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	# bytes one code point takes in UTF-8. Content-Length counts octets
127	# (RFC 9110 §8.6); a Bend String counts code points.
128	def utf8.width(+u: U32) -> Nat:
129	  Bool.pick(Nat, U32.is_lt(u, 128), 1n,
130	    Bool.pick(Nat, U32.is_lt(u, 2048), 2n,
131	      Bool.pick(Nat, U32.is_lt(u, 65536), 3n, 4n)))
132	
133	# how many bytes of UTF-8 a string is
134	def utf8.len(s: String) -> Nat:
135	  match s:
136	    case SNil{}:
137	      0n
138	    case SCon{h, t}:
139	      Nat.add(utf8.width(Char.to_u32(h)), utf8.len(t))
140	
141	# one step of the take
142	def utf8.take.step(short: Bool, h: Char, rest: Unit -> String) -> String:
143	  match short:
144	    case True{}:
145	      SNil{}
146	    case False{}:
147	      SCon{h, rest(Unit{})}
148	
149	# the front of a string that is this many bytes of UTF-8
150	def utf8.take(s: String, +n: Nat) -> String:
151	  match s:
152	    case SNil{}:
153	      SNil{}
154	    case SCon{+h, t}:
155	      +w = utf8.width(Char.to_u32(h))
156	      utf8.take.step(Nat.is_lt(n, w), h, _u => utf8.take(t, Nat.sub(n, w)))
157	
158	# one step of the drop
159	def utf8.drop.step(short: Bool, h: Char, t: String,
160	  rest: Unit -> String) -> String:
161	  match short:
162	    case True{}:
163	      SCon{h, t}
164	    case False{}:
165	      rest(Unit{})
166	
167	# the rest of a string after this many bytes of UTF-8
168	def utf8.drop(s: String, +n: Nat) -> String:
169	  match s:
170	    case SNil{}:
171	      SNil{}
172	    case SCon{+h, +t}:
173	      +w = utf8.width(Char.to_u32(h))
174	      utf8.drop.step(Nat.is_lt(n, w), h, t, _u => utf8.drop(t, Nat.sub(n, w)))
175	
176	# a decimal digit's value, or 10 when the character is not a digit
177	def digits.val.of(+u: U32) -> U32:
178	  Bool.pick(U32, Bool.and(U32.is_ge(u, 48), U32.is_le(u, 57)), U32.sub(u, 48), 10)
179	
180	# a decimal digit's value, or 10 when the character is not a digit
181	def digits.val(c: Char) -> U32:
182	  digits.val.of(Char.to_u32(c))
183	
184	# accept one digit and keep reading, or stop when it is not a digit
185	def digits.step(ok: Bool, next: Unit -> Maybe<&2, Nat>) -> Maybe<&2, Nat>:
186	  match ok:
187	    case False{}:
188	      None{}
189	    case True{}:
190	      next(Unit{})
191	
192	# read a decimal token without building Base's Nat.read ceiling
193	def digits.go(s: String, +acc: Nat, left: Nat) -> Maybe<&2, Nat>:
194	  match s left:
195	    case _ 0n:
196	      None{}
197	    case SNil{} 1n+k:
198	      Some{acc}
199	    case SCon{+h, t} 1n+k:
200	      +d = digits.val(h)
201	      digits.step(U32.is_lt(d, 10),
202	        _u => digits.go(t, Nat.add(Nat.mul(acc, 10n), U32.to_nat(d)), k))
203	
204	# a short decimal (Content-Length, max-age). Empty is none. At most 9 digits.
205	def digits.read(s: String) -> Maybe<&2, Nat>:
206	  match s:
207	    case SNil{}:
208	      None{}
209	    case SCon{h, t}:
210	      digits.go(SCon{h, t}, 0n, 9n)
211	
212	# a non-zero chunk has its data and the following CRLF
213	def chunks.ready(+after: String, +n: Nat) -> Bool:
214	  Bool.and(Bool.not(Nat.is_lt(utf8.len(after), Nat.add(n, 2n))),
215	    String.starts_with(utf8.drop(after, n), "\r\n"))
216	
217	# the next scan step, or why this chunk header is not usable
218	type Next is Data:
219	  Stop{}
220	  Go{cut: Cut}
221	  Reject{why: String}
222	
223	# one chunk header: reject non-hex sizes, stop on the 0 chunk, else continue
224	def chunks.next.of(zero: Bool, ready: Bool, +after: String, +n: Nat) -> Next:
225	  match zero ready:
226	    case True{} _:
227	      Stop{}
228	    case False{} False{}:
229	      Reject{"the chunked body stopped short"}
230	    case False{} True{}:
231	      Go{divide(utf8.drop(after, Nat.add(n, 2n)), "\r\n")}
232	
233	# hex check, then the length
234	def chunks.next.hex(+before: String, +after: String, ok: Bool) -> Next:
235	  match ok:
236	    case False{}:
237	      Reject{"chunk size is not hexadecimal"}
238	    case True{}:
239	      +n = hexlen(before)
240	      chunks.next.of(Nat.is_eq(n, 0n), chunks.ready(after, n), after, n)
241	
242	# classify one chunk header (RFC 9112 §7.1)
243	def chunks.next(+before: String, +after: String) -> Next:
244	  chunks.next.hex(before, after, hex.well(chunks.token(before)))
245	
246	# apply one scan step
247	def chunks.scan.step(step: Next, rest: Cut -> Maybe<&2, String>)
248	  -> Maybe<&2, String>:
249	  match step:
250	    case Stop{}:
251	      None{}
252	    case Reject{why}:
253	      Some{why}
254	    case Go{cut}:
255	      rest(cut)
256	
257	# None when every chunk size is hex and the 0 chunk is reached
258	def chunks.scan(fuel: Nat, c: Cut) -> Maybe<&2, String>:
259	  match fuel c:
260	    case 0n _:
261	      Some{"the chunked body is truncated"}
262	    case 1n+f NoCut{}:
263	      None{}
264	    case 1n+f Cut{before, +after}:
265	      chunks.scan.step(chunks.next(before, after), cut => chunks.scan(f, cut))
266	
267	# a zero chunk ends the body; anything after it is a trailer (RFC 9112 §7.1)
268	def chunks.more(+n: Nat, +after: String, rest: Unit -> String, zero: Bool)
269	  -> String:
270	  match zero:
271	    case True{}:
272	      ""
273	    case False{}:
274	      utf8.take(after, n)
275	        ++ rest(Unit{})
276	
277	# a chunked body put back together (RFC 9112 §7.1)
278	def chunks(fuel: Nat, c: Cut) -> String:
279	  match fuel c:
280	    case 0n _:
281	      ""
282	    case 1n+f NoCut{}:
283	      ""
284	    case 1n+f Cut{before, +after}:
285	      +n = hexlen(before)
286	      chunks.more(n, after,
287	        _u => chunks(f, divide(utf8.drop(after, Nat.add(n, 2n)), "\r\n")),
288	        Nat.is_eq(n, 0n))
289	
290	# a Transfer-Encoding: chunked body as the octets it stands for
291	def dechunk(+s: String) -> String:
292	  chunks(String.length(s), divide(s, "\r\n"))
293	
294	# whether a head line names this header (field names are case-insensitive:
295	# RFC 9110 §5.1)
296	def head.hit(h: String, +name: String) -> Bool:
297	  String.starts_with(String.to_lower(h), name ++ ":")
298	
299	# this line's value when it is the header asked for
300	def head.pick(hit: Bool, h: String, name: String, rest: String) -> String:
301	  match hit:
302	    case True{}:
303	      String.trim(String.drop(h, Nat.add(String.length(name), 1n)))
304	    case False{}:
305	      rest
306	
307	# the value a head gave a header, "" when it gave none
308	def head.go(ls: List<&2, String>, +name: String) -> String:
309	  match ls:
310	    case []:
311	      ""
312	    case +h <> t:
313	      head.pick(head.hit(h, name), h, name, head.go(t, name))
314	
315	# this line's trimmed field value
316	def head.value(h: String, name: String) -> String:
317	  String.trim(String.drop(h, Nat.add(String.length(name), 1n)))
318	
319	# cons a value when the line is the header asked for
320	def head.values.cons(hit: Bool, value: String, rest: Unit -> List<&2, String>)
321	  -> List<&2, String>:
322	  match hit:
323	    case False{}:
324	      rest(Unit{})
325	    case True{}:
326	      value <> rest(Unit{})
327	
328	# every value a head gave a header, in order (RFC 9112 §6.3 lists Content-Length)
329	def head.values(ls: List<&2, String>, +name: String) -> List<&2, String>:
330	  match ls:
331	    case []:
332	      []
333	    case +h <> t:
334	      head.values.cons(head.hit(h, name), head.value(h, name),
335	        _u => head.values(t, name))
336	
337	# a field value still holding a line break is obs-fold, which we refuse
338	def field.folded(+value: String) -> Bool:
339	  Bool.or(String.contains(value, "\n"), String.contains(value, "\r"))
340	
341	# a trimmed field value, or none when it still contains obs-fold
342	def field.keep(name: String, +value: String, folded: Bool) -> Maybe<&2, Header>:
343	  match folded:
344	    case True{}:
345	      None{}
346	    case False{}:
347	      Some{H{name, value}}
348	
349	# name and trimmed value from a cut at the first colon
350	def head.from_kept(before: String, +after: String) -> Maybe<&2, Header>:
351	  +value = String.trim(after)
352	  field.keep(before, value, field.folded(value))
353	
354	# one header line as a Header, or none when it has no colon
355	def head.from_cut(c: Cut) -> Maybe<&2, Header>:
356	  match c:
357	    case NoCut{}:
358	      None{}
359	    case Cut{before, after}:
360	      head.from_kept(before, after)
361	
362	# one header line as a Header, or none when it has no colon
363	def head.line(h: String) -> Maybe<&2, Header>:
364	  head.from_cut(divide(h, ":"))
365	
366	# prepend a parsed header when present
367	def head.cons(m: Maybe<&2, Header>, rest: List<&2, Header>) -> List<&2, Header>:
368	  match m:
369	    case None{}:
370	      rest
371	    case Some{hdr}:
372	      hdr <> rest
373	
374	# header lines after the status line as a list of fields
375	def head.list(ls: List<&2, String>) -> List<&2, Header>:
376	  match ls:
377	    case []:
378	      []
379	    case h <> t:
380	      head.cons(head.line(h), head.list(t))
381	
382	# one request header line
383	def header.line(h: Header) -> String:
384	  match h:
385	    case H{name, value}:
386	      name ++ ": " ++ value ++ "\r\n"
387	
388	# the value when this field is the one asked for
389	def headers.find.pick(value: String, hit: Bool, rest: Unit -> String) -> String:
390	  match hit:
391	    case True{}:
392	      value
393	    case False{}:
394	      rest(Unit{})
395	
396	# case-insensitive field lookup (RFC 9110 §5.1)
397	def headers.find.go(hs: List<&2, Header>, +name: String) -> String:
398	  match hs:
399	    case []:
400	      ""
401	    case H{n, v} <> t:
402	      headers.find.pick(v, String.eq(String.to_lower(n), name),
403	        _u => headers.find.go(t, name))
404	
405	# the value of a field, "" when it is absent
406	def headers.find(hs: List<&2, Header>, +name: String) -> String:
407	  headers.find.go(hs, String.to_lower(name))
408	
409	# extra headers rendered in order
410	def headers.lines(hs: List<&2, Header>) -> String:
411	  match hs:
412	    case []:
413	      ""
414	    case h <> t:
415	      header.line(h) ++ headers.lines(t)
416	
417	# Content-Length line when the body is not empty (RFC 9110 §8.6)
418	def clen.line(+n: Nat, empty: Bool) -> String:
419	  match empty:
420	    case True{}:
421	      ""
422	    case False{}:
423	      "Content-Length: " ++ Nat.show(n) ++ "\r\n"
424	
425	# a request-line and headers (RFC 9112 §3, §5). Absolute-path request-target
426	# (RFC 9112 §3.2.1). Connection: close so the connection end frames the body
427	# when no Content-Length / chunked framing applies (RFC 9112 §9.6 / §6.3).
428	def request(method: String, host: String, path: String,
429	  headers: List<&2, Header>, +body: String) -> String:
430	  +n = utf8.len(body)
431	  method ++ " " ++ path ++ " HTTP/1.1\r\n"
432	    ++ "Host: " ++ host ++ "\r\n"
433	    ++ "User-Agent: ezhttp\r\n"
434	    ++ "Accept: */*\r\n"
435	    ++ "Connection: close\r\n"
436	    ++ headers.lines(headers)
437	    ++ clen.line(n, Nat.is_eq(n, 0n))
438	    ++ "\r\n"
439	    ++ body
440	
441	# the port a scheme implies: 443 for a secure one, 80 otherwise (RFC 9110
442	# §4.2.1, §4.2.2)
443	def port.dflt(secure: Bool) -> U32:
444	  match secure:
445	    case True{}:
446	      443
447	    case False{}:
448	      80
449	
450	# the Host field value once it is known whether the port is the default
451	def authority.of(host: String, +port: U32, dflt: Bool) -> String:
452	  match dflt:
453	    case True{}:
454	      host
455	    case False{}:
456	      host ++ ":" ++ U32.show(port)
457	
458	# the Host field value: the host, and the port after a colon unless it is the
459	# scheme's default (RFC 9110 §7.2)
460	def authority(secure: Bool, host: String, +port: U32) -> String:
461	  authority.of(host, port, U32.is_eq(port, port.dflt(secure)))
462	
463	# the request a client sends to host and port, over TLS when secure
464	def request.at(method: String, secure: Bool, host: String, port: U32,
465	  path: String, headers: List<&2, Header>, body: String) -> String:
466	  request(method, authority(secure, host, port), path, headers, body)
467	
468	# GET with optional headers
469	def get_req(host: String, path: String, headers: List<&2, Header>) -> String:
470	  request("GET", host, path, headers, "")
471	
472	# HEAD with optional headers (RFC 9110 §9.3.2): same as GET, no body
473	def head_req(host: String, path: String, headers: List<&2, Header>) -> String:
474	  request("HEAD", host, path, headers, "")
475	
476	# POST with body and optional headers
477	def post_req(host: String, path: String, headers: List<&2, Header>,
478	  body: Body.Body) -> String:
479	  request("POST", host, path, headers, Body.body.payload(body))
480	
481	# PUT with body and optional headers (RFC 9110 §9.3.4)
482	def put_req(host: String, path: String, headers: List<&2, Header>,
483	  body: Body.Body) -> String:
484	  request("PUT", host, path, headers, Body.body.payload(body))
485	
486	# DELETE with body and optional headers (RFC 9110 §9.3.5)
487	def delete_req(host: String, path: String, headers: List<&2, Header>,
488	  body: Body.Body) -> String:
489	  request("DELETE", host, path, headers, Body.body.payload(body))
490	
491	# OPTIONS with optional headers (RFC 9110 §9.3.7). No request body.
492	def options_req(host: String, path: String, headers: List<&2, Header>) -> String:
493	  request("OPTIONS", host, path, headers, "")
494	
495	# GET, HEAD, and OPTIONS are safe (RFC 9110 §9.2.1). Tokens are case-sensitive.
496	def method.safe(+method: String) -> Bool:
497	  Bool.or(String.eq(method, "GET"),
498	    Bool.or(String.eq(method, "HEAD"), String.eq(method, "OPTIONS")))
499	
500	# safe methods, plus PUT and DELETE, are idempotent (RFC 9110 §9.2.2)
501	def method.idempotent(+method: String) -> Bool:
502	  Bool.or(method.safe(method),
503	    Bool.or(String.eq(method, "PUT"), String.eq(method, "DELETE")))
504	
505	# the rest of a token once this character is known
506	def token.ok.step(space: Bool, rest: Unit -> Bool) -> Bool:
507	  match space:
508	    case True{}:
509	      False{}
510	    case False{}:
511	      rest(Unit{})
512	
513	# a bearer token has no whitespace (RFC 6750 §2.1)
514	def token.ok(s: String) -> Bool:
515	  match s:
516	    case SNil{}:
517	      True{}
518	    case SCon{h, t}:
519	      token.ok.step(Char.is_space(h), _u => token.ok(t))
520	
521	# origin-form request-target: absolute-path, optional query (RFC 9112 §3.2.1)
522	def target.origin(path: String) -> Bool:
523	  String.starts_with(path, "/")
524	
525	# asterisk-form is only `*` and only for OPTIONS (RFC 9112 §3.2.4)
526	def target.asterisk(method: String, star: Bool) -> Bool:
527	  match star:
528	    case False{}:
529	      False{}
530	    case True{}:
531	      String.eq(method, "OPTIONS")
532	
533	# origin-form, or OPTIONS asterisk-form
534	def target.form(method: String, path: String, absolute: Bool) -> Bool:
535	  match absolute:
536	    case True{}:
537	      True{}
538	    case False{}:
539	      target.asterisk(method, String.eq(path, "*"))
540	
541	# a body against the length its head promised
542	def parse.short(status: U32, headers: List<&2, Header>, n: Nat, body: String,
543	  short: Bool) -> Reply:
544	  match short:
545	    case True{}:
546	      Torn{"the response body stopped before its Content-Length"}
547	    case False{}:
548	      Reply{status, headers, utf8.take(body, n)}
549	
550	# a body framed by Content-Length (RFC 9110 §8.6 / RFC 9112 §6.3)
551	def parse.clen(status: U32, headers: List<&2, Header>, +n: Nat, +body: String)
552	  -> Reply:
553	  parse.short(status, headers, n, body, Nat.is_lt(utf8.len(body), n))
554	
555	# Content-Length when present; else the rest of the connection is the body
556	def parse.len(status: U32, headers: List<&2, Header>, m: Maybe<&2, Nat>,
557	  body: String) -> Reply:
558	  match m:
559	    case None{}:
560	      Reply{status, headers, body}
561	    case Some{n}:
562	      parse.clen(status, headers, n, body)
563	
564	# every Content-Length text equals the first
565	def clen.agree.step(same: Bool, rest: Unit -> Bool) -> Bool:
566	  match same:
567	    case False{}:
568	      False{}
569	    case True{}:
570	      rest(Unit{})
571	
572	# the tail of a Content-Length list against the first value
573	def clen.agree.go(rest: List<&2, String>, +h: String) -> Bool:
574	  match rest:
575	    case []:
576	      True{}
577	    case x <> r:
578	      clen.agree.step(String.eq(x, h), _u => clen.agree.go(r, h))
579	
580	# duplicate Content-Length fields must be the same digits (RFC 9112 §6.3)
581	def clen.agree(vs: List<&2, String>) -> Bool:
582	  match vs:
583	    case []:
584	      True{}
585	    case h <> t:
586	      clen.agree.go(t, h)
587	
588	# whether any Content-Length field was present
589	def clen.any(vs: List<&2, String>) -> Bool:
590	  match vs:
591	    case []:
592	      False{}
593	    case h <> t:
594	      True{}
595	
596	# a chunked body, or why the chunk framing was rejected
597	def parse.chunked(status: U32, headers: List<&2, Header>, body: String,
598	  bad: Maybe<&2, String>) -> Reply:
599	  match bad:
600	    case None{}:
601	      Reply{status, headers, dechunk(body)}
602	    case Some{why}:
603	      Torn{why}
604	
605	# scan chunk sizes, then decode when they are hex and closed by 0
606	def parse.chunks(status: U32, headers: List<&2, Header>, +body: String) -> Reply:
607	  parse.chunked(status, headers, body,
608	    chunks.scan(String.length(body), divide(body, "\r\n")))
609	
610	# Transfer-Encoding together with Content-Length is a bad message
611	def parse.te.clash(status: U32, headers: List<&2, Header>, body: String,
612	  present: Bool) -> Reply:
613	  match present:
614	    case True{}:
615	      Torn{"Content-Length and Transfer-Encoding conflict"}
616	    case False{}:
617	      parse.chunks(status, headers, body)
618	
619	# chunked framing, or Content-Length, or the rest of the connection
620	def parse.te(status: U32, headers: List<&2, Header>, +lens: List<&2, String>,
621	  +body: String, chunked: Bool) -> Reply:
622	  match chunked:
623	    case False{}:
624	      parse.len(status, headers, digits.read(first(lens)), body)
625	    case True{}:
626	      parse.te.clash(status, headers, body, clen.any(lens))
627	
628	# disagreeing Content-Length values are torn before framing
629	def parse.agree(status: U32, headers: List<&2, Header>, te: String,
630	  +lens: List<&2, String>, body: String, ok: Bool) -> Reply:
631	  match ok:
632	    case False{}:
633	      Torn{"Content-Length values disagree"}
634	    case True{}:
635	      parse.te(status, headers, lens, body,
636	        String.contains(String.to_lower(te), "chunked"))
637	
638	# the headers that decide the framing (RFC 9112 §6.3)
639	def parse.frame(status: U32, headers: List<&2, Header>, te: String,
640	  +lens: List<&2, String>, body: String) -> Reply:
641	  parse.agree(status, headers, te, lens, body, clen.agree(lens))
642	
643	# a head whose status line has been read (RFC 9112 §4)
644	def parse.status(m: Maybe<&2, U32>, +ls: List<&2, String>, body: String)
645	  -> Reply:
646	  match m:
647	    case None{}:
648	      Torn{"the response has no status line"}
649	    case Some{n}:
650	      +hs = head.list(ls)
651	      parse.frame(n, hs, head.go(ls, "transfer-encoding"),
652	        head.values(ls, "content-length"), body)
653	
654	# the status code a head's first line names, if it names one (RFC 9112 §4)
655	def status.of(ls: List<&2, String>) -> Maybe<&2, U32>:
656	  U32.read(second(String.split(first(ls), ' ')))
657	
658	# the head's lines, with the status line read off the first
659	def parse.head(+ls: List<&2, String>, body: String) -> Reply:
660	  parse.status(status.of(ls), ls, body)
661	
662	# a response divided into its head and everything after the blank line
663	# (RFC 9112 §2.1: header section ends at empty line)
664	def parse.cut(c: Cut) -> Reply:
665	  match c:
666	    case NoCut{}:
667	      Torn{"the response head has no blank line after it"}
668	    case Cut{before, after}:
669	      parse.head(String.lines(before), after)
670	
671	# the status, headers, and body of a raw response
672	def parse(raw: String) -> Reply:
673	  parse.cut(divide(raw, "\r\n\r\n"))
674	
675	# a parsed response on one line, for a test to read
676	def show(r: Reply) -> String:
677	  match r:
678	    case Torn{why}:
679	      "torn " ++ why
680	    case Reply{status, headers, body}:
681	      U32.show(status) ++ " " ++ body
682	
683	# --- inbound request (server) and outbound response (server) ---
684	
685	# a request that came apart, or the reason it would not (RFC 9112 §3)
686	type Request is Data:
687	  Bad{why: String}
688	  Request{method: String, target: String, headers: List<&2, Header>,
689	    body: String}
690	
691	# a status code and its reason-phrase
692	type Phrase is Data:
693	  P{code: U32, text: String}
694	
695	# the reason-phrases RFC 9110 §15 names (RFC 6585 §4 for 429)
696	def reasons() -> List<&2, Phrase>:
697	  [P{200, "OK"}, P{201, "Created"}, P{202, "Accepted"}, P{204, "No Content"},
698	    P{301, "Moved Permanently"}, P{302, "Found"}, P{303, "See Other"},
699	    P{304, "Not Modified"}, P{307, "Temporary Redirect"},
700	    P{308, "Permanent Redirect"}, P{400, "Bad Request"},
701	    P{401, "Unauthorized"}, P{403, "Forbidden"}, P{404, "Not Found"},
702	    P{405, "Method Not Allowed"}, P{409, "Conflict"}, P{410, "Gone"},
703	    P{413, "Content Too Large"}, P{415, "Unsupported Media Type"},
704	    P{422, "Unprocessable Content"}, P{429, "Too Many Requests"},
705	    P{500, "Internal Server Error"}, P{501, "Not Implemented"},
706	    P{502, "Bad Gateway"}, P{503, "Service Unavailable"},
707	    P{504, "Gateway Timeout"}]
708	
709	# this phrase when its code is the one asked for, else the rest's
710	def reason.pick(text: String, hit: Bool, rest: Unit -> String) -> String:
711	  match hit:
712	    case True{}:
713	      text
714	    case False{}:
715	      rest(Unit{})
716	
717	# the phrase a list gives a code, "" when it gives none
718	def reason.in(ps: List<&2, Phrase>, +code: U32) -> String:
719	  match ps:
720	    case []:
721	      ""
722	    case P{c, text} <> t:
723	      reason.pick(text, U32.is_eq(code, c), _u => reason.in(t, code))
724	
725	# the reason-phrase for a status code (RFC 9112 §4); "" for one not listed
726	def reason(+code: U32) -> String:
727	  reason.in(reasons(), code)
728	
729	# status-line + headers + body (RFC 9112 §4, §5). Connection: close ends the
730	# exchange after one response.
731	def respond(+status: U32, headers: List<&2, Header>, +body: String) -> String:
732	  +n = utf8.len(body)
733	  "HTTP/1.1 " ++ U32.show(status) ++ " " ++ reason(status) ++ "\r\n"
734	    ++ "Connection: close\r\n"
735	    ++ headers.lines(headers)
736	    ++ clen.line(n, Nat.is_eq(n, 0n))
737	    ++ "\r\n"
738	    ++ body
739	
740	# 204 and 304 are terminated by the header section (RFC 9110 §15.3.5, §15.4.5)
741	def status.nocontent(+code: U32) -> Bool:
742	  Bool.or(U32.is_eq(code, 204), U32.is_eq(code, 304))
743	
744	# drop a 204/304 body; any other status keeps it
745	def respond.of.body(+status: U32, headers: List<&2, Header>, body: String,
746	  drop: Bool) -> String:
747	  match drop:
748	    case True{}:
749	      respond(status, headers, "")
750	    case False{}:
751	      respond(status, headers, body)
752	
753	# format a structured Reply as a response message
754	def respond.of(r: Reply) -> String:
755	  match r:
756	    case Torn{why}:
757	      respond(500, [], why)
758	    case Reply{+status, headers, body}:
759	      respond.of.body(status, headers, body, status.nocontent(status))
760	
761	# HEAD carries no message body; any other method keeps the body (RFC 9110 §9.3.2)
762	def reply.for.pick(reply: Reply, head: Bool) -> Reply:
763	  match reply head:
764	    case Torn{why} _:
765	      Torn{why}
766	    case Reply{status, headers, body} False{}:
767	      Reply{status, headers, body}
768	    case Reply{status, headers, body} True{}:
769	      Reply{status, headers, ""}
770	
771	# drop a HEAD response body before it is written
772	def reply.for(method: String, reply: Reply) -> Reply:
773	  reply.for.pick(reply, String.eq(method, "HEAD"))
774	
775	# the method token, or "" when the request did not parse
776	def method.of(req: Request) -> String:
777	  match req:
778	    case Bad{why}:
779	      ""
780	    case Request{method, target, headers, body}:
781	      method
782	
783	# request body against Content-Length
784	def ask.short(method: String, target: String, headers: List<&2, Header>,
785	  n: Nat, body: String, short: Bool) -> Request:
786	  match short:
787	    case True{}:
788	      Bad{"the request body stopped before its Content-Length"}
789	    case False{}:
790	      Request{method, target, headers, utf8.take(body, n)}
791	
792	# a request body framed by Content-Length (RFC 9110 §8.6 / RFC 9112 §6.3)
793	def ask.clen(method: String, target: String, headers: List<&2, Header>,
794	  +n: Nat, +body: String) -> Request:
795	  ask.short(method, target, headers, n, body, Nat.is_lt(utf8.len(body), n))
796	
797	# Content-Length when present; else the rest of the connection is the body
798	def ask.len(method: String, target: String, headers: List<&2, Header>,
799	  m: Maybe<&2, Nat>, body: String) -> Request:
800	  match m:
801	    case None{}:
802	      Request{method, target, headers, body}
803	    case Some{n}:
804	      ask.clen(method, target, headers, n, body)
805	
806	# a chunked request body, or why the chunk framing was rejected
807	def ask.chunked(method: String, target: String, headers: List<&2, Header>,
808	  body: String, bad: Maybe<&2, String>) -> Request:
809	  match bad:
810	    case None{}:
811	      Request{method, target, headers, dechunk(body)}
812	    case Some{why}:
813	      Bad{why}
814	
815	# scan chunk sizes, then decode when they are hex and closed by 0
816	def ask.chunks(method: String, target: String, headers: List<&2, Header>,
817	  +body: String) -> Request:
818	  ask.chunked(method, target, headers, body,
819	    chunks.scan(String.length(body), divide(body, "\r\n")))
820	
821	# Transfer-Encoding together with Content-Length is a bad request
822	def ask.te.clash(method: String, target: String, headers: List<&2, Header>,
823	  body: String, present: Bool) -> Request:
824	  match present:
825	    case True{}:
826	      Bad{"Content-Length and Transfer-Encoding conflict"}
827	    case False{}:
828	      ask.chunks(method, target, headers, body)
829	
830	# chunked framing, or Content-Length, or the rest of the connection
831	def ask.te(method: String, target: String, headers: List<&2, Header>,
832	  +lens: List<&2, String>, +body: String, chunked: Bool) -> Request:
833	  match chunked:
834	    case False{}:
835	      ask.len(method, target, headers, digits.read(first(lens)), body)
836	    case True{}:
837	      ask.te.clash(method, target, headers, body, clen.any(lens))
838	
839	# disagreeing Content-Length values are bad before framing
840	def ask.agree(method: String, target: String, headers: List<&2, Header>,
841	  te: String, +lens: List<&2, String>, body: String, ok: Bool) -> Request:
842	  match ok:
843	    case False{}:
844	      Bad{"Content-Length values disagree"}
845	    case True{}:
846	      ask.te(method, target, headers, lens, body,
847	        String.contains(String.to_lower(te), "chunked"))
848	
849	# the headers that decide request framing (RFC 9112 §6.3)
850	def ask.frame(method: String, target: String, headers: List<&2, Header>,
851	  te: String, +lens: List<&2, String>, body: String) -> Request:
852	  ask.agree(method, target, headers, te, lens, body, clen.agree(lens))
853	
854	# origin-form, or a bad request when the target is not an absolute-path
855	def ask.origin(method: String, target: String, +ls: List<&2, String>,
856	  body: String, ok: Bool) -> Request:
857	  match ok:
858	    case False{}:
859	      Bad{"the request-target is not in origin-form"}
860	    case True{}:
861	      +hs = head.list(ls)
862	      ask.frame(method, target, hs, head.go(ls, "transfer-encoding"),
863	        head.values(ls, "content-length"), body)
864	
865	# request-line: method SP request-target SP HTTP-version (RFC 9112 §3)
866	def ask.line(+method: String, +target: String, +ls: List<&2, String>,
867	  body: String) -> Request:
868	  ask.origin(method, target, ls, body,
869	    target.form(method, target, target.origin(target)))
870	
871	# three fields of the request-line, or torn
872	def ask.parts(ps: List<&2, String>, +ls: List<&2, String>, body: String)
873	  -> Request:
874	  match ps:
875	    case []:
876	      Bad{"the request has no request line"}
877	    case m <> rest:
878	      match rest:
879	        case []:
880	          Bad{"the request line has no target"}
881	        case t <> _ver:
882	          ask.line(m, t, ls, body)
883	
884	# the head's lines, with the request-line read off the first
885	def ask.head(+ls: List<&2, String>, body: String) -> Request:
886	  match ls:
887	    case []:
888	      Bad{"the request has no request line"}
889	    case _:
890	      ask.parts(String.split(first(ls), ' '), ls, body)
891	
892	# a request divided into its head and everything after the blank line
893	def ask.cut(c: Cut) -> Request:
894	  match c:
895	    case NoCut{}:
896	      Bad{"the request head has no blank line after it"}
897	    case Cut{before, after}:
898	      ask.head(String.lines(before), after)
899	
900	# the method, target, headers, and body of a raw request
901	def ask(raw: String) -> Request:
902	  ask.cut(divide(raw, "\r\n\r\n"))
903	
904	# a parsed request on one line, for a test to read
905	def ask.show(r: Request) -> String:
906	  match r:
907	    case Bad{why}:
908	      "bad " ++ why
909	    case Request{method, target, headers, body}:
910	      method ++ " " ++ target ++ " " ++ body
911	
912	# --- when a response has all arrived (RFC 9112 §6.3) ---
913	
914	# how a response's body is framed
915	type Frame is Data:
916	  Bare{}
917	  Sized{n: Nat}
918	  Chunked{}
919	  Closed{}
920	
921	# 204 and 304 carry no body; a status line that did not parse is framed by
922	# its headers
923	def status.bare(m: Maybe<&2, U32>) -> Bool:
924	  match m:
925	    case None{}:
926	      False{}
927	    case Some{n}:
928	      status.nocontent(n)
929	
930	# a Content-Length that reads as a number, or the close when none does
931	def frame.sized(m: Maybe<&2, Nat>) -> Frame:
932	  match m:
933	    case None{}:
934	      Closed{}
935	    case Some{n}:
936	      Sized{n}
937	
938	# Content-Length values that agree frame the body; any others leave the close
939	def frame.agree(+lens: List<&2, String>, ok: Bool) -> Frame:
940	  match ok:
941	    case False{}:
942	      Closed{}
943	    case True{}:
944	      frame.sized(digits.read(first(lens)))
945	
946	# chunked framing wins over Content-Length (RFC 9112 §6.3 item 4)
947	def frame.te(+lens: List<&2, String>, chunked: Bool) -> Frame:
948	  match chunked:
949	    case True{}:
950	      Chunked{}
951	    case False{}:
952	      frame.agree(lens, clen.agree(lens))
953	
954	# the framing of a response: none when bare (a reply to HEAD, a 204 or a 304),
955	# else Transfer-Encoding chunked, else Content-Length, else the close
956	def frame(bare: Bool, te: String, +lens: List<&2, String>) -> Frame:
957	  match bare:
958	    case True{}:
959	      Bare{}
960	    case False{}:
961	      frame.te(lens, String.contains(String.to_lower(te), "chunked"))
962	
963	# a zero chunk's trailer section has ended: at once, or after its fields
964	def chunks.trailer(+after: String) -> Bool:
965	  Bool.or(String.starts_with(after, "\r\n"), String.contains(after, "\r\n\r\n"))
966	
967	# a chunk that has all arrived: on to the next chunk header, else not yet
968	def chunks.ended.data(+after: String, +n: Nat, ready: Bool,
969	  rest: Cut -> Bool) -> Bool:
970	  match ready:
971	    case False{}:
972	      False{}
973	    case True{}:
974	      rest(divide(utf8.drop(after, Nat.add(n, 2n)), "\r\n"))
975	
976	# a chunk of size n: the last one when n is 0
977	def chunks.ended.size(+after: String, +n: Nat, zero: Bool,
978	  rest: Cut -> Bool) -> Bool:
979	  match zero:
980	    case True{}:
981	      chunks.trailer(after)
982	    case False{}:
983	      chunks.ended.data(after, n, chunks.ready(after, n), rest)
984	
985	# a chunk header: a size that is not hex ends the read (the parse rejects it)
986	def chunks.ended.hex(+before: String, +after: String, ok: Bool,
987	  rest: Cut -> Bool) -> Bool:
988	  match ok:
989	    case False{}:
990	      True{}
991	    case True{}:
992	      +n = hexlen(before)
993	      chunks.ended.size(after, n, Nat.is_eq(n, 0n), rest)
994	
995	# a chunk header that has arrived, or not yet
996	def chunks.ended.at(c: Cut, rest: Cut -> Bool) -> Bool:
997	  match c:
998	    case NoCut{}:
999	      False{}
1000	    case Cut{+before, +after}:
1001	      chunks.ended.hex(before, after, hex.well(chunks.token(before)), rest)
1002	
1003	# whether a chunked body has reached the end of its last chunk
1004	def chunks.ended(fuel: Nat, c: Cut) -> Bool:
1005	  match fuel:
1006	    case 0n:
1007	      False{}
1008	    case 1n+f:
1009	      chunks.ended.at(c, cut => chunks.ended(f, cut))
1010	
1011	# whether a body has all arrived under its framing
1012	def whole.of(f: Frame, +body: String) -> Bool:
1013	  match f:
1014	    case Bare{}:
1015	      True{}
1016	    case Sized{n}:
1017	      Bool.not(Nat.is_lt(utf8.len(body), n))
1018	    case Chunked{}:
1019	      chunks.ended(String.length(body), divide(body, "\r\n"))
1020	    case Closed{}:
1021	      False{}
1022	
1023	# a response whose head has ended, or not yet
1024	def whole.cut(asked: Bool, c: Cut) -> Bool:
1025	  match c:
1026	    case NoCut{}:
1027	      False{}
1028	    case Cut{before, after}:
1029	      +ls = String.lines(before)
1030	      whole.of(frame(Bool.or(asked, status.bare(status.of(ls))),
1031	        head.go(ls, "transfer-encoding"), head.values(ls, "content-length")),
1032	        after)
1033	
1034	# whether the text received so far is a whole response to a request with
1035	# this method (RFC 9112 §6.3); a response framed by the close never is
1036	def whole(+method: String, raw: String) -> Bool:
1037	  whole.cut(String.eq(method, "HEAD"), divide(raw, "\r\n\r\n"))