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	import bend-kit-bytes@0.3.2.0/bytes.bend as Bytes
6	
7	# secs + nanos / 10^9 seconds, with nanos below 10^9: -0.5 s is Duration{-1, 500000000}.
8	type Duration is Data:
9	  Duration{secs: Int.I64, nanos: U32}
10	
11	# A Duration since 1970-01-01T00:00:00Z. Days are 86400 s: there are no leap seconds.
12	type Instant is Data:
13	  Instant{secs: Int.I64, nanos: U32}
14	
15	# A proleptic Gregorian date. The conversions and formats cover years 0 to 9999.
16	type Date is Data:
17	  Date{year: U32, month: U32, day: U32}
18	
19	type DateTime is Data:
20	  DateTime{date: Date, hour: U32, min: U32, sec: U32, nanos: U32}
21	
22	def i64(x: U32) -> Int.I64:
23	  Int.I64.from_u32(x)
24	
25	# The signed 32-bit value of x, widened.
26	def i64s(x: U32) -> Int.I64:
27	  match x:
28	    case U32{w}:
29	      Int.I64{Int.Int.sext(64n, 32n, w)}
30	
31	# hi * 2^32 + lo, as the bits of an I64.
32	def i64.of(hi: U32, lo: U32) -> Int.I64:
33	  Int.I64.or(Int.I64.shl(i64(hi), 32n), i64(lo))
34	
35	# Duration
36	# --------
37	
38	def Duration.zero() -> Duration:
39	  Duration{i64(0), 0}
40	
41	def Duration.of_secs(s: Int.I64) -> Duration:
42	  Duration{s, 0}
43	
44	def Duration.of_ms(+ms: U32) -> Duration:
45	  Duration{i64((ms / 1000 : U32)), ((ms % 1000 : U32) * 1000000 : U32)}
46	
47	# Whole milliseconds, rounded down.
48	def Duration.to_ms(d: Duration) -> Int.I64:
49	  match d:
50	    case Duration{s, n}:
51	      Int.I64.add(Int.I64.mul(s, i64(1000)), i64((n / 1000000 : U32)))
52	
53	def Duration.to_nat.of(m: Maybe<&2, Nat>, +per: Nat, +n: U32) -> Nat:
54	  match m:
55	    case None{}:
56	      0n
57	    case Some{s}:
58	      (s * per + U32.to_nat(n) : Nat)
59	
60	# Whole milliseconds, rounded down; 0 when d is negative.
61	def Duration.to_ms_nat(d: Duration) -> Nat:
62	  match d:
63	    case Duration{s, n}:
64	      Duration.to_nat.of(Int.I64.to_nat(s), 1000n, (n / 1000000 : U32))
65	
66	# Whole microseconds, rounded down; 0 when d is negative.
67	def Duration.to_us_nat(d: Duration) -> Nat:
68	  match d:
69	    case Duration{s, n}:
70	      Duration.to_nat.of(Int.I64.to_nat(s), 1000000n, (n / 1000 : U32))
71	
72	def Duration.carry(c: Bool, s: Int.I64, +n: U32) -> Duration:
73	  match c:
74	    case True{}:
75	      Duration{Int.I64.add(s, i64(1)), (n - 1000000000 : U32)}
76	    case False{}:
77	      Duration{s, n}
78	
79	def Duration.add(a: Duration, b: Duration) -> Duration:
80	  match a b:
81	    case Duration{sa, na} Duration{sb, nb}:
82	      +n = (na + nb : U32)
83	      Duration.carry(U32.is_ge(n, 1000000000), Int.I64.add(sa, sb), n)
84	
85	# n is na - nb, wrapped when na < nb.
86	def Duration.borrow(c: Bool, s: Int.I64, +n: U32) -> Duration:
87	  match c:
88	    case True{}:
89	      Duration{Int.I64.sub(s, i64(1)), (n + 1000000000 : U32)}
90	    case False{}:
91	      Duration{s, n}
92	
93	def Duration.sub(a: Duration, b: Duration) -> Duration:
94	  match a b:
95	    case Duration{sa, +na} Duration{sb, +nb}:
96	      Duration.borrow(U32.is_lt(na, nb), Int.I64.sub(sa, sb), (na - nb : U32))
97	
98	def Duration.neg(d: Duration) -> Duration:
99	  Duration.sub(Duration.zero(), d)
100	
101	def Duration.cmp.then(c: Cmp, +na: U32, +nb: U32) -> Cmp:
102	  match c:
103	    case EQ{}:
104	      U32.cmp(na, nb)
105	    case LT{}:
106	      LT{}
107	    case GT{}:
108	      GT{}
109	
110	def Duration.cmp(a: Duration, b: Duration) -> Cmp:
111	  match a b:
112	    case Duration{sa, na} Duration{sb, nb}:
113	      Duration.cmp.then(Int.I64.cmp(sa, sb), na, nb)
114	
115	# Instant
116	# -------
117	
118	def Instant.epoch() -> Instant:
119	  Instant{i64(0), 0}
120	
121	def Instant.of_unix(s: Int.I64) -> Instant:
122	  Instant{s, 0}
123	
124	def Instant.of(d: Duration) -> Instant:
125	  match d:
126	    case Duration{s, n}:
127	      Instant{s, n}
128	
129	def Instant.since_epoch(i: Instant) -> Duration:
130	  match i:
131	    case Instant{s, n}:
132	      Duration{s, n}
133	
134	def Instant.add(i: Instant, d: Duration) -> Instant:
135	  Instant.of(Duration.add(Instant.since_epoch(i), d))
136	
137	# a - b.
138	def Instant.since(a: Instant, b: Instant) -> Duration:
139	  Duration.sub(Instant.since_epoch(a), Instant.since_epoch(b))
140	
141	def Instant.cmp(a: Instant, b: Instant) -> Cmp:
142	  Duration.cmp(Instant.since_epoch(a), Instant.since_epoch(b))
143	
144	# Clocks
145	# ------
146	
147	# (secs hi, secs lo, nanos) of CLOCK_MONOTONIC, from an unspecified start.
148	def mono.raw() -> IO(U32 & U32 & U32):
149	  import "./effs/time.c"
150	  import "./effs/time.js"
151	
152	# (secs hi, secs lo, nanos) of CLOCK_REALTIME, since the Unix epoch.
153	def wall.raw() -> IO(U32 & U32 & U32):
154	  import "./effs/time.c"
155	  import "./effs/time.js"
156	
157	def raw.dur(r: U32 & U32 & U32) -> Duration:
158	  (hi, lo, n) = r
159	  Duration{i64.of(hi, lo), n}
160	
161	# Time since an unspecified start that never goes back. Use it to measure spans.
162	def mono() -> IO(Duration):
163	  do IO<Duration>:
164	    r : U32 & U32 & U32 <- mono.raw()
165	    return raw.dur(r)
166	
167	# Monotonic milliseconds. Pure cores that take a Nat `now` in ms take this.
168	def mono.ms() -> IO(Nat):
169	  do IO<Nat>:
170	    d : Duration <- mono()
171	    return Duration.to_ms_nat(d)
172	
173	# Monotonic microseconds.
174	def mono.us() -> IO(Nat):
175	  do IO<Nat>:
176	    d : Duration <- mono()
177	    return Duration.to_us_nat(d)
178	
179	# The wall clock. It can jump when the system time is set.
180	def now() -> IO(Instant):
181	  do IO<Instant>:
182	    r : U32 & U32 & U32 <- wall.raw()
183	    return Instant.of(raw.dur(r))
184	
185	# Dates
186	# -----
187	
188	def Date.is_leap(+y: U32) -> Bool:
189	  Bool.and(U32.is_eq((y % 4 : U32), 0),
190	    Bool.or(U32.is_ne((y % 100 : U32), 0), U32.is_eq((y % 400 : U32), 0)))
191	
192	# 0 for a month outside 1 to 12.
193	def Date.days_in_month(+y: U32, +m: U32) -> U32:
194	  Bool.pick(U32, U32.is_eq(m, 2), Bool.pick(U32, Date.is_leap(y), 29, 28),
195	    Bool.pick(U32, Bool.and(U32.is_ge(m, 1), U32.is_le(m, 12)),
196	      (30 + ((m + (m >> 3n)) .&. 1) : U32), 0))
197	
198	def Date.valid(d: Date) -> Bool:
199	  match d:
200	    case Date{+y, +m, +dd}:
201	      Bool.and(U32.is_le(y, 9999),
202	        Bool.and(U32.is_ge(dd, 1), U32.is_le(dd, Date.days_in_month(y, m))))
203	
204	# z counts days from -0400-03-01, so every date from year 0 has z > 0 in a U32.
205	# The civil-days algorithm is Howard Hinnant's, with the year starting in March.
206	def Z.EPOCH() -> U32:
207	  865565
208	
209	def Date.to_z.at(+y: U32, +mp: U32, +d: U32) -> U32:
210	  +era = (y / 400 : U32)
211	  +yoe = (y - era * 400 : U32)
212	  +doy = ((153 * mp + 2) / 5 + d - 1 : U32)
213	  (era * 146097 + yoe * 365 + yoe / 4 - yoe / 100 + doy : U32)
214	
215	def Date.to_z.go(jf: Bool, +y: U32, +m: U32, +d: U32) -> U32:
216	  match jf:
217	    case True{}:
218	      Date.to_z.at((y + 399 : U32), (m + 9 : U32), d)
219	    case False{}:
220	      Date.to_z.at((y + 400 : U32), (m - 3 : U32), d)
221	
222	def Date.to_z(d: Date) -> U32:
223	  match d:
224	    case Date{+y, +m, +dd}:
225	      Date.to_z.go(U32.is_le(m, 2), y, m, dd)
226	
227	def Date.of_z.fin(lo: Bool, +y: U32, +mp: U32, +d: U32) -> Date:
228	  match lo:
229	    case True{}:
230	      Date{(y - 400 : U32), (mp + 3 : U32), d}
231	    case False{}:
232	      Date{(y - 399 : U32), (mp - 9 : U32), d}
233	
234	def Date.of_z(+z: U32) -> Date:
235	  +era = (z / 146097 : U32)
236	  +doe = (z - era * 146097 : U32)
237	  +yoe = ((doe - doe / 1460 + doe / 36524 - doe / 146096) / 365 : U32)
238	  +doy = (doe - (365 * yoe + yoe / 4 - yoe / 100) : U32)
239	  +mp = ((5 * doy + 2) / 153 : U32)
240	  Date.of_z.fin(U32.is_lt(mp, 10), (yoe + era * 400 : U32), mp,
241	    (doy - (153 * mp + 2) / 5 + 1 : U32))
242	
243	# Days since 1970-01-01.
244	def Date.to_days(d: Date) -> Int.I64:
245	  Int.I64.sub(i64(Date.to_z(d)), i64(Z.EPOCH()))
246	
247	def Date.of_z.if(ok: Bool, +z: U32) -> Maybe<&2, Date>:
248	  match ok:
249	    case True{}:
250	      Some{Date.of_z(z)}
251	    case False{}:
252	      None{}
253	
254	# The date days after 1970-01-01, or None outside 0000-01-01 to 9999-12-31.
255	def Date.of_days(days: Int.I64) -> Maybe<&2, Date>:
256	  +z = Int.I64.add(days, i64(Z.EPOCH()))
257	  Date.of_z.if(Bool.and(Int.I64.is_ge(z, i64(146037)), Int.I64.is_le(z, i64(3798461))),
258	    Int.I64.to_u32(z))
259	
260	# 1 for Monday to 7 for Sunday, as in ISO 8601.
261	def Date.weekday(d: Date) -> U32:
262	  ((Date.to_z(d) + 2) % 7 + 1 : U32)
263	
264	# Date and time
265	# -------------
266	
267	def DateTime.valid(t: DateTime) -> Bool:
268	  match t:
269	    case DateTime{d, h, mi, s, n}:
270	      Bool.and(Date.valid(d), Bool.and(U32.is_le(h, 23),
271	        Bool.and(U32.is_le(mi, 59), Bool.and(U32.is_le(s, 59), U32.is_lt(n, 1000000000)))))
272	
273	# The instant of a UTC date and time. It does not check t; see DateTime.valid.
274	def DateTime.to_instant(t: DateTime) -> Instant:
275	  match t:
276	    case DateTime{d, h, mi, s, n}:
277	      Instant{Int.I64.add(Int.I64.mul(Date.to_days(d), i64(86400)),
278	        i64((h * 3600 + mi * 60 + s : U32))), n}
279	
280	def DateTime.at(m: Maybe<&2, Date>, +sod: U32, n: U32) -> Maybe<&2, DateTime>:
281	  match m:
282	    case None{}:
283	      None{}
284	    case Some{d}:
285	      Some{DateTime{d, (sod / 3600 : U32), (sod / 60 % 60 : U32), (sod % 60 : U32), n}}
286	
287	# r is secs % 86400, which has the sign of secs.
288	def DateTime.floor(neg: Bool, q: Int.I64, r: Int.I64, n: U32) -> Maybe<&2, DateTime>:
289	  match neg:
290	    case True{}:
291	      DateTime.at(Date.of_days(Int.I64.sub(q, i64(1))), (Int.I64.to_u32(r) + 86400 : U32), n)
292	    case False{}:
293	      DateTime.at(Date.of_days(q), Int.I64.to_u32(r), n)
294	
295	# The UTC date and time of i, or None outside years 0 to 9999.
296	def DateTime.of_instant(i: Instant) -> Maybe<&2, DateTime>:
297	  match i:
298	    case Instant{+s, n}:
299	      +r = Int.I64.mod(s, i64(86400))
300	      DateTime.floor(Int.I64.is_neg(r), Int.I64.div(s, i64(86400)), r, n)
301	
302	# Text
303	# ----
304	
305	def pad(+x: U32, w: Nat) -> String:
306	  Fmt.Fmt.pad_left(U32.show(x), w, '0')
307	
308	# Milliseconds with six decimal places.
309	def Duration.show_ms.pos(d: Duration) -> String:
310	  match d:
311	    case Duration{s, +n}:
312	      Int.I64.show(Duration.to_ms(Duration{s, n})) ++ "." ++ pad((n % 1000000 : U32), 6n)
313	
314	def Duration.show_ms.sign(neg: Bool, d: Duration) -> String:
315	  match neg:
316	    case True{}:
317	      "-" ++ Duration.show_ms.pos(Duration.neg(d))
318	    case False{}:
319	      Duration.show_ms.pos(d)
320	
321	def Duration.show_ms(d: Duration) -> String:
322	  match d:
323	    case Duration{+s, n}:
324	      Duration.show_ms.sign(Int.I64.is_neg(s), Duration{s, n})
325	
326	# The digits of n / 10^(9 - w), with trailing zeros cut. n is not 0.
327	def frac.go(f: Nat, z: Bool, +n: U32, +w: Nat) -> String:
328	  match f:
329	    case 0n:
330	      pad(n, w)
331	    case 1n+g:
332	      match z:
333	        case True{}:
334	          +m = (n / 10 : U32)
335	          frac.go(g, U32.is_eq((m % 10 : U32), 0), m, (w - 1n : Nat))
336	        case False{}:
337	          pad(n, w)
338	
339	def frac(+n: U32) -> String:
340	  Bool.pick(String, U32.is_eq(n, 0), "", SCon{'.', frac.go(8n, U32.is_eq((n % 10 : U32), 0), n, 9n)})
341	
342	def DateTime.rfc3339(t: DateTime) -> String:
343	  match t:
344	    case DateTime{Date{y, mo, d}, h, mi, s, n}:
345	      String.concat([pad(y, 4n), "-", pad(mo, 2n), "-", pad(d, 2n), "T", pad(h, 2n), ":",
346	        pad(mi, 2n), ":", pad(s, 2n), frac(n), "Z"])
347	
348	def fmt.map(~f: DateTime -> String, m: Maybe<&2, DateTime>) -> Maybe<&2, String>:
349	  match m:
350	    case None{}:
351	      None{}
352	    case Some{t}:
353	      Some{f(t)}
354	
355	# RFC 3339 in UTC, such as 1985-04-12T23:20:50.52Z. The fraction has no trailing zeros, and is left out when 0.
356	def rfc3339(i: Instant) -> Maybe<&2, String>:
357	  fmt.map(~DateTime.rfc3339, DateTime.of_instant(i))
358	
359	def WEEKDAYS() -> List<&2, String>:
360	  ["Mon", "Tue", "Wed", "Thu", "Fri", "Sat", "Sun"]
361	
362	def MONTHS() -> List<&2, String>:
363	  ["Jan", "Feb", "Mar", "Apr", "May", "Jun", "Jul", "Aug", "Sep", "Oct", "Nov", "Dec"]
364	
365	def name(xs: List<&2, String>, +i: U32) -> String:
366	  Maybe.default(&2, String, List.get(&2, String, xs, U32.to_nat(i)), "")
367	
368	def DateTime.http_date(t: DateTime) -> String:
369	  match t:
370	    case DateTime{+date, h, mi, s, n}:
371	      Date{y, mo, d} = date
372	      String.concat([name(WEEKDAYS(), (Date.weekday(date) - 1 : U32)), ", ", pad(d, 2n), " ",
373	        name(MONTHS(), (mo - 1 : U32)), " ", pad(y, 4n), " ", pad(h, 2n), ":", pad(mi, 2n), ":",
374	        pad(s, 2n), " GMT"])
375	
376	# IMF-fixdate (RFC 9110 §5.6.7), such as Sun, 06 Nov 1994 08:49:37 GMT. It drops the fraction of a second.
377	def http_date(i: Instant) -> Maybe<&2, String>:
378	  fmt.map(~DateTime.http_date, DateTime.of_instant(i))
379	
380	# Parsers
381	# -------
382	
383	# A parser state: the numbers read so far, newest first, and the text left.
384	type P is Data:
385	  P{vals: List<&2, U32>, rest: String}
386	
387	def is_digit(+c: U32) -> Bool:
388	  Bool.and(U32.is_ge(c, 48), U32.is_le(c, 57))
389	
390	def digits.go(n: Nat, s: String, +acc: U32, ok: Bool) -> Maybe<&1, U32 & String>:
391	  match n:
392	    case 0n:
393	      match ok:
394	        case True{}:
395	          Some{(acc, s)}
396	        case False{}:
397	          None{}
398	    case 1n+k:
399	      match s:
400	        case SNil{}:
401	          None{}
402	        case SCon{Chr{+c}, t}:
403	          digits.go(k, t, (acc * 10 + c - 48 : U32), Bool.and(ok, is_digit(c)))
404	
405	def push(vs: List<&2, U32>, r: Maybe<&1, U32 & String>) -> Maybe<&2, P>:
406	  match r:
407	    case None{}:
408	      None{}
409	    case Some{(v, t)}:
410	      Some{P{Con{v, vs}, t}}
411	
412	# Exactly n digits.
413	def num(n: Nat, p: P) -> Maybe<&2, P>:
414	  match p:
415	    case P{vs, s}:
416	      push(vs, digits.go(n, s, 0, True{}))
417	
418	def lit.if(ok: Bool, vs: List<&2, U32>, t: String) -> Maybe<&2, P>:
419	  match ok:
420	    case True{}:
421	      Some{P{vs, t}}
422	    case False{}:
423	      None{}
424	
425	# One char that is a or b.
426	def lit2(+a: U32, +b: U32, p: P) -> Maybe<&2, P>:
427	  match p:
428	    case P{vs, s}:
429	      match s:
430	        case SNil{}:
431	          None{}
432	        case SCon{Chr{+c}, t}:
433	          lit.if(Bool.or(U32.is_eq(c, a), U32.is_eq(c, b)), vs, t)
434	
435	def lit(+c: U32, p: P) -> Maybe<&2, P>:
436	  lit2(c, c, p)
437	
438	def text(+w: String, p: P) -> Maybe<&2, P>:
439	  match p:
440	    case P{vs, +s}:
441	      +n = String.length(w)
442	      lit.if(String.eq(String.take(s, n), w), vs, String.drop(s, n))
443	
444	def at.head(+s: String) -> Bool:
445	  match s:
446	    case SNil{}:
447	      False{}
448	    case SCon{Chr{+c}, t}:
449	      is_digit(c)
450	
451	# Digits after the first nine are read and dropped. d says whether s starts with a digit.
452	def secfrac.go(s: String, d: Bool, +mul: U32, +acc: U32, +k: U32) -> U32 & U32 & String:
453	  match s:
454	    case SNil{}:
455	      (k, acc, SNil{})
456	    case SCon{Chr{+c}, +t}:
457	      match d:
458	        case True{}:
459	          secfrac.go(t, at.head(t), (mul / 10 : U32), (acc + (c - 48) * mul : U32), (k + 1 : U32))
460	        case False{}:
461	          (k, acc, SCon{Chr{c}, t})
462	
463	def secfrac.fin(vs: List<&2, U32>, r: U32 & U32 & String) -> Maybe<&2, P>:
464	  (k, n, t) = r
465	  lit.if(U32.is_gt(k, 0), Con{n, vs}, t)
466	
467	def secfrac.if(dot: Bool, vs: List<&2, U32>, +s: String) -> Maybe<&2, P>:
468	  match dot:
469	    case True{}:
470	      +t = String.drop(s, 1n)
471	      secfrac.fin(vs, secfrac.go(t, at.head(t), 100000000, 0, 0))
472	    case False{}:
473	      Some{P{Con{0, vs}, s}}
474	
475	# An optional '.' and one or more digits, as nanoseconds.
476	def secfrac(p: P) -> Maybe<&2, P>:
477	  match p:
478	    case P{vs, +s}:
479	      secfrac.if(String.starts_with(s, "."), vs, s)
480	
481	def zone.num(+neg: U32, vs: List<&2, U32>, t: String) -> Maybe<&2, P>:
482	  do Maybe<&2, P>:
483	    a : P <- num(2n, P{Con{neg, vs}, t})
484	    b : P <- lit(58, a)
485	    num(2n, b)
486	
487	def zone.if(z: Bool, plus: Bool, minus: Bool, vs: List<&2, U32>, t: String) -> Maybe<&2, P>:
488	  match z:
489	    case True{}:
490	      Some{P{Con{0, Con{0, Con{0, vs}}}, t}}
491	    case False{}:
492	      match plus:
493	        case True{}:
494	          zone.num(0, vs, t)
495	        case False{}:
496	          match minus:
497	            case True{}:
498	              zone.num(1, vs, t)
499	            case False{}:
500	              None{}
501	
502	# Z, or +hh:mm or -hh:mm, as (sign, hh, mm) with sign 1 for west of UTC.
503	def zone(p: P) -> Maybe<&2, P>:
504	  match p:
505	    case P{vs, s}:
506	      match s:
507	        case SNil{}:
508	          None{}
509	        case SCon{Chr{+c}, t}:
510	          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)
511	
512	def index.go(xs: List<&2, String>, +w: String, +i: U32) -> U32:
513	  match xs:
514	    case Nil{}:
515	      i
516	    case Con{x, rest}:
517	      Bool.pick(U32, String.eq(x, w), i, index.go(rest, w, (i + 1 : U32)))
518	
519	# One of names, as its index.
520	def word(+names: List<&2, String>, p: P) -> Maybe<&2, P>:
521	  match p:
522	    case P{vs, +s}:
523	      +i = index.go(names, String.take(s, 3n), 0)
524	      lit.if(U32.is_lt(i, U32.from_nat(List.length(&2, String, names))), Con{i, vs}, String.drop(s, 3n))
525	
526	def mk.if(ok: Bool, t: DateTime) -> Maybe<&2, Instant>:
527	  match ok:
528	    case True{}:
529	      Some{DateTime.to_instant(t)}
530	    case False{}:
531	      None{}
532	
533	def mk(+t: DateTime) -> Maybe<&2, Instant>:
534	  mk.if(DateTime.valid(t), t)
535	
536	def rfc3339.shift(m: Maybe<&2, Instant>, +west: U32, +hh: U32, +mm: U32) -> Maybe<&2, Instant>:
537	  match m:
538	    case None{}:
539	      None{}
540	    case Some{i}:
541	      +off = Duration.of_secs(i64((hh * 3600 + mm * 60 : U32)))
542	      Bool.pick(Maybe<&2, Instant>, Bool.and(U32.is_le(hh, 23), U32.is_le(mm, 59)),
543	        Some{Instant.add(i, Bool.pick(Duration, U32.is_eq(west, 1), off, Duration.neg(off)))}, None{})
544	
545	def rfc3339.fin(p: P) -> Maybe<&2, Instant>:
546	  match p:
547	    case P{Con{mm, Con{hh, Con{west, Con{n, Con{s, Con{mi, Con{h, Con{d, Con{mo, Con{y, Nil{}}}}}}}}}}}, SNil{}}:
548	      rfc3339.shift(mk(DateTime{Date{y, mo, d}, h, mi, s, n}), west, hh, mm)
549	    case _:
550	      None{}
551	
552	# An RFC 3339 date-time (§5.6), such as 1985-04-12T23:20:50.52Z or 1996-12-19T16:39:57-08:00.
553	# T and Z may be lowercase. A leap second (:60) is refused, as Instant has none.
554	def rfc3339.parse(s: String) -> Maybe<&2, Instant>:
555	  do Maybe<&2, Instant>:
556	    a : P <- num(4n, P{Nil{}, s})
557	    b : P <- lit(45, a)
558	    c : P <- num(2n, b)
559	    d : P <- lit(45, c)
560	    e : P <- num(2n, d)
561	    f : P <- lit2(84, 116, e)
562	    g : P <- num(2n, f)
563	    h : P <- lit(58, g)
564	    i : P <- num(2n, h)
565	    j : P <- lit(58, i)
566	    k : P <- num(2n, j)
567	    l : P <- secfrac(k)
568	    m : P <- zone(l)
569	    rfc3339.fin(m)
570	
571	def http_date.fin(p: P) -> Maybe<&2, Instant>:
572	  match p:
573	    case P{Con{s, Con{mi, Con{h, Con{y, Con{mo, Con{d, Con{wd, Nil{}}}}}}}}, SNil{}}:
574	      mk(DateTime{Date{y, (mo + 1 : U32), d}, h, mi, s, 0})
575	    case _:
576	      None{}
577	
578	# An IMF-fixdate (RFC 9110 §5.6.7), such as Sun, 06 Nov 1994 08:49:37 GMT.
579	# The day name must be one of the seven, but it is not checked against the date.
580	def http_date.parse(s: String) -> Maybe<&2, Instant>:
581	  do Maybe<&2, Instant>:
582	    a : P <- word(WEEKDAYS(), P{Nil{}, s})
583	    b : P <- text(", ", a)
584	    c : P <- num(2n, b)
585	    d : P <- lit(32, c)
586	    e : P <- word(MONTHS(), d)
587	    f : P <- lit(32, e)
588	    g : P <- num(4n, f)
589	    h : P <- lit(32, g)
590	    i : P <- num(2n, h)
591	    j : P <- lit(58, i)
592	    k : P <- num(2n, j)
593	    l : P <- lit(58, k)
594	    m : P <- num(2n, l)
595	    n : P <- text(" GMT", m)
596	    http_date.fin(n)
597	
598	# Time zones
599	# ----------
600	
601	# A local time type: seconds east of UTC, whether it is daylight time, and its abbreviation.
602	type Ttype is Data:
603	  Ttype{utoff: Int.I64, dst: Bool, abbr: String}
604	
605	# From at on, local time follows types[idx].
606	type Trans is Data:
607	  Trans{at: Int.I64, idx: U32}
608	
609	# A TZif zone (RFC 8536): transitions in time order, local time types, and the footer TZ string ("" in version 1).
610	type Zone is Data:
611	  Zone{trans: List<&2, Trans>, types: List<&2, Ttype>, tz: String}
612	
613	# n bytes of a byte string, big-endian.
614	def be(n: Nat, s: String, +acc: U32) -> U32:
615	  match n:
616	    case 0n:
617	      acc
618	    case 1n+k:
619	      match s:
620	        case SNil{}:
621	          acc
622	        case SCon{Chr{c}, t}:
623	          be(k, t, ((acc << 8n) .|. c : U32))
624	
625	def be32(+s: String, n: Nat) -> U32:
626	  be(4n, String.drop(s, n), 0)
627	
628	def u8(+s: String, n: Nat) -> U32:
629	  be(1n, String.drop(s, n), 0)
630	
631	def tzif.size(t8: Bool) -> Nat:
632	  match t8:
633	    case True{}:
634	      8n
635	    case False{}:
636	      4n
637	
638	def tzif.time(t8: Bool, +s: String) -> Int.I64:
639	  match t8:
640	    case True{}:
641	      i64.of(be32(s, 0n), be32(s, 4n))
642	    case False{}:
643	      i64s(be32(s, 0n))
644	
645	# ts holds the transition times and ks their type indexes.
646	def tzif.trans(n: Nat, +t8: Bool, +ts: String, +ks: String) -> List<&2, Trans>:
647	  match n:
648	    case 0n:
649	      Nil{}
650	    case 1n+k:
651	      Con{Trans{tzif.time(t8, ts), u8(ks, 0n)},
652	        tzif.trans(k, t8, String.drop(ts, tzif.size(t8)), String.drop(ks, 1n))}
653	
654	# The NUL-terminated abbreviation at byte i of chars.
655	def tzif.abbr(chars: String, +i: U32) -> String:
656	  name(String.split(String.drop(chars, U32.to_nat(i)), Chr{0}), 0)
657	
658	def tzif.types(n: Nat, +s: String, +chars: String) -> List<&2, Ttype>:
659	  match n:
660	    case 0n:
661	      Nil{}
662	    case 1n+k:
663	      Con{Ttype{i64s(be32(s, 0n)), U32.is_ne(u8(s, 4n), 0), tzif.abbr(chars, u8(s, 5n))},
664	        tzif.types(k, String.drop(s, 6n), chars)}
665	
666	def tzif.if(ok: Bool, z: Zone) -> Maybe<&2, Zone>:
667	  match ok:
668	    case True{}:
669	      Some{z}
670	    case False{}:
671	      None{}
672	
673	# Header counts, in RFC 8536 order: isut, isstd, leap, time, type, char.
674	def tzif.count(+h: String, i: Nat) -> Nat:
675	  U32.to_nat(be32(h, (20n + 4n * i : Nat)))
676	
677	# The data block's size in bytes, for header h.
678	def tzif.bsize(+t8: Bool, +h: String) -> Nat:
679	  +tc = tzif.count(h, 3n)
680	  (tc * tzif.size(t8) + tc + tzif.count(h, 4n) * 6n + tzif.count(h, 5n) +
681	    tzif.count(h, 2n) * (tzif.size(t8) + 4n) + tzif.count(h, 1n) + tzif.count(h, 0n) : Nat)
682	
683	# h starts at a header; its data block follows it. Version 2+ blocks have 8-byte times and a footer.
684	def tzif.block(+t8: Bool, +h: String) -> Maybe<&2, Zone>:
685	  +d = String.drop(h, 44n)
686	  +tc = tzif.count(h, 3n)
687	  +ty = tzif.count(h, 4n)
688	  +at = (tc * tzif.size(t8) + tc : Nat)
689	  +foot = String.drop(d, tzif.bsize(t8, h))
690	  tzif.if(Bool.and(String.starts_with(h, "TZif"), Bool.and(Nat.is_gt(ty, 0n),
691	      Nat.is_le((44n + tzif.bsize(t8, h) : Nat), String.length(h)))),
692	    Zone{tzif.trans(tc, t8, d, String.drop(d, (tc * tzif.size(t8) : Nat))),
693	      tzif.types(ty, String.drop(d, at), String.take(String.drop(d, (at + ty * 6n : Nat)), tzif.count(h, 5n))),
694	      Bool.pick(String, t8, name(String.split(foot, '\n'), 1), "")})
695	
696	def tzif.go(v2: Bool, +s: String) -> Maybe<&2, Zone>:
697	  match v2:
698	    case True{}:
699	      tzif.block(True{}, String.drop(s, (44n + tzif.bsize(False{}, s) : Nat)))
700	    case False{}:
701	      tzif.block(False{}, s)
702	
703	# A TZif file, such as one from /usr/share/zoneinfo. Versions 2 and up use their 64-bit block.
704	# ponytail: reads the bytes as a byte String; walk Bytes directly if zone files get big.
705	def tzif.parse(b: Bytes.Bytes) -> Maybe<&2, Zone>:
706	  +s = Bytes.to_string(b)
707	  tzif.go(U32.is_ge(u8(s, 4n), 50), s)
708	
709	# POSIX TZ offsets are seconds west of UTC; transition times are seconds from local midnight.
710	type TzField is Data:
711	  TzField{value: U32, rest: String}
712	
713	type TzText is Data:
714	  TzText{value: String, rest: String}
715	
716	type TzClock is Data:
717	  TzClock{value: Int.I64, rest: String}
718	
719	type TzDay is Data:
720	  Julian{day: U32}
721	  Ordinal{day: U32}
722	  MonthWeek{month: U32, week: U32, weekday: U32}
723	
724	type TzDate is Data:
725	  TzDate{day: TzDay, seconds: Int.I64}
726	
727	type TzDayPart is Data:
728	  TzDayPart{day: TzDay, rest: String}
729	
730	type TzDatePart is Data:
731	  TzDatePart{date: TzDate, rest: String}
732	
733	type TzRule is Data:
734	  TzRule{std: Ttype, daylight: Ttype, start: TzDate, end: TzDate}
735	
736	def tz.digit(+c: U32) -> Bool:
737	  Bool.and(U32.is_ge(c, 48), U32.is_le(c, 57))
738	
739	def tz.alpha(+c: U32) -> Bool:
740	  Bool.or(Bool.and(U32.is_ge(c, 65), U32.is_le(c, 90)),
741	    Bool.and(U32.is_ge(c, 97), U32.is_le(c, 122)))
742	
743	def tz.quoted(+c: U32) -> Bool:
744	  Bool.or(tz.alpha(c), Bool.or(tz.digit(c), Bool.or(U32.is_eq(c, 43), U32.is_eq(c, 45))))
745	
746	def tz.number.stop(seen: Bool, acc: U32, s: String) -> Maybe<&2, TzField>:
747	  match seen:
748	    case True{}:
749	      Some{TzField{acc, s}}
750	    case False{}:
751	      None{}
752	
753	def tz.number.step(digit: Bool, c: U32, t: String, acc: U32, seen: Bool, next: Unit -> Maybe<&2, TzField>) -> Maybe<&2, TzField>:
754	  match digit:
755	    case True{}:
756	      next(Unit{})
757	    case False{}:
758	      tz.number.stop(seen, acc, SCon{Chr{c}, t})
759	
760	# Three digits suffice for POSIX hour, day, and month fields.
761	def tz.number.go(s: String, +acc: U32, +seen: Bool) -> Maybe<&2, TzField>:
762	  match s:
763	    case SNil{}:
764	      tz.number.stop(seen, acc, SNil{})
765	    case SCon{Chr{+c}, +t}:
766	      tz.number.step(Bool.and(tz.digit(c), U32.is_lt(acc, 100)),
767	        c, t, acc, seen, _ => tz.number.go(t, ((acc * 10 + c - 48) : U32), True{}))
768	
769	def tz.number(s: String) -> Maybe<&2, TzField>:
770	  tz.number.go(s, 0, False{})
771	
772	def tz.name.valid(ok: Bool, name: String, rest: String) -> Maybe<&2, TzText>:
773	  match ok:
774	    case True{}:
775	      Some{TzText{name, rest}}
776	    case False{}:
777	      None{}
778	
779	def tz.name.done(rev: String, rest: String) -> Maybe<&2, TzText>:
780	  +name = String.reverse(rev)
781	  tz.name.valid(Nat.is_ge(String.length(name), 3n), name, rest)
782	
783	def tz.name.empty(quoted: Bool, rev: String) -> Maybe<&2, TzText>:
784	  match quoted:
785	    case True{}:
786	      None{}
787	    case False{}:
788	      tz.name.done(rev, SNil{})
789	
790	def tz.name.branch(continue: Bool, rev: String, c: U32, rest: String, next: Unit -> Maybe<&2, TzText>) -> Maybe<&2, TzText>:
791	  match continue:
792	    case True{}:
793	      next(Unit{})
794	    case False{}:
795	      tz.name.done(rev, SCon{Chr{c}, rest})
796	
797	def tz.name.allowed(ok: Bool, next: Unit -> Maybe<&2, TzText>) -> Maybe<&2, TzText>:
798	  match ok:
799	    case True{}:
800	      next(Unit{})
801	    case False{}:
802	      None{}
803	
804	def tz.name.quoted(end: Bool, valid: Bool, rev: String, rest: String, next: Unit -> Maybe<&2, TzText>) -> Maybe<&2, TzText>:
805	  match end:
806	    case True{}:
807	      tz.name.done(rev, rest)
808	    case False{}:
809	      tz.name.allowed(valid, next)
810	
811	def tz.name.char(quoted: Bool, end: Bool, alpha: Bool, valid: Bool, rev: String, c: U32, rest: String,
812	  next: Unit -> Maybe<&2, TzText>) -> Maybe<&2, TzText>:
813	  match quoted:
814	    case True{}:
815	      tz.name.quoted(end, valid, rev, rest, next)
816	    case False{}:
817	      tz.name.branch(alpha, rev, c, rest, next)
818	
819	def tz.name.go(s: String, +rev: String, +quoted: Bool) -> Maybe<&2, TzText>:
820	  match s:
821	    case SNil{}:
822	      tz.name.empty(quoted, rev)
823	    case SCon{Chr{+c}, +t}:
824	      tz.name.char(quoted, U32.is_eq(c, 62), tz.alpha(c), tz.quoted(c), rev, c, t,
825	        _ => tz.name.go(t, SCon{Chr{c}, rev}, quoted))
826	
827	def tz.name(s: String) -> Maybe<&2, TzText>:
828	  match s:
829	    case SCon{Chr{60}, t}:
830	      tz.name.go(t, SNil{}, True{})
831	    case _:
832	      tz.name.go(s, SNil{}, False{})
833	
834	def tz.field.valid(ok: Bool, n: U32, rest: String) -> Maybe<&2, TzField>:
835	  match ok:
836	    case True{}:
837	      Some{TzField{n, rest}}
838	    case False{}:
839	      None{}
840	
841	def tz.clock.tail(r: TzField, limit: U32) -> Maybe<&2, TzField>:
842	  match r:
843	    case TzField{+n, rest}:
844	      tz.field.valid(U32.is_le(n, limit), n, rest)
845	
846	def tz.clock.part(s: String) -> Maybe<&2, TzField>:
847	  match s:
848	    case SCon{Chr{58}, t}:
849	      do Maybe<&2, TzField>:
850	        n : TzField <- tz.number(t)
851	        tz.clock.tail(n, 59)
852	    case _:
853	      Some{TzField{0, s}}
854	
855	def tz.clock.valid(ok: Bool, +value: Int.I64, negative: Bool, rest: String) -> Maybe<&2, TzClock>:
856	  match ok:
857	    case False{}:
858	      None{}
859	    case True{}:
860	      Some{TzClock{Bool.pick(Int.I64, negative, Int.I64.neg(value), value), rest}}
861	
862	def tz.clock.seconds(sec: TzField, +hours: U32, +minutes: U32, +max: U32, negative: Bool) -> Maybe<&2, TzClock>:
863	  match sec:
864	    case TzField{+seconds, rest}:
865	      tz.clock.valid(U32.is_le(hours, max),
866	        i64((hours * 3600 + minutes * 60 + seconds : U32)), negative, rest)
867	
868	def tz.clock.minutes(m: TzField, +hours: U32, +max: U32, +negative: Bool) -> Maybe<&2, TzClock>:
869	  match m:
870	    case TzField{+minutes, rest}:
871	      do Maybe<&2, TzClock>:
872	        sec : TzField <- tz.clock.part(rest)
873	        tz.clock.seconds(sec, hours, minutes, max, negative)
874	def tz.clock.finish(h: TzField, +max: U32, +negative: Bool) -> Maybe<&2, TzClock>:
875	  match h:
876	    case TzField{+hours, rest}:
877	      do Maybe<&2, TzClock>:
878	        m : TzField <- tz.clock.part(rest)
879	        tz.clock.minutes(m, hours, max, negative)
880	
881	
882	def tz.clock.read(s: String, max: U32, negative: Bool) -> Maybe<&2, TzClock>:
883	  do Maybe<&2, TzClock>:
884	    h : TzField <- tz.number(s)
885	    tz.clock.finish(h, max, negative)
886	def tz.clock.sign(s: String, max: U32) -> Maybe<&2, TzClock>:
887	  match s:
888	    case SCon{Chr{45}, t}:
889	      tz.clock.read(t, max, True{})
890	    case SCon{Chr{43}, t}:
891	      tz.clock.read(t, max, False{})
892	    case _:
893	      tz.clock.read(s, max, False{})
894	
895	
896	def tz.day.valid(ok: Bool, d: TzDay, rest: String) -> Maybe<&2, TzDayPart>:
897	  match ok:
898	    case True{}:
899	      Some{TzDayPart{d, rest}}
900	    case False{}:
901	      None{}
902	
903	def tz.day.j(r: TzField) -> Maybe<&2, TzDayPart>:
904	  match r:
905	    case TzField{+n, rest}:
906	      tz.day.valid(Bool.and(U32.is_ge(n, 1), U32.is_le(n, 365)), Julian{n}, rest)
907	
908	def tz.day.n(r: TzField) -> Maybe<&2, TzDayPart>:
909	  match r:
910	    case TzField{+n, rest}:
911	      tz.day.valid(U32.is_le(n, 365), Ordinal{n}, rest)
912	
913	def tz.after(c: Char, s: String) -> String:
914	  match s:
915	    case SCon{h, t}:
916	      Bool.pick(String, Char.is_eq(h, c), t, SNil{})
917	    case SNil{}:
918	      SNil{}
919	
920	def tz.day.weekday(c: TzField, +month: U32, +week: U32) -> Maybe<&2, TzDayPart>:
921	  match c:
922	    case TzField{+weekday, rest}:
923	      tz.day.valid(Bool.and(U32.is_ge(month, 1), Bool.and(U32.is_le(month, 12),
924	        Bool.and(U32.is_ge(week, 1), Bool.and(U32.is_le(week, 5), U32.is_le(weekday, 6))))),
925	        MonthWeek{month, week, weekday}, rest)
926	
927	def tz.day.week(b: TzField, month: U32) -> Maybe<&2, TzDayPart>:
928	  match b:
929	    case TzField{week, rest}:
930	      do Maybe<&2, TzDayPart>:
931	        c : TzField <- tz.number(tz.after('.', rest))
932	        tz.day.weekday(c, month, week)
933	
934	def tz.day.month(a: TzField) -> Maybe<&2, TzDayPart>:
935	  match a:
936	    case TzField{month, rest}:
937	      do Maybe<&2, TzDayPart>:
938	        b : TzField <- tz.number(tz.after('.', rest))
939	        tz.day.week(b, month)
940	
941	def tz.day.m(s: String) -> Maybe<&2, TzDayPart>:
942	  do Maybe<&2, TzDayPart>:
943	    a : TzField <- tz.number(s)
944	    tz.day.month(a)
945	
946	def tz.day(s: String) -> Maybe<&2, TzDayPart>:
947	  match s:
948	    case SCon{Chr{74}, t}:
949	      do Maybe<&2, TzDayPart>:
950	        n : TzField <- tz.number(t)
951	        tz.day.j(n)
952	    case SCon{Chr{77}, t}:
953	      tz.day.m(t)
954	    case _:
955	      do Maybe<&2, TzDayPart>:
956	        n : TzField <- tz.number(s)
957	        tz.day.n(n)
958	
959	def tz.date.clock(d: TzDay, r: TzClock) -> Maybe<&2, TzDatePart>:
960	  match r:
961	    case TzClock{secs, end}:
962	      Some{TzDatePart{TzDate{d, secs}, end}}
963	
964	def tz.date.time(d: TzDay, rest: String) -> Maybe<&2, TzDatePart>:
965	  match rest:
966	    case SCon{Chr{47}, t}:
967	      do Maybe<&2, TzDatePart>:
968	        r : TzClock <- tz.clock.sign(t, 167)
969	        tz.date.clock(d, r)
970	    case _:
971	      Some{TzDatePart{TzDate{d, i64(7200)}, rest}}
972	
973	def tz.date.part(r: TzDayPart) -> Maybe<&2, TzDatePart>:
974	  match r:
975	    case TzDayPart{d, rest}:
976	      tz.date.time(d, rest)
977	
978	def tz.date(s: String) -> Maybe<&2, TzDatePart>:
979	  do Maybe<&2, TzDatePart>:
980	    r : TzDayPart <- tz.day(s)
981	    tz.date.part(r)
982	
983	def tz.rule.end(ok: Bool, standard: Ttype, daylight: Ttype, start: TzDate, end: TzDate) -> Maybe<&2, TzRule>:
984	  match ok:
985	    case True{}:
986	      Some{TzRule{standard, daylight, start, end}}
987	    case False{}:
988	      None{}
989	
990	def tz.rule.finish(b: TzDatePart, standard: Ttype, daylight: Ttype, start: TzDate) -> Maybe<&2, TzRule>:
991	  match b:
992	    case TzDatePart{end, rest}:
993	      tz.rule.end(String.is_empty(rest), standard, daylight, start, end)
994	
995	def tz.rule.start(a: TzDatePart, +standard: Ttype, +daylight: Ttype) -> Maybe<&2, TzRule>:
996	  match a:
997	    case TzDatePart{start, rest}:
998	      do Maybe<&2, TzRule>:
999	        b : TzDatePart <- tz.date(tz.after(',', rest))
1000	        tz.rule.finish(b, standard, daylight, start)
1001	
1002	def tz.rule.dates(+standard: Ttype, +daylight: Ttype, rest: String) -> Maybe<&2, TzRule>:
1003	  do Maybe<&2, TzRule>:
1004	    a : TzDatePart <- tz.date(tz.after(',', rest))
1005	    tz.rule.start(a, standard, daylight)
1006	
1007	def tz.rule.dstclock(r: TzClock, standard: Ttype, abbr: String) -> Maybe<&2, TzRule>:
1008	  match r:
1009	    case TzClock{west, rest}:
1010	      tz.rule.dates(standard, Ttype{Int.I64.neg(west), True{}, abbr}, rest)
1011	
1012	def tz.rule.offset(standard: Ttype, abbr: String, west: Int.I64, rest: String) -> Maybe<&2, TzRule>:
1013	  match rest:
1014	    case SCon{Chr{44}, t}:
1015	      tz.rule.dates(standard, Ttype{Int.I64.sub(i64(3600), west), True{}, abbr}, rest)
1016	    # POSIX leaves absent DST dates to the implementation; use the common US rules.
1017	    case SNil{}:
1018	      tz.rule.end(True{}, standard, Ttype{Int.I64.sub(i64(3600), west), True{}, abbr},
1019	        TzDate{MonthWeek{3, 2, 0}, i64(7200)}, TzDate{MonthWeek{11, 1, 0}, i64(7200)})
1020	    case _:
1021	      do Maybe<&2, TzRule>:
1022	        r : TzClock <- tz.clock.sign(rest, 24)
1023	        tz.rule.dstclock(r, standard, abbr)
1024	
1025	def tz.rule.named(name: TzText, standard: Ttype, west: Int.I64) -> Maybe<&2, TzRule>:
1026	  match name:
1027	    case TzText{abbr, rest}:
1028	      tz.rule.offset(standard, abbr, west, rest)
1029	
1030	def tz.rule.dst(+standard: Ttype, west: Int.I64, rest: String) -> Maybe<&2, TzRule>:
1031	  match rest:
1032	    case SNil{}:
1033	      Some{TzRule{standard, standard, TzDate{Ordinal{0}, i64(0)}, TzDate{Ordinal{0}, i64(0)}}}
1034	    case _:
1035	      do Maybe<&2, TzRule>:
1036	        name : TzText <- tz.name(rest)
1037	        tz.rule.named(name, standard, west)
1038	
1039	def tz.rule.stdclock(offset: TzClock, abbr: String) -> Maybe<&2, TzRule>:
1040	  match offset:
1041	    case TzClock{+west, rest}:
1042	      tz.rule.dst(Ttype{Int.I64.neg(west), False{}, abbr}, west, rest)
1043	
1044	def tz.rule.standard(name: TzText) -> Maybe<&2, TzRule>:
1045	  match name:
1046	    case TzText{abbr, rest}:
1047	      do Maybe<&2, TzRule>:
1048	        offset : TzClock <- tz.clock.sign(rest, 24)
1049	        tz.rule.stdclock(offset, abbr)
1050	
1051	def tz.rule(s: String) -> Maybe<&2, TzRule>:
1052	  do Maybe<&2, TzRule>:
1053	    name : TzText <- tz.name(s)
1054	    tz.rule.standard(name)
1055	
1056	# The day number of a rule in year y, relative to January 1.
1057	def tz.day.index(d: TzDay, +y: U32) -> U32:
1058	  match d:
1059	    case Julian{+n}:
1060	      (n - 1 + Bool.pick(U32, Bool.and(Date.is_leap(y), U32.is_ge(n, 60)), 1, 0) : U32)
1061	    case Ordinal{n}:
1062	      n
1063	    case MonthWeek{+month, +week, +weekday}:
1064	      +first_day = (Date.weekday(Date{y, month, 1}) % 7 : U32)
1065	      +day = (1 + ((weekday + 7 - first_day) % 7) + (week - 1) * 7 : U32)
1066	      +last = Date.days_in_month(y, month)
1067	      +actual = Bool.pick(U32, U32.is_gt(day, last), (day - 7 : U32), day)
1068	      Int.I64.to_u32(Int.I64.sub(Date.to_days(Date{y, month, actual}), Date.to_days(Date{y, 1, 1})))
1069	
1070	def tz.date.utc(d: TzDate, +y: U32, west: Int.I64) -> Int.I64:
1071	  match d:
1072	    case TzDate{day, sec}:
1073	      Int.I64.add(Int.I64.mul(Int.I64.add(Date.to_days(Date{y, 1, 1}), i64(tz.day.index(day, y))), i64(86400)),
1074	        Int.I64.add(sec, west))
1075	
1076	# Apply the two transitions for the UTC year and its neighbors. A /time may cross a year boundary.
1077	type TzEvent is Data:
1078	  TzEvent{when: Int.I64, dst: Bool}
1079	
1080	def tz.event.select(newer: Bool, old: Maybe<&2, TzEvent>, when: Int.I64, dst: Bool) -> Maybe<&2, TzEvent>:
1081	  match newer:
1082	    case True{}:
1083	      Some{TzEvent{when, dst}}
1084	    case False{}:
1085	      old
1086	
1087	def tz.event.new(+now: Int.I64, old: Maybe<&2, TzEvent>, +when: Int.I64, dst: Bool) -> Maybe<&2, TzEvent>:
1088	  match old:
1089	    case None{}:
1090	      tz.event.select(Int.I64.is_le(when, now), None{}, when, dst)
1091	    case Some{TzEvent{+prev, flag}}:
1092	      tz.event.select(Bool.and(Int.I64.is_le(when, now), Int.I64.is_gt(when, prev)),
1093	        Some{TzEvent{prev, flag}}, when, dst)
1094	
1095	def tz.event.year(+now: Int.I64, old: Maybe<&2, TzEvent>, +r: TzRule, +y: U32) -> Maybe<&2, TzEvent>:
1096	  match r:
1097	    case TzRule{Ttype{+off, _, _}, Ttype{+dstoff, _, _}, +start, +end}:
1098	      +first = tz.event.new(now, old, tz.date.utc(start, y, Int.I64.neg(off)), True{})
1099	      tz.event.new(now, first, tz.date.utc(end, y, Int.I64.neg(dstoff)), False{})
1100	
1101	def tz.event.prev(+now: Int.I64, old: Maybe<&2, TzEvent>, +r: TzRule, +y: U32) -> Maybe<&2, TzEvent>:
1102	  match y:
1103	    case 0:
1104	      old
1105	    case _:
1106	      tz.event.year(now, old, r, (y - 1 : U32))
1107	
1108	def tz.event.next.if(valid: Bool, now: Int.I64, old: Maybe<&2, TzEvent>, r: TzRule, y: U32) -> Maybe<&2, TzEvent>:
1109	  match valid:
1110	    case True{}:
1111	      tz.event.year(now, old, r, (y + 1 : U32))
1112	    case False{}:
1113	      old
1114	def tz.event.next(+now: Int.I64, old: Maybe<&2, TzEvent>, +r: TzRule, +y: U32) -> Maybe<&2, TzEvent>:
1115	  tz.event.next.if(U32.is_lt(y, 9999), now, old, r, y)
1116	
1117	
1118	def tz.event.type(ev: Maybe<&2, TzEvent>, +r: TzRule) -> Ttype:
1119	  match ev:
1120	    case Some{TzEvent{when, dst}}:
1121	      match r:
1122	        case TzRule{standard, daylight, start, end}:
1123	          Bool.pick(Ttype, dst, daylight, standard)
1124	    case None{}:
1125	      match r:
1126	        case TzRule{standard, daylight, start, end}:
1127	          standard
1128	
1129	def tz.rule.at(+r: TzRule, +secs: Int.I64, +year: U32) -> Ttype:
1130	  +a = tz.event.prev(secs, None{}, r, year)
1131	  +b = tz.event.year(secs, a, r, year)
1132	  tz.event.type(tz.event.next(secs, b, r, year), r)
1133	
1134	def tz.rule.date(d: Maybe<&2, DateTime>, r: TzRule, secs: Int.I64) -> Maybe<&2, Ttype>:
1135	  match d:
1136	    case None{}:
1137	      None{}
1138	    case Some{DateTime{Date{y, m, day}, h, mi, second, nanos}}:
1139	      Some{tz.rule.at(r, secs, y)}
1140	
1141	def tz.rule.lookup(rule: Maybe<&2, TzRule>, +secs: Int.I64) -> Maybe<&2, Ttype>:
1142	  match rule:
1143	    case None{}:
1144	      None{}
1145	    case Some{r}:
1146	      tz.rule.date(DateTime.of_instant(Instant.of_unix(secs)), r, secs)
1147	
1148	# The type index at secs: the last transition at or before it, or type 0 before the first.
1149	# ponytail: linear scan; bisect an Array if lookups get hot.
1150	def Zone.find(ts: List<&2, Trans>, +secs: Int.I64, +cur: U32) -> U32:
1151	  match ts:
1152	    case Nil{}:
1153	      cur
1154	    case Con{Trans{t, k}, rest}:
1155	      Zone.find(rest, secs, Bool.pick(U32, Int.I64.is_le(t, secs), k, cur))
1156	def Zone.last.go(ts: List<&2, Trans>, +secs: Int.I64, +last: Int.I64) -> Bool:
1157	  match ts:
1158	    case Nil{}:
1159	      Int.I64.is_gt(secs, last)
1160	    case Con{Trans{t, k}, rest}:
1161	      Zone.last.go(rest, secs, t)
1162	def Zone.last(ts: List<&2, Trans>, secs: Int.I64) -> Bool:
1163	  match ts:
1164	    case Nil{}:
1165	      True{}
1166	    case Con{Trans{t, k}, rest}:
1167	      Zone.last.go(rest, secs, t)
1168	
1169	
1170	def Zone.at.fallback(m: Maybe<&2, Ttype>, types: List<&2, Ttype>, ts: List<&2, Trans>, secs: Int.I64) -> Maybe<&2, Ttype>:
1171	  match m:
1172	    case Some{t}:
1173	      Some{t}
1174	    case None{}:
1175	      List.get(&2, Ttype, types, U32.to_nat(Zone.find(ts, secs, 0)))
1176	def Zone.at.footer(use: Bool, tz: String, types: List<&2, Ttype>, ts: List<&2, Trans>, +secs: Int.I64) -> Maybe<&2, Ttype>:
1177	  match use:
1178	    case False{}:
1179	      List.get(&2, Ttype, types, U32.to_nat(Zone.find(ts, secs, 0)))
1180	    case True{}:
1181	      Zone.at.fallback(tz.rule.lookup(tz.rule(tz), secs), types, ts, secs)
1182	
1183	def Zone.at.tz(empty: Bool, tz: String, types: List<&2, Ttype>, +ts: List<&2, Trans>, +secs: Int.I64) -> Maybe<&2, Ttype>:
1184	  match empty:
1185	    case True{}:
1186	      List.get(&2, Ttype, types, U32.to_nat(Zone.find(ts, secs, 0)))
1187	    case False{}:
1188	      Zone.at.footer(Zone.last(ts, secs), tz, types, ts, secs)
1189	
1190	
1191	
1192	# The local time type at i. The footer applies strictly after the final explicit transition.
1193	def Zone.at(z: Zone, i: Instant) -> Maybe<&2, Ttype>:
1194	  match z i:
1195	    case Zone{ts, types, +tz} Instant{s, n}:
1196	      Zone.at.tz(String.eq(tz, ""), tz, types, ts, s)
1197	
1198	def Zone.local.at(m: Maybe<&2, Ttype>, i: Instant) -> Maybe<&2, DateTime>:
1199	  match m:
1200	    case None{}:
1201	      None{}
1202	    case Some{Ttype{off, dst, abbr}}:
1203	      DateTime.of_instant(Instant.add(i, Duration.of_secs(off)))
1204	
1205	# The local date and time at i in zone z.
1206	def Zone.local(z: Zone, +i: Instant) -> Maybe<&2, DateTime>:
1207	  Zone.local.at(Zone.at(z, i), i)