schema Components minInclusive and minExclusive

It is an for both and to be specified for the same datatype.

minExclusive < maxInclusive

It is an for the value specified for to be greater than or equal to the value specified for for the same datatype.

minExclusive valid restriction

It is an if any of the following conditions is true:

is among the members of of and is less than the of the parent

is among the members of of and is greater the of the parent

is among the members of of and is less than the of the parent

is among the members of of and is greater than or equal to the of the parent

minInclusive

minInclusive is the of the for a datatype with the property. The value of minInclusive be in the of the .

provides for:

Constraining a to values with a specific .

The following is the definition of a datatype which limits values to integers greater than or equal to 100, using .

]]> The minInclusive Schema Component A value from the of the . A . Optional. An annotation.

If is true, then types for which the current type is the cannot specify a value for other than .

XML Representation of minInclusive Schema Components

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

A value in an is facet-valid with respect to if:

if the property in is true, then the value be numerically greater than or equal to ;

if the property in is false (i.e., is one of the date and time related datatypes), then the value be chronologically greater than or equal to ;

Constraints on minInclusive Schema Components minInclusive < maxExclusive

It is an for the value specified for to be greater than or equal to the value specified for for the same datatype.

minInclusive valid restriction

It is an if any of the following conditions is true:

is among the members of of and is less than the of the parent

is among the members of of and is greater the of the parent

is among the members of of and is less than or equal to the of the parent

is among the members of of and is greater than or equal to the of the parent

totalDigits

totalDigits controls the maximum number of values in the of datatypes from , by restricting it to numbers that are expressible as i × 10^-n where i and n are integers such that |i| < 10^totalDigits and 0 <= n <= totalDigits. The value of totalDigits be a .

The term totalDigits is chosen to reflect the fact that it restricts the to those values that can be represented lexically using at most totalDigits digits. Note that it does not restrict the directly; a lexical representation that adds additional leading zero digits or trailing fractional zero digits is still permitted.

The totalDigits Schema Component A . A . Optional. An annotation.

If is true, then types for which the current type is the cannot specify a value for other than .

XML Representation of totalDigits Schema Components

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

A value in a is facet-valid with respect to if:

that value is expressible as i × 10^-n where i and n are integers such that |i| < 10^ and 0 <= n <= .

Constraints on totalDigits Schema Components totalDigits valid restriction

It is an if is among the members of of and is greater than the of the parent

fractionDigits

fractionDigits controls the size of the minimum difference between values in the of datatypes from decimal, by restricting the to numbers that are expressible as i × 10^-n where i and n are integers and 0 <= n <= fractionDigits. The value of fractionDigits be a .

The term fractionDigits is chosen to reflect the fact that it restricts the to those values that can be represented lexically using at most fractionDigits to the right of the decimal point. Note that it does not restrict the directly; a non- that adds additional leading zero digits or trailing fractional 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 .

]]> The fractionDigits Schema Component A . A . Optional. An annotation.

If is true, then types for which the current type is the cannot specify a value for other than .

XML Representation of fractionDigits Schema Components

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

A value in a is facet-valid with respect to if:

that value is expressible as i × 10^-n where i and n are integers and 0 <= n <= .

Constraints on fractionDigits Schema Components fractionDigits less than or equal to totalDigits

It is an for to be greater than .

fractionDigits valid restriction

It is an if is among the members of of and is greater than the of the parent .

Conformance

This specification describes two levels of conformance for datatype processors. The first is required of all processors. Support for the other will depend on the application environments for which the processor is intended.

Minimally conforming processors completely and correctly implement the and .

Processors which accept schemas in the form of XML documents as described in (and other relevant portions of ) are additionally said to provide conformance to the XML Representation of Schemas, and , when processing schema documents, completely and correctly implement all s in this specification, and adhere exactly to the specifications in (and other relevant portions of ) for mapping the contents of such documents to schema components for use in validation.

By separating the conformance requirements relating to the concrete syntax of XML schema documents, this specification admits processors which validate using schemas stored in optimized binary representations, dynamically created schemas represented as programming language data structures, or implementations in which particular schemas are compiled into executable code such as C or Java. Such processors can be said to be minimally conforming but not necessarily in conformance to the XML Representation of Schemas.

Schema for Datatype Definitions (normative) DTD for Datatype Definitions (non-normative) Temporary Stuff (to be added elsewhere)

All processors support year values with a minimum of 4 digits (i.e., YYYY) and a minimum fractional second precision of milliseconds or three decimal digits (i.e. s.sss). However, processors set an application-defined limit on the maximum number of digits they are prepared to support in these two cases, in which case that application-defined maximum number be clearly documented.

Constructed datatypes are those that are defined in terms of other datatypes.

Derived datatypes are those that are by restiction or extension.

Built-up Value Spaces

Some datatypes, such as , 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. An optional property is permitted but not required to have the special value absent.

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; see for a discussion of ordinary versus precision-carrying numbers. The numbers generally used in describing datatypes are &decimal;s and &integer;s.

An enumerated constant is an undefined thing whose only property is that it is unequal to any other constants and to any member of any defined datatype.

(There are a few constants which are specified by name to be members of the value space of more than one primitive datatype. Such constants are differentiated by their name and associated datatype; this is because members of the value space of distinct primitive datatypes are always distinct. Apart from that, constants are differentiated one from the other by their name. They have no other inherent properties; their effect is defined in the context in which they occur. Examples of constants are positiveInfinity and absent.

Numerical Values

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

If m and n are numbers, then m div n is the greatest integer in m / n .

If m and n are numbers, then m mod n is (m / n) − ( m n) .

n 1 is a convenient and short way of expressing the greatest integer in n.

Precision

Numbers are sometimes thought of as including both a numerical value and a precision. Precision can be thought of as a band plus or minus from the numerical value itself. For example, five plus-or-minus two or two million to the nearest thousand.

There is a smaller class of precision numbers which do not require the plus-or-minus in order to indicate their precision. They indicate their precision by the number of digits to the right of the decimal point. 5.0 has precision plus-or-minus 0.05, but 5.00 has precision plus-or-minus 0.005.

There is also a kind of precision where the plus-or-minus is expressed as a percentage (or other proportion) of the numerical value, rather than an exact value: 15 plus-or-minus 10 percent or 15000 plus-or-minus 10 percent, where the same percentage indicates a different absolute precision depending on the size. This kind of precision is properly called geometric precision; the absolute precision first described is properly called arithmetic precision.

A close approximation to geometric precision also can, for some combinations of numerical value and precision, be indicated without the plus-or-minus: The precision is indicated by the total number of digits (not counting leading zero digits). 5.0 has precision plus-or-minus 1 percent but 5.00 has precision plus-or-minus one-tenth percent.

Geometric precision doesn't quite match with the digit count. 5.0 and 50 both have precision plus-or-minus 1 percent but 1.5 and 15 both have precision plus-or-minus 3 percent. For various reasons we choose to call this digit-count precision floating-point precision.

The datatype described in this specification embodies both arithmetic and floating-point precision for numbers whose numerical values are &decimal;s, with arithmetic precision describable simply by the number of fraction digits. It turns out that for these particular precision numbers, there is a relation between the arithmetic precision (expressed as the number of fraction digits) and floating-point precision (expressed as the total number of digits, excluding redundant leading zero digits). If a is the arithmetic precision of a number whose numerical value is n, then the floating-point precision is (log(| n − 10^a |) + 1) 1 . This formula, of course, doesn't work for numerical value zero. In that case, we find it convenient (and consonant with established practice) to freeze floating-point precision at 1 and still allow various arithmetic precision values.

One point needs to be made about the notations and the precisions they can indicate. It's impossible for ordinary decimal notation to indicate a positive arithmetic precision (as in one million to the nearest thousand); this needs scientific notation: 1000E3 (or 1.000E6).

Exact Lexical Mappings

Numerals and Fragments Thereof digit0-9 unsignedNoDecimalPtNumeral+ signedDecimalPtNumeral(+ | -) noDecimalPtNumeral(+ | -)? fracFrag+ unsignedDecimalPtNumeral ( . ?) | (. ) unsignedFullDecimalPtNumeral . decimalPtNumeral(+ | -)? unsignedScientificNotationNumeral ( | ) (e | E) scientificNotationNumeral (+ | -)? Some numerical datatypes include some or all of three non-numerical values: positiveInfinity, negativeInfinity, and notANumber. Their lexical spaces include non-numeral lexical representations for these non-numeric values: Special Non-numerical Lexical Representations Used With Numerical Datatypes numericalSpecialRep INF | +INF | -INF | NaN

Date/time Values

RQ-122 (define dateTime value space)

Much of the material defining the various date/time datatypes is found here and is or will be referenced in the sections defining each individual date/time datatype. See e.g. .

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.

Dates and Times in the Real World

Except for the tables of lengths of months and occurrences of leap-seconds, this section is informative, not normative.

There are various concepts involving dates (counting days) and times (counting moments) that have developed over the millenia. This section does not pretend to be a complete tutorial on the history; it only discusses the methods which are necessary to understand just which set of the possible reasonable choices has been adopted for Schema date/time datatypes.

Seconds, Minutes, and Days

A day is, at least approximately, the time of one rotation of the Earth about its axis with respect to the Sun. Each day is divided into 24 hours; each hour into 60 minutes, and each minute usually into 60 seconds. (The hedges in those sentences are deliberate, and their resolution shows why one must be careful to insure that all users of Schema date/time datatypes are in fact correctly using the same datatype.) For the purposes of this section and the next, a day always begins and ends when the rotation of the Earth about its axis places the Sun exactly (at least for UT1, and approximately for the others) overhead (at its zenith) at 0 degrees longitude.

Thus a day is (usually) 86400 (= 60 × 60 × 24) seconds.

Universal Time 1 (UT1) is real time: One day is (exactly, or at least as close as can be astronomically measured) one revolution of the Earth about its axis with respect to the Sun. The day is divided into 86400 equal-length seconds, which may vary in length from day to day. International Atomic Time (TAI or Temps Atomique International) is time measured in seconds as established by a collection of atomic clocks maintained by various national standards agencies. The time counts that Schema has chosen to represent are based on : Universal Coordinated Time (UTC) is an adaptation of TAI which closely approximates UT1 by adding leap-seconds to selected days. Relations between them are as follows:

TAI seconds are all the same length, and there are exactly 86400 seconds in each day.

UT1 seconds vary in length, but there are exactly 86400 seconds each day. Days always have the sun at zenith at noon in Greenwich, England. (As a historical note, the TAI second, defined in 1956 in terms of the excitation frequency of Cesium atoms, was chosen to be the average length of a UT1 second during the year 1900.)

Noon of TAI days do not necessarily match the Sun at the zenith. In 1958, TAI was promulgated and synchronized with UT1. Since then, the difference has been slowly increasing, with a given number of seconds from that date measured in UT1 coming later than that same number measured in TAI.

seconds are the same as TAI seconds, but day boundaries are kept approximately in sync with UT1 by adding an extra leap-second or so to a day once in a while; therefore occasionally a day is not exactly 86400 seconds. In 1972, was synchronized with TAI (and UT1) to lock them all together retroactively to the date when TAI was synchronized with UT1. is now kept within 0.9 seconds of UT1 by an international standards organization which declares on an ad hoc basis when additional leap-seconds are added (or subtracted, although the physical situations that might require substraction seem unlikely to occur). As of 2003, the difference between the two is 32 seconds. New leap-seconds are always added immediately preceding midnight (when the Earth's rotation puts the Sun opposite the noon zenith) at 0 degrees longitude (i.e., midnight in the timezone so determined).

As of the writing of this specification, leap-seconds have been added to at the end of each of the following days (as identified by the Gregorian calendar, see ), and no future leap-seconds have been announced:

Date Number of Leap-seconds Date Number of Leap-seconds

1960-12-31 1.422818 1975-12-31 1

1961-07-31 0.224752 1976-12-31 1

1961-01-31 0.198288 1977-12-31 1

1963-10-30 0.8514208 1978-12-31 1

1963-12-31 0.0685152 1989-12-31 1

1964-03-31 0.217936 1981-06-30 1

1964-08-31 0.298288 1982-06-30 1

1964-01-31 0.258112 1983-06-30 1

1965-02-28 0.176464 1985-06-30 1

1965-06-30 0.258112 1987-12-31 1

1965-08-31 0.180352 1989-12-31 1

1965-12-31 0.158112 1990-12-31 1

1968-01-31 1.872512 1992-06-30 1

1971-12-31 3.814318 1993-06-30 1

1972-06-30 1 1994-06-30 1

1972-12-31 1 1995-12-31 1

1973-12-31 1 1997-06-30 1

1974-12-31 1 1998-12-31 1

Date	Number of Leap-seconds	Date	Number of Leap-seconds
1960-12-31	1.422818	1975-12-31	1
1961-07-31	0.224752	1976-12-31	1
1961-01-31	0.198288	1977-12-31	1
1963-10-30	0.8514208	1978-12-31	1
1963-12-31	0.0685152	1989-12-31	1
1964-03-31	0.217936	1981-06-30	1
1964-08-31	0.298288	1982-06-30	1
1964-01-31	0.258112	1983-06-30	1
1965-02-28	0.176464	1985-06-30	1
1965-06-30	0.258112	1987-12-31	1
1965-08-31	0.180352	1989-12-31	1
1965-12-31	0.158112	1990-12-31	1
1968-01-31	1.872512	1992-06-30	1
1971-12-31	3.814318	1993-06-30	1
1972-06-30	1	1994-06-30	1
1972-12-31	1	1995-12-31	1
1973-12-31	1	1997-06-30	1
1974-12-31	1	1998-12-31	1

Leap-seconds added prior to 1972-06-30 (when 's first post-adoption leap-second was added) were inherited from previous standard times. (Data in the table was derived from data provided by the US Naval Observatory.)

There are inherently no precise measurements of the difference between UT1 on the one hand and proleptic (i.e., used to measure times prior to their adoption) TAI and on the other before 1958, although they are known (by virtue of early astornomical records) to differ from UT1 by several hours around year 0000. Users must be aware that they differ, if they deal with extremely accurate measures over widely separated moments, and must be sure they know which system is being used.

Schema date/time datatypes (except ) are leap-second-aware; that is to say, they use rather than UT1 or TAI. is a special case; it is not leap-second aware, but the algorithm for adding durations to or subtracting them from other date/time datatypes compensates.

Counting Days: Years and Months

Once one decides on how many seconds are in each day, one must also count the days—and months and years. The standard used for Schema date/time datatypes is the so-called Gregorian calendar. Since days are (generally) 86400 seconds, and one wants each year to correspond to one complete cycle of the Earth around the Sun (which is not exactly a multiple of 86400 seconds), and traditionally months have various numbers of days, the following algorithm was chosen to determine which days fell in which months in which years: Counting from an agreed-upon arbitrary day, years are numbered consecutively, each year has 12 months (numbered 1 through 12, as well as named) within it, and each day has between 28 and 31 days (also numbered from 1), depending on the month and year according to the following table:

Month	Nbr of Days
1 (January)	31
2 (February)	If the associated year is divisble by 400, or by 4 but not 100, then 29; otherwise 28
3 (March)	31
4 (April)	30
5 (May)	31
6 (June)	30
7 (July)	31
8 (August)	31
9 (September)	30
10 (October)	31
11 (November)	30
12 (December)	31

For example, the three numbers (year, month, and day) for 20 January 2003 (2003-01-20) are 2003, 1, and 20 respectively.

RQ-123 (year 0000 in date/time datatypes)

The following rewrite includes allowing year 0000 (1 BCE) and redefining all the lexical representations with negative years from that specified in Schema 1.0, as warned in a Note in Schema 1.0 2E. A formal Note calling attention to this change elsewhere in the "normative" part of this specification will be added.

The count of years, months, and days were made official and locked to real time by decree of (the Roman Catholic) Pope Gregory in 1582 (from which comes the name Gregorian). Since then, and somewhat even before, days had been counted with reasonable historical accuracy so that the Gregorian calendar algorithm can even be used proleptically, i.e., to establish dates prior to its official adoption. By relatively recent convention (it began to be adopted by astronomers during the 1800s), there is a year numbered zero; this makes calculating the difference between two dates easier. The year called 1 of the Common Era (1 CE, or 1 AD) is numbered one; the preceding year is numbered zero, not minus one. (Warning: The date using the proleptic Gregorian calendar will not generally be the same for a given day as the date using the Julian calendar which was in common use prior to the adoption of the Gregorian calendar, nor will Gregorian years before the Common Era (BCE, or BC) be numbered the same as with the current standard negative numbering.)

There are also standard schemes for numbering days without reference to months and years. The most common is the modified Julian date (MJD), which counts days from 17 Nov 1858 (1858-11-17). The older count is the Julian date (JD), which sets its zero day exactly 2,400,000.5 days earlier than MJD. (JD days begin at noon!) Schema, however, counts seconds rather than days and arbitrarily begins its initial moment at the beginning of 1 Jan 1 CE (0001-01-01), to describe certain functions. (Since a schema implementation need not expose this count, implementers are free to use other base moments and/or to count by days, providing they retain awareness of leap-seconds.)

Note that the JD day-counting scheme is not the same as the Julian calendar which was supplanted by the Gregorian calendar described above.

Timezones: When does a Day Start?

All of the preceding discussion applies to real times at the Greenwich meridian, the meridian where longitude is 0 degrees. Human society has found it convenient to have noon all over the globe at least approximately when the Sun is overhead—and more recently also to have moments numbered the same in nearby localities, with the differences between separated localities well-known. Thus the invention of timezones. A timezone is a way of describing a local time by specifying the number of hours and minutes which must be added to the standard time to get the local time. The standard time is selected to be that where noon is when the Sun is exactly overhead at 0 degrees longitude; is officially locked to that particular timezone. Schema date/time datatypes (except ) are timezone-sensitive; that is to say, they retain knowledge of a timezone if one is specified in a lexical representation.

A moment in time is like a point on a line; the point does not change if we change where we put zero on the line, but the number we use to represent that point changes. Similarly, when one specifies a moment in time, one can specify the same moment regardless of which timezone one specifies, but the numbers one uses for year, month, day, hour, minute, and second will be different.

The Seven-property Model

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; the Gregorian calendar algorithm, modified for leap-seconds, is the isomorphism from the first to the second and is one-to-one. For definiteness, we choose to model the first using five &integer; and one &decimal; properties. We superimpose the second by providing one &decimal;-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 timezone. Values for the six primary properties are always stored in , so having the timezone makes it possible to calculate the corresponding raw values, as they would be reckoned in that timezone. Properties of

Date/time Seven-property Models

year an &integer; month an &integer; between 1 and 12 inclusive day an &integer; between 1 and 28, 29, 30, or 31 inclusive, depending on and hour an &integer; between 0 and 23 inclusive, or 24 if both and are zero minute an &integer; between 0 and 59 inclusive second a &decimal; greater than or equal 0, less than 60 except as prescribed in the table of leap-seconds in ; must be less than 60 if is absent. timezone an &integer; between −840 and 840 inclusive

The model just described is called herein the seven-property model for date/time datatypes. It is used as is for ; all other date/time datatypes except 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 property, like , is always permitted to have the value absent.)

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

Leap-seconds are not permitted when is absent, because the presence of a leap-second value together with particular and values determines a so it might as well be explicit. (All date/time datatypes that do not require to be absent also prohibit that value for and .)

While calculating, property values from the 1971-12-31T00:00:00 are used to fill in for those that are absent, except that if is absent but is not, the largest permitted day for that month is used. 1971-12-31T00:00:00 happens to permit both the maximum number of days and the maximum number of seconds.

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 absent and the other's is not, and using maximum and minimum values for the one whose is actually absent changes the resulting (strict) inequality, the original two values are incomparable.

Lexical Mappings

Each lexical representation is made up of certain date/time fragments, each of which corresponds to a particular property of the datatype value. They are defined by the following productions. Date/time Lexical Representation Fragments yearFrag -? ((1-9 +)) | (0 )) monthFrag (0 1-9) | (1 01) dayFrag (0-2 ) | (3 01) hourFrag (01 ) | (2 0-4) minuteFrag 0-5 secondFrag 0-6 (. +)? timezoneFragZ | ((+ | -) (0 | 1 0-4) : )

Each fragment other than defines a subset of the of ; the corresponding is the lexical mapping restricted to that subset. These fragment lexical mappings are combined separately for each date/time datatype (other than ) to make up the complete lexical mapping for that datatype. The mapping is used to obtain the value of the property, the mapping is used to obtain the value of the property, etc. Each datatype which specifies some properties to be mandatorily absent also does not permit the corresponding lexical fragments in its lexical representations.

(The redundancy between Z, +00:00, and -00:00, and the possibility of trailing fractional 0 digits for , are the only redundancies preventing these mappings from being one-to-one.)

The following fragment canonical mappings for each value-object property are combined as appropriate to make the for each date/time datatype (other than ):

Function Definitions

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.

Generic Number-related Functions

The following functions are used with various numeric and date/time datatypes. Auxiliary Functions for Operating on Numeral Fragments digitValue &integer;a nonnegative &integer; less than ten dmatches

Maps each digit to its numerical value.

Return

0 when d = 0 ,

1 when d = 1 ,

2 when d = 2 ,

etc.

digitSequenceValue &integer;a nonnegative &integer; Sa finite sequence of &string;s, each term matching .

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

Return the sum of (S_i) × 10^{length(S)−i} where i runs over the domain of S. fractionDigitSequenceValue &integer;a nonnegative &integer; Sa finite sequence of &string;s, each term matching .

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

Return the sum of (S_i) − 10⁻ⁱ where i runs over the domain of S. fractionFragValue &decimal;a nonnegative &decimal; Nmatches

Maps a to the appropriate fractional &decimal;.

N is necessarily the left-to-right concatenation of a finite sequence S of &string;s, each term matching . Return (S). Generic Numeral-to-Number Lexical Mappings unsignedNoDecimalMap &integer;a nonnegative &integer; Nmatches

Maps an to its numerical value.

N is the left-to-right concatenation of a finite sequence S of &string;s, each term matching . Return (S). noDecimalMap &integer;a nonnegative &integer; Nmatches

Maps an to its numerical value.

N necessarily consists of an optional sign(+ or -) and then a &string; U that matches . Return

−(U) when - is present, and

(U) otherwise.

unsignedDecimalPtMap &decimal;a nonnegative &decimal; Dmatches

Maps an to its numerical value.

D necessarily consists of an optional &string; N matching , a decimal point, and then an optional &string; F matching . Return

(N) when F is not present,

(F) when N is not present, and

(N) + (F) otherwise.

decimalPtMap &decimal;a &decimal; Nmatches

Maps a to its numerical value.

N necessarily consists of an optional sign(+ or -) and then an instance U of . Return

−(U) when - is present, and

(U) otherwise.

scientificMap &decimal; Nmatches

Maps a to its numerical value.

N necessarily consists of an instance C of either or , either an e or an E, and then an instance E of . Return

(C) − 10 ^ (E) when a . is present in N, and

(C) − 10 ^ (E) otherwise.

Auxiliary Functions for Producing Numeral Fragments digit matches ibetween 0 and 9 inclusive

Maps each &integer; between 0 and 9 to the corresponding .

Return

0 when i = 0 ,

1 when i = 1 ,

2 when i = 2 ,

etc.

digitRemainderSeq sequence of &integer;ssequence of nonnegative &integer;s ia nonnegative &integer;

Maps each nonnegative &integer; to a sequence of &integer;s used by to ultimately create an .

Return that sequence s for which

s₀ = i and

s_j+1 = s_j 10 .

digitSeq sequence of &integer;ssequence of &integer;s where each term is between 0 and 9 inclusive ia nonnegative &integer;

Maps each nonnegative &integer; to a sequence of &integer;s used by to create an .

Return that sequence s for which s_j =(i)_j 10 . lastSignificantDigit &integer;a nonnegative &integer; sa sequence of nonnegative &integer;s

Maps a sequence of nonnegative &integer;s to the index of the first zero term.

Return the smallest nonnegative &integer; j such that s(i)_j+1 is 0. FractionDigitRemainderSeq sequence of &decimal;sa sequence of nonnegative &decimal;s fnonnegative and less than 1

Maps each nonnegative &decimal; less than 1 to a sequence of &decimal;s used by to ultimately create an .

Return that sequence s for which

s₀ = f − 10 , and

s_j+1 = (s_j 1) − 10 .

fractionDigitSeq sequence of &integer;sa sequence of integer;s where each term is between 0 and 9 inclusive fnonnegative and less than 1

Maps each nonnegative &decimal; less than 1 to a sequence of &integer;s used by to ultimately create an .

Return that sequence s for which s_j = (f)_j 1 . fractionDigitsCanonicalFragmentMap matches fnonnegative and less than 1

Maps each nonnegative &decimal; less than 1 to a &string; used by to create an .

Return ((f)₀) &concat; . . . &concat; ((f)_((f))) . Generic Number to Numeral Canonical Mappings unsignedNoDecimalPtCanonicalMap matches ia nonnegative &integer;

Maps a nonnegative &integer; to a , its .

Return ((i)_((i))) &concat; . . . &concat; ((i)₀) . (Note that the concatenation is in reverse order.) noDecimalPtCanonicalMap matches ian &integer;

Maps an &integer; to a , its .

Return

- &concat; (−i) when i is negative,

(i) otherwise.

unsignedDecimalPtCanonicalMap matches na nonnegative &decimal;

Maps a nonnegative &decimal; to a , its .

Return (n1) &concat; . &concat; (n1) . decimalPtCanonicalMap matches na &decimal;

Maps a &decimal; to a , its .

Return

- &concat; (−i) when i is negative,

(i) otherwise.

unsignedScientificCanonicalMap matches na nonnegative &decimal;

Maps a nonnegative &decimal; to a , its .

Return (n / 10^log(n) 1) &concat; E &concat; (log(n) 1) scientificCanonicalMap matches na &decimal;

Maps a &decimal; to a , its .

Return

- &concat; (−n) when n is negative,

(i) otherwise.

For example:

123.4567 1 = 0.4567 and 123.4567 1 = 123 .

(123) is 123 , 12 , 1 , 0 , 0 , . . . .

(123) is 3 , 2 , 1 , 0 , 0 , . . . .

((123)) = 2 (Sequences count from 0.)

(123) = 123

(0.4567) is 4.567 , 5.67 , 6.7 , 7 , 0 , 0 , . . . .

(0.4567) is 4 , 5 , 6 , 7 , 0 , 0 , . . . .

((0.4567)) = 3

(0.4567) = 4567

(123.4567) = 123.4567

Lexical Mapping for Non-numerical s Used With Numerical Datatypes specialRepValue one of positiveInfinity, negativeInfinity, or notANumber. Smatches

Maps the lexical representations of s used with some numerical datatypes to those s.

Return

positiveInfinity when S is INF or +INF,

negativeInfinity when S is -INF, and

notANumber when S is NaN

Canonical Mapping for Non-numerical s Used With Numerical Datatypes specialRepCanonicalMap matches cone of positiveInfinity, negativeInfinity, and notANumber

Maps the s used with some numerical datatypes to their canonical representations.

Return

INF when c is positiveInfinity

-INF when c is negativeInfinity

NaN when c is notANumber

Auxilliary Functions for Reading Instances of decimalPtPrecision &integer;an &integer; LEXmatches

Maps a onto an &integer; presumably intended as the of a value.

LEX necessarily contains a decimal point (.) and may optionally contain a following F consisting of some number n of s. Return

n when F is present, and

0 otherwise.

scientificPrecision &integer;an &integer; LEXmatches

Maps a onto an &integer; presumably intended as the of a value.

LEX necessarily contains a or C preceeding an exponent indicator (E or e, and a following E. Return

−(E) when C is a , and

(C) − (E) otherwise.

Lexical Mapping precisionDecimalLexicalMap a value LEXmatches

Maps a onto a complete value.

pD be a complete value.

Set pD's to

(LEX) when LEX is an instance of ,

(LEX) when LEX is an instance of and

(LEX) otherwise.

set pD's to

0 when LEX is a ,

(LEX) when LEX is a ,

(LEX) when LEX is a , and

absent otherwise

Set pD's to

absent when LEX is NaN

negative when the first character of LEX is -, and

positive otherwise.

The algorithm for has not yet been written. Canonical Mapping precisionDecimalCanonicalMap a &string; matching pDa value

Maps a to its , a .

(TBD) -related Definitions

The following functions are primarily used with the datatype and its derivatives. Auxiliary -related Functions Operating on Representation Fragments duYearFragmentMap &integer;a nonnegative &integer; Ymatches

Maps a to an &integer;, intended as part of the value of the property of a value.

Y is necessarily the letter Y followed by a numeral N: Return (N). duMonthFragmentMap &integer;a nonnegative &integer; Mmatches

Maps a to an &integer;, intended as part of the value of the property of a value.

M is necessarily the letter M followed by a numeral N: Return (N). duDayFragmentMap &integer;a nonnegative &integer; Dmatches

Maps a to an &integer;, intended as part of the value of the property of a value.

D is necessarily the letter D followed by a numeral N: Return (N). duHourFragmentMap &integer;a nonnegative &integer; Hmatches

Maps a to an &integer;, intended as part of the value of the property of a value.

D is necessarily the letter D followed by a numeral N: Return (N). duMinuteFragmentMap &integer;a nonnegative &integer; Mmatches

Maps a to an &integer;, intended as part of the value of the property of a value.

M is necessarily the letter M followed by a numeral N: Return (N). duSecondFragmentMap &decimal;a nonnegative &decimal; Smatches

Maps a to a &decimal;, intended as part of the value of the property of a value.

S is necessarily S followed by a numeral N: Return

(N) when . occurs in N, and

(N) otherwise.

duYearMonthFragmentMap &integer;a nonnegative &integer; YMmatches

Maps a into an &integer;, intended as part of the property of a value.

YM necessarily consists of an instance Y of and/or an instance M of :

y be (Y) (or 0 if Y is not present) and

m be (M) (or 0 if M is not present).

Return 12 × y + m . duTimeFragmentMap &decimal;a nonnegative &decimal; Tmatches

Maps a into a &decimal;, intended as part of the property of a value.

T necessarily consists of an instance H of , and/or an instance M of , and/or an instance S of .

h be (H) (or 0 if H is not present),

m be (M) (or 0 if M is not present), and

s be (S) (or 0 if S is not present).

Return 3600 × h + 60 × m + s . duDayTimeFragmentMap &decimal;a nonnegative &decimal; DTmatches

Maps a into a &decimal;, which is the potential value of the property of a value.

DT necesarily consists of an instance D of and/or an instance T of .

d be (D) (or 0 if D is not present) and

t be (T) (or 0 if T is not present).

Return 86400 × d + t . The Lexical Mapping durationMap a complete value DURmatches

Separates the into the month part and the seconds part, then maps them into the and of the value.

DUR consists of possibly a leading -, followed by P and then an instance Y of and/or an instance D of : Return a whose

value is

0 if Y is not present,

−(Y) if both - and Y are present, and

(Y) otherwise.

and whose

value is

0 if D is not present,

−(D) if both - and D are present, and

(D) otherwise.

The Lexical Mapping yearMonthDurationMap a complete value YMmatches

Maps the lexical representation into the of a value. (A 's is always zero.) is a restriction of .

YM necessarily consists of an optional leading -, followed by P and then an instance Y of : Return a whose

value is

−(Y) if - is present in YM and

(Y) otherwise, and

value is (necessarily) 0.

The Lexical Mapping dayTimeDurationMap a complete value DTa value

Maps the lexical representation into the of a value. (A 's is always zero.) is a restriction of .

DT necessarily consists of possibly a leading -, followed by P and then an instance D of : Return a whose

value is (necessarily) 0, and

value is

−(D) if - is present in DT and

(D) otherwise.

Auxiliary -related Functions Producing Representation Fragments duYearMonthCanonicalFragmentMap a &string; matching yma nonnegative &integer;

Maps a nonnegative &integer;, presumably the absolute value of the of a value, to a , a fragment of a .

y be ym 12 , and

m be ym 12 ,

Return

(y) &concat; Y &concat; (m) &concat; M when neither y nor m is zero,

(y) &concat; Y when y is not zero but m is, and

(m) &concat; M when y is zero.

duDayCanonicalFragmentMap a &string; matching da nonnegative &integer;

Maps a nonnegative &integer;, presumably the day normalized value from the of a value, to a , a fragment of a .

Return

(d) &concat; D when d is not zero, and

the empty string () when d is zero.

duHourCanonicalFragmentMap a &string; matching ha nonnegative &integer;

Maps a nonnegative &integer;, presumably the hour normalized value from the of a value, to a , a fragment of a .

Return

(h) &concat; H when h is not zero, and

the empty string () when h is zero.

duMinuteCanonicalFragmentMap a &string; matching ma nonnegative &integer;

Maps a nonnegative &integer;, presumably the minute normalized value from the of a value, to a , a fragment of a .

Return

(m) &concat; M when m is not zero, and

the empty string () when m is zero.

duSecondCanonicalFragmentMap matches sa nonnegative &decimal;

Maps a nonnegative &decimal;, presumably the second normalized value from the of a value, to a , a fragment of a .

Return

(s) &concat; S when s is a non-zero integer,

(s) &concat; S when s is not an integer, and

the empty string () when s is zero.

duTimeCanonicalFragmentMap a &string; matching ha nonnegative &integer; ma nonnegative &integer; sa nonnegative &decimal;

Maps three nonnegative numbers, presumably the hour, minute, and second normalized values from a 's , to a , a fragment of a .

Return

T &concat; (h) &concat; (m) &concat; (s) when h, m, and s are not all zero, and

the empty string () when all arguments are zero.

duDayTimeCanonicalFragmentMap matches ssa nonnegative &decimal;

Maps a nonnegative &decimal;, presumably the absolute value of the of a value, to a , a fragment of a .

d is ss 86400 ,

h is (ss 86400) 3600 ,

m is (ss 3600) 60 , and

s is ss 60 ,

Return

(d) &concat; (h, m, s) when ss is not zero and

T0S when ss is zero.

The Canonical Mapping durationCanonicalMap matches va complete value

Maps a 's property values to fragments and combines the fragments into a complete .

m be v's ,

s be v's , and

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

Return

sgn &concat; P &concat; (| m |) &concat; (| s |) when neither m nor s is zero,

sgn &concat; P &concat; (| m |) when m is not zero but s is, and

sgn &concat; P &concat; (| s |) when m is zero.

The Canonical Mapping yearMonthDurationCanonicalMap matches yma complete value

Maps a 's value to a . (The value is necessarily zero and is ignored.) is a restriction of .

m be ym's and

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

Return sgn &concat; P &concat; (| m |) . The Canonical Mapping dayTimeDurationCanonicalMap matches dta complete value

Maps a 's value to a . (The value is necessarily zero and is ignored.) is a restriction of .

s be dt's and

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

Return sgn &concat; P &concat; (| s |) .

Date/time-related Definitions

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 timezone changes (as when converting to and from raw values) and when adding values to or subtracting them from values. Date/time Datatype Normalizing Procedures normalizeMonth yran &integer; moan &integer;

Add (mo − 1) 12 to yr.

Set mo to (mo − 1) 12 .

normalizeDay yran &integer; moan &integer; daan &integer;

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

(yr, mo)

Repeat until da is positive and not greater than the limit specified in the table of day limits in (which depends on yr and mo):

If da exceeds the upper limit from the table then:

Subtract that limit from da.

Add 1 to mo.

(yr, mo)

If da is not positive then:

Subtract 1 from mo.

(yr, mo)

Add the new upper limit from the table to da.

normalizeMinute yran &integer; moan &integer; daan &integer; hran &integer; mian &integer;

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

Add mi 60 to hr.

Set mi to mi 60 .

Add hr 24 to da.

Set hr to hr 24 .

(yr, mo, da).

lsiNormalizeSecond yran &integer; yran &integer; daan &integer; hran &integer; mian &integer; sea &decimal;

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

Add se 60 to mi.

Set se to se 60 .

(yr, mo, da, hr, mi).

lssNormalizeSecond yr an &integer; mo an &integer; da an &integer; hr an &integer; mi an &integer; se a &decimal;

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

(yr, mo, da).

Add 60 × mi + 3600 × hr to se .

Set mi and hr to zero.

Repeat until se is nonnegative and less than 86400 plus the number of leap-seconds specified by the leap-second table in (which depends on yr, mo, and da):

If se equals or exceeds 86400 plus the upper limit from the table then:

Subtract (86400 plus that leap-second count) from se.

Add 1 to da.

If se is negative then:

Subtract 1 from da.

Add 86400 plus the new leap-second count from the table to se.

(yr, mo, da).

If se is less than 86340 then:

Set mi to se 60.

Set se to se 60.

If se is not less than 86340 then:

Set mi to 1439.

Subtract 86340 from se.

(yr, mo, da, hr, mi)

The raw-value functions following all have very similar algorithms

Raw Properties of Date/time Seven-property Models rawYear &integer;an &integer; dta value

Returns the raw year value of a , i.e., the local timezone year, as opposed to the year. (This matters only near the year boundaries.)

yr be 1971 when dt's is absent, and dt's otherwise,

mo be 12 or dt's , similarly,

da be (the limit specified in the table of day limits in (which depends on yr and mo)) or dt's , similarly,

hr be 0 or dt's , similarly, and

mi be 0 or dt's , similarly.

Add to mi

(yr, mo, da, hr, mi).

If or dt's is absent, return dt's ; otherwise, return yr.

rawMonth &integer;an &integer; dta value

Returns the raw month value of a , i.e., the local timezone month, as opposed to the month. (This matters only near the month boundaries.)

yr be 1971 when dt's is absent, and dt's otherwise,

mo be 12 or dt's , similarly,

da be (the limit specified in the table of day limits in (which depends on yr and mo)) or dt's , similarly,

hr be 0 or dt's , similarly, and

mi be 0 or dt's , similarly.

Add to mi

(yr, mo, da, hr, mi).

If or dt's is absent, return dt's ; otherwise, return mo.

rawDay &integer;an &integer; dta value

Returns the raw day value of a , i.e., the local timezone day, as opposed to the day.

yr be 1971 when dt's is absent, and dt's otherwise,

mo be 12 or dt's , similarly,

da be (the limit specified in the table of day limits in (which depends on yr and mo)) or dt's , similarly,

hr be 0 or dt's , similarly, and

mi be 0 or dt's , similarly.

Add to mi

(yr, mo, da, hr, mi).

If or dt's is absent, return dt's ; otherwise, return da.

rawHour &integer;an &integer; dta value

Returns the raw hour value of a , i.e., the local timezone hour, as opposed to the hour.

yr be 1971 when dt's is absent, and dt's otherwise,

mo be 12 or dt's , similarly,

da be (the limit specified in the table of day limits in (which depends on yr and mo)) or dt's , similarly,

hr be 0 or dt's , similarly, and

mi be 0 or dt's , similarly.

Add to mi

(yr, mo, da, hr, mi).

If or dt's is absent, return dt's ; otherwise, return hr.

rawMinute &integer;an &integer; dta value

Returns the raw minute value of a , i.e., the local timezone minute, as opposed to the minute.

yr be 1971 when dt's is absent, and dt's otherwise,

mo be 12 or dt's , similarly,

da be (the limit specified in the table of day limits in (which depends on yr and mo)) or dt's , similarly,

hr be 0 or dt's , similarly, and

mi be 0 or dt's , similarly.

Add to mi

(yr, mo, da, hr, mi).

If or dt's is absent, return dt's ; otherwise, return mi.

rawSecond &decimal;a &decimal; dta value

Returns the raw second value of a , i.e., the local timezone second, as opposed to the second; however, for seconds, there is no difference.

Return value unchanged. setDateTimeFromRaw dta value rawYran &integer; rawMoan &integer; rawDaan &integer; rawHran &integer; rawMian &integer; rawSean &decimal;

Sets the properties of a from the raw values provided (the local timezone values, as opposed to the values). absent values are given default values for computation, but ultimately absent properties remain absent.

yr be rawYear when rawYear is not absent, dt's when dt's is not absent but rawYear is, and 1971 otherwise,

mo be rawMo, dt's , or 12, similarly,

da be rawDa, dt's , or the limit specified in the table of day limits in (which depends on yr and mo), similarly,

hr be rawHr, dt's , or 0, similarly,

mi be rawMi, dt's , or 0, similarly, and

se be rawSe, dt's , or 0, similarly.

If dt's is not absent,

Subtract from mi

(yr,mo,da,hr,mi).

Set to yr when is not absent, to mo when is not absent, etc.

Time on Timeline for Date/time Seven-property Models timeOnTimeline &decimal;a &decimal; dta value

Maps a value to the &decimal; representing its position on the time line.

yr be 1970 when dt's is absent, and dt's − 1 otherwise,

mo be 12 or dt's , similarly,

da be (the limit specified in the table of day limits) − 1 or (dt's ) − 1 , similarly,

hr be 0 or dt's , similarly, and

mi be 0 or dt's , similarly.

()

Set ToTl to 31536000 × yr .

(Leap-year Days, , and )

Add 86400 × (yr 400 − yr 100 + yr 4) to ToTl.

Add 86400 × (total number of days in months less than mo, from table in ) to ToTl

Add 86400 × da to ToTl.

(, , and )

Add 3600 × hr + 60 × mi + se to ToTl.

Return ToTl.

Partial Date/time Lexical Mappings yearFragValue &integer;an &integer; YRmatches

Maps a , part of a 's , onto an &integer;, presumably the property of a value.

Return (YR) monthFragValue &integer;an &integer; MOmatches

Maps a , part of a 's , onto an &integer;, presumably the property of a value.

Return (MO) dayFragValue &integer;an &integer; DAmatches

Maps a , part of a 's , onto an &integer;, presumably the property of a value.

Return (DA) hourFragValue &integer;an &integer; HRmatches

Maps a , part of a 's , onto an &integer;, presumably the property of a value.

Return (HR) minuteFragValue &integer;an &integer; MImatches

Maps a , part of a 's , onto an &integer;, presumably the property of a value.

Return (MI) secondFragValue &decimal;a &decimal; SEmatches

Maps a , part of a 's , onto a &decimal;, presumably the property of a value.

Return

(SE) when no decimal point occurs in SE, and

(SE) otherwise.

timezoneFragValue &integer;an &integer; TZmatches

Maps a , part of a 's , onto an &integer;, presumably the property of a value.

TZ necessarily consists of either just Z, or a sign (+ or -) followed by an instance H of , a colon, and an instance M of Return

0 when TZ is Z,

−((H) × 60 + (M)) when the sign is -, and

(H) × 60 + (M) otherwise.

Lexical Mapping gDayLexicalRep a complete value LEXmatches

Maps a to a value.

LEX necessarily includes an instance D of , optionally followed by an instance T of . gD be a complete value with all property values absent.

Set gD's to (T) when T is present and absent otherwise.

(gD, absent, absent, (D), absent, absent, absent)

Return gD.

Auxiliary Functions for Date/time Canonical Mappings unsTwoDigitCanonicalFragmentMap matches ia nonnegative &integer; less than 100

Maps a nonnegative &integer; less than 100 onto an unsigned always-two-digit numeral.

Return (i 10) &concat; (i 10) fourDigitCanonicalFragmentMap matches ian &integer; whose absolute value is less than 10000

Maps an &integer; between -10000 and 10000 onto an always-four-digit numeral.

Return

- &concat; (−i 100) &concat; (−i 100) when i is negative,

(i 100) &concat; (i 100) otherwise.

Partial Date/time Canonical Mappings yearCanonicalFragmentMap matches yan &integer;

Maps an &integer;, presumably the property of a value, onto a , part of a 's .

Return

(y) when |y| > 9999 .

(y) otherwise.

monthCanonicalFragmentMap matches man &integer; between 1 and 12 inclusive

Maps an &integer;, presumably the property of a value, onto a , part of a 's .

Return (m) dayCanonicalFragmentMap matches dan &integer; between 1 and 31 inclusive (may be limited further depending on associated and )

Maps an &integer;, presumably the property of a value, onto a , part of a 's .

Return (d) hourCanonicalFragmentMap matches han &integer; between 0 and 23 inclusive.

Maps an &integer;, presumably the property of a value, onto a , part of a 's .

Return (h) minuteCanonicalFragmentMap matches man &integer; between 0 and 59 inclusive.

Maps an &integer;, presumably the property of a value, onto a , part of a 's .

Return (m) secondCanonicalFragmentMap matches sa nonnegative &decimal; less than 70

Maps a &decimal;, presumably the property of a value, onto a , part of a 's .

Return

(s) when s is an integer, and

(s1) &concat; . &concat; (s1) otherwise.

timezoneCanonicalFragmentMap matches tan &integer; between −840 and 840 inclusive

Maps an &integer;, presumably the property of a value, onto a , part of a 's .

Return

Z when t is zero,

- &concat; (−t 60) &concat; : &concat; (−t 60) when t is negative, and

+ &concat; (t 60) &concat; : &concat; (t 60) otherwise.

Canonical Mapping gDayCanonicalRep matches gDa complete value

Maps a value to a .

Return

--- &concat; () when is absent, and

--- &concat; ((gD)) &concat; () otherwise.

Datatypes and Facets ISO 8601 Date and Time Formats It is likely that this Appendix will be deleted once all date/time datatype descriptions are written to the new format using the seven-property model, as illustrated in . ISO 8601 Conventions

The datatypes , , , , , , , and use lexical formats inspired by . Following , the lexical forms of these datatypes can include only the characters #20 through #7F. This appendix provides more detail on the ISO formats and discusses some deviations from them for the datatypes defined in this specification.

"specifies the representation of dates in the proleptic Gregorian calendar and times and representations of periods of time". The proleptic Gregorian calendar includes dates prior to 1582 (the year it came into use as an ecclesiastical calendar). It should be pointed out that the datatypes described in this specification do not cover all the types of data covered by , nor do they support all the lexical representations for those types of data.

lexical formats are described using "pictures" in which characters are used in place of decimal digits. The allowed decimal digits are (#x30-#x39). For the primitive datatypes , , , , , , and . these characters have the following meanings:

C -- represents a digit used in the thousands and hundreds components, the "century" component, of the time element "year". Legal values are from 0 to 9.

Y -- represents a digit used in the tens and units components of the time element "year". Legal values are from 0 to 9.

M -- represents a digit used in the time element "month". The two digits in a MM format can have values from 1 to 12.

D -- represents a digit used in the time element "day". The two digits in a DD format can have values from 1 to 28 if the month value equals 2, 1 to 29 if the month value equals 2 and the year is a leap year, 1 to 30 if the month value equals 4, 6, 9 or 11, and 1 to 31 if the month value equals 1, 3, 5, 7, 8, 10 or 12.

h -- represents a digit used in the time element "hour". The two digits in a hh format can have values from 0 to 24. If the value of the hour element is 24 then the values of the minutes element and the seconds element must be 00 and 00.

m -- represents a digit used in the time element "minute". The two digits in a mm format can have values from 0 to 59.

s -- represents a digit used in the time element "second". The two digits in a ss format can have values from 0 to 60. In the formats described in this specification the whole number of seconds be followed by decimal seconds to an arbitrary level of precision. This is represented in the picture by "ss.sss". A value of 60 or more is allowed only in the case of leap seconds.

Strictly speaking, a value of 60 or more is not sensible unless the month and day could represent March 31, June 30, September 30, or December 31 in . Because the leap second is added or subtracted as the last second of the day in time, the long (or short) minute could occur at other times in local time. In cases where the leap second is used with an inappropriate month and day it, and any fractional seconds, should considered as added or subtracted from the following minute.

For all the information items indicated by the above characters, leading zeros are required where indicated.

In addition to the above, certain characters are used as designators and appear as themselves in lexical formats.

T -- is used as time designator to indicate the start of the representation of the time of day in .

Z -- is used as time-zone designator, immediately (without a space) following a data element expressing the time of day in Coordinated Universal Time () in , , , , , , , and .

In the lexical format for the following characters are also used as designators and appear as themselves in lexical formats:

P -- is used as the time duration designator, preceding a data element representing a given duration of time.

Y -- follows the number of years in a time duration.

M -- follows the number of months or minutes in a time duration.

D -- follows the number of days in a time duration.

H -- follows the number of hours in a time duration.

S -- follows the number of seconds in a time duration.

The values of the Year, Month, Day, Hour and Minutes components are not restricted but allow an arbitrary integer. Similarly, the value of the Seconds component allows an arbitrary decimal. Thus, the lexical format for and datatypes derived from it does not follow the alternative format of § 5.5.3.2.1 of .

Truncated and Reduced Formats

supports a variety of "truncated" formats in which some of the characters on the left of specific formats, for example, the century, can be omitted. Truncated formats are, in general, not permitted for the datatypes defined in this specification with three exceptions. The datatype uses a truncated format for which represents an instant of time that recurs every day. Similarly, the and datatypes use left-truncated formats for . The datatype uses a right and left truncated format for .

also supports a variety of "reduced" or right-truncated formats in which some of the characters to the right of specific formats, such as the time specification, can be omitted. Right truncated formats are also, in general, not permitted for the datatypes defined in this specification with the following exceptions: right-truncated representations of are used as lexical representations for , , .

Deviations from ISO 8601 Formats Sign Allowed

An optional minus sign is allowed immediately preceding, without a space, the lexical representations for , , , , .

No Year Zero

The year "0000" is an illegal year value.

More Than 9999 Years

To accommodate year values greater than 9999, more than four digits are allowed in the year representations of , , , and . This follows .

Time zone permitted

The lexical representations for the datatypes , , , , and permit an optional trailing time zone specificiation.

Adding durations to dateTimes It is expected that this Appendix will be replaced by a short function definition building upon those already defined herein, which will be placed with the other function definitions in and referenced in .

Given a S and a D, this appendix specifies how to compute a 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 is within a specific time period. This appendix also addresses the addition of s to the datatypes , , , and , which can be viewed as a set of s. In such cases, the addition is made to the first or starting in the set.

This is a logical explanation of the process. Actual implementations are free to optimize as long as they produce the same results. The calculation uses the notation S[year] to represent the year field of S, S[month] to represent the month field, and so on. It also depends on the following functions:

fQuotient(a, b) = the greatest integer less than or equal to a/b

fQuotient(-1,3) = -1

fQuotient(0,3)...fQuotient(2,3) = 0

fQuotient(3,3) = 1

fQuotient(3.123,3) = 1

modulo(a, b) = a - fQuotient(a,b)*b

modulo(-1,3) = 2

modulo(0,3)...modulo(2,3) = 0...2

modulo(3,3) = 0

modulo(3.123,3) = 0.123

fQuotient(a, low, high) = fQuotient(a - low, high - low)

fQuotient(0, 1, 13) = -1

fQuotient(1, 1, 13) ... fQuotient(12, 1, 13) = 0

fQuotient(13, 1, 13) = 1

fQuotient(13.123, 1, 13) = 1

modulo(a, low, high) = modulo(a - low, high - low) + low

modulo(0, 1, 13) = 12

modulo(1, 1, 13) ... modulo(12, 1, 13) = 1...12

modulo(13, 1, 13) = 1

modulo(13.123, 1, 13) = 1.123

maximumDayInMonthFor(yearValue, monthValue) =

M := modulo(monthValue, 1, 13)

Y := yearValue + fQuotient(monthValue, 1, 13)

Return a value based on M and Y:

31	M = January, March, May, July, August, October, or December
30	M = April, June, September, or November
29	M = February AND (modulo(Y, 400) = 0 OR (modulo(Y, 100) != 0) AND modulo(Y, 4) = 0)
28	Otherwise

Algorithm

Essentially, this calculation is equivalent to separating D into <year,month> and <day,hour,minute,second> fields. The <year,month> is added to S. If the day is out of range, it is pinned to be within range. Thus April 31 turns into April 30. Then the <day,hour,minute,second> is added. This latter addition can cause the year and month to change.

Leap seconds are handled by the computation by treating them as overflows. Essentially, a value of 60 seconds in S is treated as if it were a duration of 60 seconds added to S (with a zero seconds field). All calculations thereafter 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 is the responsibility of the . 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 .

The following is the precise specification. These steps must be followed in the same order. If a field in D is not specified, it is treated as if it were zero. If a field in S is not specified, it is treated in the calculation as if it were the minimum allowed value in that field, however, after the calculation is concluded, the corresponding field in E is removed (set to unspecified).

Months (may be modified additionally below)

temp := S[month] + D[month]

E[month] := modulo(temp, 1, 13)

carry := fQuotient(temp, 1, 13)

Years (may be modified additionally below)

E[year] := S[year] + D[year] + carry

Zone

E[zone] := S[zone]

Seconds

temp := S[second] + D[second]

E[second] := modulo(temp, 60)

carry := fQuotient(temp, 60)

Minutes

temp := S[minute] + D[minute] + carry

E[minute] := modulo(temp, 60)

carry := fQuotient(temp, 60)

Hours

temp := S[hour] + D[hour] + carry

E[hour] := modulo(temp, 24)

carry := fQuotient(temp, 24)

Days

if S[day] > maximumDayInMonthFor(E[year], E[month])

tempDays := maximumDayInMonthFor(E[year], E[month])

else if S[day] < 1

tempDays := 1

else

tempDays := S[day]

E[day] := tempDays + D[day] + carry

START LOOP

IF E[day] < 1

E[day] := E[day] + maximumDayInMonthFor(E[year], E[month] - 1)

carry := -1

ELSE IF E[day] > maximumDayInMonthFor(E[year], E[month])

E[day] := E[day] - maximumDayInMonthFor(E[year], E[month])

carry := 1

ELSE EXIT LOOP

temp := E[month] + carry

E[month] := modulo(temp, 1, 13)

E[year] := E[year] + fQuotient(temp, 1, 13)

GOTO START LOOP

Examples:

dateTime	duration	result
2000-01-12T12:13:14Z	P1Y3M5DT7H10M3.3S	2001-04-17T19:23:17.3Z
2000-01	-P3M	1999-10
2000-01-12	PT33H	2000-01-13

Commutativity and Associativity

Time durations are added by simply adding each of their fields, respectively, without overflow.

The order of addition of durations to instants is 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

Regular Expressions

A R is a sequence of characters that denote a set of strings L(R). When used to constrain a , a regular expression R asserts that only strings in L(R) are valid literals for values of that type.

Unlike some popular regular expression languages (including those defined by Perl and standard Unix utilities), the regular expression language defined here implicitly anchors all regular expressions at the head and tail, as the most common use of regular expressions in is to match entire literals. For example, a datatype from such that all values must begin with the character A (#x41) and end with the character Z (#x5a) would be defined as follows:

In regular expression languages that are not implicitly anchored at the head and tail, it is customary to write the equivalent regular expression as:

^A.*Z$

where "^" anchors the pattern at the head and "$" anchors at the tail.

In those rare cases where an unanchored match is desired, including .* at the beginning and ending of the regular expression will achieve the desired results. For example, a datatype from string such that all values must contain at least 3 consecutive A (#x41) characters somewhere within the value could be defined as follows:

A regular expression is composed from zero or more es, separated by | characters.

Regular Expression regExp ( '|' )*

For all es S, and for all s T, valid s R are: Denoting the set of strings L(R) containing:

(empty string) the set containing just the empty string

S all strings in L(S)

S|T all strings in L(S) and all strings in L(T)

For all es S, and for all s T, valid s R are:	Denoting the set of strings L(R) containing:
(empty string)	the set containing just the empty string
S	all strings in L(S)
S\|T	all strings in L(S) and all strings in L(T)

A branch consists of zero or more s, concatenated together.

Branch branch *

For all s S, and for all es T, valid es R are: Denoting the set of strings L(R) containing:

S all strings in L(S)

ST all strings st with s in L(S) and t in L(T)

For all s S, and for all es T, valid es R are:	Denoting the set of strings L(R) containing:
S	all strings in L(S)
ST	all strings st with s in L(S) and t in L(T)

A piece is an , possibly followed by a .

Piece piece ?

For all s S and non-negative integers n, m such that n <= m, valid s R are: Denoting the set of strings L(R) containing:

S all strings in L(S)

S? the empty string, and all strings in L(S).

S* All strings in L(S?) and all strings st with s in L(S*) and t in L(S). ( all concatenations of zero or more strings from L(S) )

S+ All strings st with s in L(S) and t in L(S*). ( all concatenations of one or more strings from L(S) )

S{n,m} All strings st with s in L(S) and t in L(S{n-1,m-1}). ( All sequences of at least n, and at most m, strings from L(S) )

S{n} All strings in L(S{n,n}). ( All sequences of exactly n strings from L(S) )

S{n,} All strings in L(S{n}S*) ( All sequences of at least n, strings from L(S) )

S{0,m} All strings st with s in L(S?) and t in L(S{0,m-1}). ( All sequences of at most m, strings from L(S) )

S{0,0} The set containing only the empty string

For all s S and non-negative integers n, m such that n <= m, valid s R are:	Denoting the set of strings L(R) containing:
S	all strings in L(S)
S?	the empty string, and all strings in L(S).
S*	All strings in L(S?) and all strings st with s in L(S*) and t in L(S). ( all concatenations of zero or more strings from L(S) )
S+	All strings st with s in L(S) and t in L(S*). ( all concatenations of one or more strings from L(S) )
S{n,m}	All strings st with s in L(S) and t in L(S{n-1,m-1}). ( All sequences of at least n, and at most m, strings from L(S) )
S{n}	All strings in L(S{n,n}). ( All sequences of exactly n strings from L(S) )
S{n,}	All strings in L(S{n}S*) ( All sequences of at least n, strings from L(S) )
S{0,m}	All strings st with s in L(S?) and t in L(S{0,m-1}). ( All sequences of at most m, strings from L(S) )
S{0,0}	The set containing only the empty string

The regular expression language in the Perl Programming Language does not include a quantifier of the form S{,m}, since it is logically equivalent to S{0,m}. We have, therefore, left this logical possibility out of the regular expression language defined by this specification.

A quantifier is one of ?, *, +, {n,m} or {n,}, which have the meanings defined in the table above.

Quanitifer quantifier [?*+] | ( '{' '}' ) quantity | | quantRange ',' quantMin ',' QuantExact [0-9]+

An atom is either a , a , or a parenthesized .

Atom atom | | ( '(' ')' )

For all s c, es C, and s S, valid s R are: Denoting the set of strings L(R) containing:

c the single string consisting only of c

C all strings in L(C)

(S) all strings in L(S)

For all s c, es C, and s S, valid s R are:	Denoting the set of strings L(R) containing:
c	the single string consisting only of c
C	all strings in L(C)
(S)	all strings in L(S)

A metacharacter is either ., \, ?, *, +, {, } (, ), [ or ]. These characters have special meanings in s, but can be escaped to form s that denote the sets of strings containing only themselves, i.e., an escaped behaves like a .

A normal character is any XML character that is not a metacharacter. In s, a normal character is an atom that denotes the singleton set of strings containing only itself.

Normal Character Char [^.\?*+()|#x5B#x5D]

Note that a can be represented either as itself, or with a character reference.

Character Classes

A character class is an R that identifies a set of characters C(R). The set of strings L(R) denoted by a character class R contains one single-character string "c" for each character c in C(R).

Character Class charClass | |

A character class is either a or a .

A character class expression is a surrounded by [ and ] characters. For all character groups G, [G] is a valid character class expression, identifying the set of characters C([G]) = C(G).

Character Class Expression charClassExpr '[' ']'

A character group is either a , a , or a .

Character Group charGroup | |

A positive character group consists of one or more s or s, concatenated together. A positive character group identifies the set of characters containing all of the characters in all of the sets identified by its constituent ranges or escapes.

Positive Character Group posCharGroup ( | )+

For all s R, all s E, and all s P, valid s G are: Identifying the set of characters C(G) containing:

R all characters in C(R).

E all characters in C(E).

RP all characters in C(R) and all characters in C(P).

EP all characters in C(E) and all characters in C(P).

For all s R, all s E, and all s P, valid s G are:	Identifying the set of characters C(G) containing:
R	all characters in C(R).
E	all characters in C(E).
RP	all characters in C(R) and all characters in C(P).
EP	all characters in C(E) and all characters in C(P).

A negative character group is a preceded by the ^ character. For all s P, ^P is a valid negative character group, and C(^P) contains all XML characters that are not in C(P).

Negative Character Group negCharGroup '^'

A character class subtraction is a subtracted from a or , using the - character.

Character Class Subtraction charClassSub ( | ) '-'

For any or G, and any C, G-C is a valid , identifying the set of all characters in C(G) that are not also in C(C).

A character range R identifies a set of characters C(R) containing all XML characters with UCS code points in a specified range.

Character Range charRange | seRange '-' charOrEsc | XmlChar [^\#x2D#x5B#x5D]

A single XML character is a that identifies the set of characters containing only itself. All XML characters are valid character ranges, except as follows:

The [, ], - and \ characters are not valid character ranges;

The ^ character is only valid at the beginning of a if it is part of a

A also be written in the form s-e, identifying the set that contains all XML characters with UCS code points greater than or equal to the code point of s, but not greater than the code point of e.

s-e is a valid character range iff:

s is a , or an XML character;

s is not \

If s is the first character in a , then s is not ^

e is a , or an XML character;

e is not \ or [; and

The code point of e is greater than or equal to the code point of s;

The code point of a is the code point of the single character in the set of characters that it identifies.

Character Class Escapes

A character class escape is a short sequence of characters that identifies predefined character class. The valid character class escapes are the s, the s, and the s (including the s).

Character Class Escape charClassEsc ( | | | )

A single character escape identifies a set containing a only one character -- usually because that character is difficult or impossible to write directly into a .

Single Character Escape SingleCharEsc '\' [nrt\|.?*+(){}#x2D#x5B#x5D#x5E]

The valid s are: Identifying the set of characters C(R) containing:

\n the newline character (#xA)

\r the return character (#xD)

\t the tab character (#x9)

\\ \

\| |

\. .

\- -

\^ ^

\? ?

\* *

\+ +

\{ {

\} }

$ (

$ )

\[ [

\] ]

The valid s are:	Identifying the set of characters C(R) containing:
`\n`	the newline character (#xA)
`\r`	the return character (#xD)
`\t`	the tab character (#x9)
`\\`	\
`\\|`	\|
`\.`	.
`\-`	-
`\^`	^
`\?`	?
`\*`	*
`\+`	+
`\{`	{
`\}`	}
`\(`	(
`\)`	)
`\[`	[
`\]`	]

specifies a number of possible values for the "General Category" property and provides mappings from code points to specific character properties. The set containing all characters that have property X, can be identified with a category escape \p{X}. The complement of this set is specified with the category escape \P{X}. ([\P{X}] = [^\p{X}]).

Category Escape catEsc '\p{' '}' complEsc '\P{' '}' charProp |

is subject to future revision. For example, the mapping from code points to character properties might be updated. All processors support the character properties defined in the version of that is current at the time this specification became a W3C Recommendation. However, implementors are encouraged to support the character properties defined in any future version.

The following table specifies the recognized values of the "General Category" property.

Category	Property	Meaning
Letters	L	All Letters
	Lu	uppercase
	Ll	lowercase
	Lt	titlecase
	Lm	modifier
	Lo	other

Marks	M	All Marks
	Mn	nonspacing
	Mc	spacing combining
	Me	enclosing

Numbers	N	All Numbers
	Nd	decimal digit
	Nl	letter
	No	other

Punctuation	P	All Punctuation
	Pc	connector
	Pd	dash
	Ps	open
	Pe	close
	Pi	initial quote (may behave like Ps or Pe depending on usage)
	Pf	final quote (may behave like Ps or Pe depending on usage)
	Po	other

Separators	Z	All Separators
	Zs	space
	Zl	line
	Zp	paragraph

Symbols	S	All Symbols
	Sm	math
	Sc	currency
	Sk	modifier
	So	other

Other	C	All Others
	Cc	control
	Cf	format
	Co	private use
	Cn	not assigned

Categories IsCategory | | | | | | Letters 'L' [ultmo]? Marks 'M' [nce]? Numbers 'N' [dlo]? Punctuation 'P' [cdseifo]? Separators 'Z' [slp]? Symbols 'S' [mcko]? Others 'C' [cfon]?

The properties mentioned above exclude the Cs property. The Cs property identifies "surrogate" characters, which do not occur at the level of the "character abstraction" that XML instance documents operate on.

groups code points into a number of blocks such as Basic Latin (i.e., ASCII), Latin-1 Supplement, Hangul Jamo, CJK Compatibility, etc. The set containing all characters that have block name X (with all white space stripped out), can be identified with a block escape \p{IsX}. The complement of this set is specified with the block escape \P{IsX}. ([\P{IsX}] = [^\p{IsX}]).

Block Escape IsBlock 'Is' [a-zA-Z0-9#x2D]+

The following table specifies the recognized block names (for more information, see the "Blocks.txt" file in ).

Start Code	End Code	Block Name	Start Code	End Code	Block Name
#x0000	#x007F	BasicLatin	#x0080	#x00FF	Latin-1Supplement
#x0100	#x017F	LatinExtended-A	#x0180	#x024F	LatinExtended-B
#x0250	#x02AF	IPAExtensions	#x02B0	#x02FF	SpacingModifierLetters
#x0300	#x036F	CombiningDiacriticalMarks	#x0370	#x03FF	Greek
#x0400	#x04FF	Cyrillic	#x0530	#x058F	Armenian
#x0590	#x05FF	Hebrew	#x0600	#x06FF	Arabic
#x0700	#x074F	Syriac	#x0780	#x07BF	Thaana
#x0900	#x097F	Devanagari	#x0980	#x09FF	Bengali
#x0A00	#x0A7F	Gurmukhi	#x0A80	#x0AFF	Gujarati
#x0B00	#x0B7F	Oriya	#x0B80	#x0BFF	Tamil
#x0C00	#x0C7F	Telugu	#x0C80	#x0CFF	Kannada
#x0D00	#x0D7F	Malayalam	#x0D80	#x0DFF	Sinhala
#x0E00	#x0E7F	Thai	#x0E80	#x0EFF	Lao
#x0F00	#x0FFF	Tibetan	#x1000	#x109F	Myanmar
#x10A0	#x10FF	Georgian	#x1100	#x11FF	HangulJamo
#x1200	#x137F	Ethiopic	#x13A0	#x13FF	Cherokee
#x1400	#x167F	UnifiedCanadianAboriginalSyllabics	#x1680	#x169F	Ogham
#x16A0	#x16FF	Runic	#x1780	#x17FF	Khmer
#x1800	#x18AF	Mongolian	#x1E00	#x1EFF	LatinExtendedAdditional
#x1F00	#x1FFF	GreekExtended	#x2000	#x206F	GeneralPunctuation
#x2070	#x209F	SuperscriptsandSubscripts	#x20A0	#x20CF	CurrencySymbols
#x20D0	#x20FF	CombiningMarksforSymbols	#x2100	#x214F	LetterlikeSymbols
#x2150	#x218F	NumberForms	#x2190	#x21FF	Arrows
#x2200	#x22FF	MathematicalOperators	#x2300	#x23FF	MiscellaneousTechnical
#x2400	#x243F	ControlPictures	#x2440	#x245F	OpticalCharacterRecognition
#x2460	#x24FF	EnclosedAlphanumerics	#x2500	#x257F	BoxDrawing
#x2580	#x259F	BlockElements	#x25A0	#x25FF	GeometricShapes
#x2600	#x26FF	MiscellaneousSymbols	#x2700	#x27BF	Dingbats
#x2800	#x28FF	BraillePatterns	#x2E80	#x2EFF	CJKRadicalsSupplement
#x2F00	#x2FDF	KangxiRadicals	#x2FF0	#x2FFF	IdeographicDescriptionCharacters
#x3000	#x303F	CJKSymbolsandPunctuation	#x3040	#x309F	Hiragana
#x30A0	#x30FF	Katakana	#x3100	#x312F	Bopomofo
#x3130	#x318F	HangulCompatibilityJamo	#x3190	#x319F	Kanbun
#x31A0	#x31BF	BopomofoExtended	#x3200	#x32FF	EnclosedCJKLettersandMonths
#x3300	#x33FF	CJKCompatibility	#x3400	#x4DB5	CJKUnifiedIdeographsExtensionA
#x4E00	#x9FFF	CJKUnifiedIdeographs	#xA000	#xA48F	YiSyllables
#xA490	#xA4CF	YiRadicals	#xAC00	#xD7A3	HangulSyllables

			#xE000	#xF8FF	PrivateUse
#xF900	#xFAFF	CJKCompatibilityIdeographs	#xFB00	#xFB4F	AlphabeticPresentationForms
#xFB50	#xFDFF	ArabicPresentationForms-A	#xFE20	#xFE2F	CombiningHalfMarks
#xFE30	#xFE4F	CJKCompatibilityForms	#xFE50	#xFE6F	SmallFormVariants
#xFE70	#xFEFE	ArabicPresentationForms-B	#xFEFF	#xFEFF	Specials
#xFF00	#xFFEF	HalfwidthandFullwidthForms	#xFFF0	#xFFFD	Specials

The blocks mentioned above exclude the HighSurrogates, LowSurrogates and HighPrivateUseSurrogates blocks. These blocks identify "surrogate" characters, which do not occur at the level of the "character abstraction" that XML instance documents operate on.

is subject to future revision. For example, the grouping of code points into blocks might be updated. All processors support the blocks defined in the version of that is current at the time this specification became a W3C Recommendation. However, implementors are encouraged to support the blocks defined in any future version of the Unicode Standard.

For example, the for identifying the ASCII characters is \p{IsBasicLatin}.

A multi-character escape provides a simple way to identify a commonly used set of characters:

Multi-Character Escape MultiCharEsc '\' [sSiIcCdDwW] WildcardEsc '.'

Character sequence Equivalent

. [^\n\r]

\s [#x20\t\n\r]

\S [^\s]

\i the set of initial name characters, those ed by Letter | '_' | ':'

\I [^\i]

\c the set of name characters, those ed by NameChar

\C [^\c]

\d \p{Nd}

\D [^\d]

\w [#x0000-#x10FFFF]-[\p{P}\p{Z}\p{C}] (all characters except the set of "punctuation", "separator" and "other" characters)

\W [^\w]

Character sequence	Equivalent
.	[^\n\r]
\s	[#x20\t\n\r]
\S	[^\s]
\i	the set of initial name characters, those ed by Letter \| '_' \| ':'
\I	[^\i]
\c	the set of name characters, those ed by NameChar
\C	[^\c]
\d	\p{Nd}
\D	[^\d]
\w	[#x0000-#x10FFFF]-[\p{P}\p{Z}\p{C}] (all characters except the set of "punctuation", "separator" and "other" characters)
\W	[^\w]

The language defined here does not attempt to provide a general solution to "regular expressions" over UCS character sequences. In particular, it does not easily provide for matching sequences of base characters and combining marks. The language is targeted at support of "Level 1" features as defined in . It is hoped that future versions of this specification will provide support for "Level 2" features.

Changes since version 1.0 Changes Already Made

A number of proposals for final wording satisfying various approved requirements for Schema 1.1 are included in the prose of this document. Only one has been formally accepted by the WG: the rewrite of (including the new derived datatypes and ), in , and ; even that new approved text has a few improvements proffered. The new writeups of , , , and are included herein but have not yet received final approval by the WG. In versions of this draft that show add/del markup, the unapproved new material is marked as revision text. (Approved changes are not marked as revisions.)

Datatypes, Facets and Related Rewrites

The model of an abstract datatype is being made more precise and explicit. has mostly been rewritten, but there is still discussion within the WG as to the final form; this text has not been formally blessed by the WG. In versions of this specification that show adds and dels, this material shaws as a proposed change. Driving this new text is not only a desire on the part of the WG to make it more precise and explicit but also a specific formal requirement to redo the handling of facets (RQ-24 (systematic facets)). The primary intent of this requirement was to move the description of equality, identity, and order to .

RQ-24 (systematic facets: separate identity and equality) directed that we provide for equality that in some cases was different from identity. Most datatypes still use identity as their equality, but the new precisionDecimal and the redesigned date/time datatypes will not. It is also intended that and will use this capability to separate minus zero from plus zero; they will be non-identical but equal (see RQ-140).

The of the component for list datatypes is now always false, reflecting the fact that datatypes are not ordered (except by the trivial order), and hence cannot reasonably be bounded.

Units of length have been selected for all datatypes that are permitted the length &cfacet; (RQ-6 (length for [almost] all primitive types)).

Numerical Datatypes

The datatype has been added. It differs from in that values corry not ony numerical value but also precision Precision is explained in . The writeup in has not yet been approved by the WG. In versions of this specification that show adds and dels, this material shows as a proposed change.

Date/time Datatypes

RQ-2 (canonical rep of duration) resulted in the adoption of a new two-property model for and the rewriting of . A few additional changes have been proposed, and in versions of this specification that show adds and dels these changes are so marked. In addition, two new derived datatypes ( and ) have been added in satisfaction of RQ-20 (ordered duration types).

RQ-122 (define dateTime value space) has resulted in a revision of the value space for all date/time datatypes (except , which was changed as a result of another requirement). The most visible effect of this change was to cause the values to retain knowledge of their timezone, which is explained in the new material. The new version specifies a seven-property model used uniformly for values in all of these datatypes, described in . Only has been rewritten to match this new generic approach; the other date/time datatype descriptions will be rewritten in a future draft. These rewrites and the new have not yet been approved by the WG; in versions of this specification that show adds and dels, this material shows as a proposed change. In addition to the normative material, the nonnormative was added to explain in more detail the model of dates and times behind the seven-property model, so that there will be no confusion about the handling of such things as leap-seconds.

The seven property model rewrite of date/time datatype descriptions includes a carefully crafted definition of order that insures that for repeating datatypes (time, gDay, etc.), timezoned values will be compared as though they are on the same "calendar day" ("raw" property values) so that in any given timezone, the days start at "raw" 00:00:00 and end not quite including "raw" 24:00:00. Days are not 00:00:00Z to 24:00:00Z in timezones other than Z. This covers the requirements of RQ-13 (time zone crosses date line). In addition, in satisfaction of RQ-123 (year 0000 in date/time datatypes), the lexical representation 0000 for years is made legal and the mapping of values with negative years onto the timeline has been changed to match. E.g., the year 0000 is 1 B.C.E., the year −0001 is 2 B.C.E., etc. (This is a change from version 1.0 of this specification.)

Specific Outstanding Issues

In addition to the changes already made, the Working Group has decided on a number of further changes which have not yet been reflected in this draft. These are indicated throughout the text as issues, including more or less detail on the intended resolution. The ones remaining in this draft are summarized below, linked to their occurrence in the text above, where more detail can be found, including links to the original requirement or other point of origin.

Glossary (non-normative)

The listing below is for the benefit of readers of a printed version of this document: it collects together all the definitions which appear in the document above.

An XSL macro is used to collect definitions from throughout the spec and gather them here for easy reference. References Normative World Wide Web Consortium. XML Base. Available at: http://www.w3.org/TR/2001/REC-xmlbase-20010627/ IEEE. IEEE Standard for Binary Floating-Point Arithmetic. See http://standards.ieee.org/reading/ieee/std_public/description/busarch/754-1985_desc.html World Wide Web Consortium. XML Linking Language (XLink). Available at: &xlink;. Note: only the URI reference escaping procedure defined in Section 5.4 is normatively referenced. Extensible Markup Language (XML) 1.0, Second EditionThird Edition, Tim Bray et al., eds., W3C, 6 October 20004 February 2004. See http://www.w3.org/TR/2000/REC-xml-20001006http://www.w3.org/TR/2004/REC-xml-20040204/ XML Schema Version 1.1 Part 1: Structures. Available at: http://www.w3.org/TR/2001/REC-xmlschema-1-20010502/ &xsdl; XML Schema Requirements , Ashok Malhotra and Murray Maloney, eds., W3C, 15 February 1999. See http://www.w3.org/TR/1999/NOTE-xml-schema-req-19990215 World Wide Web Consortium. Namespaces in XML. Available at: &xmlnsspec; Tim Berners-Lee, et. al. RFC 2396: Uniform Resource Identifiers (URI): Generic Syntax.. 1998. Available at: http://www.ietf.org/rfc/rfc2396.txt RFC 2732: Format for Literal IPv6 Addresses in URL's. 1999. Available at: http://www.ietf.org/rfc/rfc2732.txt N. Freed and N. Borenstein. RFC 2045: Multipurpose Internet Mail Extensions (MIME) Part One: Format of Internet Message Bodies. 1996. Available at: http://www.ietf.org/rfc/rfc2045.txt H. Alvestrand, ed. RFC 3066: Tags for the Identification of Languages 1995. Available at: http://www.ietf.org/rfc/rfc3066.txt William D Clinger. How to Read Floating Point Numbers Accurately. In Proceedings of Conference on Programming Language Design and Implementation, pages 92-101. Available at: ftp://ftp.ccs.neu.edu/pub/people/will/howtoread.ps The Unicode Consortium. The Unicode Character Database. Available at: http://www.unicode.org/Public/3.1-Update/UnicodeCharacterDatabase-3.1.0.html Non-normative XML Schema Requirements , Ashok Malhotra and Murray Maloney, eds., W3C, 15 February 1999. See http://www.w3.org/TR/1999/NOTE-xml-schema-req-19990215 M. Dürst and M. Suignard . Internationalized Resource Identifiers 2002. Available at: http://www.w3.org/International/iri-edit/draft-duerst-iri-08.txt World Wide Web Consortium. Ruby Annotation. Available at: http://www.w3.org/TR/2001/REC-ruby-20010531 World Wide Web Consortium. Hypertext Markup Language, version 4.01. Available at: &html4; World Wide Web Consortium. XML Schema Language: Part 0 Primer. Available at: &primer; Mark Davis. Unicode Regular Expression Guidelines, 1988. Available at: http://www.unicode.org/unicode/reports/tr18/ The Perl Programming Language. See http://www.perl.com/pub/language/info/software.html ISO (International Organization for Standardization). ISO/IEC 9075-2:1999, Information technology --- Database languages --- SQL --- Part 2: Foundation (SQL/Foundation). [Geneva]: International Organization for Standardization, 1999. See http://www.iso.ch/cate/d26197.html International Earth Rotation Service (IERS). See http://maia.usno.navy.mil ISO (International Organization for Standardization). Representations of dates and times, 1988-06-15. ISO (International Organization for Standardization). Representations of dates and times, draft revision, 1998. ISO (International Organization for Standardization). Representations of dates and times, second edition, 2000-12-15. ISO (International Organization for Standardization). Language-independent Datatypes. See http://www.iso.ch/cate/d19346.html World Wide Web Consortium. RDF Schema Specification. Available at: http://www.w3.org/TR/2000/CR-rdf-schema-20000327/ Information about Leap Seconds Available at: http://tycho.usno.navy.mil/leapsec.990505.html World Wide Web Consortium. Extensible Stylesheet Language (XSL). Available at: