2.5.1.1 Atomic datatypes

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

2.5.1.2 List datatypes

Several type systems (such as the one described in [ISO 11404]) treat ·list· datatypes as special cases of the more general notions of aggregate or collection datatypes.

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

[Definition:]   The ·atomic· or ·union· datatype that participates in the definition of a ·list· datatype is known as the itemType of that ·list· datatype.

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

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

A ·list· datatype can be ·derived· from an ·atomic· datatype whose ·lexical space· allows space (such as string or anyURI)or a ·union· datatype any of whose {member type definitions}'s ·lexical space· allows space. In such a case, regardless of the input, list items will be separated at space boundaries.

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

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

When a datatype is ·derived· from a ·list· datatype, the following ·constraining facet·s apply:

• ·length·
• ·maxLength·
• ·minLength·
• ·enumeration·
• ·pattern·
• ·whiteSpace·

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

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

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

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

2.5.1.3 Union datatypes

The ·value space· and ·lexical space· of a ·union· datatype are the union of the ·value space·s and ·lexical space·s of its ·memberTypes·. ·union· datatypes are always ·derived·. Currently, there are no ·built-in· ·union· datatypes.

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

Any number (greater than 1) of ·atomic· or ·list· ·datatype·s can participate in a ·union· type.

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

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

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

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

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

2.5.2.1 Derived by restriction

[Definition:]  A datatype is said to be ·derived· by restriction from another datatype when values for zero or more ·constraining facet·s are specified that serve to constrain its ·value space· and/or its ·lexical space· to a subset of those of its ·base type·.

[Definition:]  Every datatype that is ·derived· by restriction is defined in terms of an existing datatype, referred to as its base type. base types can be either ·primitive· or ·derived·.

2.5.2.2 Derived by list

A ·list· datatype can be ·derived· from another datatype (its ·itemType·) by creating a ·value space· that consists of a finite-length sequence of values of its ·itemType·.

2.5.2.3 Derived by union

One datatype can be ·derived· from one or more datatypes by ·union·ing their ·value space·s and, consequently, their ·lexical space·s.

3.2.1.1 Constraining facets

string has the following ·constraining facets·:

• length
• minLength
• maxLength
• pattern
• enumeration
• whiteSpace

3.2.1.2 Derived datatypes

The following ·built-in· datatypes are ·derived· from string:

• normalizedString

3.2.2.1 Lexical representation

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

3.2.2.2 Canonical representation

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

3.2.2.3 Constraining facets

boolean has the following ·constraining facets·:

• pattern
• whiteSpace

3.2.3.1 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.

3.2.3.2 Canonical representation

The canonical representation for decimal is defined by prohibiting certain options from the 3.2.3.1 Lexical representation. 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.

3.2.3.3 Constraining facets

decimal has the following ·constraining facets·:

• totalDigits
• fractionDigits
• pattern
• whiteSpace
• enumeration
• maxInclusive
• maxExclusive
• minInclusive
• minExclusive

3.2.3.4 Derived datatypes

The following ·built-in· datatypes are ·derived· from decimal:

• integer

3.2.4.1 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 ·must· be an integer. The mantissa must be a decimal number. The representations for exponent and mantissa must follow the lexical rules for integer and decimal. 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.

3.2.4.2 Canonical representation

The canonical representation for float is defined by prohibiting certain options from the 3.2.4.1 Lexical representation. 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.

3.2.4.3 Constraining facets

float has the following ·constraining facets·:

• pattern
• enumeration
• whiteSpace
• maxInclusive
• maxExclusive
• minInclusive
• minExclusive

3.2.5.1 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 ·must· be an integer. The mantissa must be a decimal number. The representations for exponent and mantissa must follow the lexical rules for integer and decimal. 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 double.

3.2.5.2 Canonical representation

The canonical representation for double is defined by prohibiting certain options from the 3.2.5.1 Lexical representation. 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.

3.2.5.3 Constraining facets

double has the following ·constraining facets·:

• pattern
• enumeration
• whiteSpace
• maxInclusive
• maxExclusive
• minInclusive
• minExclusive

3.2.6.1 Lexical representation

The lexical representation for duration is the [ISO 8601] extended format PnYn MnDTnH nMnS, where nY represents the number of years, nM the number of months, nD the number of days, 'T' is the date/time separator, nH the number of hours, nM the number of minutes and nS the number of seconds. The number of seconds can include decimal digits to arbitrary precision.

The values of the Year, Month, Day, Hour and Minutes components are not restricted but allow an arbitrary unsigned integer, i.e., an integer that conforms to the pattern [0-9]+.. Similarly, the value of the Seconds component allows an arbitrary unsigned decimal. Following [ISO 8601], at least one digit must follow the decimal point if it appears. That is, the value of the Seconds component must conform to the pattern [0-9]+(\.[0-9]+)?. Thus, the lexical representation of duration does not follow the alternative format of § 5.5.3.2.1 of [ISO 8601].

An optional preceding minus sign ('-') is allowed, to indicate a negative duration. If the sign is omitted a positive duration is indicated. See also D ISO 8601 Date and Time Formats.

For example, to indicate a duration of 1 year, 2 months, 3 days, 10 hours, and 30 minutes, one would write: P1Y2M3DT10H30M. One could also indicate a duration of minus 120 days as: -P120D.

Reduced precision and truncated representations of this format are allowed provided they conform to the following:

• If the number of years, months, days, hours, minutes, or seconds in any expression equals zero, the number and its corresponding designator ·may· be omitted. However, at least one number and its designator ·must· be present.
• The seconds part ·may· have a decimal fraction.
• The designator 'T' must be absent if and only if all of the time items are absent. The designator 'P' must always be present.

For example, P1347Y, P1347M and P1Y2MT2H are all allowed; P0Y1347M and P0Y1347M0D are allowed. P-1347M is not allowed although -P1347M is allowed. P1Y2MT is not allowed.

3.2.6.2 Order relation on duration

In general, the ·order-relation· on duration is a partial order since there is no determinate relationship between certain durations such as one month (P1M) and 30 days (P30D). The ·order-relation· of two duration values x and y is x < y iff s+x < s+y for each qualified dateTime s in the list below. These values for s cause the greatest deviations in the addition of dateTimes and durations. Addition of durations to time instants is defined in E Adding durations to dateTimes.

• 1696-09-01T00:00:00Z
• 1697-02-01T00:00:00Z
• 1903-03-01T00:00:00Z
• 1903-07-01T00:00:00Z

The following table shows the strongest relationship that can be determined between example durations. The symbol <> means that the order relation is indeterminate. Note that because of leap-seconds, a seconds field can vary from 59 to 60. However, because of the way that addition is defined in E Adding durations to dateTimes, they are still totally ordered.

Implementations are free to optimize the computation of the ordering relationship. For example, the following table can be used to compare durations of a small number of months against days.

3.2.6.3 Facet Comparison for durations

In comparing duration values with minInclusive, minExclusive, maxInclusive and maxExclusive facet values indeterminate comparisons should be considered as "false".

3.2.6.4 Totally ordered durations

Certain derived datatypes of durations can be guaranteed have a total order. For this, they must have fields from only one row in the list below and the time zone must either be required or prohibited.

• year, month
• day, hour, minute, second

For example, a datatype could be defined to correspond to the [SQL] datatype Year-Month interval that required a four digit year field and a two digit month field but required all other fields to be unspecified. This datatype could be defined as below and would have a total order.

<simpleType name='SQL-Year-Month-Interval'>
    <restriction base='duration'>
      <pattern value='P\p{Nd}{4}Y\p{Nd}{2}M'/>
    </restriction>
</simpleType>

3.2.6.5 Constraining facets

duration has the following ·constraining facets·:

• pattern
• enumeration
• whiteSpace
• maxInclusive
• maxExclusive
• minInclusive
• minExclusive

3.2.7.4 Order relation on dateTime

In general, the ·order-relation· 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 E Adding durations to dateTimes

• 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:

1. For each i in {year, month, day, hour, minute, second}
   1. If P[i] and Q[i] are both not specified, continue to the next i
   2. If P[i] is not specified and Q[i] is, or vice versa, stop and return P <> Q
   3. If P[i] < Q[i], stop and return P < Q
   4. If P[i] > Q[i], stop and return P > Q
2. Stop and return P = Q

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

1. P < Q if P < (Q with time zone +14:00)
2. P > Q if P > (Q with time zone -14:00)
3. 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:

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

Examples:

3.2.7.5 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.

3.2.7.6 Constraining facets

dateTime has the following ·constraining facets