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

3.3.2.2 Lexical representation

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

3.3.2.3 Canonical representation

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

3.3.3.2 Canonical representation

The ·canonical representation· for decimal is defined by prohibiting certain options from the Lexical ↓representation↓↑Mapping↑ (§3.3.3.1).  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.

3.3.5.2 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.

3.3.5.3 Canonical representation

The ·canonical representation· for float is defined by prohibiting certain options from the Lexical representation (§3.3.5.2).  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.

3.3.6.2 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.

3.3.6.3 Canonical representation

The ·canonical representation· for double is defined by prohibiting certain options from the Lexical representation (§3.3.6.2).  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.

3.3.7.2 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 integer. Similarly, the value of the Seconds component allows an arbitrary decimal. 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 ISO 8601 Date and Time Formats (§G).

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' shall be absent 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.

3.3.7.4 Order relation on duration

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 Adding durations to dateTimes (§H), 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.

3.3.7.5 Facet Comparison for durations

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

3.3.7.6 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>

3.3.8.2 Lexical representation

The ·lexical space· 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 zeroes are prohibited, and '0000' is prohibited (see the Note above (§3.3.8); 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 ·value space· 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 Adding durations to dateTimes (§H).

3.3.8.3 Canonical representation

3.3.8.5 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 zeroes 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, ·UTC·; 'Z' is its ·canonical representation·.

When a timezone is added to a ·UTC· 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.

3.3.8.6 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 ·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 Adding durations to dateTimes (§H)

• 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:

3.3.8.7 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.