Every supports the notion of equality, with the following rules:

On every datatype, the operation Equal is defined in terms of the equality property of the : for any values a, b drawn from the , Equal(a,b) is true if a = b, and false otherwise.

By definition, given A and B where A and B are not related by , for every pair of values a from A and b from B, a != b.

An order relation on a is a mathematical relation which imposes a total order on the members of the .

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

order relations have the following rules:

A is bounded above if there exists a unique value U in the such that, for all values v in the , v <= U. The value U is said to be an upper bound of the .

A is bounded below if there exists a unique value L in the space such that, for all values v in the , L <= v. The value L is then said to be a lower bound of the .

A datatype is bounded if its has both an and a .

Every has associated with it the concept of cardinality. Some s are finite, some are countably infinite while still others are uncountably 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:

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.

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

For and datatypes from , length is measured in units of code points. For and datatypes from , length is measured in octets (8 bits) of binary data. For datatypes by , length is measured in list items.

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

For and datatypes from , minLength is measured in units of code points. For and datatypes from , minLength is measured in octets (8 bits) of binary data. For datatypes by , length is measured in list items.

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

For and datatypes from , maxLength is measured in units of code points. For and datatypes from , maxLength is measured in octets (8 bits) of binary data. For datatypes by , length is measured in list items.

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 .

enumeration constrains the to a specified set of values.

enumeration does not impose an order relation on the it creates; the property of the datatype involved remains that of the .

maxInclusive is the of the for a datatype with the property. The value is inclusive in the sense that the value is itself included in the . The value of maxInclusive  be of the same type as the .

maxExclusive is the of the for a datatype with the property. The value is exclusive in the sense that the value is itself excluded from the . The value of maxExclusive must be of the same type as the .

minInclusive is the of the for a datatype with the property. The value is inclusive in the sense that the value is itself included in the . The value of minInclusive must be of the same type as the .

minExclusive is the of the for a datatype with the property. The value is exclusive in the sense that the value is itself excluded from the for the datatype. The value of minExclusive  be of the same type as the .

precision is the maximum number of decimal digits in values of datatypes from . The value of precision  be a .

scale is the maximum number of decimal digits in the fractional part of values of datatypes from . The value of scale   be a .

encoding is the encoded form of the of datatypes from . The value of encoding  be one of {hex, base64}.

If the value of encoding is hex then each binary octet is encoded as a character tuple, consisting the two hexadecimal digits ([0-9a-fA-F]) representing the octet code. For example, "20" is the hex encoding for the US-ASCII space character.

If the value of encoding is base64 then the entire binary stream is encoding using the Base64 Content-Transfer-Encoding defined in Section 6.8 .

duration is the duration of values for the datatype and datatypes from . The value of duration   be a .

period is the frequency of recurrence for values for the datatype and datatypes from . The value of period   be .

datatypes may 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.

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 whitespace separated sequence of literals of the datatype of the items in the (where whitespace es S in ).

A datatype can be from an datatype whose allows whitespace. In such a case, regardless of the input, list items will be separated at whitespace boundaries.

When a datatype is from a datatype, the following s may be used:

For each of the above s, the unit of length is measured in number of list items.

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

Any number (greater than 1) of or s may participate in a type. The order in which the participating types are specified in the definition (that is, the order of the <simpleType> children of the <union> element) is significant. During validation, an element or attribute's value is validated against the participating types 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. See and for more details.

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

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 zero, positive and negative infinity and not-a-number have 0, -0, INF, -INF and NaN, respectively.

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

The canonical representation for float is defined by prohibiting certain options from the . Specifically, the preceding optional "+" sign is prohibited from the mantissa. The exponent must be indicated by "E" ande number representations must be normalized such that for non-zero numbers there is a single non-zero digit to the left of the decimal point. Leading and trailing zeroes are disallowed in the mantissa and leading zeroes are disallowed in the exponent.

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.

The special values positive and negative zero, positive and negative infinity and not-a-number have 0, -0, INF, -INF and NaN, respectively.

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

The canonical representation for double is defined by prohibiting certain options from the . Specifically, the preceding optional "+" sign is prohibited from the mantissa. The exponent must be indicated by "E" ande number representations must be normalized such that for non-zero numbers there is a single non-zero digit to the left of the decimal point. Leading and trailing zeroes are disallowed in the mantissa and leading zeroes are disallowed in the exponent.

decimal has a lexical representation consisting of a finite-length sequence of decimal digits separated by a period as a decimal indicator, in accordance with the scale and precision facets, with an optional leading sign. 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.

The canonical representation for decimal is defined by prohibiting certain options from the . Specifically, the preceding optional "+" sign is prohibited. Leading zeroes are prohibited. Trailing zeroes to the right of the decimal point are also prohibited.

A single lexical representation, similar to the representations allowed by , is allowed for timeDuration. This lexical representation is the 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 integer. Similarly, the value of the Seconds component allows an arbitrary decimal, that is they do not follow the alternative format of § 5.5.3.2.1 of .

An optional preceding minus sign ('-') is allowed, to indicate a negative duration. If the sign is omitted a positive duration is indicated. See also .

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:

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

A single lexical representation, which is a subset of the lexical representations allowed by , is allowed for recurringDuration. This lexical representation is the extended format CCYY-MM-DDThh:mm:ss.sss where "CC" represents the century, "YY" the year, "MM" the month and "DD" the day, preceded by an optional leading sign to indicate a negative number. If the sign is omitted, "+" is assumed. The letter "T" is the date/time separator and "hh", "mm", "ss.sss" represent hour, minute and second respectively. Additional digits can be used to increase the precision of fractional seconds if desired. To accommodate year values greater than 9999 additional digits can be added to the left of this representation. The year 0000 is prohibited.

This representation can be immediately followed by a "Z" to indicate Coordinated Universal Time (UTC). To indicate the time zone, i.e. the difference between the local time and Coordinated Universal Time, the difference immediately follows the time and consists of a sign, + or -, followed by hh:mm. See also .

The derived datatype uses the same lexical representation. Other derived datatypes , , and use truncated versions of this lexical representation.

The canonical representation for recurringDuration is defined by prohibiting certain options from the . Specifically, the preceding optional "+" sign is prohibited and the time zone must be Coordinated Universal Time (UTC) and be indicated by a "Z".

The of uriReference is the set of strings that the URI-reference production in Section 4 of .

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

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.