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Date Representation, Julian Day, dimensional numbers

Date Representation

Here are John Randall's notes from 4/12/05 on how to represent and manipulate dates comprehensively and uniformly. Also, there's a suggestion from Neville Holmes on using dimensional, as opposed to the usual, dimensionless, numbers to better represent dates.

Specifying dates

1. Julian day: a single integer.
2. YMD: a list of <year> <month> <day>.
3. String representing a date.


We propose two verbs

jday: rank 1 1 1
jdate: rank _ 1 0

These are obverses of each other. The idea is that jday operating on a date gives a Julian day, and that jdate operating on a Julian day gives a date.

Monadic forms

jday <y m d>--><D>

Rank is 1, so we can convert a list of dates to days.

jdate <D>--><y m d>

Rank is _, so we can convert a list of days to dates.

Dyadic forms

For dates represented as strings, we need to specify the format. This is supplied as the left argument.

<format string> jday <date string>--><D>

Left rank 1, right rank 1.

<format string> jdate <D>--><date string>

Left rank 1, right rank 0 (or possibly _, since we are most likely to be applying a fixed format string to a list of dates).

Unix DATE Command Manual Page

DATE(1)				 User Commands			       DATE(1)

       date - print or set the system date and time

       date [OPTION]... [+FORMAT]
       date [-u|--utc|--universal] [MMDDhhmm[[CC]YY][.ss]]

       Display the current time in the given FORMAT, or set the system date.

       -d, --date=STRING
	      display time described by STRING, not 'now'

       -f, --file=DATEFILE
	      like --date once for each line of DATEFILE

       -r, --reference=FILE
	      display the last modification time of FILE

       -R, --rfc-2822
	      output date and time in RFC 2822 format

	      output date and time in RFC 3339 format.	TIMESPEC='date', 'sec-
	      onds', or 'ns' for date and time to the indicated precision.

       -s, --set=STRING
	      set time described by STRING

       -u, --utc, --universal
	      print or set Coordinated Universal Time

       --help display this help and exit

	      output version information and exit

       FORMAT controls the output.  The only valid option for the second  form
       specifies Coordinated Universal Time.  Interpreted sequences are:

       %%     a literal %

       %a     locale's abbreviated weekday name (e.g., Sun)

       %A     locale's full weekday name (e.g., Sunday)

       %b     locale's abbreviated month name (e.g., Jan)

       %B     locale's full month name (e.g., January)

       %c     locale's date and time (e.g., Thu Mar  3 23:05:25 2005)

       %C     century; like %Y, except omit last two digits (e.g., 21)

       %d     day of month (e.g, 01)

       %D     date; same as %m/%d/%y

       %e     day of month, space padded; same as %_d

       %F     full date; same as %Y-%m-%d

       %g     last two digits of year of ISO week number (see %G)

       %G     year of ISO week number (see %V); normally useful only with %V

       %h     same as %b

       %H     hour (00..23)

       %I     hour (01..12)

       %j     day of year (001..366)

       %k     hour ( 0..23)

       %l     hour ( 1..12)

       %m     month (01..12)

       %M     minute (00..59)

       %n     a newline

       %N     nanoseconds (000000000..999999999)

       %p     locale's equivalent of either AM or PM; blank if not known

       %P     like %p, but lower case

       %r     locale's 12-hour clock time (e.g., 11:11:04 PM)

       %R     24-hour hour and minute; same as %H:%M

       %s     seconds since 1970-01-01 00:00:00 UTC

       %S     second (00..60)

       %t     a tab

       %T     time; same as %H:%M:%S

       %u     day of week (1..7); 1 is Monday

       %U     week number of year, with Sunday as first day of week (00..53)

       %V     ISO week number, with Monday as first day of week (01..53)

       %w     day of week (0..6); 0 is Sunday

       %W     week number of year, with Monday as first day of week (00..53)

       %x     locale's date representation (e.g., 12/31/99)

       %X     locale's time representation (e.g., 23:13:48)

       %y     last two digits of year (00..99)

       %Y     year

       %z     +hhmm numeric timezone (e.g., -0400)

       %:z    +hh:mm numeric timezone (e.g., -04:00)

       %::z   +hh:mm:ss numeric time zone (e.g., -04:00:00)

       %:::z  numeric  time  zone  with	 :  to necessary precision (e.g., -04,

       %Z     alphabetic time zone abbreviation (e.g., EDT)

       By default, date	 pads  numeric	fields	with  zeroes.	The  following
       optional flags may follow '%':

	      - (hyphen) do not pad the field _ (underscore) pad with spaces 0
	      (zero) pad with zeros ^ use upper case if possible #  use	 oppo-
	      site case if possible

       After  any  flags  comes	 an optional field width, as a decimal number;
       then an optional modifier, which is either E to use the locale's alter-
       nate  representations  if available, or O to use the locale's alternate
       numeric symbols if available.

       TZ     Specifies the timezone, unless overridden by command line param-
	      eters.  If neither is specified, the setting from /etc/localtime
	      is used.

       Written by David MacKenzie.

       Report bugs to <>.

       Copyright © 2006 Free Software Foundation, Inc.
       This is free software.  You may redistribute copies  of	it  under  the
       terms	   of	    the	     GNU      General	   Public      License
       <>.	There is NO WARRANTY,  to  the
       extent permitted by law.

       The  full documentation for date is maintained as a Texinfo manual.  If
       the info and date programs are properly installed  at  your  site,  the

	      info date

       should give you access to the complete manual.

date 5.97			   May 2006			       DATE(1)

Suggestion to Use Dimensional Numbers in Date Representation

The following is a slightly re-formatted version of an e-mail from Neville Holmes suggesting how we might incorporate dimensional numbers into J in order to represent dates. "Dimensional numbers" means numbers with units of measurement embedded in them. For instance, a distance might be in units of meters or light-years.

Date:	 Sun, 20 Mar 2005 17:46:22 +1100
From:	 "neville holmes" <holmeswn@YAHOO.COM.AU>
Subject: Re: [Jforum] Units calculations in J?

Preamble Against Building Dimensional Analysis into J

It seems to me that it would be unwise to build dimensional analysis into J. Firstly, it would make the interpreter much more complex, and thus probably slower. Secondly it would make the notation much more complex, which would raise the barrier for casual users and beginners, who are all too often overlooked. Thirdly, there is no single system of units in use, and the ISO system of units is arguably defective anyway. Fourthly, the people who use dimensioned values are primarily engineers and scientists who are probably better suited by being given application packages.

One exception is monetary values, and I have occasionally toyed with the idea that the imaginary part of ordinary numbers could appropriately [be] treated as money to keep it out of the way of real numbers, at least during addition and subtraction.

Exception to this Opposition in Case of Date Values

However, there is one class of very awkward values which I believe J could consistently, conveniently and compatibly handle to the great benefit of casual and inexpert users at least. I refer to time intervals and dates. The following explanation is drawn from my memory of trying to design a decent pocket calculator some years ago, and I hope its fragmentary nature will convey the basic idea satisfactorily.

Examples of time intervals

    4w5              four weeks and five days
    _4w5d6h23m45.23  weeks through to seconds, negative

Examples of dates

    1066y4m1         first of April 1066
     2005y3m17d12    mid  St Patrick's day this year.

In brief, any such value with a month is a date. Maybe a "date" with a 0 year could be this year, and there is a host of other possiblities for special representations.

Arithmetic on dates

Dates could be subtracted to give time intervals. Time intervals could be added to or subtracted from dates. Maybe 1y0&| or something similar could be applied to a date to give the week of the year, and 1m0&| to give the day of the week, and so on. Otherwise, arithmetic on dates would give a domain error.

Arithmetic on time intervals

Ordinary values could generally be applied to time intervals to yield time intervals. Time intervals could be added to, subtracted from, or remaindered into time intervals to yield time intervals, and they could be divided to yield ordinary numbers. (Note that %&1m0 could be used to convert a time interval into an ordinary number giving the value in minutes.) Otherwise, domain errors.

Further Possibilities

There are a lot of further possibilities which it seems superfluous to do more than name at this stage:

  • clock times
  • lunar calendar
  • rates

There are also some matters of details to be considered, such as:

  • disambiguating the "m" between month and minute
  • formatting
  • handling BC
  • mixing other formats

Clearly there's quite a bit of design to be done, but the effect on existing code should be nil, and the complications for the interpreter should be fairly small as what's being done is primarly adding a couple of new types of exact numeric values with very limited domains.

I would suggest that the value of this extension for casual and everyday users would repay the implementation effort, and the capability could attract new users.

Neville Holmes, P.O.Box 404, Mowbray 7248, Tasmania
Normal e-mail:

Scan of Original Notes - Annotated

JohnsNotesOnDateRepresentation1 50.jpg

Scan of Julian Day Conversion Program in C

JohnsNotesOnDateRepresentation2 50.jpg

Scan of Unix DATE Command Man Page (from April 2002)

JohnsNotesOnDateRepresentation3 50.jpg JohnsNotesOnDateRepresentation4 50.jpg