1	# Clocks, Duration and Instant, Gregorian dates, RFC 3339 and HTTP-date text, and TZif time zones. Source: https://github.com/paymog/bend-kit/tree/main/time
2	import Base
3	import bend-kit-int@0.2.0.0/int.bend as Int
4	import bend-kit-fmt@0.1.0.0/fmt.bend as Fmt
5	# bend-kit-bytes@0.3.0.0
6	import 0x49814d83de8f70993a43e1002be29ecd/bytes.bend as Bytes
7	
8	# secs + nanos / 10^9 seconds, with nanos below 10^9: -0.5 s is Duration{-1, 500000000}.
9	type Duration is Data:
10	  Duration{secs: Int.I64, nanos: U32}
11	
12	# A Duration since 1970-01-01T00:00:00Z. Days are 86400 s: there are no leap seconds.
13	type Instant is Data:
14	  Instant{secs: Int.I64, nanos: U32}
15	
16	# A proleptic Gregorian date. The conversions and formats cover years 0 to 9999.
17	type Date is Data:
18	  Date{year: U32, month: U32, day: U32}
19	
20	type DateTime is Data:
21	  DateTime{date: Date, hour: U32, min: U32, sec: U32, nanos: U32}
22	
23	def i64(x: U32) -> Int.I64:
24	  Int.I64.from_u32(x)
25	
26	# The signed 32-bit value of x, widened.
27	def i64s(x: U32) -> Int.I64:
28	  match x:
29	    case U32{w}:
30	      Int.I64{Int.Int.sext(64n, 32n, w)}
31	
32	# hi * 2^32 + lo, as the bits of an I64.
33	def i64.of(hi: U32, lo: U32) -> Int.I64:
34	  Int.I64.or(Int.I64.shl(i64(hi), 32n), i64(lo))
35	
36	# Duration
37	# --------
38	
39	def Duration.zero() -> Duration:
40	  Duration{i64(0), 0}
41	
42	def Duration.of_secs(s: Int.I64) -> Duration:
43	  Duration{s, 0}
44	
45	def Duration.of_ms(+ms: U32) -> Duration:
46	  Duration{i64((ms / 1000 : U32)), ((ms % 1000 : U32) * 1000000 : U32)}
47	
48	# Whole milliseconds, rounded down.
49	def Duration.to_ms(d: Duration) -> Int.I64:
50	  match d:
51	    case Duration{s, n}:
52	      Int.I64.add(Int.I64.mul(s, i64(1000)), i64((n / 1000000 : U32)))
53	
54	def Duration.to_nat.of(m: Maybe<&2, Nat>, +per: Nat, +n: U32) -> Nat:
55	  match m:
56	    case None{}:
57	      0n
58	    case Some{s}:
59	      (s * per + U32.to_nat(n) : Nat)
60	
61	# Whole milliseconds, rounded down; 0 when d is negative.
62	def Duration.to_ms_nat(d: Duration) -> Nat:
63	  match d:
64	    case Duration{s, n}:
65	      Duration.to_nat.of(Int.I64.to_nat(s), 1000n, (n / 1000000 : U32))
66	
67	# Whole microseconds, rounded down; 0 when d is negative.
68	def Duration.to_us_nat(d: Duration) -> Nat:
69	  match d:
70	    case Duration{s, n}:
71	      Duration.to_nat.of(Int.I64.to_nat(s), 1000000n, (n / 1000 : U32))
72	
73	def Duration.carry(c: Bool, s: Int.I64, +n: U32) -> Duration:
74	  match c:
75	    case True{}:
76	      Duration{Int.I64.add(s, i64(1)), (n - 1000000000 : U32)}
77	    case False{}:
78	      Duration{s, n}
79	
80	def Duration.add(a: Duration, b: Duration) -> Duration:
81	  match a b:
82	    case Duration{sa, na} Duration{sb, nb}:
83	      +n = (na + nb : U32)
84	      Duration.carry(U32.is_ge(n, 1000000000), Int.I64.add(sa, sb), n)
85	
86	# n is na - nb, wrapped when na < nb.
87	def Duration.borrow(c: Bool, s: Int.I64, +n: U32) -> Duration:
88	  match c:
89	    case True{}:
90	      Duration{Int.I64.sub(s, i64(1)), (n + 1000000000 : U32)}
91	    case False{}:
92	      Duration{s, n}
93	
94	def Duration.sub(a: Duration, b: Duration) -> Duration:
95	  match a b:
96	    case Duration{sa, +na} Duration{sb, +nb}:
97	      Duration.borrow(U32.is_lt(na, nb), Int.I64.sub(sa, sb), (na - nb : U32))
98	
99	def Duration.neg(d: Duration) -> Duration:
100	  Duration.sub(Duration.zero(), d)
101	
102	def Duration.cmp.then(c: Cmp, +na: U32, +nb: U32) -> Cmp:
103	  match c:
104	    case EQ{}:
105	      U32.cmp(na, nb)
106	    case LT{}:
107	      LT{}
108	    case GT{}:
109	      GT{}
110	
111	def Duration.cmp(a: Duration, b: Duration) -> Cmp:
112	  match a b:
113	    case Duration{sa, na} Duration{sb, nb}:
114	      Duration.cmp.then(Int.I64.cmp(sa, sb), na, nb)
115	
116	# Instant
117	# -------
118	
119	def Instant.epoch() -> Instant:
120	  Instant{i64(0), 0}
121	
122	def Instant.of_unix(s: Int.I64) -> Instant:
123	  Instant{s, 0}
124	
125	def Instant.of(d: Duration) -> Instant:
126	  match d:
127	    case Duration{s, n}:
128	      Instant{s, n}
129	
130	def Instant.since_epoch(i: Instant) -> Duration:
131	  match i:
132	    case Instant{s, n}:
133	      Duration{s, n}
134	
135	def Instant.add(i: Instant, d: Duration) -> Instant:
136	  Instant.of(Duration.add(Instant.since_epoch(i), d))
137	
138	# a - b.
139	def Instant.since(a: Instant, b: Instant) -> Duration:
140	  Duration.sub(Instant.since_epoch(a), Instant.since_epoch(b))
141	
142	def Instant.cmp(a: Instant, b: Instant) -> Cmp:
143	  Duration.cmp(Instant.since_epoch(a), Instant.since_epoch(b))
144	
145	# Clocks
146	# ------
147	
148	# (secs hi, secs lo, nanos) of CLOCK_MONOTONIC, from an unspecified start.
149	def mono.raw() -> IO(U32 & U32 & U32):
150	  import "./effs/time.c"
151	  import "./effs/time.js"
152	
153	# (secs hi, secs lo, nanos) of CLOCK_REALTIME, since the Unix epoch.
154	def wall.raw() -> IO(U32 & U32 & U32):
155	  import "./effs/time.c"
156	  import "./effs/time.js"
157	
158	def raw.dur(r: U32 & U32 & U32) -> Duration:
159	  (hi, lo, n) = r
160	  Duration{i64.of(hi, lo), n}
161	
162	# Time since an unspecified start that never goes back. Use it to measure spans.
163	def mono() -> IO(Duration):
164	  do IO<Duration>:
165	    r : U32 & U32 & U32 <- mono.raw()
166	    return raw.dur(r)
167	
168	# Monotonic milliseconds. Pure cores that take a Nat `now` in ms take this.
169	def mono.ms() -> IO(Nat):
170	  do IO<Nat>:
171	    d : Duration <- mono()
172	    return Duration.to_ms_nat(d)
173	
174	# Monotonic microseconds.
175	def mono.us() -> IO(Nat):
176	  do IO<Nat>:
177	    d : Duration <- mono()
178	    return Duration.to_us_nat(d)
179	
180	# The wall clock. It can jump when the system time is set.
181	def now() -> IO(Instant):
182	  do IO<Instant>:
183	    r : U32 & U32 & U32 <- wall.raw()
184	    return Instant.of(raw.dur(r))
185	
186	# Dates
187	# -----
188	
189	def Date.is_leap(+y: U32) -> Bool:
190	  Bool.and(U32.is_eq((y % 4 : U32), 0),
191	    Bool.or(U32.is_ne((y % 100 : U32), 0), U32.is_eq((y % 400 : U32), 0)))
192	
193	# 0 for a month outside 1 to 12.
194	def Date.days_in_month(+y: U32, +m: U32) -> U32:
195	  Bool.pick(U32, U32.is_eq(m, 2), Bool.pick(U32, Date.is_leap(y), 29, 28),
196	    Bool.pick(U32, Bool.and(U32.is_ge(m, 1), U32.is_le(m, 12)),
197	      (30 + ((m + (m >> 3n)) .&. 1) : U32), 0))
198	
199	def Date.valid(d: Date) -> Bool:
200	  match d:
201	    case Date{+y, +m, +dd}:
202	      Bool.and(U32.is_le(y, 9999),
203	        Bool.and(U32.is_ge(dd, 1), U32.is_le(dd, Date.days_in_month(y, m))))
204	
205	# z counts days from -0400-03-01, so every date from year 0 has z > 0 in a U32.
206	# The civil-days algorithm is Howard Hinnant's, with the year starting in March.
207	def Z.EPOCH() -> U32:
208	  865565
209	
210	def Date.to_z.at(+y: U32, +mp: U32, +d: U32) -> U32:
211	  +era = (y / 400 : U32)
212	  +yoe = (y - era * 400 : U32)
213	  +doy = ((153 * mp + 2) / 5 + d - 1 : U32)
214	  (era * 146097 + yoe * 365 + yoe / 4 - yoe / 100 + doy : U32)
215	
216	def Date.to_z.go(jf: Bool, +y: U32, +m: U32, +d: U32) -> U32:
217	  match jf:
218	    case True{}:
219	      Date.to_z.at((y + 399 : U32), (m + 9 : U32), d)
220	    case False{}:
221	      Date.to_z.at((y + 400 : U32), (m - 3 : U32), d)
222	
223	def Date.to_z(d: Date) -> U32:
224	  match d:
225	    case Date{+y, +m, +dd}:
226	      Date.to_z.go(U32.is_le(m, 2), y, m, dd)
227	
228	def Date.of_z.fin(lo: Bool, +y: U32, +mp: U32, +d: U32) -> Date:
229	  match lo:
230	    case True{}:
231	      Date{(y - 400 : U32), (mp + 3 : U32), d}
232	    case False{}:
233	      Date{(y - 399 : U32), (mp - 9 : U32), d}
234	
235	def Date.of_z(+z: U32) -> Date:
236	  +era = (z / 146097 : U32)
237	  +doe = (z - era * 146097 : U32)
238	  +yoe = ((doe - doe / 1460 + doe / 36524 - doe / 146096) / 365 : U32)
239	  +doy = (doe - (365 * yoe + yoe / 4 - yoe / 100) : U32)
240	  +mp = ((5 * doy + 2) / 153 : U32)
241	  Date.of_z.fin(U32.is_lt(mp, 10), (yoe + era * 400 : U32), mp,
242	    (doy - (153 * mp + 2) / 5 + 1 : U32))
243	
244	# Days since 1970-01-01.
245	def Date.to_days(d: Date) -> Int.I64:
246	  Int.I64.sub(i64(Date.to_z(d)), i64(Z.EPOCH()))
247	
248	def Date.of_z.if(ok: Bool, +z: U32) -> Maybe<&2, Date>:
249	  match ok:
250	    case True{}:
251	      Some{Date.of_z(z)}
252	    case False{}:
253	      None{}
254	
255	# The date days after 1970-01-01, or None outside 0000-01-01 to 9999-12-31.
256	def Date.of_days(days: Int.I64) -> Maybe<&2, Date>:
257	  +z = Int.I64.add(days, i64(Z.EPOCH()))
258	  Date.of_z.if(Bool.and(Int.I64.is_ge(z, i64(146037)), Int.I64.is_le(z, i64(3798461))),
259	    Int.I64.to_u32(z))
260	
261	# 1 for Monday to 7 for Sunday, as in ISO 8601.
262	def Date.weekday(d: Date) -> U32:
263	  ((Date.to_z(d) + 2) % 7 + 1 : U32)
264	
265	# Date and time
266	# -------------
267	
268	def DateTime.valid(t: DateTime) -> Bool:
269	  match t:
270	    case DateTime{d, h, mi, s, n}:
271	      Bool.and(Date.valid(d), Bool.and(U32.is_le(h, 23),
272	        Bool.and(U32.is_le(mi, 59), Bool.and(U32.is_le(s, 59), U32.is_lt(n, 1000000000)))))
273	
274	# The instant of a UTC date and time. It does not check t; see DateTime.valid.
275	def DateTime.to_instant(t: DateTime) -> Instant:
276	  match t:
277	    case DateTime{d, h, mi, s, n}:
278	      Instant{Int.I64.add(Int.I64.mul(Date.to_days(d), i64(86400)),
279	        i64((h * 3600 + mi * 60 + s : U32))), n}
280	
281	def DateTime.at(m: Maybe<&2, Date>, +sod: U32, n: U32) -> Maybe<&2, DateTime>:
282	  match m:
283	    case None{}:
284	      None{}
285	    case Some{d}:
286	      Some{DateTime{d, (sod / 3600 : U32), (sod / 60 % 60 : U32), (sod % 60 : U32), n}}
287	
288	# r is secs % 86400, which has the sign of secs.
289	def DateTime.floor(neg: Bool, q: Int.I64, r: Int.I64, n: U32) -> Maybe<&2, DateTime>:
290	  match neg:
291	    case True{}:
292	      DateTime.at(Date.of_days(Int.I64.sub(q, i64(1))), (Int.I64.to_u32(r) + 86400 : U32), n)
293	    case False{}:
294	      DateTime.at(Date.of_days(q), Int.I64.to_u32(r), n)
295	
296	# The UTC date and time of i, or None outside years 0 to 9999.
297	def DateTime.of_instant(i: Instant) -> Maybe<&2, DateTime>:
298	  match i:
299	    case Instant{+s, n}:
300	      +r = Int.I64.mod(s, i64(86400))
301	      DateTime.floor(Int.I64.is_neg(r), Int.I64.div(s, i64(86400)), r, n)
302	
303	# Text
304	# ----
305	
306	def pad(+x: U32, w: Nat) -> String:
307	  Fmt.Fmt.pad_left(U32.show(x), w, '0')
308	
309	# Milliseconds with six decimal places.
310	def Duration.show_ms.pos(d: Duration) -> String:
311	  match d:
312	    case Duration{s, +n}:
313	      Int.I64.show(Duration.to_ms(Duration{s, n})) ++ "." ++ pad((n % 1000000 : U32), 6n)
314	
315	def Duration.show_ms.sign(neg: Bool, d: Duration) -> String:
316	  match neg:
317	    case True{}:
318	      "-" ++ Duration.show_ms.pos(Duration.neg(d))
319	    case False{}:
320	      Duration.show_ms.pos(d)
321	
322	def Duration.show_ms(d: Duration) -> String:
323	  match d:
324	    case Duration{+s, n}:
325	      Duration.show_ms.sign(Int.I64.is_neg(s), Duration{s, n})
326	
327	# The digits of n / 10^(9 - w), with trailing zeros cut. n is not 0.
328	def frac.go(f: Nat, z: Bool, +n: U32, +w: Nat) -> String:
329	  match f:
330	    case 0n:
331	      pad(n, w)
332	    case 1n+g:
333	      match z:
334	        case True{}:
335	          +m = (n / 10 : U32)
336	          frac.go(g, U32.is_eq((m % 10 : U32), 0), m, (w - 1n : Nat))
337	        case False{}:
338	          pad(n, w)
339	
340	def frac(+n: U32) -> String:
341	  Bool.pick(String, U32.is_eq(n, 0), "", SCon{'.', frac.go(8n, U32.is_eq((n % 10 : U32), 0), n, 9n)})
342	
343	def DateTime.rfc3339(t: DateTime) -> String:
344	  match t:
345	    case DateTime{Date{y, mo, d}, h, mi, s, n}:
346	      String.concat([pad(y, 4n), "-", pad(mo, 2n), "-", pad(d, 2n), "T", pad(h, 2n), ":",
347	        pad(mi, 2n), ":", pad(s, 2n), frac(n), "Z"])
348	
349	def fmt.map(~f: DateTime -> String, m: Maybe<&2, DateTime>) -> Maybe<&2, String>:
350	  match m:
351	    case None{}:
352	      None{}
353	    case Some{t}:
354	      Some{f(t)}
355	
356	# RFC 3339 in UTC, such as 1985-04-12T23:20:50.52Z. The fraction has no trailing zeros, and is left out when 0.
357	def rfc3339(i: Instant) -> Maybe<&2, String>:
358	  fmt.map(~DateTime.rfc3339, DateTime.of_instant(i))
359	
360	def WEEKDAYS() -> List<&2, String>:
361	  ["Mon", "Tue", "Wed", "Thu", "Fri", "Sat", "Sun"]
362	
363	def MONTHS() -> List<&2, String>:
364	  ["Jan", "Feb", "Mar", "Apr", "May", "Jun", "Jul", "Aug", "Sep", "Oct", "Nov", "Dec"]
365	
366	def name(xs: List<&2, String>, +i: U32) -> String:
367	  Maybe.default(&2, String, List.get(&2, String, xs, U32.to_nat(i)), "")
368	
369	def DateTime.http_date(t: DateTime) -> String:
370	  match t:
371	    case DateTime{+date, h, mi, s, n}:
372	      Date{y, mo, d} = date
373	      String.concat([name(WEEKDAYS(), (Date.weekday(date) - 1 : U32)), ", ", pad(d, 2n), " ",
374	        name(MONTHS(), (mo - 1 : U32)), " ", pad(y, 4n), " ", pad(h, 2n), ":", pad(mi, 2n), ":",
375	        pad(s, 2n), " GMT"])
376	
377	# IMF-fixdate (RFC 9110 §5.6.7), such as Sun, 06 Nov 1994 08:49:37 GMT. It drops the fraction of a second.
378	def http_date(i: Instant) -> Maybe<&2, String>:
379	  fmt.map(~DateTime.http_date, DateTime.of_instant(i))
380	
381	# Parsers
382	# -------
383	
384	# A parser state: the numbers read so far, newest first, and the text left.
385	type P is Data:
386	  P{vals: List<&2, U32>, rest: String}
387	
388	def is_digit(+c: U32) -> Bool:
389	  Bool.and(U32.is_ge(c, 48), U32.is_le(c, 57))
390	
391	def digits.go(n: Nat, s: String, +acc: U32, ok: Bool) -> Maybe<&1, U32 & String>:
392	  match n:
393	    case 0n:
394	      match ok:
395	        case True{}:
396	          Some{(acc, s)}
397	        case False{}:
398	          None{}
399	    case 1n+k:
400	      match s:
401	        case SNil{}:
402	          None{}
403	        case SCon{Chr{+c}, t}:
404	          digits.go(k, t, (acc * 10 + c - 48 : U32), Bool.and(ok, is_digit(c)))
405	
406	def push(vs: List<&2, U32>, r: Maybe<&1, U32 & String>) -> Maybe<&2, P>:
407	  match r:
408	    case None{}:
409	      None{}
410	    case Some{(v, t)}:
411	      Some{P{Con{v, vs}, t}}
412	
413	# Exactly n digits.
414	def num(n: Nat, p: P) -> Maybe<&2, P>:
415	  match p:
416	    case P{vs, s}:
417	      push(vs, digits.go(n, s, 0, True{}))
418	
419	def lit.if(ok: Bool, vs: List<&2, U32>, t: String) -> Maybe<&2, P>:
420	  match ok:
421	    case True{}:
422	      Some{P{vs, t}}
423	    case False{}:
424	      None{}
425	
426	# One char that is a or b.
427	def lit2(+a: U32, +b: U32, p: P) -> Maybe<&2, P>:
428	  match p:
429	    case P{vs, s}:
430	      match s:
431	        case SNil{}:
432	          None{}
433	        case SCon{Chr{+c}, t}:
434	          lit.if(Bool.or(U32.is_eq(c, a), U32.is_eq(c, b)), vs, t)
435	
436	def lit(+c: U32, p: P) -> Maybe<&2, P>:
437	  lit2(c, c, p)
438	
439	def text(+w: String, p: P) -> Maybe<&2, P>:
440	  match p:
441	    case P{vs, +s}:
442	      +n = String.length(w)
443	      lit.if(String.eq(String.take(s, n), w), vs, String.drop(s, n))
444	
445	def at.head(+s: String) -> Bool:
446	  match s:
447	    case SNil{}:
448	      False{}
449	    case SCon{Chr{+c}, t}:
450	      is_digit(c)
451	
452	# Digits after the first nine are read and dropped. d says whether s starts with a digit.
453	def secfrac.go(s: String, d: Bool, +mul: U32, +acc: U32, +k: U32) -> U32 & U32 & String:
454	  match s:
455	    case SNil{}:
456	      (k, acc, SNil{})
457	    case SCon{Chr{+c}, +t}:
458	      match d:
459	        case True{}:
460	          secfrac.go(t, at.head(t), (mul / 10 : U32), (acc + (c - 48) * mul : U32), (k + 1 : U32))
461	        case False{}:
462	          (k, acc, SCon{Chr{c}, t})
463	
464	def secfrac.fin(vs: List<&2, U32>, r: U32 & U32 & String) -> Maybe<&2, P>:
465	  (k, n, t) = r
466	  lit.if(U32.is_gt(k, 0), Con{n, vs}, t)
467	
468	def secfrac.if(dot: Bool, vs: List<&2, U32>, +s: String) -> Maybe<&2, P>:
469	  match dot:
470	    case True{}:
471	      +t = String.drop(s, 1n)
472	      secfrac.fin(vs, secfrac.go(t, at.head(t), 100000000, 0, 0))
473	    case False{}:
474	      Some{P{Con{0, vs}, s}}
475	
476	# An optional '.' and one or more digits, as nanoseconds.
477	def secfrac(p: P) -> Maybe<&2, P>:
478	  match p:
479	    case P{vs, +s}:
480	      secfrac.if(String.starts_with(s, "."), vs, s)
481	
482	def zone.num(+neg: U32, vs: List<&2, U32>, t: String) -> Maybe<&2, P>:
483	  do Maybe<&2, P>:
484	    a : P <- num(2n, P{Con{neg, vs}, t})
485	    b : P <- lit(58, a)
486	    num(2n, b)
487	
488	def zone.if(z: Bool, plus: Bool, minus: Bool, vs: List<&2, U32>, t: String) -> Maybe<&2, P>:
489	  match z:
490	    case True{}:
491	      Some{P{Con{0, Con{0, Con{0, vs}}}, t}}
492	    case False{}:
493	      match plus:
494	        case True{}:
495	          zone.num(0, vs, t)
496	        case False{}:
497	          match minus:
498	            case True{}:
499	              zone.num(1, vs, t)
500	            case False{}:
501	              None{}
502	
503	# Z, or +hh:mm or -hh:mm, as (sign, hh, mm) with sign 1 for west of UTC.
504	def zone(p: P) -> Maybe<&2, P>:
505	  match p:
506	    case P{vs, s}:
507	      match s:
508	        case SNil{}:
509	          None{}
510	        case SCon{Chr{+c}, t}:
511	          zone.if(Bool.or(U32.is_eq(c, 90), U32.is_eq(c, 122)), U32.is_eq(c, 43), U32.is_eq(c, 45), vs, t)
512	
513	def index.go(xs: List<&2, String>, +w: String, +i: U32) -> U32:
514	  match xs:
515	    case Nil{}:
516	      i
517	    case Con{x, rest}:
518	      Bool.pick(U32, String.eq(x, w), i, index.go(rest, w, (i + 1 : U32)))
519	
520	# One of names, as its index.
521	def word(+names: List<&2, String>, p: P) -> Maybe<&2, P>:
522	  match p:
523	    case P{vs, +s}:
524	      +i = index.go(names, String.take(s, 3n), 0)
525	      lit.if(U32.is_lt(i, U32.from_nat(List.length(&2, String, names))), Con{i, vs}, String.drop(s, 3n))
526	
527	def mk.if(ok: Bool, t: DateTime) -> Maybe<&2, Instant>:
528	  match ok:
529	    case True{}:
530	      Some{DateTime.to_instant(t)}
531	    case False{}:
532	      None{}
533	
534	def mk(+t: DateTime) -> Maybe<&2, Instant>:
535	  mk.if(DateTime.valid(t), t)
536	
537	def rfc3339.shift(m: Maybe<&2, Instant>, +west: U32, +hh: U32, +mm: U32) -> Maybe<&2, Instant>:
538	  match m:
539	    case None{}:
540	      None{}
541	    case Some{i}:
542	      +off = Duration.of_secs(i64((hh * 3600 + mm * 60 : U32)))
543	      Bool.pick(Maybe<&2, Instant>, Bool.and(U32.is_le(hh, 23), U32.is_le(mm, 59)),
544	        Some{Instant.add(i, Bool.pick(Duration, U32.is_eq(west, 1), off, Duration.neg(off)))}, None{})
545	
546	def rfc3339.fin(p: P) -> Maybe<&2, Instant>:
547	  match p:
548	    case P{Con{mm, Con{hh, Con{west, Con{n, Con{s, Con{mi, Con{h, Con{d, Con{mo, Con{y, Nil{}}}}}}}}}}}, SNil{}}:
549	      rfc3339.shift(mk(DateTime{Date{y, mo, d}, h, mi, s, n}), west, hh, mm)
550	    case _:
551	      None{}
552	
553	# An RFC 3339 date-time (§5.6), such as 1985-04-12T23:20:50.52Z or 1996-12-19T16:39:57-08:00.
554	# T and Z may be lowercase. A leap second (:60) is refused, as Instant has none.
555	def rfc3339.parse(s: String) -> Maybe<&2, Instant>:
556	  do Maybe<&2, Instant>:
557	    a : P <- num(4n, P{Nil{}, s})
558	    b : P <- lit(45, a)
559	    c : P <- num(2n, b)
560	    d : P <- lit(45, c)
561	    e : P <- num(2n, d)
562	    f : P <- lit2(84, 116, e)
563	    g : P <- num(2n, f)
564	    h : P <- lit(58, g)
565	    i : P <- num(2n, h)
566	    j : P <- lit(58, i)
567	    k : P <- num(2n, j)
568	    l : P <- secfrac(k)
569	    m : P <- zone(l)
570	    rfc3339.fin(m)
571	
572	def http_date.fin(p: P) -> Maybe<&2, Instant>:
573	  match p:
574	    case P{Con{s, Con{mi, Con{h, Con{y, Con{mo, Con{d, Con{wd, Nil{}}}}}}}}, SNil{}}:
575	      mk(DateTime{Date{y, (mo + 1 : U32), d}, h, mi, s, 0})
576	    case _:
577	      None{}
578	
579	# An IMF-fixdate (RFC 9110 §5.6.7), such as Sun, 06 Nov 1994 08:49:37 GMT.
580	# The day name must be one of the seven, but it is not checked against the date.
581	def http_date.parse(s: String) -> Maybe<&2, Instant>:
582	  do Maybe<&2, Instant>:
583	    a : P <- word(WEEKDAYS(), P{Nil{}, s})
584	    b : P <- text(", ", a)
585	    c : P <- num(2n, b)
586	    d : P <- lit(32, c)
587	    e : P <- word(MONTHS(), d)
588	    f : P <- lit(32, e)
589	    g : P <- num(4n, f)
590	    h : P <- lit(32, g)
591	    i : P <- num(2n, h)
592	    j : P <- lit(58, i)
593	    k : P <- num(2n, j)
594	    l : P <- lit(58, k)
595	    m : P <- num(2n, l)
596	    n : P <- text(" GMT", m)
597	    http_date.fin(n)
598	
599	# Time zones
600	# ----------
601	
602	# A local time type: seconds east of UTC, whether it is daylight time, and its abbreviation.
603	type Ttype is Data:
604	  Ttype{utoff: Int.I64, dst: Bool, abbr: String}
605	
606	# From at on, local time follows types[idx].
607	type Trans is Data:
608	  Trans{at: Int.I64, idx: U32}
609	
610	# A TZif zone (RFC 8536): transitions in time order, local time types, and the footer TZ string ("" in version 1).
611	type Zone is Data:
612	  Zone{trans: List<&2, Trans>, types: List<&2, Ttype>, tz: String}
613	
614	# n bytes of a byte string, big-endian.
615	def be(n: Nat, s: String, +acc: U32) -> U32:
616	  match n:
617	    case 0n:
618	      acc
619	    case 1n+k:
620	      match s:
621	        case SNil{}:
622	          acc
623	        case SCon{Chr{c}, t}:
624	          be(k, t, ((acc << 8n) .|. c : U32))
625	
626	def be32(+s: String, n: Nat) -> U32:
627	  be(4n, String.drop(s, n), 0)
628	
629	def u8(+s: String, n: Nat) -> U32:
630	  be(1n, String.drop(s, n), 0)
631	
632	def tzif.size(t8: Bool) -> Nat:
633	  match t8:
634	    case True{}:
635	      8n
636	    case False{}:
637	      4n
638	
639	def tzif.time(t8: Bool, +s: String) -> Int.I64:
640	  match t8:
641	    case True{}:
642	      i64.of(be32(s, 0n), be32(s, 4n))
643	    case False{}:
644	      i64s(be32(s, 0n))
645	
646	# ts holds the transition times and ks their type indexes.
647	def tzif.trans(n: Nat, +t8: Bool, +ts: String, +ks: String) -> List<&2, Trans>:
648	  match n:
649	    case 0n:
650	      Nil{}
651	    case 1n+k:
652	      Con{Trans{tzif.time(t8, ts), u8(ks, 0n)},
653	        tzif.trans(k, t8, String.drop(ts, tzif.size(t8)), String.drop(ks, 1n))}
654	
655	# The NUL-terminated abbreviation at byte i of chars.
656	def tzif.abbr(chars: String, +i: U32) -> String:
657	  name(String.split(String.drop(chars, U32.to_nat(i)), Chr{0}), 0)
658	
659	def tzif.types(n: Nat, +s: String, +chars: String) -> List<&2, Ttype>:
660	  match n:
661	    case 0n:
662	      Nil{}
663	    case 1n+k:
664	      Con{Ttype{i64s(be32(s, 0n)), U32.is_ne(u8(s, 4n), 0), tzif.abbr(chars, u8(s, 5n))},
665	        tzif.types(k, String.drop(s, 6n), chars)}
666	
667	def tzif.if(ok: Bool, z: Zone) -> Maybe<&2, Zone>:
668	  match ok:
669	    case True{}:
670	      Some{z}
671	    case False{}:
672	      None{}
673	
674	# Header counts, in RFC 8536 order: isut, isstd, leap, time, type, char.
675	def tzif.count(+h: String, i: Nat) -> Nat:
676	  U32.to_nat(be32(h, (20n + 4n * i : Nat)))
677	
678	# The data block's size in bytes, for header h.
679	def tzif.bsize(+t8: Bool, +h: String) -> Nat:
680	  +tc = tzif.count(h, 3n)
681	  (tc * tzif.size(t8) + tc + tzif.count(h, 4n) * 6n + tzif.count(h, 5n) +
682	    tzif.count(h, 2n) * (tzif.size(t8) + 4n) + tzif.count(h, 1n) + tzif.count(h, 0n) : Nat)
683	
684	# h starts at a header; its data block follows it. Version 2+ blocks have 8-byte times and a footer.
685	def tzif.block(+t8: Bool, +h: String) -> Maybe<&2, Zone>:
686	  +d = String.drop(h, 44n)
687	  +tc = tzif.count(h, 3n)
688	  +ty = tzif.count(h, 4n)
689	  +at = (tc * tzif.size(t8) + tc : Nat)
690	  +foot = String.drop(d, tzif.bsize(t8, h))
691	  tzif.if(Bool.and(String.starts_with(h, "TZif"), Bool.and(Nat.is_gt(ty, 0n),
692	      Nat.is_le((44n + tzif.bsize(t8, h) : Nat), String.length(h)))),
693	    Zone{tzif.trans(tc, t8, d, String.drop(d, (tc * tzif.size(t8) : Nat))),
694	      tzif.types(ty, String.drop(d, at), String.take(String.drop(d, (at + ty * 6n : Nat)), tzif.count(h, 5n))),
695	      Bool.pick(String, t8, name(String.split(foot, '\n'), 1), "")})
696	
697	def tzif.go(v2: Bool, +s: String) -> Maybe<&2, Zone>:
698	  match v2:
699	    case True{}:
700	      tzif.block(True{}, String.drop(s, (44n + tzif.bsize(False{}, s) : Nat)))
701	    case False{}:
702	      tzif.block(False{}, s)
703	
704	# A TZif file, such as one from /usr/share/zoneinfo. Versions 2 and up use their 64-bit block.
705	# ponytail: reads the bytes as a byte String; walk Bytes directly if zone files get big.
706	def tzif.parse(b: Bytes.Bytes) -> Maybe<&2, Zone>:
707	  +s = Bytes.to_string(b)
708	  tzif.go(U32.is_ge(u8(s, 4n), 50), s)
709	
710	# POSIX TZ offsets are seconds west of UTC; transition times are seconds from local midnight.
711	type TzField is Data:
712	  TzField{value: U32, rest: String}
713	
714	type TzText is Data:
715	  TzText{value: String, rest: String}
716	
717	type TzClock is Data:
718	  TzClock{value: Int.I64, rest: String}
719	
720	type TzDay is Data:
721	  Julian{day: U32}
722	  Ordinal{day: U32}
723	  MonthWeek{month: U32, week: U32, weekday: U32}
724	
725	type TzDate is Data:
726	  TzDate{day: TzDay, seconds: Int.I64}
727	
728	type TzDayPart is Data:
729	  TzDayPart{day: TzDay, rest: String}
730	
731	type TzDatePart is Data:
732	  TzDatePart{date: TzDate, rest: String}
733	
734	type TzRule is Data:
735	  TzRule{std: Ttype, daylight: Ttype, start: TzDate, end: TzDate}
736	
737	def tz.digit(+c: U32) -> Bool:
738	  Bool.and(U32.is_ge(c, 48), U32.is_le(c, 57))
739	
740	def tz.alpha(+c: U32) -> Bool:
741	  Bool.or(Bool.and(U32.is_ge(c, 65), U32.is_le(c, 90)),
742	    Bool.and(U32.is_ge(c, 97), U32.is_le(c, 122)))
743	
744	def tz.quoted(+c: U32) -> Bool:
745	  Bool.or(tz.alpha(c), Bool.or(tz.digit(c), Bool.or(U32.is_eq(c, 43), U32.is_eq(c, 45))))
746	
747	def tz.number.stop(seen: Bool, acc: U32, s: String) -> Maybe<&2, TzField>:
748	  match seen:
749	    case True{}:
750	      Some{TzField{acc, s}}
751	    case False{}:
752	      None{}
753	
754	def tz.number.step(digit: Bool, c: U32, t: String, acc: U32, seen: Bool, next: Unit -> Maybe<&2, TzField>) -> Maybe<&2, TzField>:
755	  match digit:
756	    case True{}:
757	      next(Unit{})
758	    case False{}:
759	      tz.number.stop(seen, acc, SCon{Chr{c}, t})
760	
761	# Three digits suffice for POSIX hour, day, and month fields.
762	def tz.number.go(s: String, +acc: U32, +seen: Bool) -> Maybe<&2, TzField>:
763	  match s:
764	    case SNil{}:
765	      tz.number.stop(seen, acc, SNil{})
766	    case SCon{Chr{+c}, +t}:
767	      tz.number.step(Bool.and(tz.digit(c), U32.is_lt(acc, 100)),
768	        c, t, acc, seen, _ => tz.number.go(t, ((acc * 10 + c - 48) : U32), True{}))
769	
770	def tz.number(s: String) -> Maybe<&2, TzField>:
771	  tz.number.go(s, 0, False{})
772	
773	def tz.name.valid(ok: Bool, name: String, rest: String) -> Maybe<&2, TzText>:
774	  match ok:
775	    case True{}:
776	      Some{TzText{name, rest}}
777	    case False{}:
778	      None{}
779	
780	def tz.name.done(rev: String, rest: String) -> Maybe<&2, TzText>:
781	  +name = String.reverse(rev)
782	  tz.name.valid(Nat.is_ge(String.length(name), 3n), name, rest)
783	
784	def tz.name.empty(quoted: Bool, rev: String) -> Maybe<&2, TzText>:
785	  match quoted:
786	    case True{}:
787	      None{}
788	    case False{}:
789	      tz.name.done(rev, SNil{})
790	
791	def tz.name.branch(continue: Bool, rev: String, c: U32, rest: String, next: Unit -> Maybe<&2, TzText>) -> Maybe<&2, TzText>:
792	  match continue:
793	    case True{}:
794	      next(Unit{})
795	    case False{}:
796	      tz.name.done(rev, SCon{Chr{c}, rest})
797	
798	def tz.name.allowed(ok: Bool, next: Unit -> Maybe<&2, TzText>) -> Maybe<&2, TzText>:
799	  match ok:
800	    case True{}:
801	      next(Unit{})
802	    case False{}:
803	      None{}
804	
805	def tz.name.quoted(end: Bool, valid: Bool, rev: String, rest: String, next: Unit -> Maybe<&2, TzText>) -> Maybe<&2, TzText>:
806	  match end:
807	    case True{}:
808	      tz.name.done(rev, rest)
809	    case False{}:
810	      tz.name.allowed(valid, next)
811	
812	def tz.name.char(quoted: Bool, end: Bool, alpha: Bool, valid: Bool, rev: String, c: U32, rest: String,
813	  next: Unit -> Maybe<&2, TzText>) -> Maybe<&2, TzText>:
814	  match quoted:
815	    case True{}:
816	      tz.name.quoted(end, valid, rev, rest, next)
817	    case False{}:
818	      tz.name.branch(alpha, rev, c, rest, next)
819	
820	def tz.name.go(s: String, +rev: String, +quoted: Bool) -> Maybe<&2, TzText>:
821	  match s:
822	    case SNil{}:
823	      tz.name.empty(quoted, rev)
824	    case SCon{Chr{+c}, +t}:
825	      tz.name.char(quoted, U32.is_eq(c, 62), tz.alpha(c), tz.quoted(c), rev, c, t,
826	        _ => tz.name.go(t, SCon{Chr{c}, rev}, quoted))
827	
828	def tz.name(s: String) -> Maybe<&2, TzText>:
829	  match s:
830	    case SCon{Chr{60}, t}:
831	      tz.name.go(t, SNil{}, True{})
832	    case _:
833	      tz.name.go(s, SNil{}, False{})
834	
835	def tz.field.valid(ok: Bool, n: U32, rest: String) -> Maybe<&2, TzField>:
836	  match ok:
837	    case True{}:
838	      Some{TzField{n, rest}}
839	    case False{}:
840	      None{}
841	
842	def tz.clock.tail(r: TzField, limit: U32) -> Maybe<&2, TzField>:
843	  match r:
844	    case TzField{+n, rest}:
845	      tz.field.valid(U32.is_le(n, limit), n, rest)
846	
847	def tz.clock.part(s: String) -> Maybe<&2, TzField>:
848	  match s:
849	    case SCon{Chr{58}, t}:
850	      do Maybe<&2, TzField>:
851	        n : TzField <- tz.number(t)
852	        tz.clock.tail(n, 59)
853	    case _:
854	      Some{TzField{0, s}}
855	
856	def tz.clock.valid(ok: Bool, +value: Int.I64, negative: Bool, rest: String) -> Maybe<&2, TzClock>:
857	  match ok:
858	    case False{}:
859	      None{}
860	    case True{}:
861	      Some{TzClock{Bool.pick(Int.I64, negative, Int.I64.neg(value), value), rest}}
862	
863	def tz.clock.seconds(sec: TzField, +hours: U32, +minutes: U32, +max: U32, negative: Bool) -> Maybe<&2, TzClock>:
864	  match sec:
865	    case TzField{+seconds, rest}:
866	      tz.clock.valid(U32.is_le(hours, max),
867	        i64((hours * 3600 + minutes * 60 + seconds : U32)), negative, rest)
868	
869	def tz.clock.minutes(m: TzField, +hours: U32, +max: U32, +negative: Bool) -> Maybe<&2, TzClock>:
870	  match m:
871	    case TzField{+minutes, rest}:
872	      do Maybe<&2, TzClock>:
873	        sec : TzField <- tz.clock.part(rest)
874	        tz.clock.seconds(sec, hours, minutes, max, negative)
875	def tz.clock.finish(h: TzField, +max: U32, +negative: Bool) -> Maybe<&2, TzClock>:
876	  match h:
877	    case TzField{+hours, rest}:
878	      do Maybe<&2, TzClock>:
879	        m : TzField <- tz.clock.part(rest)
880	        tz.clock.minutes(m, hours, max, negative)
881	
882	
883	def tz.clock.read(s: String, max: U32, negative: Bool) -> Maybe<&2, TzClock>:
884	  do Maybe<&2, TzClock>:
885	    h : TzField <- tz.number(s)
886	    tz.clock.finish(h, max, negative)
887	def tz.clock.sign(s: String, max: U32) -> Maybe<&2, TzClock>:
888	  match s:
889	    case SCon{Chr{45}, t}:
890	      tz.clock.read(t, max, True{})
891	    case SCon{Chr{43}, t}:
892	      tz.clock.read(t, max, False{})
893	    case _:
894	      tz.clock.read(s, max, False{})
895	
896	
897	def tz.day.valid(ok: Bool, d: TzDay, rest: String) -> Maybe<&2, TzDayPart>:
898	  match ok:
899	    case True{}:
900	      Some{TzDayPart{d, rest}}
901	    case False{}:
902	      None{}
903	
904	def tz.day.j(r: TzField) -> Maybe<&2, TzDayPart>:
905	  match r:
906	    case TzField{+n, rest}:
907	      tz.day.valid(Bool.and(U32.is_ge(n, 1), U32.is_le(n, 365)), Julian{n}, rest)
908	
909	def tz.day.n(r: TzField) -> Maybe<&2, TzDayPart>:
910	  match r:
911	    case TzField{+n, rest}:
912	      tz.day.valid(U32.is_le(n, 365), Ordinal{n}, rest)
913	
914	def tz.after(c: Char, s: String) -> String:
915	  match s:
916	    case SCon{h, t}:
917	      Bool.pick(String, Char.is_eq(h, c), t, SNil{})
918	    case SNil{}:
919	      SNil{}
920	
921	def tz.day.weekday(c: TzField, +month: U32, +week: U32) -> Maybe<&2, TzDayPart>:
922	  match c:
923	    case TzField{+weekday, rest}:
924	      tz.day.valid(Bool.and(U32.is_ge(month, 1), Bool.and(U32.is_le(month, 12),
925	        Bool.and(U32.is_ge(week, 1), Bool.and(U32.is_le(week, 5), U32.is_le(weekday, 6))))),
926	        MonthWeek{month, week, weekday}, rest)
927	
928	def tz.day.week(b: TzField, month: U32) -> Maybe<&2, TzDayPart>:
929	  match b:
930	    case TzField{week, rest}:
931	      do Maybe<&2, TzDayPart>:
932	        c : TzField <- tz.number(tz.after('.', rest))
933	        tz.day.weekday(c, month, week)
934	
935	def tz.day.month(a: TzField) -> Maybe<&2, TzDayPart>:
936	  match a:
937	    case TzField{month, rest}:
938	      do Maybe<&2, TzDayPart>:
939	        b : TzField <- tz.number(tz.after('.', rest))
940	        tz.day.week(b, month)
941	
942	def tz.day.m(s: String) -> Maybe<&2, TzDayPart>:
943	  do Maybe<&2, TzDayPart>:
944	    a : TzField <- tz.number(s)
945	    tz.day.month(a)
946	
947	def tz.day(s: String) -> Maybe<&2, TzDayPart>:
948	  match s:
949	    case SCon{Chr{74}, t}:
950	      do Maybe<&2, TzDayPart>:
951	        n : TzField <- tz.number(t)
952	        tz.day.j(n)
953	    case SCon{Chr{77}, t}:
954	      tz.day.m(t)
955	    case _:
956	      do Maybe<&2, TzDayPart>:
957	        n : TzField <- tz.number(s)
958	        tz.day.n(n)
959	
960	def tz.date.clock(d: TzDay, r: TzClock) -> Maybe<&2, TzDatePart>:
961	  match r:
962	    case TzClock{secs, end}:
963	      Some{TzDatePart{TzDate{d, secs}, end}}
964	
965	def tz.date.time(d: TzDay, rest: String) -> Maybe<&2, TzDatePart>:
966	  match rest:
967	    case SCon{Chr{47}, t}:
968	      do Maybe<&2, TzDatePart>:
969	        r : TzClock <- tz.clock.sign(t, 167)
970	        tz.date.clock(d, r)
971	    case _:
972	      Some{TzDatePart{TzDate{d, i64(7200)}, rest}}
973	
974	def tz.date.part(r: TzDayPart) -> Maybe<&2, TzDatePart>:
975	  match r:
976	    case TzDayPart{d, rest}:
977	      tz.date.time(d, rest)
978	
979	def tz.date(s: String) -> Maybe<&2, TzDatePart>:
980	  do Maybe<&2, TzDatePart>:
981	    r : TzDayPart <- tz.day(s)
982	    tz.date.part(r)
983	
984	def tz.rule.end(ok: Bool, standard: Ttype, daylight: Ttype, start: TzDate, end: TzDate) -> Maybe<&2, TzRule>:
985	  match ok:
986	    case True{}:
987	      Some{TzRule{standard, daylight, start, end}}
988	    case False{}:
989	      None{}
990	
991	def tz.rule.finish(b: TzDatePart, standard: Ttype, daylight: Ttype, start: TzDate) -> Maybe<&2, TzRule>:
992	  match b:
993	    case TzDatePart{end, rest}:
994	      tz.rule.end(String.is_empty(rest), standard, daylight, start, end)
995	
996	def tz.rule.start(a: TzDatePart, +standard: Ttype, +daylight: Ttype) -> Maybe<&2, TzRule>:
997	  match a:
998	    case TzDatePart{start, rest}:
999	      do Maybe<&2, TzRule>:
1000	        b : TzDatePart <- tz.date(tz.after(',', rest))
1001	        tz.rule.finish(b, standard, daylight, start)
1002	
1003	def tz.rule.dates(+standard: Ttype, +daylight: Ttype, rest: String) -> Maybe<&2, TzRule>:
1004	  do Maybe<&2, TzRule>:
1005	    a : TzDatePart <- tz.date(tz.after(',', rest))
1006	    tz.rule.start(a, standard, daylight)
1007	
1008	def tz.rule.dstclock(r: TzClock, standard: Ttype, abbr: String) -> Maybe<&2, TzRule>:
1009	  match r:
1010	    case TzClock{west, rest}:
1011	      tz.rule.dates(standard, Ttype{Int.I64.neg(west), True{}, abbr}, rest)
1012	
1013	def tz.rule.offset(standard: Ttype, abbr: String, west: Int.I64, rest: String) -> Maybe<&2, TzRule>:
1014	  match rest:
1015	    case SCon{Chr{44}, t}:
1016	      tz.rule.dates(standard, Ttype{Int.I64.sub(i64(3600), west), True{}, abbr}, rest)
1017	    # POSIX leaves absent DST dates to the implementation; use the common US rules.
1018	    case SNil{}:
1019	      tz.rule.end(True{}, standard, Ttype{Int.I64.sub(i64(3600), west), True{}, abbr},
1020	        TzDate{MonthWeek{3, 2, 0}, i64(7200)}, TzDate{MonthWeek{11, 1, 0}, i64(7200)})
1021	    case _:
1022	      do Maybe<&2, TzRule>:
1023	        r : TzClock <- tz.clock.sign(rest, 24)
1024	        tz.rule.dstclock(r, standard, abbr)
1025	
1026	def tz.rule.named(name: TzText, standard: Ttype, west: Int.I64) -> Maybe<&2, TzRule>:
1027	  match name:
1028	    case TzText{abbr, rest}:
1029	      tz.rule.offset(standard, abbr, west, rest)
1030	
1031	def tz.rule.dst(+standard: Ttype, west: Int.I64, rest: String) -> Maybe<&2, TzRule>:
1032	  match rest:
1033	    case SNil{}:
1034	      Some{TzRule{standard, standard, TzDate{Ordinal{0}, i64(0)}, TzDate{Ordinal{0}, i64(0)}}}
1035	    case _:
1036	      do Maybe<&2, TzRule>:
1037	        name : TzText <- tz.name(rest)
1038	        tz.rule.named(name, standard, west)
1039	
1040	def tz.rule.stdclock(offset: TzClock, abbr: String) -> Maybe<&2, TzRule>:
1041	  match offset:
1042	    case TzClock{+west, rest}:
1043	      tz.rule.dst(Ttype{Int.I64.neg(west), False{}, abbr}, west, rest)
1044	
1045	def tz.rule.standard(name: TzText) -> Maybe<&2, TzRule>:
1046	  match name:
1047	    case TzText{abbr, rest}:
1048	      do Maybe<&2, TzRule>:
1049	        offset : TzClock <- tz.clock.sign(rest, 24)
1050	        tz.rule.stdclock(offset, abbr)
1051	
1052	def tz.rule(s: String) -> Maybe<&2, TzRule>:
1053	  do Maybe<&2, TzRule>:
1054	    name : TzText <- tz.name(s)
1055	    tz.rule.standard(name)
1056	
1057	# The day number of a rule in year y, relative to January 1.
1058	def tz.day.index(d: TzDay, +y: U32) -> U32:
1059	  match d:
1060	    case Julian{+n}:
1061	      (n - 1 + Bool.pick(U32, Bool.and(Date.is_leap(y), U32.is_ge(n, 60)), 1, 0) : U32)
1062	    case Ordinal{n}:
1063	      n
1064	    case MonthWeek{+month, +week, +weekday}:
1065	      +first_day = (Date.weekday(Date{y, month, 1}) % 7 : U32)
1066	      +day = (1 + ((weekday + 7 - first_day) % 7) + (week - 1) * 7 : U32)
1067	      +last = Date.days_in_month(y, month)
1068	      +actual = Bool.pick(U32, U32.is_gt(day, last), (day - 7 : U32), day)
1069	      Int.I64.to_u32(Int.I64.sub(Date.to_days(Date{y, month, actual}), Date.to_days(Date{y, 1, 1})))
1070	
1071	def tz.date.utc(d: TzDate, +y: U32, west: Int.I64) -> Int.I64:
1072	  match d:
1073	    case TzDate{day, sec}:
1074	      Int.I64.add(Int.I64.mul(Int.I64.add(Date.to_days(Date{y, 1, 1}), i64(tz.day.index(day, y))), i64(86400)),
1075	        Int.I64.add(sec, west))
1076	
1077	# Apply the two transitions for the UTC year and its neighbors. A /time may cross a year boundary.
1078	type TzEvent is Data:
1079	  TzEvent{when: Int.I64, dst: Bool}
1080	
1081	def tz.event.select(newer: Bool, old: Maybe<&2, TzEvent>, when: Int.I64, dst: Bool) -> Maybe<&2, TzEvent>:
1082	  match newer:
1083	    case True{}:
1084	      Some{TzEvent{when, dst}}
1085	    case False{}:
1086	      old
1087	
1088	def tz.event.new(+now: Int.I64, old: Maybe<&2, TzEvent>, +when: Int.I64, dst: Bool) -> Maybe<&2, TzEvent>:
1089	  match old:
1090	    case None{}:
1091	      tz.event.select(Int.I64.is_le(when, now), None{}, when, dst)
1092	    case Some{TzEvent{+prev, flag}}:
1093	      tz.event.select(Bool.and(Int.I64.is_le(when, now), Int.I64.is_gt(when, prev)),
1094	        Some{TzEvent{prev, flag}}, when, dst)
1095	
1096	def tz.event.year(+now: Int.I64, old: Maybe<&2, TzEvent>, +r: TzRule, +y: U32) -> Maybe<&2, TzEvent>:
1097	  match r:
1098	    case TzRule{Ttype{+off, _, _}, Ttype{+dstoff, _, _}, +start, +end}:
1099	      +first = tz.event.new(now, old, tz.date.utc(start, y, Int.I64.neg(off)), True{})
1100	      tz.event.new(now, first, tz.date.utc(end, y, Int.I64.neg(dstoff)), False{})
1101	
1102	def tz.event.prev(+now: Int.I64, old: Maybe<&2, TzEvent>, +r: TzRule, +y: U32) -> Maybe<&2, TzEvent>:
1103	  match y:
1104	    case 0:
1105	      old
1106	    case _:
1107	      tz.event.year(now, old, r, (y - 1 : U32))
1108	
1109	def tz.event.next.if(valid: Bool, now: Int.I64, old: Maybe<&2, TzEvent>, r: TzRule, y: U32) -> Maybe<&2, TzEvent>:
1110	  match valid:
1111	    case True{}:
1112	      tz.event.year(now, old, r, (y + 1 : U32))
1113	    case False{}:
1114	      old
1115	def tz.event.next(+now: Int.I64, old: Maybe<&2, TzEvent>, +r: TzRule, +y: U32) -> Maybe<&2, TzEvent>:
1116	  tz.event.next.if(U32.is_lt(y, 9999), now, old, r, y)
1117	
1118	
1119	def tz.event.type(ev: Maybe<&2, TzEvent>, +r: TzRule) -> Ttype:
1120	  match ev:
1121	    case Some{TzEvent{when, dst}}:
1122	      match r:
1123	        case TzRule{standard, daylight, start, end}:
1124	          Bool.pick(Ttype, dst, daylight, standard)
1125	    case None{}:
1126	      match r:
1127	        case TzRule{standard, daylight, start, end}:
1128	          standard
1129	
1130	def tz.rule.at(+r: TzRule, +secs: Int.I64, +year: U32) -> Ttype:
1131	  +a = tz.event.prev(secs, None{}, r, year)
1132	  +b = tz.event.year(secs, a, r, year)
1133	  tz.event.type(tz.event.next(secs, b, r, year), r)
1134	
1135	def tz.rule.date(d: Maybe<&2, DateTime>, r: TzRule, secs: Int.I64) -> Maybe<&2, Ttype>:
1136	  match d:
1137	    case None{}:
1138	      None{}
1139	    case Some{DateTime{Date{y, m, day}, h, mi, second, nanos}}:
1140	      Some{tz.rule.at(r, secs, y)}
1141	
1142	def tz.rule.lookup(rule: Maybe<&2, TzRule>, +secs: Int.I64) -> Maybe<&2, Ttype>:
1143	  match rule:
1144	    case None{}:
1145	      None{}
1146	    case Some{r}:
1147	      tz.rule.date(DateTime.of_instant(Instant.of_unix(secs)), r, secs)
1148	
1149	# The type index at secs: the last transition at or before it, or type 0 before the first.
1150	# ponytail: linear scan; bisect an Array if lookups get hot.
1151	def Zone.find(ts: List<&2, Trans>, +secs: Int.I64, +cur: U32) -> U32:
1152	  match ts:
1153	    case Nil{}:
1154	      cur
1155	    case Con{Trans{t, k}, rest}:
1156	      Zone.find(rest, secs, Bool.pick(U32, Int.I64.is_le(t, secs), k, cur))
1157	def Zone.last.go(ts: List<&2, Trans>, +secs: Int.I64, +last: Int.I64) -> Bool:
1158	  match ts:
1159	    case Nil{}:
1160	      Int.I64.is_gt(secs, last)
1161	    case Con{Trans{t, k}, rest}:
1162	      Zone.last.go(rest, secs, t)
1163	def Zone.last(ts: List<&2, Trans>, secs: Int.I64) -> Bool:
1164	  match ts:
1165	    case Nil{}:
1166	      True{}
1167	    case Con{Trans{t, k}, rest}:
1168	      Zone.last.go(rest, secs, t)
1169	
1170	
1171	def Zone.at.fallback(m: Maybe<&2, Ttype>, types: List<&2, Ttype>, ts: List<&2, Trans>, secs: Int.I64) -> Maybe<&2, Ttype>:
1172	  match m:
1173	    case Some{t}:
1174	      Some{t}
1175	    case None{}:
1176	      List.get(&2, Ttype, types, U32.to_nat(Zone.find(ts, secs, 0)))
1177	def Zone.at.footer(use: Bool, tz: String, types: List<&2, Ttype>, ts: List<&2, Trans>, +secs: Int.I64) -> Maybe<&2, Ttype>:
1178	  match use:
1179	    case False{}:
1180	      List.get(&2, Ttype, types, U32.to_nat(Zone.find(ts, secs, 0)))
1181	    case True{}:
1182	      Zone.at.fallback(tz.rule.lookup(tz.rule(tz), secs), types, ts, secs)
1183	
1184	def Zone.at.tz(empty: Bool, tz: String, types: List<&2, Ttype>, +ts: List<&2, Trans>, +secs: Int.I64) -> Maybe<&2, Ttype>:
1185	  match empty:
1186	    case True{}:
1187	      List.get(&2, Ttype, types, U32.to_nat(Zone.find(ts, secs, 0)))
1188	    case False{}:
1189	      Zone.at.footer(Zone.last(ts, secs), tz, types, ts, secs)
1190	
1191	
1192	
1193	# The local time type at i. The footer applies strictly after the final explicit transition.
1194	def Zone.at(z: Zone, i: Instant) -> Maybe<&2, Ttype>:
1195	  match z i:
1196	    case Zone{ts, types, +tz} Instant{s, n}:
1197	      Zone.at.tz(String.eq(tz, ""), tz, types, ts, s)
1198	
1199	def Zone.local.at(m: Maybe<&2, Ttype>, i: Instant) -> Maybe<&2, DateTime>:
1200	  match m:
1201	    case None{}:
1202	      None{}
1203	    case Some{Ttype{off, dst, abbr}}:
1204	      DateTime.of_instant(Instant.add(i, Duration.of_secs(off)))
1205	
1206	# The local date and time at i in zone z.
1207	def Zone.local(z: Zone, +i: Instant) -> Maybe<&2, DateTime>:
1208	  Zone.local.at(Zone.at(z, i), i)