1	# ezhttp/src/http: HTTP/1.1 message text for client and server — request and
2	# response formatting/parsing — with no sockets. Semantics follow RFC 9110;
3	# message syntax and framing follow RFC 9112. TLS is outside this module.
4	import Base
5	import ./body.bend as Body
6	
7	# a string divided at the first occurrence of a pattern, or not divided at all
8	type Cut is Data:
9	  NoCut{}
10	  Cut{before: String, after: String}
11	
12	# one header field name and value (RFC 9110 §5 / RFC 9112 §5)
13	type Header is Data:
14	  H{name: String, value: String}
15	
16	# what a response turned out to be: status, headers, framed body — or why not
17	type Reply is Data:
18	  Torn{why: String}
19	  Reply{status: U32, headers: List<&2, Header>, body: String}
20	
21	# the first of a list of pieces, "" when there are none
22	def first(ps: List<&2, String>) -> String:
23	  match ps:
24	    case []:
25	      ""
26	    case h <> t:
27	      h
28	
29	# the second of a list of pieces, "" when there is no second
30	def second(ps: List<&2, String>) -> String:
31	  match ps:
32	    case []:
33	      ""
34	    case h <> t:
35	      first(t)
36	
37	# one char of the divide, put back on the front of what the rest found
38	def divide.push(h: Char, r: Cut) -> Cut:
39	  match r:
40	    case NoCut{}:
41	      NoCut{}
42	    case Cut{before, after}:
43	      Cut{SCon{h, before}, after}
44	
45	# one step of the walk; rest is a thunk so Bool.pick does not force recursion
46	def divide.step(here: Bool, h: Char, t: String, n: Nat,
47	  rest: Unit -> Cut) -> Cut:
48	  match here:
49	    case True{}:
50	      Cut{"", String.drop(SCon{h, t}, n)}
51	    case False{}:
52	      divide.push(h, rest(Unit{}))
53	
54	# the walk: stop at the first hit
55	def divide.go(s: String, +pat: String, +n: Nat) -> Cut:
56	  match s:
57	    case SNil{}:
58	      NoCut{}
59	    case SCon{+h, +t}:
60	      divide.step(String.starts_with(SCon{h, t}, pat), h, t, n,
61	        _u => divide.go(t, pat, n))
62	
63	# a string in two halves around the first occurrence of a pattern
64	def divide(s: String, +pat: String) -> Cut:
65	  divide.go(s, pat, String.length(pat))
66	
67	# the value of one hex digit's code point, or 16 when it is not one
68	def hex.of(+u: U32) -> U32:
69	  Bool.pick(U32, Bool.and(U32.is_ge(u, 48), U32.is_le(u, 57)), U32.sub(u, 48),
70	    Bool.pick(U32, Bool.and(U32.is_ge(u, 97), U32.is_le(u, 102)), U32.sub(u, 87),
71	      Bool.pick(U32, Bool.and(U32.is_ge(u, 65), U32.is_le(u, 70)), U32.sub(u, 55),
72	        16)))
73	
74	# the value of one hex digit, or 16 when the char is not one
75	def hex.val(c: Char) -> U32:
76	  hex.of(Char.to_u32(c))
77	
78	# one step of the hex read
79	def hex.step(done: Bool, acc: Nat, rest: Unit -> Nat) -> Nat:
80	  match done:
81	    case True{}:
82	      acc
83	    case False{}:
84	      rest(Unit{})
85	
86	# the hex digits at the front of a string, read until one is not a digit
87	def hex.go(s: String, +acc: Nat) -> Nat:
88	  match s:
89	    case SNil{}:
90	      acc
91	    case SCon{+h, t}:
92	      +v = hex.val(h)
93	      hex.step(U32.is_ge(v, 16), acc,
94	        _u => hex.go(t, Nat.add(Nat.mul(acc, 16n), U32.to_nat(v))))
95	
96	# chunk-size from a chunk header (RFC 9112 §7.1); extensions after `;` ignored
97	def hexlen(s: String) -> Nat:
98	  hex.go(String.trim(first(String.split(s, ';'))), 0n)
99	
100	# whether a character is a hex digit
101	def hex.digit(c: Char) -> Bool:
102	  U32.is_lt(hex.val(c), 16)
103	
104	# the rest of a hex token once the first digit is known
105	def hex.rest(token: String, good: Bool) -> Bool:
106	  match token good:
107	    case _ False{}:
108	      False{}
109	    case SNil{} True{}:
110	      True{}
111	    case SCon{h, t} True{}:
112	      hex.rest(t, hex.digit(h))
113	
114	# a chunk-size token is one or more hex digits (RFC 9112 §7.1)
115	def hex.well(token: String) -> Bool:
116	  match token:
117	    case SNil{}:
118	      False{}
119	    case SCon{h, t}:
120	      hex.rest(t, hex.digit(h))
121	
122	# the chunk-size token, extensions after `;` removed
123	def chunks.token(before: String) -> String:
124	  String.trim(first(String.split(before, ';')))
125	
126	# octets one code point takes in UTF-8, for a text written onto the wire
127	# (RFC 3629 §3). Content-Length counts octets (RFC 9110 §8.6); a Bend String
128	# counts code points.
129	def utf8.width(+u: U32) -> Nat:
130	  Bool.pick(Nat, U32.is_lt(u, 128), 1n,
131	    Bool.pick(Nat, U32.is_lt(u, 2048), 2n,
132	      Bool.pick(Nat, U32.is_lt(u, 65536), 3n, 4n)))
133	
134	# how many octets of UTF-8 a text is
135	def utf8.len(s: String) -> Nat:
136	  match s:
137	    case SNil{}:
138	      0n
139	    case SCon{h, t}:
140	      Nat.add(utf8.width(Char.to_u32(h)), utf8.len(t))
141	
142	# What is received is octets, one character each (SPEC.md HTTP-BODY-1): the
143	# octs.* walks below count a character as one octet.
144	
145	# octets one received character stands for: one
146	def octs.width(+_u: U32) -> Nat:
147	  1n
148	
149	# how many octets a received text is
150	def octs.len(s: String) -> Nat:
151	  match s:
152	    case SNil{}:
153	      0n
154	    case SCon{h, t}:
155	      Nat.add(octs.width(Char.to_u32(h)), octs.len(t))
156	
157	# one step of the take
158	def octs.take.step(short: Bool, h: Char, rest: Unit -> String) -> String:
159	  match short:
160	    case True{}:
161	      SNil{}
162	    case False{}:
163	      SCon{h, rest(Unit{})}
164	
165	# the front of a string that is this many bytes of UTF-8
166	def octs.take(s: String, +n: Nat) -> String:
167	  match s:
168	    case SNil{}:
169	      SNil{}
170	    case SCon{+h, t}:
171	      +w = octs.width(Char.to_u32(h))
172	      octs.take.step(Nat.is_lt(n, w), h, _u => octs.take(t, Nat.sub(n, w)))
173	
174	# one step of the drop
175	def octs.drop.step(short: Bool, h: Char, t: String,
176	  rest: Unit -> String) -> String:
177	  match short:
178	    case True{}:
179	      SCon{h, t}
180	    case False{}:
181	      rest(Unit{})
182	
183	# the rest of a string after this many bytes of UTF-8
184	def octs.drop(s: String, +n: Nat) -> String:
185	  match s:
186	    case SNil{}:
187	      SNil{}
188	    case SCon{+h, +t}:
189	      +w = octs.width(Char.to_u32(h))
190	      octs.drop.step(Nat.is_lt(n, w), h, t, _u => octs.drop(t, Nat.sub(n, w)))
191	
192	# a decimal digit's value, or 10 when the character is not a digit
193	def digits.val.of(+u: U32) -> U32:
194	  Bool.pick(U32, Bool.and(U32.is_ge(u, 48), U32.is_le(u, 57)), U32.sub(u, 48), 10)
195	
196	# a decimal digit's value, or 10 when the character is not a digit
197	def digits.val(c: Char) -> U32:
198	  digits.val.of(Char.to_u32(c))
199	
200	# accept one digit and keep reading, or stop when it is not a digit
201	def digits.step(ok: Bool, next: Unit -> Maybe<&2, Nat>) -> Maybe<&2, Nat>:
202	  match ok:
203	    case False{}:
204	      None{}
205	    case True{}:
206	      next(Unit{})
207	
208	# read a decimal token without building Base's Nat.read ceiling
209	def digits.go(s: String, +acc: Nat, left: Nat) -> Maybe<&2, Nat>:
210	  match s left:
211	    case _ 0n:
212	      None{}
213	    case SNil{} 1n+k:
214	      Some{acc}
215	    case SCon{+h, t} 1n+k:
216	      +d = digits.val(h)
217	      digits.step(U32.is_lt(d, 10),
218	        _u => digits.go(t, Nat.add(Nat.mul(acc, 10n), U32.to_nat(d)), k))
219	
220	# a short decimal (Content-Length, max-age). Empty is none. At most 9 digits.
221	def digits.read(s: String) -> Maybe<&2, Nat>:
222	  match s:
223	    case SNil{}:
224	      None{}
225	    case SCon{h, t}:
226	      digits.go(SCon{h, t}, 0n, 9n)
227	
228	# one step of the count: a character wider than what is still asked for
229	# means the string is longer
230	def octs.has.step(short: Bool, rest: Unit -> Bool) -> Bool:
231	  match short:
232	    case True{}:
233	      True{}
234	    case False{}:
235	      rest(Unit{})
236	
237	# whether a string is at least this many bytes of UTF-8, walking no further
238	# than that many (octs.len walks all of it)
239	def octs.has(s: String, +n: Nat) -> Bool:
240	  match s:
241	    case SNil{}:
242	      Bool.not(Nat.is_lt(0n, n))
243	    case SCon{+h, t}:
244	      +w = octs.width(Char.to_u32(h))
245	      octs.has.step(Nat.is_lt(n, w), _u => octs.has(t, Nat.sub(n, w)))
246	
247	# a non-zero chunk has its data and the following CRLF
248	def chunks.ready(+after: String, +n: Nat) -> Bool:
249	  Bool.and(octs.has(after, Nat.add(n, 2n)),
250	    String.starts_with(octs.drop(after, n), "\r\n"))
251	
252	# the next scan step, or why this chunk header is not usable
253	type Next is Data:
254	  Stop{}
255	  Go{cut: Cut}
256	  Reject{why: String}
257	
258	# one chunk header: reject non-hex sizes, stop on the 0 chunk, else continue
259	def chunks.next.of(zero: Bool, ready: Bool, +after: String, +n: Nat) -> Next:
260	  match zero ready:
261	    case True{} _:
262	      Stop{}
263	    case False{} False{}:
264	      Reject{"the chunked body stopped short"}
265	    case False{} True{}:
266	      Go{divide(octs.drop(after, Nat.add(n, 2n)), "\r\n")}
267	
268	# hex check, then the length
269	def chunks.next.hex(+before: String, +after: String, ok: Bool) -> Next:
270	  match ok:
271	    case False{}:
272	      Reject{"chunk size is not hexadecimal"}
273	    case True{}:
274	      +n = hexlen(before)
275	      chunks.next.of(Nat.is_eq(n, 0n), chunks.ready(after, n), after, n)
276	
277	# classify one chunk header (RFC 9112 §7.1)
278	def chunks.next(+before: String, +after: String) -> Next:
279	  chunks.next.hex(before, after, hex.well(chunks.token(before)))
280	
281	# apply one scan step
282	def chunks.scan.step(step: Next, rest: Cut -> Maybe<&2, String>)
283	  -> Maybe<&2, String>:
284	  match step:
285	    case Stop{}:
286	      None{}
287	    case Reject{why}:
288	      Some{why}
289	    case Go{cut}:
290	      rest(cut)
291	
292	# None when every chunk size is hex and the 0 chunk is reached
293	def chunks.scan(fuel: Nat, c: Cut) -> Maybe<&2, String>:
294	  match fuel c:
295	    case 0n _:
296	      Some{"the chunked body is truncated"}
297	    case 1n+f NoCut{}:
298	      None{}
299	    case 1n+f Cut{before, +after}:
300	      chunks.scan.step(chunks.next(before, after), cut => chunks.scan(f, cut))
301	
302	# a zero chunk ends the body; anything after it is a trailer (RFC 9112 §7.1)
303	def chunks.more(+n: Nat, +after: String, rest: Unit -> String, zero: Bool)
304	  -> String:
305	  match zero:
306	    case True{}:
307	      ""
308	    case False{}:
309	      octs.take(after, n)
310	        ++ rest(Unit{})
311	
312	# a chunked body put back together (RFC 9112 §7.1)
313	def chunks(fuel: Nat, c: Cut) -> String:
314	  match fuel c:
315	    case 0n _:
316	      ""
317	    case 1n+f NoCut{}:
318	      ""
319	    case 1n+f Cut{before, +after}:
320	      +n = hexlen(before)
321	      chunks.more(n, after,
322	        _u => chunks(f, divide(octs.drop(after, Nat.add(n, 2n)), "\r\n")),
323	        Nat.is_eq(n, 0n))
324	
325	# a Transfer-Encoding: chunked body as the octets it stands for
326	def dechunk(+s: String) -> String:
327	  chunks(String.length(s), divide(s, "\r\n"))
328	
329	# whether a head line names this header (field names are case-insensitive:
330	# RFC 9110 §5.1)
331	def head.hit(h: String, +name: String) -> Bool:
332	  String.starts_with(String.to_lower(h), name ++ ":")
333	
334	# this line's value when it is the header asked for
335	def head.pick(hit: Bool, h: String, name: String, rest: String) -> String:
336	  match hit:
337	    case True{}:
338	      String.trim(String.drop(h, Nat.add(String.length(name), 1n)))
339	    case False{}:
340	      rest
341	
342	# the value a head gave a header, "" when it gave none
343	def head.go(ls: List<&2, String>, +name: String) -> String:
344	  match ls:
345	    case []:
346	      ""
347	    case +h <> t:
348	      head.pick(head.hit(h, name), h, name, head.go(t, name))
349	
350	# this line's trimmed field value
351	def head.value(h: String, name: String) -> String:
352	  String.trim(String.drop(h, Nat.add(String.length(name), 1n)))
353	
354	# cons a value when the line is the header asked for
355	def head.values.cons(hit: Bool, value: String, rest: Unit -> List<&2, String>)
356	  -> List<&2, String>:
357	  match hit:
358	    case False{}:
359	      rest(Unit{})
360	    case True{}:
361	      value <> rest(Unit{})
362	
363	# every value a head gave a header, in order (RFC 9112 §6.3 lists Content-Length)
364	def head.values(ls: List<&2, String>, +name: String) -> List<&2, String>:
365	  match ls:
366	    case []:
367	      []
368	    case +h <> t:
369	      head.values.cons(head.hit(h, name), head.value(h, name),
370	        _u => head.values(t, name))
371	
372	# a field value still holding a line break is obs-fold, which we refuse
373	def field.folded(+value: String) -> Bool:
374	  Bool.or(String.contains(value, "\n"), String.contains(value, "\r"))
375	
376	# a trimmed field value, or none when it still contains obs-fold
377	def field.keep(name: String, +value: String, folded: Bool) -> Maybe<&2, Header>:
378	  match folded:
379	    case True{}:
380	      None{}
381	    case False{}:
382	      Some{H{name, value}}
383	
384	# name and trimmed value from a cut at the first colon
385	def head.from_kept(before: String, +after: String) -> Maybe<&2, Header>:
386	  +value = String.trim(after)
387	  field.keep(before, value, field.folded(value))
388	
389	# one header line as a Header, or none when it has no colon
390	def head.from_cut(c: Cut) -> Maybe<&2, Header>:
391	  match c:
392	    case NoCut{}:
393	      None{}
394	    case Cut{before, after}:
395	      head.from_kept(before, after)
396	
397	# one header line as a Header, or none when it has no colon
398	def head.line(h: String) -> Maybe<&2, Header>:
399	  head.from_cut(divide(h, ":"))
400	
401	# prepend a parsed header when present
402	def head.cons(m: Maybe<&2, Header>, rest: List<&2, Header>) -> List<&2, Header>:
403	  match m:
404	    case None{}:
405	      rest
406	    case Some{hdr}:
407	      hdr <> rest
408	
409	# header lines after the status line as a list of fields
410	def head.list(ls: List<&2, String>) -> List<&2, Header>:
411	  match ls:
412	    case []:
413	      []
414	    case h <> t:
415	      head.cons(head.line(h), head.list(t))
416	
417	# one request header line
418	def header.line(h: Header) -> String:
419	  match h:
420	    case H{name, value}:
421	      name ++ ": " ++ value ++ "\r\n"
422	
423	# the value when this field is the one asked for
424	def headers.find.pick(value: String, hit: Bool, rest: Unit -> String) -> String:
425	  match hit:
426	    case True{}:
427	      value
428	    case False{}:
429	      rest(Unit{})
430	
431	# case-insensitive field lookup (RFC 9110 §5.1)
432	def headers.find.go(hs: List<&2, Header>, +name: String) -> String:
433	  match hs:
434	    case []:
435	      ""
436	    case H{n, v} <> t:
437	      headers.find.pick(v, String.eq(String.to_lower(n), name),
438	        _u => headers.find.go(t, name))
439	
440	# the value of a field, "" when it is absent
441	def headers.find(hs: List<&2, Header>, +name: String) -> String:
442	  headers.find.go(hs, String.to_lower(name))
443	
444	# extra headers rendered in order
445	def headers.lines(hs: List<&2, Header>) -> String:
446	  match hs:
447	    case []:
448	      ""
449	    case h <> t:
450	      header.line(h) ++ headers.lines(t)
451	
452	# the Content-Length field when the body is not empty (RFC 9110 §8.6)
453	def clen.field(+n: Nat, empty: Bool) -> List<&2, Header>:
454	  match empty:
455	    case True{}:
456	      []
457	    case False{}:
458	      [H{"Content-Length", Nat.show(n)}]
459	
460	# Content-Length line when the body is not empty (RFC 9110 §8.6)
461	def clen.line(+n: Nat, empty: Bool) -> String:
462	  headers.lines(clen.field(n, empty))
463	
464	# the fields a request names: the ones ezhttp writes a default for, the ones
465	# it always computes, and every other (SPEC.md HTTP-CLI-8)
466	type Field is Data:
467	  FHost{}
468	  FAgent{}
469	  FAccept{}
470	  FConn{}
471	  FClen{}
472	  FOther{}
473	
474	# a field's place in the order above
475	def field.rank(f: Field) -> U32:
476	  match f:
477	    case FHost{}:
478	      0
479	    case FAgent{}:
480	      1
481	    case FAccept{}:
482	      2
483	    case FConn{}:
484	      3
485	    case FClen{}:
486	      4
487	    case FOther{}:
488	      5
489	
490	# whether two fields are the same one
491	def field.same(a: Field, b: Field) -> Bool:
492	  U32.is_eq(field.rank(a), field.rank(b))
493	
494	# a lower-case name that is not content-length
495	def field.of.clen(hit: Bool) -> Field:
496	  match hit:
497	    case True{}:
498	      FClen{}
499	    case False{}:
500	      FOther{}
501	
502	# a lower-case name that is not connection
503	def field.of.conn(hit: Bool, +l: String) -> Field:
504	  match hit:
505	    case True{}:
506	      FConn{}
507	    case False{}:
508	      field.of.clen(String.eq(l, "content-length"))
509	
510	# a lower-case name that is not accept
511	def field.of.accept(hit: Bool, +l: String) -> Field:
512	  match hit:
513	    case True{}:
514	      FAccept{}
515	    case False{}:
516	      field.of.conn(String.eq(l, "connection"), l)
517	
518	# a lower-case name that is not user-agent
519	def field.of.agent(hit: Bool, +l: String) -> Field:
520	  match hit:
521	    case True{}:
522	      FAgent{}
523	    case False{}:
524	      field.of.accept(String.eq(l, "accept"), l)
525	
526	# a lower-case name that is not host
527	def field.of.host(hit: Bool, +l: String) -> Field:
528	  match hit:
529	    case True{}:
530	      FHost{}
531	    case False{}:
532	      field.of.agent(String.eq(l, "user-agent"), l)
533	
534	# the field a lower-case name names
535	def field.of(+l: String) -> Field:
536	  field.of.host(String.eq(l, "host"), l)
537	
538	# the field a name names, compared case-insensitively (RFC 9110 §5.1)
539	def field.name(name: String) -> Field:
540	  field.of(String.to_lower(name))
541	
542	# the field a header line names
543	def header.field(h: Header) -> Field:
544	  match h:
545	    case H{name, value}:
546	      field.name(name)
547	
548	# keep a header in front of the rest, or not
549	def fields.put(keep: Bool, h: Header, rest: List<&2, Header>)
550	  -> List<&2, Header>:
551	  match keep:
552	    case True{}:
553	      h <> rest
554	    case False{}:
555	      rest
556	
557	# the headers that name one field, in order
558	def fields.of(+f: Field, hs: List<&2, Header>) -> List<&2, Header>:
559	  match hs:
560	    case []:
561	      []
562	    case +h <> t:
563	      fields.put(field.same(f, header.field(h)), h, fields.of(f, t))
564	
565	# the caller's fields of a name, or the default when it gave none
566	def fields.or(given: List<&2, Header>, dflt: List<&2, Header>)
567	  -> List<&2, Header>:
568	  match given:
569	    case []:
570	      dflt
571	    case h <> t:
572	      h <> t
573	
574	# a request's header fields for a body of n octets: Host, User-Agent and
575	# Accept (the caller's, or the default), Connection: close, the caller's other
576	# fields, Content-Length.
577	# A caller's Connection or Content-Length is not sent: Connection: close lets
578	# the connection end frame the body when no Content-Length / chunked framing
579	# applies (RFC 9112 §9.6 / §6.3), and the body's length is computed.
580	def request.fields.n(host: String, +hs: List<&2, Header>, +n: Nat)
581	  -> List<&2, Header>:
582	  List.append(&2, Header, fields.or(fields.of(FHost{}, hs), [H{"Host", host}]),
583	    List.append(&2, Header,
584	      fields.or(fields.of(FAgent{}, hs), [H{"User-Agent", "ezhttp"}]),
585	      List.append(&2, Header,
586	        fields.or(fields.of(FAccept{}, hs), [H{"Accept", "*/*"}]),
587	        H{"Connection", "close"}
588	          <> List.append(&2, Header, fields.of(FOther{}, hs),
589	            clen.field(n, Nat.is_eq(n, 0n))))))
590	
591	# a request's header fields for a text body: the fields for its UTF-8 octets
592	def request.fields(host: String, +hs: List<&2, Header>, +body: String)
593	  -> List<&2, Header>:
594	  request.fields.n(host, hs, utf8.len(body))
595	
596	# a request-line and headers (RFC 9112 §3, §5). Absolute-path request-target
597	# (RFC 9112 §3.2.1); the fields are request.fields'.
598	def request(method: String, host: String, path: String,
599	  headers: List<&2, Header>, +body: String) -> String:
600	  method ++ " " ++ path ++ " HTTP/1.1\r\n"
601	    ++ headers.lines(request.fields(host, headers, body))
602	    ++ "\r\n"
603	    ++ body
604	
605	# the port a scheme implies: 443 for a secure one, 80 otherwise (RFC 9110
606	# §4.2.1, §4.2.2)
607	def port.dflt(secure: Bool) -> U32:
608	  match secure:
609	    case True{}:
610	      443
611	    case False{}:
612	      80
613	
614	# the Host field value once it is known whether the port is the default
615	def authority.of(host: String, +port: U32, dflt: Bool) -> String:
616	  match dflt:
617	    case True{}:
618	      host
619	    case False{}:
620	      host ++ ":" ++ U32.show(port)
621	
622	# the Host field value: the host, and the port after a colon unless it is the
623	# scheme's default (RFC 9110 §7.2)
624	def authority(secure: Bool, host: String, +port: U32) -> String:
625	  authority.of(host, port, U32.is_eq(port, port.dflt(secure)))
626	
627	# the request a client sends to host and port, over TLS when secure
628	def request.at(method: String, secure: Bool, host: String, port: U32,
629	  path: String, headers: List<&2, Header>, body: String) -> String:
630	  request(method, authority(secure, host, port), path, headers, body)
631	
632	# the request text for a body of n octets that is sent after it as its own
633	# octets: the request line, the fields for n octets, and the blank line
634	def request.head(method: String, host: String, path: String,
635	  headers: List<&2, Header>, +n: Nat) -> String:
636	  method ++ " " ++ path ++ " HTTP/1.1\r\n"
637	    ++ headers.lines(request.fields.n(host, headers, n))
638	    ++ "\r\n"
639	
640	# the request text a client sends to host and port ahead of n octets
641	def request.head.at(method: String, secure: Bool, host: String, port: U32,
642	  path: String, headers: List<&2, Header>, n: Nat) -> String:
643	  request.head(method, authority(secure, host, port), path, headers, n)
644	
645	# GET with optional headers
646	def get_req(host: String, path: String, headers: List<&2, Header>) -> String:
647	  request("GET", host, path, headers, "")
648	
649	# HEAD with optional headers (RFC 9110 §9.3.2): same as GET, no body
650	def head_req(host: String, path: String, headers: List<&2, Header>) -> String:
651	  request("HEAD", host, path, headers, "")
652	
653	# POST with body and optional headers
654	def post_req(host: String, path: String, headers: List<&2, Header>,
655	  body: String) -> String:
656	  request("POST", host, path, headers, body)
657	
658	# PUT with body and optional headers (RFC 9110 §9.3.4)
659	def put_req(host: String, path: String, headers: List<&2, Header>,
660	  body: String) -> String:
661	  request("PUT", host, path, headers, body)
662	
663	# DELETE with body and optional headers (RFC 9110 §9.3.5)
664	def delete_req(host: String, path: String, headers: List<&2, Header>,
665	  body: String) -> String:
666	  request("DELETE", host, path, headers, body)
667	
668	# OPTIONS with optional headers (RFC 9110 §9.3.7). No request body.
669	def options_req(host: String, path: String, headers: List<&2, Header>) -> String:
670	  request("OPTIONS", host, path, headers, "")
671	
672	# GET, HEAD, and OPTIONS are safe (RFC 9110 §9.2.1). Tokens are case-sensitive.
673	def method.safe(+method: String) -> Bool:
674	  Bool.or(String.eq(method, "GET"),
675	    Bool.or(String.eq(method, "HEAD"), String.eq(method, "OPTIONS")))
676	
677	# safe methods, plus PUT and DELETE, are idempotent (RFC 9110 §9.2.2)
678	def method.idempotent(+method: String) -> Bool:
679	  Bool.or(method.safe(method),
680	    Bool.or(String.eq(method, "PUT"), String.eq(method, "DELETE")))
681	
682	# the rest of a token once this character is known
683	def token.ok.step(space: Bool, rest: Unit -> Bool) -> Bool:
684	  match space:
685	    case True{}:
686	      False{}
687	    case False{}:
688	      rest(Unit{})
689	
690	# a bearer token has no whitespace (RFC 6750 §2.1)
691	def token.ok(s: String) -> Bool:
692	  match s:
693	    case SNil{}:
694	      True{}
695	    case SCon{h, t}:
696	      token.ok.step(Char.is_space(h), _u => token.ok(t))
697	
698	# origin-form request-target: absolute-path, optional query (RFC 9112 §3.2.1)
699	def target.origin(path: String) -> Bool:
700	  String.starts_with(path, "/")
701	
702	# asterisk-form is only `*` and only for OPTIONS (RFC 9112 §3.2.4)
703	def target.asterisk(method: String, star: Bool) -> Bool:
704	  match star:
705	    case False{}:
706	      False{}
707	    case True{}:
708	      String.eq(method, "OPTIONS")
709	
710	# origin-form, or OPTIONS asterisk-form
711	def target.form(method: String, path: String, absolute: Bool) -> Bool:
712	  match absolute:
713	    case True{}:
714	      True{}
715	    case False{}:
716	      target.asterisk(method, String.eq(path, "*"))
717	
718	# a body against the length its head promised
719	def parse.short(status: U32, headers: List<&2, Header>, n: Nat, body: String,
720	  short: Bool) -> Reply:
721	  match short:
722	    case True{}:
723	      Torn{"the response body stopped before its Content-Length"}
724	    case False{}:
725	      Reply{status, headers, octs.take(body, n)}
726	
727	# a body framed by Content-Length (RFC 9110 §8.6 / RFC 9112 §6.3)
728	def parse.clen(status: U32, headers: List<&2, Header>, +n: Nat, +body: String)
729	  -> Reply:
730	  parse.short(status, headers, n, body, Nat.is_lt(octs.len(body), n))
731	
732	# Content-Length when present; else the rest of the connection is the body
733	def parse.len(status: U32, headers: List<&2, Header>, m: Maybe<&2, Nat>,
734	  body: String) -> Reply:
735	  match m:
736	    case None{}:
737	      Reply{status, headers, body}
738	    case Some{n}:
739	      parse.clen(status, headers, n, body)
740	
741	# every Content-Length text equals the first
742	def clen.agree.step(same: Bool, rest: Unit -> Bool) -> Bool:
743	  match same:
744	    case False{}:
745	      False{}
746	    case True{}:
747	      rest(Unit{})
748	
749	# the tail of a Content-Length list against the first value
750	def clen.agree.go(rest: List<&2, String>, +h: String) -> Bool:
751	  match rest:
752	    case []:
753	      True{}
754	    case x <> r:
755	      clen.agree.step(String.eq(x, h), _u => clen.agree.go(r, h))
756	
757	# duplicate Content-Length fields must be the same digits (RFC 9112 §6.3)
758	def clen.agree(vs: List<&2, String>) -> Bool:
759	  match vs:
760	    case []:
761	      True{}
762	    case h <> t:
763	      clen.agree.go(t, h)
764	
765	# whether any Content-Length field was present
766	def clen.any(vs: List<&2, String>) -> Bool:
767	  match vs:
768	    case []:
769	      False{}
770	    case h <> t:
771	      True{}
772	
773	# a chunked body, or why the chunk framing was rejected
774	def parse.chunked(status: U32, headers: List<&2, Header>, body: String,
775	  bad: Maybe<&2, String>) -> Reply:
776	  match bad:
777	    case None{}:
778	      Reply{status, headers, dechunk(body)}
779	    case Some{why}:
780	      Torn{why}
781	
782	# scan chunk sizes, then decode when they are hex and closed by 0
783	def parse.chunks(status: U32, headers: List<&2, Header>, +body: String) -> Reply:
784	  parse.chunked(status, headers, body,
785	    chunks.scan(String.length(body), divide(body, "\r\n")))
786	
787	# Transfer-Encoding together with Content-Length is a bad message
788	def parse.te.clash(status: U32, headers: List<&2, Header>, body: String,
789	  present: Bool) -> Reply:
790	  match present:
791	    case True{}:
792	      Torn{"Content-Length and Transfer-Encoding conflict"}
793	    case False{}:
794	      parse.chunks(status, headers, body)
795	
796	# chunked framing, or Content-Length, or the rest of the connection
797	def parse.te(status: U32, headers: List<&2, Header>, +lens: List<&2, String>,
798	  +body: String, chunked: Bool) -> Reply:
799	  match chunked:
800	    case False{}:
801	      parse.len(status, headers, digits.read(first(lens)), body)
802	    case True{}:
803	      parse.te.clash(status, headers, body, clen.any(lens))
804	
805	# disagreeing Content-Length values are torn before framing
806	def parse.agree(status: U32, headers: List<&2, Header>, te: String,
807	  +lens: List<&2, String>, body: String, ok: Bool) -> Reply:
808	  match ok:
809	    case False{}:
810	      Torn{"Content-Length values disagree"}
811	    case True{}:
812	      parse.te(status, headers, lens, body,
813	        String.contains(String.to_lower(te), "chunked"))
814	
815	# the headers that decide the framing (RFC 9112 §6.3)
816	def parse.frame(status: U32, headers: List<&2, Header>, te: String,
817	  +lens: List<&2, String>, body: String) -> Reply:
818	  parse.agree(status, headers, te, lens, body, clen.agree(lens))
819	
820	# a head whose status line has been read (RFC 9112 §4)
821	def parse.status(m: Maybe<&2, U32>, +ls: List<&2, String>, body: String)
822	  -> Reply:
823	  match m:
824	    case None{}:
825	      Torn{"the response has no status line"}
826	    case Some{n}:
827	      +hs = head.list(ls)
828	      parse.frame(n, hs, head.go(ls, "transfer-encoding"),
829	        head.values(ls, "content-length"), body)
830	
831	# the status code a head's first line names, if it names one (RFC 9112 §4)
832	def status.of(ls: List<&2, String>) -> Maybe<&2, U32>:
833	  U32.read(second(String.split(first(ls), ' ')))
834	
835	# the head's lines, with the status line read off the first
836	def parse.head(+ls: List<&2, String>, body: String) -> Reply:
837	  parse.status(status.of(ls), ls, body)
838	
839	# a response divided into its head and everything after the blank line
840	# (RFC 9112 §2.1: header section ends at empty line)
841	def parse.cut(c: Cut) -> Reply:
842	  match c:
843	    case NoCut{}:
844	      Torn{"the response head has no blank line after it"}
845	    case Cut{before, after}:
846	      parse.head(String.lines(before), after)
847	
848	# the status, headers, and body of a raw response
849	def parse(raw: String) -> Reply:
850	  parse.cut(divide(raw, "\r\n\r\n"))
851	
852	# a parsed response on one line, for a test to read
853	def show(r: Reply) -> String:
854	  match r:
855	    case Torn{why}:
856	      "torn " ++ why
857	    case Reply{status, headers, body}:
858	      U32.show(status) ++ " " ++ body
859	
860	# --- inbound request (server) and outbound response (server) ---
861	
862	# a request that came apart, or the reason it would not (RFC 9112 §3)
863	type Request is Data:
864	  Bad{why: String}
865	  Request{method: String, target: String, headers: List<&2, Header>,
866	    body: String}
867	
868	# a status code and its reason-phrase
869	type Phrase is Data:
870	  P{code: U32, text: String}
871	
872	# the reason-phrases RFC 9110 §15 names (RFC 6585 §4 for 429)
873	def reasons() -> List<&2, Phrase>:
874	  [P{200, "OK"}, P{201, "Created"}, P{202, "Accepted"}, P{204, "No Content"},
875	    P{301, "Moved Permanently"}, P{302, "Found"}, P{303, "See Other"},
876	    P{304, "Not Modified"}, P{307, "Temporary Redirect"},
877	    P{308, "Permanent Redirect"}, P{400, "Bad Request"},
878	    P{401, "Unauthorized"}, P{403, "Forbidden"}, P{404, "Not Found"},
879	    P{405, "Method Not Allowed"}, P{409, "Conflict"}, P{410, "Gone"},
880	    P{413, "Content Too Large"}, P{415, "Unsupported Media Type"},
881	    P{422, "Unprocessable Content"}, P{429, "Too Many Requests"},
882	    P{500, "Internal Server Error"}, P{501, "Not Implemented"},
883	    P{502, "Bad Gateway"}, P{503, "Service Unavailable"},
884	    P{504, "Gateway Timeout"}]
885	
886	# this phrase when its code is the one asked for, else the rest's
887	def reason.pick(text: String, hit: Bool, rest: Unit -> String) -> String:
888	  match hit:
889	    case True{}:
890	      text
891	    case False{}:
892	      rest(Unit{})
893	
894	# the phrase a list gives a code, "" when it gives none
895	def reason.in(ps: List<&2, Phrase>, +code: U32) -> String:
896	  match ps:
897	    case []:
898	      ""
899	    case P{c, text} <> t:
900	      reason.pick(text, U32.is_eq(code, c), _u => reason.in(t, code))
901	
902	# the reason-phrase for a status code (RFC 9112 §4); "" for one not listed
903	def reason(+code: U32) -> String:
904	  reason.in(reasons(), code)
905	
906	# status-line + headers + body (RFC 9112 §4, §5). Connection: close ends the
907	# exchange after one response.
908	def respond(+status: U32, headers: List<&2, Header>, +body: String) -> String:
909	  +n = utf8.len(body)
910	  "HTTP/1.1 " ++ U32.show(status) ++ " " ++ reason(status) ++ "\r\n"
911	    ++ "Connection: close\r\n"
912	    ++ headers.lines(headers)
913	    ++ clen.line(n, Nat.is_eq(n, 0n))
914	    ++ "\r\n"
915	    ++ body
916	
917	# 204 and 304 are terminated by the header section (RFC 9110 §15.3.5, §15.4.5)
918	def status.nocontent(+code: U32) -> Bool:
919	  Bool.or(U32.is_eq(code, 204), U32.is_eq(code, 304))
920	
921	# drop a 204/304 body; any other status keeps it
922	def respond.of.body(+status: U32, headers: List<&2, Header>, body: String,
923	  drop: Bool) -> String:
924	  match drop:
925	    case True{}:
926	      respond(status, headers, "")
927	    case False{}:
928	      respond(status, headers, body)
929	
930	# format a structured Reply as a response message
931	def respond.of(r: Reply) -> String:
932	  match r:
933	    case Torn{why}:
934	      respond(500, [], why)
935	    case Reply{+status, headers, body}:
936	      respond.of.body(status, headers, body, status.nocontent(status))
937	
938	# HEAD carries no message body; any other method keeps the body (RFC 9110 §9.3.2)
939	def reply.for.pick(reply: Reply, head: Bool) -> Reply:
940	  match reply head:
941	    case Torn{why} _:
942	      Torn{why}
943	    case Reply{status, headers, body} False{}:
944	      Reply{status, headers, body}
945	    case Reply{status, headers, body} True{}:
946	      Reply{status, headers, ""}
947	
948	# drop a HEAD response body before it is written
949	def reply.for(method: String, reply: Reply) -> Reply:
950	  reply.for.pick(reply, String.eq(method, "HEAD"))
951	
952	# the method token, or "" when the request did not parse
953	def method.of(req: Request) -> String:
954	  match req:
955	    case Bad{why}:
956	      ""
957	    case Request{method, target, headers, body}:
958	      method
959	
960	# request body against Content-Length
961	def ask.short(method: String, target: String, headers: List<&2, Header>,
962	  n: Nat, body: String, short: Bool) -> Request:
963	  match short:
964	    case True{}:
965	      Bad{"the request body stopped before its Content-Length"}
966	    case False{}:
967	      Request{method, target, headers, octs.take(body, n)}
968	
969	# a request body framed by Content-Length (RFC 9110 §8.6 / RFC 9112 §6.3)
970	def ask.clen(method: String, target: String, headers: List<&2, Header>,
971	  +n: Nat, +body: String) -> Request:
972	  ask.short(method, target, headers, n, body, Nat.is_lt(octs.len(body), n))
973	
974	# Content-Length when present; else the rest of the connection is the body
975	def ask.len(method: String, target: String, headers: List<&2, Header>,
976	  m: Maybe<&2, Nat>, body: String) -> Request:
977	  match m:
978	    case None{}:
979	      Request{method, target, headers, body}
980	    case Some{n}:
981	      ask.clen(method, target, headers, n, body)
982	
983	# a chunked request body, or why the chunk framing was rejected
984	def ask.chunked(method: String, target: String, headers: List<&2, Header>,
985	  body: String, bad: Maybe<&2, String>) -> Request:
986	  match bad:
987	    case None{}:
988	      Request{method, target, headers, dechunk(body)}
989	    case Some{why}:
990	      Bad{why}
991	
992	# scan chunk sizes, then decode when they are hex and closed by 0
993	def ask.chunks(method: String, target: String, headers: List<&2, Header>,
994	  +body: String) -> Request:
995	  ask.chunked(method, target, headers, body,
996	    chunks.scan(String.length(body), divide(body, "\r\n")))
997	
998	# Transfer-Encoding together with Content-Length is a bad request
999	def ask.te.clash(method: String, target: String, headers: List<&2, Header>,
1000	  body: String, present: Bool) -> Request:
1001	  match present:
1002	    case True{}:
1003	      Bad{"Content-Length and Transfer-Encoding conflict"}
1004	    case False{}:
1005	      ask.chunks(method, target, headers, body)
1006	
1007	# chunked framing, or Content-Length, or the rest of the connection
1008	def ask.te(method: String, target: String, headers: List<&2, Header>,
1009	  +lens: List<&2, String>, +body: String, chunked: Bool) -> Request:
1010	  match chunked:
1011	    case False{}:
1012	      ask.len(method, target, headers, digits.read(first(lens)), body)
1013	    case True{}:
1014	      ask.te.clash(method, target, headers, body, clen.any(lens))
1015	
1016	# disagreeing Content-Length values are bad before framing
1017	def ask.agree(method: String, target: String, headers: List<&2, Header>,
1018	  te: String, +lens: List<&2, String>, body: String, ok: Bool) -> Request:
1019	  match ok:
1020	    case False{}:
1021	      Bad{"Content-Length values disagree"}
1022	    case True{}:
1023	      ask.te(method, target, headers, lens, body,
1024	        String.contains(String.to_lower(te), "chunked"))
1025	
1026	# the headers that decide request framing (RFC 9112 §6.3)
1027	def ask.frame(method: String, target: String, headers: List<&2, Header>,
1028	  te: String, +lens: List<&2, String>, body: String) -> Request:
1029	  ask.agree(method, target, headers, te, lens, body, clen.agree(lens))
1030	
1031	# origin-form, or a bad request when the target is not an absolute-path
1032	def ask.origin(method: String, target: String, +ls: List<&2, String>,
1033	  body: String, ok: Bool) -> Request:
1034	  match ok:
1035	    case False{}:
1036	      Bad{"the request-target is not in origin-form"}
1037	    case True{}:
1038	      +hs = head.list(ls)
1039	      ask.frame(method, target, hs, head.go(ls, "transfer-encoding"),
1040	        head.values(ls, "content-length"), body)
1041	
1042	# request-line: method SP request-target SP HTTP-version (RFC 9112 §3)
1043	def ask.line(+method: String, +target: String, +ls: List<&2, String>,
1044	  body: String) -> Request:
1045	  ask.origin(method, target, ls, body,
1046	    target.form(method, target, target.origin(target)))
1047	
1048	# three fields of the request-line, or torn
1049	def ask.parts(ps: List<&2, String>, +ls: List<&2, String>, body: String)
1050	  -> Request:
1051	  match ps:
1052	    case []:
1053	      Bad{"the request has no request line"}
1054	    case m <> rest:
1055	      match rest:
1056	        case []:
1057	          Bad{"the request line has no target"}
1058	        case t <> _ver:
1059	          ask.line(m, t, ls, body)
1060	
1061	# the head's lines, with the request-line read off the first
1062	def ask.head(+ls: List<&2, String>, body: String) -> Request:
1063	  match ls:
1064	    case []:
1065	      Bad{"the request has no request line"}
1066	    case _:
1067	      ask.parts(String.split(first(ls), ' '), ls, body)
1068	
1069	# a request divided into its head and everything after the blank line
1070	def ask.cut(c: Cut) -> Request:
1071	  match c:
1072	    case NoCut{}:
1073	      Bad{"the request head has no blank line after it"}
1074	    case Cut{before, after}:
1075	      ask.head(String.lines(before), after)
1076	
1077	# the method, target, headers, and body of a raw request
1078	def ask(raw: String) -> Request:
1079	  ask.cut(divide(raw, "\r\n\r\n"))
1080	
1081	# a parsed request on one line, for a test to read
1082	def ask.show(r: Request) -> String:
1083	  match r:
1084	    case Bad{why}:
1085	      "bad " ++ why
1086	    case Request{method, target, headers, body}:
1087	      method ++ " " ++ target ++ " " ++ body
1088	
1089	# --- when a response has all arrived (RFC 9112 §6.3) ---
1090	
1091	# how a response's body is framed
1092	type Frame is Data:
1093	  Bare{}
1094	  Sized{n: Nat}
1095	  Chunked{}
1096	  Closed{}
1097	
1098	# 204 and 304 carry no body; a status line that did not parse is framed by
1099	# its headers
1100	def status.bare(m: Maybe<&2, U32>) -> Bool:
1101	  match m:
1102	    case None{}:
1103	      False{}
1104	    case Some{n}:
1105	      status.nocontent(n)
1106	
1107	# a 1xx status is an interim response (RFC 9110 §15.2); a status line that
1108	# did not parse is not
1109	def status.interim(m: Maybe<&2, U32>) -> Bool:
1110	  match m:
1111	    case None{}:
1112	      False{}
1113	    case Some{+n}:
1114	      Bool.and(U32.is_le(100, n), U32.is_lt(n, 200))
1115	
1116	# a Content-Length that reads as a number, or the close when none does
1117	def frame.sized(m: Maybe<&2, Nat>) -> Frame:
1118	  match m:
1119	    case None{}:
1120	      Closed{}
1121	    case Some{n}:
1122	      Sized{n}
1123	
1124	# Content-Length values that agree frame the body; any others leave the close
1125	def frame.agree(+lens: List<&2, String>, ok: Bool) -> Frame:
1126	  match ok:
1127	    case False{}:
1128	      Closed{}
1129	    case True{}:
1130	      frame.sized(digits.read(first(lens)))
1131	
1132	# chunked framing wins over Content-Length (RFC 9112 §6.3 item 4)
1133	def frame.te(+lens: List<&2, String>, chunked: Bool) -> Frame:
1134	  match chunked:
1135	    case True{}:
1136	      Chunked{}
1137	    case False{}:
1138	      frame.agree(lens, clen.agree(lens))
1139	
1140	# the framing of a response: none when bare (a reply to HEAD, a 204 or a 304),
1141	# else Transfer-Encoding chunked, else Content-Length, else the close
1142	def frame(bare: Bool, te: String, +lens: List<&2, String>) -> Frame:
1143	  match bare:
1144	    case True{}:
1145	      Bare{}
1146	    case False{}:
1147	      frame.te(lens, String.contains(String.to_lower(te), "chunked"))
1148	
1149	# a zero chunk's trailer section has ended: at once, or after its fields
1150	def chunks.trailer(+after: String) -> Bool:
1151	  Bool.or(String.starts_with(after, "\r\n"), String.contains(after, "\r\n\r\n"))
1152	
1153	# a chunk that has all arrived: on to the next chunk header, else not yet
1154	def chunks.ended.data(+after: String, +n: Nat, ready: Bool,
1155	  rest: Cut -> Bool) -> Bool:
1156	  match ready:
1157	    case False{}:
1158	      False{}
1159	    case True{}:
1160	      rest(divide(octs.drop(after, Nat.add(n, 2n)), "\r\n"))
1161	
1162	# a chunk of size n: the last one when n is 0
1163	def chunks.ended.size(+after: String, +n: Nat, zero: Bool,
1164	  rest: Cut -> Bool) -> Bool:
1165	  match zero:
1166	    case True{}:
1167	      chunks.trailer(after)
1168	    case False{}:
1169	      chunks.ended.data(after, n, chunks.ready(after, n), rest)
1170	
1171	# a chunk header: a size that is not hex ends the read (the parse rejects it)
1172	def chunks.ended.hex(+before: String, +after: String, ok: Bool,
1173	  rest: Cut -> Bool) -> Bool:
1174	  match ok:
1175	    case False{}:
1176	      True{}
1177	    case True{}:
1178	      +n = hexlen(before)
1179	      chunks.ended.size(after, n, Nat.is_eq(n, 0n), rest)
1180	
1181	# a chunk header that has arrived, or not yet
1182	def chunks.ended.at(c: Cut, rest: Cut -> Bool) -> Bool:
1183	  match c:
1184	    case NoCut{}:
1185	      False{}
1186	    case Cut{+before, +after}:
1187	      chunks.ended.hex(before, after, hex.well(chunks.token(before)), rest)
1188	
1189	# whether a chunked body has reached the end of its last chunk
1190	def chunks.ended(fuel: Nat, c: Cut) -> Bool:
1191	  match fuel:
1192	    case 0n:
1193	      False{}
1194	    case 1n+f:
1195	      chunks.ended.at(c, cut => chunks.ended(f, cut))
1196	
1197	# whether a body has all arrived under its framing
1198	def whole.of(f: Frame, +body: String) -> Bool:
1199	  match f:
1200	    case Bare{}:
1201	      True{}
1202	    case Sized{n}:
1203	      Bool.not(Nat.is_lt(octs.len(body), n))
1204	    case Chunked{}:
1205	      chunks.ended(String.length(body), divide(body, "\r\n"))
1206	    case Closed{}:
1207	      False{}
1208	
1209	# a head that is interim: whole when what follows is; else whole under the
1210	# framing it gives
1211	def whole.step(asked: Bool, +ls: List<&2, String>, +after: String,
1212	  interim: Bool, rest: Cut -> Bool) -> Bool:
1213	  match interim:
1214	    case True{}:
1215	      rest(divide(after, "\r\n\r\n"))
1216	    case False{}:
1217	      whole.of(frame(Bool.or(asked, status.bare(status.of(ls))),
1218	        head.go(ls, "transfer-encoding"), head.values(ls, "content-length")),
1219	        after)
1220	
1221	# a response whose head has ended, or not yet
1222	def whole.at(asked: Bool, c: Cut, rest: Cut -> Bool) -> Bool:
1223	  match c:
1224	    case NoCut{}:
1225	      False{}
1226	    case Cut{before, after}:
1227	      +ls = String.lines(before)
1228	      whole.step(asked, ls, after, status.interim(status.of(ls)), rest)
1229	
1230	# the heads in turn, at most `fuel` of them
1231	def whole.go(fuel: Nat, +asked: Bool, c: Cut) -> Bool:
1232	  match fuel:
1233	    case 0n:
1234	      False{}
1235	    case 1n+f:
1236	      whole.at(asked, c, cut => whole.go(f, asked, cut))
1237	
1238	# whether the text received so far is a whole response to a request with
1239	# this method (RFC 9112 §6.3), interim 1xx heads read past (RFC 9110 §15.2);
1240	# a response framed by the close never is
1241	def whole(+method: String, +raw: String) -> Bool:
1242	  whole.go(String.length(raw), String.eq(method, "HEAD"),
1243	    divide(raw, "\r\n\r\n"))
1244	
1245	# --- a response read by the request's method (RFC 9110 §15.2, §6.4.1) ---
1246	
1247	# a 1xx, 204 or 304 response has no body (RFC 9110 §6.4.1)
1248	def status.empty(+m: Maybe<&2, U32>) -> Bool:
1249	  Bool.or(status.interim(m), status.bare(m))
1250	
1251	# an interim head is skipped when more text follows it
1252	def interim.skip(m: Maybe<&2, U32>, after: String) -> Bool:
1253	  Bool.and(status.interim(m), Bool.not(String.is_empty(after)))
1254	
1255	# the final head with no body: its status and fields, an empty body
1256	def parse.to.bare(m: Maybe<&2, U32>, ls: List<&2, String>) -> Reply:
1257	  match m:
1258	    case None{}:
1259	      Torn{"the response has no status line"}
1260	    case Some{n}:
1261	      Reply{n, head.list(ls), ""}
1262	
1263	# the final head: with no body, or framed as parse frames it
1264	def parse.to.final(m: Maybe<&2, U32>, +ls: List<&2, String>, after: String,
1265	  bare: Bool) -> Reply:
1266	  match bare:
1267	    case True{}:
1268	      parse.to.bare(m, ls)
1269	    case False{}:
1270	      parse.status(m, ls, after)
1271	
1272	# an interim head is skipped, any other is the final one
1273	def parse.to.step(head: Bool, +ls: List<&2, String>, +m: Maybe<&2, U32>,
1274	  +after: String, skip: Bool, rest: Cut -> Reply) -> Reply:
1275	  match skip:
1276	    case True{}:
1277	      rest(divide(after, "\r\n\r\n"))
1278	    case False{}:
1279	      parse.to.final(m, ls, after, Bool.or(head, status.empty(m)))
1280	
1281	# a head that has ended, or the reason it has not
1282	def parse.to.at(head: Bool, c: Cut, rest: Cut -> Reply) -> Reply:
1283	  match c:
1284	    case NoCut{}:
1285	      Torn{"the response head has no blank line after it"}
1286	    case Cut{before, +after}:
1287	      +ls = String.lines(before)
1288	      +m = status.of(ls)
1289	      parse.to.step(head, ls, m, after, interim.skip(m, after), rest)
1290	
1291	# the heads in turn, at most `fuel` of them
1292	def parse.to.go(fuel: Nat, +head: Bool, c: Cut) -> Reply:
1293	  match fuel:
1294	    case 0n:
1295	      Torn{"the response head has no blank line after it"}
1296	    case 1n+f:
1297	      parse.to.at(head, c, cut => parse.to.go(f, head, cut))
1298	
1299	# the response to a request with this method (RFC 9112 §6.3): interim 1xx
1300	# heads skipped, and no body for HEAD or a 1xx, 204 or 304 final status
1301	def parse.to(+method: String, +raw: String) -> Reply:
1302	  parse.to.go(String.length(raw), String.eq(method, "HEAD"),
1303	    divide(raw, "\r\n\r\n"))
1304	
1305	# --- when a response has all arrived, judged read by read (SPEC.md HTTP-CLI-12) ---
1306	#
1307	# The client judges the text it has received after every read. Judging the
1308	# whole text each time (whole) costs the whole text each time; the state
1309	# below carries the judgement from one read to the next, so a read costs what
1310	# it brought (and the head, while no final head has ended). hear.more(
1311	# hear.of(method, a), b) is hear.of(method, a ++ b), and hear.done of it is
1312	# whole(method, a ++ b).
1313	
1314	# bytes of UTF-8 walked off the front of a string: all of it, with this many
1315	# still owed, or a stop at the first character that does not fit in what was
1316	# left, with what was left and the text from that character on
1317	type Skip is Data:
1318	  Short{owed: Nat}
1319	  Over{left: Nat, rest: String}
1320	
1321	# one step of the skip: a character wider than what is left stops it
1322	def octs.skip.step(short: Bool, +n: Nat, h: Char, t: String,
1323	  rest: Unit -> Skip) -> Skip:
1324	  match short:
1325	    case True{}:
1326	      Over{n, SCon{h, t}}
1327	    case False{}:
1328	      rest(Unit{})
1329	
1330	# walk n bytes of UTF-8 off a string, as octs.drop does, saying how it ended
1331	def octs.skip(s: String, +n: Nat) -> Skip:
1332	  match s:
1333	    case SNil{}:
1334	      Short{n}
1335	    case SCon{+h, +t}:
1336	      +w = octs.width(Char.to_u32(h))
1337	      octs.skip.step(Nat.is_lt(n, w), n, h, t, _u => octs.skip(t, Nat.sub(n, w)))
1338	
1339	# where a chunked body's walk stands: ended; waiting at a chunk header (or the
1340	# last chunk's trailer) that has not all arrived; inside a chunk's data with
1341	# octets still owed; or at the end of a chunk's data, at what should be its
1342	# CRLF. `fuel` is what chunks.ended would have left there.
1343	type Walk is Data:
1344	  Ended{}
1345	  Hold{fuel: Nat, rest: String}
1346	  Owed{fuel: Nat, owed: Nat}
1347	  Tail{fuel: Nat, left: Nat, rest: String}
1348	
1349	# a chunk's data skipped: whether its CRLF has arrived, and on to the next
1350	# chunk header when it has
1351	def walk.crlf(g: Nat, +left: Nat, +rest: String, ready: Bool,
1352	  go: String -> Walk) -> Walk:
1353	  match ready:
1354	    case True{}:
1355	      go(octs.drop(rest, Nat.add(left, 2n)))
1356	    case False{}:
1357	      Tail{g, left, rest}
1358	
1359	# a chunk's data: all of what arrived, with octets still owed, or its end
1360	def walk.data(+g: Nat, s: Skip, go: String -> Walk) -> Walk:
1361	  match s:
1362	    case Short{owed}:
1363	      Owed{g, owed}
1364	    case Over{+left, +rest}:
1365	      walk.crlf(g, left, rest, Bool.and(octs.has(rest, Nat.add(left, 2n)),
1366	        String.starts_with(rest, "\r\n")), go)
1367	
1368	# the last chunk: ended once its trailer section has
1369	def walk.trail(g: Nat, rest: String, ended: Bool) -> Walk:
1370	  match ended:
1371	    case True{}:
1372	      Ended{}
1373	    case False{}:
1374	      Hold{1n+g, rest}
1375	
1376	# a chunk of size n: the last one when n is 0
1377	def walk.size(+g: Nat, rest: String, +after: String, +n: Nat, zero: Bool,
1378	  go: String -> Walk) -> Walk:
1379	  match zero:
1380	    case True{}:
1381	      walk.trail(g, rest, chunks.trailer(after))
1382	    case False{}:
1383	      walk.data(g, octs.skip(after, n), go)
1384	
1385	# a chunk header: a size that is not hex ends the walk (the parse rejects it)
1386	def walk.hex(+g: Nat, rest: String, +before: String, +after: String, ok: Bool,
1387	  go: String -> Walk) -> Walk:
1388	  match ok:
1389	    case False{}:
1390	      Ended{}
1391	    case True{}:
1392	      +n = hexlen(before)
1393	      walk.size(g, rest, after, n, Nat.is_eq(n, 0n), go)
1394	
1395	# a chunk header that has arrived, or not yet
1396	def walk.at(+g: Nat, rest: String, c: Cut, go: String -> Walk) -> Walk:
1397	  match c:
1398	    case NoCut{}:
1399	      Hold{1n+g, rest}
1400	    case Cut{+before, +after}:
1401	      walk.hex(g, rest, before, after, hex.well(chunks.token(before)), go)
1402	
1403	# the walk of chunks.ended from the chunk header at the front of a text
1404	def walk(fuel: Nat, +rest: String) -> Walk:
1405	  match fuel:
1406	    case 0n:
1407	      Hold{0n, rest}
1408	    case 1n+f:
1409	      +g = f
1410	      walk.at(g, rest, divide(rest, "\r\n"), s => walk(g, s))
1411	
1412	# whether the walk has ended
1413	def walk.done(w: Walk) -> Bool:
1414	  match w:
1415	    case Ended{}:
1416	      True{}
1417	    case Hold{fuel, rest}:
1418	      False{}
1419	    case Owed{fuel, owed}:
1420	      False{}
1421	    case Tail{fuel, left, rest}:
1422	      False{}
1423	
1424	# the walk once m more characters, b, have arrived
1425	def walk.more(w: Walk, +m: Nat, b: String) -> Walk:
1426	  match w:
1427	    case Ended{}:
1428	      Ended{}
1429	    case Hold{fuel, rest}:
1430	      walk(Nat.add(fuel, m), rest ++ b)
1431	    case Owed{g, owed}:
1432	      +f = Nat.add(g, m)
1433	      walk.data(f, octs.skip(b, owed), s => walk(f, s))
1434	    case Tail{g, left, rest}:
1435	      +f = Nat.add(g, m)
1436	      walk.data(f, Over{left, rest ++ b}, s => walk(f, s))
1437	
1438	# where a response stands: no final head yet (with the text from the head
1439	# being read on, and the fuel whole.go would have there); no body, so whole;
1440	# framed by the close, so never whole; sized, with the octets that have
1441	# arrived; or chunked, with its walk
1442	type Hear is Data:
1443	  Heads{fuel: Nat, asked: Bool, raw: String}
1444	  Whole{}
1445	  Never{}
1446	  Count{n: Nat, have: Nat}
1447	  Walking{w: Walk}
1448	
1449	# a final head's body under its framing
1450	def hear.body(f: Frame, +after: String) -> Hear:
1451	  match f:
1452	    case Bare{}:
1453	      Whole{}
1454	    case Sized{n}:
1455	      Count{n, octs.len(after)}
1456	    case Chunked{}:
1457	      Walking{walk(String.length(after), after)}
1458	    case Closed{}:
1459	      Never{}
1460	
1461	# an interim head: on to the next; a final one: its body
1462	def hear.step(asked: Bool, +ls: List<&2, String>, +after: String,
1463	  interim: Bool, go: String -> Hear) -> Hear:
1464	  match interim:
1465	    case True{}:
1466	      go(after)
1467	    case False{}:
1468	      hear.body(frame(Bool.or(asked, status.bare(status.of(ls))),
1469	        head.go(ls, "transfer-encoding"), head.values(ls, "content-length")),
1470	        after)
1471	
1472	# a head that has ended, or not yet
1473	def hear.at(+g: Nat, +asked: Bool, raw: String, c: Cut, go: String -> Hear)
1474	  -> Hear:
1475	  match c:
1476	    case NoCut{}:
1477	      Heads{1n+g, asked, raw}
1478	    case Cut{before, after}:
1479	      +ls = String.lines(before)
1480	      hear.step(asked, ls, after, status.interim(status.of(ls)), go)
1481	
1482	# the heads in turn, as whole.go reads them
1483	def hear.go(fuel: Nat, +asked: Bool, +raw: String) -> Hear:
1484	  match fuel:
1485	    case 0n:
1486	      Heads{0n, asked, raw}
1487	    case 1n+f:
1488	      +g = f
1489	      hear.at(g, asked, raw, divide(raw, "\r\n\r\n"), s => hear.go(g, asked, s))
1490	
1491	# where a response to a request with this method stands, read from the
1492	# whole text received so far
1493	def hear.of(+method: String, +raw: String) -> Hear:
1494	  hear.go(String.length(raw), String.eq(method, "HEAD"), raw)
1495	
1496	# whether the response has all arrived
1497	def hear.done(h: Hear) -> Bool:
1498	  match h:
1499	    case Heads{fuel, asked, raw}:
1500	      False{}
1501	    case Whole{}:
1502	      True{}
1503	    case Never{}:
1504	      False{}
1505	    case Count{n, have}:
1506	      Bool.not(Nat.is_lt(have, n))
1507	    case Walking{w}:
1508	      walk.done(w)
1509	
1510	# where a response stands once more text, b, has arrived
1511	def hear.more(h: Hear, +b: String) -> Hear:
1512	  match h:
1513	    case Heads{fuel, asked, raw}:
1514	      hear.go(Nat.add(fuel, String.length(b)), asked, raw ++ b)
1515	    case Whole{}:
1516	      Whole{}
1517	    case Never{}:
1518	      Never{}
1519	    case Count{n, have}:
1520	      Count{n, Nat.add(have, octs.len(b))}
1521	    case Walking{w}:
1522	      Walking{walk.more(w, String.length(b), b)}
1523	
1524	# --- a response's reason phrase (RFC 9112 §4) ---
1525	
1526	# a reason phrase with the CR its line ended with removed; a reason-phrase
1527	# itself holds no CR (RFC 9112 §4)
1528	def phrase.chop.at(
1529	  cr: Bool,
1530	  ch: Char,
1531	  tl: String,
1532	  rest: Unit -> String
1533	) -> String:
1534	  match cr tl:
1535	    case True{} SNil{}:
1536	      SNil{}
1537	    case True{} SCon{x, xt}:
1538	      SCon{ch, rest(Unit{})}
1539	    case False{} _:
1540	      SCon{ch, rest(Unit{})}
1541	
1542	# the text of a reason phrase, a final CR removed
1543	def phrase.chop(text: String) -> String:
1544	  match text:
1545	    case SNil{}:
1546	      SNil{}
1547	    case SCon{+ch, +tl}:
1548	      phrase.chop.at(Char.is_eq(ch, '\r'), ch, tl, _u => phrase.chop(tl))
1549	
1550	# what follows the status code's SP: the reason phrase; none without that SP
1551	def phrase.code(cut: Cut) -> String:
1552	  match cut:
1553	    case NoCut{}:
1554	      ""
1555	    case Cut{before, after}:
1556	      phrase.chop(after)
1557	
1558	# what follows the version's SP: the status code, an SP and the reason
1559	def phrase.after(cut: Cut) -> String:
1560	  match cut:
1561	    case NoCut{}:
1562	      ""
1563	    case Cut{before, after}:
1564	      phrase.code(divide(after, " "))
1565	
1566	# a status line's reason phrase (RFC 9112 §4: HTTP-version SP status-code SP
1567	# [ reason-phrase ]), empty when the line has fewer than two SPs
1568	def phrase.line(line: String) -> String:
1569	  phrase.after(divide(line, " "))
1570	
1571	# an interim head is skipped, any other gives the reason on its first line
1572	def phrase.to.step(
1573	  +ls: List<&2, String>,
1574	  +after: String,
1575	  skip: Bool,
1576	  rest: Cut -> String
1577	) -> String:
1578	  match skip:
1579	    case True{}:
1580	      rest(divide(after, "\r\n\r\n"))
1581	    case False{}:
1582	      phrase.line(first(ls))
1583	
1584	# a head that has ended, or none
1585	def phrase.to.at(cut: Cut, rest: Cut -> String) -> String:
1586	  match cut:
1587	    case NoCut{}:
1588	      ""
1589	    case Cut{before, +after}:
1590	      +ls = String.lines(before)
1591	      phrase.to.step(ls, after, interim.skip(status.of(ls), after), rest)
1592	
1593	# the heads in turn, at most `fuel` of them
1594	def phrase.to.go(fuel: Nat, cut: Cut) -> String:
1595	  match fuel:
1596	    case 0n:
1597	      ""
1598	    case 1n+f:
1599	      phrase.to.at(cut, next => phrase.to.go(f, next))
1600	
1601	# the reason phrase of the head parse.to stops at: interim 1xx heads with
1602	# text after them skipped, empty when no head ends
1603	def phrase.to(+raw: String) -> String:
1604	  phrase.to.go(String.length(raw), divide(raw, "\r\n\r\n"))