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1	/******************************************************************************
2
3	Library: ISO8601.PL
4	Copyright (c) 2004-2005 Daniel L. Dudley
5
6	Purpose: ISO 8601 (and European civil calendar) compliant library of date
7	and time (clock) related predicates. That is, an ISO 8601 handler.
8
9	Author: Daniel L. Dudley
10	Created: 2004-02-18
11
12	******************************************************************************/
13
14
15	:- object(iso8601).
16
17	:- info([
18	version is 1.0,
19	author is 'Daniel L. Dudley',
20	date is 2005/04/11,
21	comment is 'ISO 8601 (and European civil calendar) compliant library of date predicates.',
22	remarks is [
23	'Scope:' - 'This object currently provides a powerful, versatile and efficient set of date-handling predicates, which--thanks to Logtalk--may be used as is on a wide range of Prolog compilers. Besides taking time to familiarize oneself with each predicate, the user should take note of the following information.',
24	'Validation of dates: ' - 'Date parts are not validated--that is the caller''s responsibility! However, not being quite heartless yet, we do provide a predicate for this purpose.',
25	'Date arithmetic:' - 'Many of the examples illustrate a simplified method of doing date arithmetic. Note, however, that we do not generally recommend this practice--it is all too easy to make mistakes. The safest way of finding the day difference between two dates is to first convert the dates to their Julian day numbers and then subtract one from the other. Similarly, the safe way to add or subtract a day offset to a particular date is to first convert the date to its Julian day number, add or subtract the day offset, and then convert the result to its corresponding date.',
26	'BC years' - 'ISO 8601 specifies that the Gregorian calendar be used, yet requires that years prior to 1 AD be handled arithmetically, i.e., the year we know as 1 BC is year 0, 2 BC is year -1, 3 BC is year -2 and so on. We do not follow ISO 8601 with regard to the handling of BC years. Our date predicates will accept and interpret an input year 0 as 1 BC; however, a negative year, Year, should always be interpreted as abs(Year) =:= Year BC. We believe that the average person will find our handling of BC years more user-friendly than the ISO 8601 one, but we encourage feedback from users with a view to a possible change in future versions.',
27	'Week numbers:' - 'It is possible for a day (date) to have a week number that belongs to another year. Up to three of the first days of a calendar year may belong to the last week (number) of the prior calendar year, and up to three days of the last days of a calendar year may belong to the first week (number) of the next calendar year. It for this reason that the Week parameter in date/6-7 is a compound term, namely week(WeekNo,ActualYear).',
28	'Computation of Gregorian Easter Sunday:' - 'The algorithm is based upon the "Gaussian rule". Proleptic use is limited to years > 1582 AD, that is, after the introduction of the Gregorian calendar.',
29	'Some Christian feast day offsets from Easter Sunday:' - 'Carnival Monday: -48 days, Mardi Gras (Shrove Tuesday): -47 days, Ash Wednesday: -46 days, Palm Sunday: -7 days, Easter Friday: -2 days, Easter Saturday: -1 day, Easter Monday: +1 day, Ascension of Christ: +39 days, Whitsunday: +49 days, Whitmonday: +50 days, Feast of Corpus Christi: +60 days.'
30	]]).
31
32	% CORE PREDICATES:
33
34	:- public(date/4).
35	:- mode(date(?integer, ?integer, ?integer, ?integer), zero_or_one).
36	:- info(date/4, [
37	comment is 'Get the system date and/or its Julian Day # or convert a Julian Day # to/from given date parts.',
38	arguments is [
39	'JD' - 'Julian day serial number',
40	'Year' - '0 or negative if converted BC year, positive otherwise',
41	'Month' - 'Normally an integer between 1 and 12 inclusive',
42	'Day' - 'Normally an integer between 1 and 31 inclusive depending upon month'],
43	examples is [
44	'Current date (i.e., today):' - date(JD,Y,M,D) - {JD = 2453471, Y = 2005, M = 4, D = 10},
45	'Convert a date to its Julian day number:' - date(JD,2000,2,29) - {JD = 2451604},
46	'Convert a Julian day number to its date:' - date(2451604,Yr,Mth,Day) - {Yr = 2000, Mth = 2, Day = 29},
47	'What is the date of day # 60 in year 2000?' - date(J,2000,1,60) - {J = 2451604},
48	'What is the Julian of the 1st day prior to 2000-1-1?' - date(J,2000,1,0) - {J = 2451544},
49	'What is the Julian of the 60th day prior to 2000-1-1?' - date(J,2000,1,-59) - {J = 2451485},
50	'Illegal date is auto-adjusted (see also next query)' - date(JD,1900,2,29) - {JD = 2415080},
51	'This is the correct date!' - date(2415080,Y,M,D) - {Y = 1900, M = 3, D = 1}]]).
52
53	:- public(date/5).
54	:- mode(date(?integer, ?integer, ?integer, ?integer, ?integer), zero_or_one).
55	:- info(date/5, [
56	comment is 'Ditto date/4 + get/check its day-of-week #.',
57	arguments is [
58	'JD' - 'Julian day serial number',
59	'Year' - '0 or negative if converted BC year, positive otherwise',
60	'Month' - 'Normally an integer between 1 and 12 inclusive',
61	'Day' - 'Normally an integer between 1 and 31 inclusive depending upon month',
62	'DoW' - 'Day of week, where Monday=1, Tuesday=2, ..., Sunday=7'],
63	examples is [
64	'Get the Julian and the day-of-week # of a date:' - date(JD,2000,2,29,DoW) - {JD = 2451604, DoW = 2},
65	'Check the validity of a given date (day-of-week is 2, not 4):' - date(JD,2002,3,5,4) - {no},
66	'Get the Julian day of a given date if it is a Sunday:' - date(JD,2004,2,29,7) - {JD = 2453065},
67	'Get the date and day-of-week # of a Julian:' - date(2451545,Y,M,D,DoW) - {Y = 2000, M = 1, D = 1, DoW = 6}]]).
68
69	:- public(date/6).
70	:- mode(date(?integer, ?integer, ?integer, ?integer, ?integer, ?compound), zero_or_one).
71	:- info(date/6, [
72	comment is 'Ditto date/5 + get/check its week #.',
73	arguments is [
74	'JD' - 'Julian day serial number',
75	'Year' - '0 or negative if converted BC year, positive otherwise',
76	'Month' - 'Normally an integer between 1 and 12 inclusive',
77	'Day' - 'Normally an integer between 1 and 31 inclusive depending upon month',
78	'DoW' - 'Day of week, where Monday=1, Tuesday=2, ..., Sunday=7',
79	'Week' - 'Compound term, week(WeekNo,ActualYear), of a day'],
80	examples is [
81	'Get the day-of-week and week number of a date:' - date(_,2000,1,1,DoW,Wk) - {DoW = 6, Wk = week(52,1999)},
82	'Get the week number and year of this week:' - date(_,_,_,_,_,Wk) - {Wk = week(7, 2004)},
83	'Get the Julian number and the week of a date if it is a Sunday:' - date(JD,2004,2,29,7,Wk) - {JD = 2453065, Wk = week(9,2004)},
84	'Get the day-of-week and week of a Julian day number:' - date(2453066,_,_,_,DoW,Wk) - {DoW = 1, Wk = week(10,2004)},
85	'Check that given date data matches:' - date(_,2004,3,1,1,week(10,2004)) - {yes},
86	'What is the date of a day of week (default is 1) in given week # and year?' - date(_,Y,M,D,DoW,week(26,2004)) - {Y = 2004, M = 6, D = 21, DoW = 1},
87	'Ditto for Sunday:' - date(_,Y,M,D,7,week(1,2005)) - {Y = 2005, M = 1, D = 9},
88	'Ditto for Tuesday in following week:' - date(_,Y,M,D,9,week(1,2005)) - {Y = 2005, M = 1, D = 11},
89	'Ditto for Thursday in the prior week:' - date(_,Y,M,D,4,week(0,2005)) - {Y = 2004, M = 12, D = 30},
90	'Ditto for Tuesday two weeks prior:' - date(_,Y,M,D,2,week(-1,2005)) - {Y = 2004, M = 12, D = 21},
91	'Ditto for Saturday:' - date(_,Y,M,D,6,week(53,2004)) - {Y = 2005, M = 1, D = 1},
92	'Ditto for Monday (note automatic compensation of nonexistent week number):' - date(_,Y,M,D,1,week(60,2004)) - {Y = 2005, M = 2, D = 14}]]).
93
94	:- public(date/7).
95	:- mode(date(?integer, ?integer, ?integer, ?integer, ?integer, ?compound, ?integer), zero_or_one).
96	:- info(date/7, [
97	comment is 'Ditto date/6 + get/check its day-of-year #.',
98	arguments is [
99	'JD' - 'Julian day serial number',
100	'Year' - '0 or negative if converted BC year, positive otherwise',
101	'Month' - 'Normally an integer between 1 and 12 inclusive',
102	'Day' - 'Normally an integer between 1 and 31 inclusive depending upon month',
103	'DoW' - 'Day of week, where Monday=1, Tuesday=2, ..., Sunday=7',
104	'Week' - 'Compound term, week(WeekNo,ActualYear), of a day',
105	'DoY' - 'Day of year (NB! calendar year, not week # year)'],
106	examples is [
107	'Get the date and day-of-year of a Julian number:' - date(2451649,Year,Month,Day,_,_,DoY) - {Year = 2000, Month = 4, Day = 14, DoY = 105},
108	'Get the Julian number, week number and day-of-year of a date, confirming that it is a Sunday:' - date(JD,2004,2,29,7,Wk,DoY) - {JD = 2453065, Wk = week(9,2004), DoY = 60},
109	'Confirm that a date is, in fact, a specific day-of-year:' - date(_,2004,3,1,_,_,61) - {yes},
110	'Get the Julian number, week day and day-of-year of a date:' - date(JD,2004,10,18,DoW,_,DoY) - {JD = 2453297, DoW = 1, DoY = 292},
111	'Get today''s day-of-year:' - date(_,_,_,_,_,_,DoY) - {DoY = 54},
112	'Get all missing date data (excl. Julian number) for the 60th calendar day of 2004:' - date(_,2004,Month,Day,DoW,Week,60) - {Month = 2, Day = 29, DoW = 7, Week = week(9,2004)},
113	'Match given date data and, if true, return the missing data (excl. Julian number):' - date(_,2004,3,Day,DoW,Week,61) - {Day = 1, DoW = 1, Week = week(10,2004)},
114	'Ditto (the 61st day-of-year cannot be both day 1 and 2 of the month):' - date(_,2004,Month,2,DoW,Week,61) - {no}]]).
115
116	:- public(date_string/3).
117	:- mode(date_string(+atom, +integer, ?atom), zero_or_one).
118	:- mode(date_string(+atom, ?list, ?atom), zero_or_one).
119	:- info(date_string/3, [
120	comment is 'Conversion between an ISO 8601 compliant date string and its components (truncated and expanded date representations are currently unsupported). Note that date components are not validated; that is the caller''s responsibility!',
121	arguments is [
122	'Format' - 'ISO 8601 format',
123	'Components' - 'When bound and String is free, either a Julian number or a [Year,Month,Day] term; it binds to the system day/date if free When free and String is bound, it binds to an integer list representing the numeric elements of String',
124	'String' - 'ISO 8601 formatted string correspondent to Components'],
125	examples is [
126	'Date, complete, basic (section 5.2.1.1):' - date_string('YYYYMMDD',[2004,2,29],Str) - {Str = '20040229'},
127	'Date, complete, basic (section 5.2.1.1):' - date_string('YYYYMMDD',Day,'20040229') - {Day = [2004,2,29]},
128	'Date, complete, extended (section 5.2.1.1):' - date_string('YYYY-MM-DD',[2003,12,16],Str) - {Str = '2003-12-16'},
129	'Date, complete, extended (section 5.2.1.1):' - date_string('YYYY-MM-DD',Day,'2003-12-16') - {Day = [2003,12,16]},
130	'Date, complete, extended (section 5.2.1.1):' - date_string('YYYY-MM-DD',_,Str) - {Str = '2004-02-17'},
131	'Date, complete, extended (section 5.2.1.1):' - date_string('YYYY-MM-DD',Day,'2004-02-17') - {Day = [2004,2,17]},
132	'Date, reduced, month (section 5.2.1.2 a):' - date_string('YYYY-MM',[2004,9,18],Str) - {Str = '2004-09'},
133	'Date, reduced, month (section 5.2.1.2 a):' - date_string('YYYY-MM',Day,'2004-09') - {Day = [2004,9]},
134	'Date, reduced, year (section 5.2.1.2 b):' - date_string('YYYY',[1900,7,24],Str) - {Str = '1900'},
135	'Date, reduced, year (section 5.2.1.2 b):' - date_string('YYYY',Day,'1900') - {Day = [1900]},
136	'Date, reduced, century (section 5.2.1.2 c):' - date_string('YY',2456557,Str) - {Str = '20'},
137	'Date, reduced, century (section 5.2.1.2 c):' - date_string('YY',Day,'20') - {Day = [20]},
138	'Date, ordinal, complete (section 5.2.2.1):' - date_string('YYYYDDD',[2005,3,25],Str) - {Str = '2005084'},
139	'Date, ordinal, complete (section 5.2.2.1):' - date_string('YYYYDDD',Day,'2005084') - {Day = [2005,84]},
140	'Date, ordinal, extended (section 5.2.2.1):' - date_string('YYYY-DDD',[1854,12,4],Str) - {Str = '1854-338'},
141	'Date, ordinal, extended (section 5.2.2.1):' - date_string('YYYY-DDD',Day,'1854-338') - {Day = [1854,338]},
142	'Week, complete, basic (section 5.2.3.1):' - date_string('YYYYWwwD',[2000,1,2],Str) - {Str = '1999W527'},
143	'Week, complete, basic (section 5.2.3.1):' - date_string('YYYYWwwD',Day,'1999W527') - {Day = [1999,52,7]},
144	'Week, complete, extended (section 5.2.3.1):' - date_string('YYYY-Www-D',[2003,12,29],Str) - {Str = '2004-W01-1'},
145	'Week, complete, extended (section 5.2.3.1):' - date_string('YYYY-Www-D',Day,'2004-W01-1') - {Day = [2004,1,1]},
146	'Week, complete, extended (section 5.2.3.1):' - date_string('YYYY-Www-D',2453167,Str) - {Str = '2004-W24-4'},
147	'Week, complete, extended (section 5.2.3.1):' - date_string('YYYY-Www-D',Day,'2004-W24-4') - {Day = [2004,24,4]},
148	'Week, reduced, basic (section 5.2.3.2):' - date_string('YYYYWww',[2004,2,29],Str) - {Str = '2004W09'},
149	'Week, reduced, basic (section 5.2.3.2):' - date_string('YYYYWww',Day,'2004W09') - {Day = [2004,9]},
150	'Week, reduced, extended (section 5.2.3.2):' - date_string('YYYY-Www',[2004,2,29],Str) - {Str = '2004-W09'},
151	'Week, reduced, extended (section 5.2.3.2):' - date_string('YYYY-Www',Day,'2004-W09') - {Day = [2004,9]}]]).
152
153	% MISCELLANEOUS PREDICATES (GOODIES):
154
155	:- public(valid_date/3).
156	:- mode(valid_date(+integer, +integer, +integer), zero_or_one).
157	:- info(valid_date/3, [
158	comment is 'Validate a given date in the Gregorian calendar.',
159	argnames is ['Year', 'Month', 'Day'],
160	examples is [
161	'Yes, the recent millenium was a leap year:' - valid_date(2000,2,29) - {yes},
162	'2004 was also a leap year:' - valid_date(2004,2,29) - {yes},
163	'Only 30 days in April:' - valid_date(2004,4,31) - {no},
164	'1 BC was a leap year:' - valid_date(-1,2,29) - {yes}
165	]]).
166
167	:- public(leap_year/1).
168	:- mode(leap_year(?integer), zero_or_one).
169	:- info(leap_year/1, [
170	comment is 'Succeed if given year is a leap year in the Gregorian calendar.',
171	arguments is [
172	'Year' - 'The Gregorian calendar year to investigate. If free, it binds to the system year'],
173	examples is [
174	'No, the prior centenary was not a leap year:' - leap_year(1900) - {no},
175	'The recent millenium:' - leap_year(2000) - {yes},
176	'This year:' - leap_year(Year) - {Year = 2004},
177	'This year (equivalent to prior query):' - leap_year(_) - {yes},
178	'Next centennial:' - leap_year(2100) - {no},
179	'Year 0, equivalent to 1 BC:' - leap_year(0) - {yes},
180	'1 BC' - leap_year(-1) - {yes},
181	'4 BC' - leap_year(-4) - {no},
182	'5 BC' - leap_year(-5) - {yes}
183	]]).
184
185	:- public(calendar_month/3).
186	:- mode(calendar_month(?integer, ?integer, -compound), zero_or_one).
187	:- info(calendar_month/3, [
188	comment is 'Compute a calendar month.',
189	arguments is [
190	'Year' - 'The calendar year',
191	'Month' - 'The calendar month',
192	'Calendar' - 'A compound term, m/3, composed of three main arguments specifying year, month, and a list of week and week day numbers (calendar body).'],
193	examples is [
194	'Compute the calendar of March, 2005:' - calendar_month(2005, 3, Calendar) - {Calendar = m(2005, 3,[w( 9, [ 0, 1, 2, 3, 4, 5, 6]),w(10, [ 7, 8, 9, 10, 11, 12, 13]),w(11, [14, 15, 16, 17, 18, 19, 20]),w(12, [21, 22, 23, 24, 25, 26, 27]),w(13, [28, 29, 30, 31, 0, 0, 0]),w( 0, [ 0, 0, 0, 0, 0, 0, 0])])}]]).
195
196	:- public(easter_day/3).
197	:- mode(easter_day(?integer, -integer, -integer), zero_or_one).
198	:- info(easter_day/3, [
199	comment is 'Compute a Gregorian Easter Sunday.',
200	arguments is [
201	'Year' - 'Integer specifying the year to be investigated',
202	'Month' - 'Month in which Easter Sunday falls for given year',
203	'Day'- 'Day of month in which Easter Sunday falls for given year'],
204	examples is [
205	'Compute Easter Sunday for a particular year:' - easter_day(2006,Month,Day) - {Month=4, Day=16},
206	'Compute Easter Sunday for the current year:' - easter_day(Y,M,D) - {Y = 2005, M = 3, D = 27}
207	]]).
208
209
210	/************************
211	ISO 8601 DATE PREDICATES
212	************************/
213
214	%==============================================================================
215	% date(?JD, ?Year, ?Month, ?Day)
216
217	date(JD,Year,Month,Day) :-
218	( var(JD), var(Year), var(Month), var(Day)
219	-> % GET THE SYSTEM DATE AND ITS JULIAN DAY SERIAL NUMBER:
220	{'$lgt_current_date'(Year, Month, Day)}
221	; true
222	),
223	( var(JD), nonvar(Year), nonvar(Month), nonvar(Day)
224	-> % CORRIGATE BC/AD CALENDAR YEARS TO FIT 0-BASED ALGORITHM:
225	(Year < 0 -> Year1 is Year + 1 ; Year1 = Year),
226	% CONVERT DATE PARTS TO JULIAN DAY SERIAL NUMBER:
227	A is (14 - Month) // 12,
228	Y is Year1 + 4800 - A,
229	M is Month + (12 * A) - 3,
230	D is Day + ((153 * M + 2) // 5) + (365 * Y) + (Y // 4),
231	JD is D - (Y // 100) + (Y // 400) - 32045
232	; nonvar(JD),
233	% CONVERT JULIAN DAY SERIAL NUMBER TO DATE PARTS:
234	A is JD + 32045,
235	B is (4 * (A + 36524)) // 146097 - 1,
236	C is A - ((146097 * B) // 4),
237	D is ((4 * (C + 365)) // 1461) - 1,
238	E is C - ((1461 * D) // 4),
239	M is ((5 * (E - 1)) + 2) // 153,
240	Day is E - (((153 * M) + 2) // 5),
241	Month is M + (3 - (12 * (M // 10))),
242	Year1 is ((100 * B) + D - 4800 + (M // 10)),
243	% CORRIGATE 0-BASED ALGORITHM RESULT TO BC/AD CALENDAR YEARS:
244	(Year1 < 1 -> Year is Year1 - 1 ; Year = Year1)
245	).
246
247
248	%==============================================================================
249	% date(?JD, ?Year, ?Month, ?Day, ?DoW)
250
251	date(JD,Year,Month,Day,DoW) :-
252	date(JD,Year,Month,Day),
253	DoW is (JD mod 7) + 1.
254
255
256	%==============================================================================
257	% date(?JD, ?Year, ?Month, ?Day, ?DoW, ?Week)
258
259	date(JD,Year,Month,Day,DoW,week(Wk,Yr)) :-
260	( var(JD), var(Year), var(Month), var(Day), nonvar(Wk), nonvar(Yr)
261	-> (var(DoW) -> DoW = 1 ; true),
262	date(JD1,Yr,1,1,DoW1),
263	(DoW1 > 4 -> Offset = 0 ; Offset = 1),
264	JD is JD1 + ((Wk - Offset) * 7) + DoW - DoW1,
265	date(JD,Year,Month,Day)
266	; date(JD,Year,Month,Day,DoW),
267	D4 is (((JD + 31741 - (JD mod 7)) mod 146097) mod 36524) mod 1461,
268	L is D4 // 1460,
269	Wk is (((D4 - L) mod 365) + L) // 7 + 1,
270	% CORRIGATE YEAR AS NECESSARY:
271	( Month =:= 1, (Day =:= 1 ; Day =:= 2 ; Day =:= 3), Wk > 1
272	-> Yr is Year - 1
273	; ( Month =:= 12, (Day =:= 29 ; Day =:= 30 ; Day =:= 31), Wk =:= 1
274	-> Yr is Year + 1
275	; Yr = Year
276	)
277	)
278	).
279
280
281	%==============================================================================
282	% date(?JD, ?Year, ?Month, ?Day, ?DoW, ?Week, ?DoY)
283
284	date(JD,Year,Month,Day,DoW,Week,DoY) :-
285	( var(JD), nonvar(Year), (var(Month) ; var(Day)), nonvar(DoY)
286	-> date(JD1,Year,1,0),
287	JD is JD1 + DoY,
288	date(JD,Year,Month,Day,DoW,Week)
289	; date(JD,Year,Month,Day,DoW,Week),
290	date(JD1,Year,1,0),
291	DoY is JD - JD1
292	).
293
294
295	%==============================================================================
296	% date_string(+Format, ?Day, ?String)
297
298	date_string('YYYYMMDD',Day,String) :- % DATE
299	( nonvar(String)
300	-> atom_chars(String,[Y0,Y1,Y2,Y3,M0,M1,D0,D1]),
301	number_chars(Y,[Y0,Y1,Y2,Y3]),
302	number_chars(M,[M0,M1]),
303	number_chars(D,[D0,D1]),
304	Day = [Y,M,D]
305	; ((var(Day) ; Day = [Y\|_], var(Y)) -> date(_,Y,M,D) ; true),
306	(Day = [Y,M,D] -> nonvar(Y), nonvar(M), nonvar(D) ; date(Day,Y,M,D)),
307	prepend_zeros(2,D,D1),
308	prepend_zeros(2,M,M1),
309	number_codes(Y,Y1),
310	list_of_lists_to_atom([Y1,M1,D1],String)
311	).
312	date_string('YYYY-MM-DD',Day,String) :- % DATE
313	( nonvar(String)
314	-> atom_chars(String,[Y0,Y1,Y2,Y3,_,M0,M1,_,D0,D1]),
315	number_chars(Y,[Y0,Y1,Y2,Y3]),
316	number_chars(M,[M0,M1]),
317	number_chars(D,[D0,D1]),
318	Day = [Y,M,D]
319	; ((var(Day) ; Day = [Y\|_], var(Y)) -> date(_,Y,M,D) ; true),
320	(Day = [Y,M,D] -> nonvar(Y), nonvar(M), nonvar(D) ; date(Day,Y,M,D)),
321	prepend_zeros(2,D,D1),
322	prepend_zeros(2,M,M1),
323	number_codes(Y,Y1),
324	list_of_lists_to_atom([Y1,[45],M1,[45],D1],String)
325	).
326	date_string('YYYY-MM',Day,String) :- % YEAR & MONTH
327	( nonvar(String)
328	-> atom_chars(String,[Y0,Y1,Y2,Y3,_,M0,M1]),
329	number_chars(Year,[Y0,Y1,Y2,Y3]),
330	number_chars(Month,[M0,M1]),
331	Day = [Year,Month]
332	; ((var(Day) ; Day = [Y\|_], var(Y)) -> date(_,Y,M,_) ; true),
333	(Day = [Y,M,_] -> nonvar(Y), nonvar(M) ; date(Day,Y,M,_)),
334	prepend_zeros(2,M,M1),
335	number_codes(Y,Y1),
336	list_of_lists_to_atom([Y1,[45],M1],String)
337	).
338	date_string('YYYY',Day,String) :- % YEAR
339	( nonvar(String)
340	-> atom_chars(String,[Y0,Y1,Y2,Y3]),
341	number_chars(Year,[Y0,Y1,Y2,Y3]),
342	Day = [Year]
343	; ((var(Day) ; Day = [Y\|_], var(Y)) -> date(_,Y,_,_) ; true),
344	(Day = [Y\|_] -> nonvar(Y) ; date(Day,Y,_,_)),
345	number_codes(Y,Codes),
346	atom_codes(String,Codes)
347	).
348	date_string('YY',Day,String) :- % CENTURY
349	( nonvar(String)
350	-> atom_chars(String,[C0,C1]),
351	number_chars(Century,[C0,C1]),
352	Day = [Century]
353	; ((var(Day) ; Day = [Y\|_], var(Y)) -> date(_,Y,_,_) ; true),
354	(Day = [Y\|_] -> nonvar(Y) ; date(Day,Y,_,_)),
355	Y1 is Y // 100,
356	number_codes(Y1,Codes),
357	atom_codes(String,Codes)
358	).
359	date_string('YYYYDDD',Day,String) :- % YEAR & DAY-OF-YEAR
360	( nonvar(String)
361	-> atom_chars(String,[Y0,Y1,Y2,Y3,D0,D1,D2]),
362	number_chars(Year,[Y0,Y1,Y2,Y3]),
363	number_chars(DoY,[D0,D1,D2]),
364	Day = [Year,DoY]
365	; ((var(Day) ; Day = [Y\|_], var(Y)) -> date(_,Y,M,D) ; true),
366	(Day = [Y,M,D] -> nonvar(Y), nonvar(M), nonvar(D) ; JD = Day),
367	date(JD,Y,M,D,_,_,DoY),
368	prepend_zeros(3,DoY,DoY1),
369	number_codes(Y,Y1),
370	list_of_lists_to_atom([Y1,DoY1],String)
371	).
372	date_string('YYYY-DDD',Day,String) :- % YEAR & DAY-OF-YEAR
373	( nonvar(String)
374	-> atom_chars(String,[Y0,Y1,Y2,Y3,_,D0,D1,D2]),
375	number_chars(Year,[Y0,Y1,Y2,Y3]),
376	number_chars(DoY,[D0,D1,D2]),
377	Day = [Year,DoY]
378	; ((var(Day) ; Day = [Y\|_], var(Y)) -> date(_,Y,M,D) ; true),
379	(Day = [Y,M,D] -> nonvar(Y), nonvar(M), nonvar(D) ; JD = Day),
380	date(JD,Y,M,D,_,_,DoY),
381	prepend_zeros(3,DoY,DoY1),
382	number_codes(Y,Y1),
383	list_of_lists_to_atom([Y1,[45],DoY1],String)
384	).
385	date_string('YYYYWwwD',Day,String) :- % YEAR, WEEK & DAY-OF-WEEK
386	( nonvar(String)
387	-> atom_chars(String,[Y0,Y1,Y2,Y3,_,W0,W1,DoW0]),
388	number_chars(Year,[Y0,Y1,Y2,Y3]),
389	number_chars(Week,[W0,W1]),
390	number_chars(DoW,[DoW0]),
391	Day = [Year,Week,DoW]
392	; ((var(Day) ; Day = [Y\|_], var(Y)) -> date(_,Y,M,D) ; true),
393	(Day = [Y,M,D] -> nonvar(Y), nonvar(M), nonvar(D) ; JD = Day),
394	date(JD,Y,M,D,DoW,week(Wk,Yr)),
395	number_codes(Yr,Y1),
396	prepend_zeros(2,Wk,Wk1),
397	number_codes(DoW,DoW1),
398	List = [Y1,[87],Wk1,DoW1],
399	list_of_lists_to_atom(List,String)
400	).
401	date_string('YYYY-Www-D',Day,String) :- % YEAR, WEEK & DAY-OF-WEEK
402	( nonvar(String)
403	-> atom_chars(String,[Y0,Y1,Y2,Y3,_,_,W0,W1,_,DoW0]),
404	number_chars(Year,[Y0,Y1,Y2,Y3]),
405	number_chars(Week,[W0,W1]),
406	number_chars(DoW,[DoW0]),
407	Day = [Year,Week,DoW]
408	; ((var(Day) ; Day = [Y\|_], var(Y)) -> date(_,Y,M,D) ; true),
409	(Day = [Y,M,D] -> nonvar(Y), nonvar(M), nonvar(D) ; JD = Day),
410	date(JD,Y,M,D,DoW,week(Wk,Yr)),
411	number_codes(Yr,Y1),
412	prepend_zeros(2,Wk,Wk1),
413	number_codes(DoW,DoW1),
414	List = [Y1,[45,87],Wk1,[45],DoW1],
415	list_of_lists_to_atom(List,String)
416	).
417	date_string('YYYYWww',Day,String) :- % YEAR & WEEK
418	( nonvar(String)
419	-> atom_chars(String,[Y0,Y1,Y2,Y3,_,W0,W1]),
420	number_chars(Year,[Y0,Y1,Y2,Y3]),
421	number_chars(Week,[W0,W1]),
422	Day = [Year,Week]
423	; ((var(Day) ; Day = [Y\|_], var(Y)) -> date(_,Y,M,D) ; true),
424	(Day = [Y,M,D] -> nonvar(Y), nonvar(M), nonvar(D) ; JD = Day),
425	date(JD,Y,M,D,_,week(Wk,Yr)),
426	number_codes(Yr,Y1),
427	prepend_zeros(2,Wk,Wk1),
428	List = [Y1,[87],Wk1],
429	list_of_lists_to_atom(List,String)
430	).
431	date_string('YYYY-Www',Day,String) :- % YEAR & WEEK
432	( nonvar(String)
433	-> atom_chars(String,[Y0,Y1,Y2,Y3,_,_,W0,W1]),
434	number_chars(Year,[Y0,Y1,Y2,Y3]),
435	number_chars(Week,[W0,W1]),
436	Day = [Yea