1	# AWS Signature V4 signing and S3 object storage over Hairpin. Source: https://github.com/paymog/bend-kit/tree/main/sigv4
2	import Base
3	import bend-kit-crypto@0.1.1.0/crypto.bend as Crypto
4	import bend-kit-hairpin@0.1.0.0/hairpin.bend as Hairpin
5	import bend-kit-http@0.23.0.1/http.bend as Http
6	import bend-kit-time@0.1.0.0/time.bend as Time
7	# By hash, as http imports them: bend-kit-url@0.4.1.0, -bytes@0.3.0.0.
8	import 0x1f2d80f53f971b16c6de6a65cb1918ae/url.bend as Url
9	import 0xcfc8be7b076f41f95c8e118383892d55/encoding.bend as Enc
10	import 0x49814d83de8f70993a43e1002be29ecd/bytes.bend as Bytes
11	
12	# Text (path, query, header values) is a String of code points; non-ASCII is sent as UTF-8.
13	# S3 decodes and re-encodes wire escapes once; other services encode an escaped wire path twice.
14	# SigV4 encoding keeps only A-Z a-z 0-9 - _ . ~ and uses uppercase %XX.
15	# date is the x-amz-date form, YYYYMMDDTHHMMSSZ. token is "" for long-term keys.
16	type Credentials is Data:
17	  Credentials{access: String, secret: String, token: String}
18	
19	# Code points to UTF-8 octets, one Char per octet. acc is reversed.
20	def utf8.c3(three: Bool, +c: U32, acc: String) -> String:
21	  match three:
22	    case True{}:
23	      SCon{Chr{(128 + c % 64 : U32)}, SCon{Chr{(128 + c / 64 % 64 : U32)}, SCon{Chr{(224 + c / 4096 : U32)}, acc}}}
24	    case False{}:
25	      SCon{Chr{(128 + c % 64 : U32)}, SCon{Chr{(128 + c / 64 % 64 : U32)}, SCon{Chr{(128 + c / 4096 % 64 : U32)}, SCon{Chr{(240 + c / 262144 : U32)}, acc}}}}
26	
27	def utf8.c2(two: Bool, +c: U32, acc: String) -> String:
28	  match two:
29	    case True{}:
30	      SCon{Chr{(128 + c % 64 : U32)}, SCon{Chr{(192 + c / 64 : U32)}, acc}}
31	    case False{}:
32	      utf8.c3(U32.is_lt(c, 65536), c, acc)
33	
34	def utf8.c1(one: Bool, +c: U32, acc: String) -> String:
35	  match one:
36	    case True{}:
37	      SCon{Chr{c}, acc}
38	    case False{}:
39	      utf8.c2(U32.is_lt(c, 2048), c, acc)
40	
41	def utf8.go(s: String, acc: String) -> String:
42	  match s:
43	    case SNil{}:
44	      String.reverse(acc)
45	    case SCon{Chr{+c}, t}:
46	      utf8.go(t, utf8.c1(U32.is_lt(c, 128), c, acc))
47	
48	def utf8(s: String) -> String:
49	  utf8.go(s, SNil{})
50	
51	# SigV4 URI encoding of text: UTF-8, then every octet but the unreserved ones as %XX. slash keeps '/'.
52	def encode(s: String, slash: Bool) -> String:
53	  match slash:
54	    case True{}:
55	      Url.pct.encode_path(utf8(s))
56	    case False{}:
57	      Url.pct.encode_q(utf8(s))
58	
59	def dec.of(m: Maybe<&2, String>, +raw: String) -> String:
60	  match m:
61	    case None{}:
62	      raw
63	    case Some{d}:
64	      d
65	
66	# A wire component, re-encoded. A malformed escape stays literal, so its '%' is encoded.
67	def norm(s: String) -> String:
68	  +o = utf8(s)
69	  Url.pct.encode_q(dec.of(Url.pct.decode(o), o))
70	
71	def norms(xs: List<&2, String>) -> List<&2, String>:
72	  match xs:
73	    case Nil{}:
74	      Nil{}
75	    case Con{h, t}:
76	      Con{norm(h), norms(t)}
77	
78	# Non-S3 services encode the wire path a second time; '%' becomes '%25'.
79	def wire.segs(xs: List<&2, String>) -> List<&2, String>:
80	  match xs:
81	    case Nil{}:
82	      Nil{}
83	    case Con{h, t}:
84	      Con{Url.pct.encode_q(utf8(h)), wire.segs(t)}
85	
86	# Canonical URI (RFC 3986 §5.2.4 for services other than s3): "" and "." segments drop, ".." pops.
87	def dots.seg(skip: Bool, up: Bool, +seg: String, st: List<&2, String>) -> List<&2, String>:
88	  match skip up:
89	    case True{} _:
90	      st
91	    case False{} True{}:
92	      List.drop(&2, String, st, 1n)
93	    case False{} False{}:
94	      Con{seg, st}
95	
96	def dots(xs: List<&2, String>, st: List<&2, String>) -> List<&2, String>:
97	  match xs:
98	    case Nil{}:
99	      List.reverse(&2, String, st)
100	    case Con{+h, t}:
101	      dots(t, dots.seg(Bool.or(String.is_empty(h), String.eq(h, ".")), String.eq(h, ".."), h, st))
102	
103	def uri.slash(empty: Bool, trail: Bool, +body: String) -> String:
104	  match empty trail:
105	    case True{} _:
106	      "/"
107	    case False{} True{}:
108	      "/" ++ body ++ "/"
109	    case False{} False{}:
110	      "/" ++ body
111	
112	def uri.dots(+path: String) -> String:
113	  +body = String.join(wire.segs(dots(String.split(path, '/'), Nil{})), "/")
114	  +trail = Bool.or(String.ends_with(path, "/"), Bool.or(String.ends_with(path, "/."), String.ends_with(path, "/..")))
115	  uri.slash(String.is_empty(body), trail, body)
116	
117	# S3 signs the path as sent: each segment re-encoded, nothing removed.
118	def uri.s3(empty: Bool, +path: String) -> String:
119	  match empty:
120	    case True{}:
121	      "/"
122	    case False{}:
123	      String.join(norms(String.split(path, '/')), "/")
124	
125	def uri.if(s3: Bool, +path: String) -> String:
126	  match s3:
127	    case True{}:
128	      uri.s3(String.is_empty(path), path)
129	    case False{}:
130	      uri.dots(path)
131	
132	def uri(+service: String, +path: String) -> String:
133	  uri.if(String.eq(service, "s3"), path)
134	
135	# Canonical query: split on '&', each "k=v" (a bare "k" is "k="), re-encoded, sorted by key then value.
136	def pair(xs: List<&2, String>) -> Sigma<&2, &2, String, _ => String>:
137	  match xs:
138	    case Nil{}:
139	      ("", "")
140	    case Con{k, t}:
141	      (norm(k), norm(String.join(t, "=")))
142	
143	def pairs.if(empty: Bool, +h: String, rest: List<&2, Sigma<&2, &2, String, _ => String>>) -> List<&2, Sigma<&2, &2, String, _ => String>>:
144	  match empty:
145	    case True{}:
146	      rest
147	    case False{}:
148	      Con{pair(String.split(h, '=')), rest}
149	
150	def pairs(xs: List<&2, String>) -> List<&2, Sigma<&2, &2, String, _ => String>>:
151	  match xs:
152	    case Nil{}:
153	      Nil{}
154	    case Con{+h, t}:
155	      pairs.if(String.is_empty(h), h, pairs(t))
156	
157	def pair.le.of(c: Cmp, av: String, bv: String) -> Bool:
158	  match c:
159	    case LT{}:
160	      True{}
161	    case GT{}:
162	      False{}
163	    case EQ{}:
164	      String.is_le(av, bv)
165	
166	def pair.le(a: Sigma<&2, &2, String, _ => String>, b: Sigma<&2, &2, String, _ => String>) -> Bool:
167	  (ak, av) = a
168	  (bk, bv) = b
169	  pair.le.of(String.order(ak, bk), av, bv)
170	
171	def pairs.show(xs: List<&2, Sigma<&2, &2, String, _ => String>>) -> List<&2, String>:
172	  match xs:
173	    case Nil{}:
174	      Nil{}
175	    case Con{(k, v), t}:
176	      Con{k ++ "=" ++ v, pairs.show(t)}
177	
178	def query(q: String) -> String:
179	  String.join(pairs.show(List.sort(~Sigma<&2, &2, String, _ => String>, ~pair.le, pairs(String.split(q, '&')))), "&")
180	
181	# Canonical headers: lowercase names, trimmed values with space runs squashed, sorted by name,
182	# and a repeated name's values joined by ',' in the order given.
183	def squash.if(space: Bool, sp: Bool, +c: U32, rest: String) -> String:
184	  match space sp:
185	    case True{} True{}:
186	      rest
187	    case _ _:
188	      SCon{Chr{c}, rest}
189	
190	def squash(s: String, sp: Bool) -> String:
191	  match s:
192	    case SNil{}:
193	      SNil{}
194	    case SCon{Chr{+c}, t}:
195	      squash.if(U32.is_eq(c, 32), sp, c, squash(t, U32.is_eq(c, 32)))
196	
197	def hdrs.low(xs: List<&2, Sigma<&2, &2, String, _ => String>>) -> List<&2, Sigma<&2, &2, String, _ => String>>:
198	  match xs:
199	    case Nil{}:
200	      Nil{}
201	    case Con{(n, v), t}:
202	      Con{(String.to_lower(n), squash(String.trim(v), False{})), hdrs.low(t)}
203	
204	def name.le(a: Sigma<&2, &2, String, _ => String>, b: Sigma<&2, &2, String, _ => String>) -> Bool:
205	  (an, av) = a
206	  (bn, bv) = b
207	  String.is_le(an, bn)
208	
209	def grp.if(same: Bool, +n: String, +v: String, +pn: String, +pv: String, rest: List<&2, Sigma<&2, &2, String, _ => String>>) -> List<&2, Sigma<&2, &2, String, _ => String>>:
210	  match same:
211	    case True{}:
212	      Con{(pn, pv ++ "," ++ v), rest}
213	    case False{}:
214	      Con{(n, v), Con{(pn, pv), rest}}
215	
216	def grp.add(acc: List<&2, Sigma<&2, &2, String, _ => String>>, +n: String, +v: String) -> List<&2, Sigma<&2, &2, String, _ => String>>:
217	  match acc:
218	    case Nil{}:
219	      [(n, v)]
220	    case Con{(+pn, +pv), rest}:
221	      grp.if(String.eq(pn, n), n, v, pn, pv, rest)
222	
223	def grp(xs: List<&2, Sigma<&2, &2, String, _ => String>>, acc: List<&2, Sigma<&2, &2, String, _ => String>>) -> List<&2, Sigma<&2, &2, String, _ => String>>:
224	  match xs:
225	    case Nil{}:
226	      List.reverse(&2, Sigma<&2, &2, String, _ => String>, acc)
227	    case Con{(+n, +v), t}:
228	      grp(t, grp.add(acc, n, v))
229	
230	def headers(hs: List<&2, Sigma<&2, &2, String, _ => String>>) -> List<&2, Sigma<&2, &2, String, _ => String>>:
231	  grp(List.sort(~Sigma<&2, &2, String, _ => String>, ~name.le, hdrs.low(hs)), Nil{})
232	
233	def names(xs: List<&2, Sigma<&2, &2, String, _ => String>>) -> List<&2, String>:
234	  match xs:
235	    case Nil{}:
236	      Nil{}
237	    case Con{(n, v), t}:
238	      Con{n, names(t)}
239	
240	def lines(xs: List<&2, Sigma<&2, &2, String, _ => String>>) -> String:
241	  match xs:
242	    case Nil{}:
243	      ""
244	    case Con{(n, v), t}:
245	      n ++ ":" ++ v ++ "\n" ++ lines(t)
246	
247	# The SignedHeaders value for headers hs.
248	def signed(hs: List<&2, Sigma<&2, &2, String, _ => String>>) -> String:
249	  String.join(names(headers(hs)), ";")
250	
251	# The canonical request. hs must hold every header to sign, host included. phash is the
252	# payload's lowercase hex SHA-256, or "UNSIGNED-PAYLOAD".
253	def canonical(+service: String, +method: String, +path: String, +q: String, +hs: List<&2, Sigma<&2, &2, String, _ => String>>, +phash: String) -> String:
254	  +h = headers(hs)
255	  method ++ "\n" ++ uri(service, path) ++ "\n" ++ query(q) ++ "\n" ++ lines(h) ++ "\n" ++ String.join(names(h), ";") ++ "\n" ++ phash
256	
257	def scope(+date: String, +region: String, +service: String) -> String:
258	  String.take(date, 8n) ++ "/" ++ region ++ "/" ++ service ++ "/aws4_request"
259	
260	# The string to sign, from the hex SHA-256 of the canonical request.
261	def to_sign(+date: String, +scope: String, +hash: String) -> String:
262	  "AWS4-HMAC-SHA256\n" ++ date ++ "\n" ++ scope ++ "\n" ++ hash
263	
264	def header(+access: String, +scope: String, +signed: String, +sig: String) -> String:
265	  "AWS4-HMAC-SHA256 Credential=" ++ access ++ "/" ++ scope ++ ", SignedHeaders=" ++ signed ++ ", Signature=" ++ sig
266	
267	# Crypto. Errors are the crypto effect's (errno, why).
268	
269	def hex.of(r: Result<&1, &1, U32 & String, U32 & Array<U32>>) -> Result<&1, &1, U32 & String, String>:
270	  match r:
271	    case Fail{e}:
272	      Fail{e}
273	    case Done{(len, buf)}:
274	      Done{Bytes.to_hex(Bytes.Bytes{len, buf})}
275	
276	# Hex SHA-256 of a byte string.
277	def sha.words(b: Bytes.Bytes) -> IO(Result<&1, &1, U32 & String, U32 & Array<U32>>):
278	  Bytes.Bytes{+len, buf} = b
279	  Crypto.sha256.words(len, buf)
280	
281	def sha(+s: String) -> IO(Result<&1, &1, U32 & String, String>):
282	  do IO<Result<&1, &1, U32 & String, String>>:
283	    r : Result<&1, &1, U32 & String, U32 & Array<U32>> <- sha.words(Bytes.from_string(s))
284	    return hex.of(r)
285	
286	def mac.words(+kn: U32, kb: Array<U32>, d: Bytes.Bytes) -> IO(Result<&1, &1, U32 & String, U32 & Array<U32>>):
287	  Bytes.Bytes{+dn, db} = d
288	  Crypto.hmac.words("SHA256", kn, kb, dn, db)
289	
290	def words(b: Bytes.Bytes) -> Result<&1, &1, U32 & String, U32 & Array<U32>>:
291	  Bytes.Bytes{+len, buf} = b
292	  Done{(len, buf)}
293	
294	# HMAC-SHA256 of msg under the key k holds, or k's failure.
295	def mac(k: Result<&1, &1, U32 & String, U32 & Array<U32>>, +msg: String) -> IO(Result<&1, &1, U32 & String, U32 & Array<U32>>):
296	  match k:
297	    case Fail{e}:
298	      IO.pure(Result<&1, &1, U32 & String, U32 & Array<U32>>, Fail{e})
299	    case Done{(kn, kb)}:
300	      mac.words(kn, kb, Bytes.from_string(msg))
301	
302	# The signing key: HMAC(HMAC(HMAC(HMAC("AWS4" + secret, day), region), service), "aws4_request").
303	def key(+secret: String, +day: String, +region: String, +service: String) -> IO(Result<&1, &1, U32 & String, U32 & Array<U32>>):
304	  do IO<Result<&1, &1, U32 & String, U32 & Array<U32>>>:
305	    k1 : Result<&1, &1, U32 & String, U32 & Array<U32>> <- mac(words(Bytes.from_string("AWS4" ++ secret)), day)
306	    k2 : Result<&1, &1, U32 & String, U32 & Array<U32>> <- mac(k1, region)
307	    k3 : Result<&1, &1, U32 & String, U32 & Array<U32>> <- mac(k2, service)
308	    mac(k3, "aws4_request")
309	
310	def signature.of(h: Result<&1, &1, U32 & String, String>, +secret: String, +date: String, +region: String, +service: String) -> IO(Result<&1, &1, U32 & String, String>):
311	  match h:
312	    case Fail{e}:
313	      IO.pure(Result<&1, &1, U32 & String, String>, Fail{e})
314	    case Done{+hash}:
315	      do IO<Result<&1, &1, U32 & String, String>>:
316	        k : Result<&1, &1, U32 & String, U32 & Array<U32>> <- key(secret, String.take(date, 8n), region, service)
317	        s : Result<&1, &1, U32 & String, U32 & Array<U32>> <- mac(k, to_sign(date, scope(date, region, service), hash))
318	        return hex.of(s)
319	
320	# The hex signature of a canonical request.
321	def signature(+secret: String, +date: String, +region: String, +service: String, +creq: String) -> IO(Result<&1, &1, U32 & String, String>):
322	  do IO<Result<&1, &1, U32 & String, String>>:
323	    h : Result<&1, &1, U32 & String, String> <- sha(creq)
324	    signature.of(h, secret, date, region, service)
325	
326	def header.of(r: Result<&1, &1, U32 & String, String>, +access: String, +scope: String, +signed: String) -> Result<&1, &1, U32 & String, String>:
327	  match r:
328	    case Fail{e}:
329	      Fail{e}
330	    case Done{sig}:
331	      Done{header(access, scope, signed, sig)}
332	
333	# The Authorization header over exactly the headers hs: the general form, for any header set.
334	# hs must include host and x-amz-date, and x-amz-security-token for temporary credentials;
335	# creds.token is not added here (authorize.hash adds it). Send every header in hs.
336	def sign(creds: Credentials, +region: String, +service: String, +date: String, +method: String, +path: String, +q: String, +hs: List<&2, Sigma<&2, &2, String, _ => String>>, +phash: String) -> IO(Result<&1, &1, U32 & String, String>):
337	  Credentials{+access, +secret, token} = creds
338	  do IO<Result<&1, &1, U32 & String, String>>:
339	    s : Result<&1, &1, U32 & String, String> <- signature(secret, date, region, service, canonical(service, method, path, q, hs, phash))
340	    return header.of(s, access, scope(date, region, service), signed(hs))
341	
342	def token.hdr(empty: Bool, +token: String) -> List<&2, Sigma<&2, &2, String, _ => String>>:
343	  match empty:
344	    case True{}:
345	      Nil{}
346	    case False{}:
347	      [("x-amz-security-token", token)]
348	
349	# The Authorization header over host;x-amz-content-sha256;x-amz-date, plus x-amz-security-token
350	# when creds has a token. Send those headers with these values. phash: the payload's hex
351	# SHA-256, or "UNSIGNED-PAYLOAD".
352	def authorize.hash(creds: Credentials, +region: String, +service: String, +date: String, +method: String, +path: String, +q: String, +host: String, +phash: String) -> IO(Result<&1, &1, U32 & String, String>):
353	  Credentials{+access, +secret, +token} = creds
354	  sign(Credentials{access, secret, token}, region, service, date, method, path, q, Con{("host", host), Con{("x-amz-content-sha256", phash), Con{("x-amz-date", date), token.hdr(String.is_empty(token), token)}}}, phash)
355	
356	def authorize.pair(r: Result<&1, &1, U32 & String, String>, +phash: String) -> Result<&1, &1, U32 & String, String & String>:
357	  match r:
358	    case Fail{e}:
359	      Fail{e}
360	    case Done{a}:
361	      Done{(a, phash)}
362	
363	def authorize.of(h: Result<&1, &1, U32 & String, String>, creds: Credentials, +region: String, +service: String, +date: String, +method: String, +path: String, +q: String, +host: String) -> IO(Result<&1, &1, U32 & String, String & String>):
364	  match h:
365	    case Fail{e}:
366	      IO.pure(Result<&1, &1, U32 & String, String & String>, Fail{e})
367	    case Done{+phash}:
368	      do IO<Result<&1, &1, U32 & String, String & String>>:
369	        a : Result<&1, &1, U32 & String, String> <- authorize.hash(creds, region, service, date, method, path, q, host, phash)
370	        return authorize.pair(a, phash)
371	
372	# authorize.hash over the payload's SHA-256. Done{(authorization, x-amz-content-sha256)}.
373	def authorize(creds: Credentials, +region: String, +service: String, +date: String, +method: String, +path: String, +q: String, +host: String, payload: Bytes.Bytes) -> IO(Result<&1, &1, U32 & String, String & String>):
374	  do IO<Result<&1, &1, U32 & String, String & String>>:
375	    r : Result<&1, &1, U32 & String, U32 & Array<U32>> <- sha.words(payload)
376	    authorize.of(hex.of(r), creds, region, service, date, method, path, q, host)
377	
378	def token.q(empty: Bool, +token: String) -> String:
379	  match empty:
380	    case True{}:
381	      ""
382	    case False{}:
383	      "&X-Amz-Security-Token=" ++ encode(token, False{})
384	
385	# The query a presigned request adds to q, before X-Amz-Signature.
386	def presign.query(+access: String, +token: String, +scope: String, +date: String, +expires: U32, +q: String) -> String:
387	  query(q ++ "&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=" ++ encode(access ++ "/" ++ scope, False{}) ++ "&X-Amz-Date=" ++ date ++ "&X-Amz-Expires=" ++ U32.show(expires) ++ token.q(String.is_empty(token), token) ++ "&X-Amz-SignedHeaders=host")
388	
389	def presign.of(r: Result<&1, &1, U32 & String, String>, +cq: String) -> Result<&1, &1, U32 & String, String>:
390	  match r:
391	    case Fail{e}:
392	      Fail{e}
393	    case Done{sig}:
394	      Done{cq ++ "&X-Amz-Signature=" ++ sig}
395	
396	def presign.go(+creds: Credentials, +region: String, +service: String, +date: String, +method: String, +path: String, +q: String, +host: String, +expires: U32) -> IO(Result<&1, &1, U32 & String, String>):
397	  Credentials{+access, +secret, +token} = creds
398	  +cq = presign.query(access, token, scope(date, region, service), date, expires, q)
399	  do IO<Result<&1, &1, U32 & String, String>>:
400	    s : Result<&1, &1, U32 & String, String> <- signature(secret, date, region, service, canonical(service, method, path, cq, [("host", host)], "UNSIGNED-PAYLOAD"))
401	    return presign.of(s, cq)
402	
403	def presign.if(ok: Bool, +creds: Credentials, +region: String, +service: String, +date: String, +method: String, +path: String, +q: String, +host: String, +expires: U32) -> IO(Result<&1, &1, U32 & String, String>):
404	  match ok:
405	    case True{}:
406	      presign.go(creds, region, service, date, method, path, q, host, expires)
407	    case False{}:
408	      IO.pure(Result<&1, &1, U32 & String, String>, Fail{(22, "sigv4: expires must be 1 to 604800 seconds")})
409	
410	# A presigned URL's query, signing host only over UNSIGNED-PAYLOAD, valid for expires seconds,
411	# 1 to 604800 (else Fail EINVAL). Request https://{host}{path}?{result} with no auth headers.
412	def presign(+creds: Credentials, +region: String, +service: String, +date: String, +method: String, +path: String, +q: String, +host: String, +expires: U32) -> IO(Result<&1, &1, U32 & String, String>):
413	  presign.if(Bool.and(U32.is_lt(0, expires), U32.is_le(expires, 604800)), creds, region, service, date, method, path, q, host, expires)
414	
415	# ---- S3
416	
417	# Path: {endpoint}/{bucket}/{key}. Virtual: {bucket}.{endpoint host}/{key}.
418	type Style is Data:
419	  Path{}
420	  Virtual{}
421	
422	# endpoint: scheme://host[:port], as https://s3.us-east-1.amazonaws.com or http://127.0.0.1:9000. Its path is ignored.
423	type Config is Data:
424	  Config{endpoint: String, region: String, style: Style, creds: Credentials}
425	
426	type Client is Type:
427	  Client{cfg: Config, http: Hairpin.Client}
428	
429	# ErrNet: no response. ErrSign: the signer failed. ErrConfig: a bad endpoint or a missing setting.
430	# ErrS3: any status outside 2xx, redirects included, with S3's error Code and Message ("" when there is no
431	# error body, as for HEAD). ErrXml: a 2xx body that is not the XML asked for, with its text.
432	type Err is Data:
433	  ErrNet{e: Http.Err}
434	  ErrSign{code: U32, why: String}
435	  ErrConfig{why: String}
436	  ErrS3{status: U32, code: String, message: String}
437	  ErrXml{body: String}
438	
439	# etag keeps S3's quotes. modified is S3's ISO 8601 text.
440	type Object is Data:
441	  Object{key: String, size: Nat, etag: String, modified: String}
442	
443	# next: the continuation token when S3 cut the listing off.
444	type Page is Data:
445	  Page{objects: List<&2, Object>, prefixes: List<&2, String>, next: Maybe<&2, String>}
446	
447	# From a HEAD: Content-Length, ETag, Content-Type, and Last-Modified.
448	type Meta is Data:
449	  Meta{size: Nat, etag: String, mime: String, modified: String}
450	
451	# ---- config
452	
453	# Redirects come back as ErrS3: a signed request must not follow one.
454	def new(cfg: Config) -> Client:
455	  Client{cfg, Hairpin.redirect(Hairpin.new(), Http.ModeManual{})}
456	
457	def close(c: Client) -> IO(Unit):
458	  Client{cfg, http} = c
459	  Hairpin.close(http)
460	
461	# Up to n more tries after a connect error, a timeout, or 408, 429, 500, 502, 503, or 504. The signature stays valid for 15 minutes.
462	def retry(c: Client, n: U32) -> Client:
463	  Client{cfg, http} = c
464	  Client{cfg, Hairpin.retry(http, n)}
465	
466	def timeout(c: Client, ms: U32) -> Client:
467	  Client{cfg, http} = c
468	  Client{cfg, Hairpin.timeout(http, ms)}
469	
470	# AWS itself: https://s3.{region}.amazonaws.com, virtual-hosted.
471	def aws(+region: String, creds: Credentials) -> Config:
472	  Config{"https://s3." ++ region ++ ".amazonaws.com", region, Virtual{}, creds}
473	
474	def env(r: Result<&1, &1, U32 & String, String>) -> String:
475	  match r:
476	    case Fail{e}:
477	      ""
478	    case Done{s}:
479	      s
480	
481	def or(+a: String, b: String) -> String:
482	  Bool.pick(String, String.is_empty(a), b, a)
483	
484	def from_env.cfg(custom: Bool, +region: String, endpoint: String, creds: Credentials) -> Config:
485	  match custom:
486	    case True{}:
487	      Config{endpoint, region, Path{}, creds}
488	    case False{}:
489	      aws(region, creds)
490	
491	def from_env.if(missing: Bool, access: String, secret: String, token: String, region: String, +endpoint: String) ->
492	    Result<&1, &1, Err, Config>:
493	  match missing:
494	    case True{}:
495	      Fail{ErrConfig{"AWS_ACCESS_KEY_ID and AWS_SECRET_ACCESS_KEY must be set"}}
496	    case False{}:
497	      Done{from_env.cfg(Bool.not(String.is_empty(endpoint)), region, endpoint, Credentials{access, secret, token})}
498	
499	def from_env.of(+access: String, +secret: String, token: String, region: String, endpoint: String) -> Result<&1, &1, Err, Config>:
500	  from_env.if(Bool.or(String.is_empty(access), String.is_empty(secret)), access, secret, token, region, endpoint)
501	
502	# AWS_ACCESS_KEY_ID, AWS_SECRET_ACCESS_KEY, AWS_SESSION_TOKEN; AWS_REGION, else AWS_DEFAULT_REGION, else us-east-1;
503	# AWS_ENDPOINT_URL_S3, else AWS_ENDPOINT_URL. A custom endpoint is path-style, as MinIO wants; AWS is virtual-hosted.
504	def from_env() -> IO(Result<&1, &1, Err, Config>):
505	  do IO<Result<&1, &1, Err, Config>>:
506	    a : Result<&1, &1, U32 & String, String> <- IO.get_env("AWS_ACCESS_KEY_ID")
507	    s : Result<&1, &1, U32 & String, String> <- IO.get_env("AWS_SECRET_ACCESS_KEY")
508	    t : Result<&1, &1, U32 & String, String> <- IO.get_env("AWS_SESSION_TOKEN")
509	    r : Result<&1, &1, U32 & String, String> <- IO.get_env("AWS_REGION")
510	    dr : Result<&1, &1, U32 & String, String> <- IO.get_env("AWS_DEFAULT_REGION")
511	    e3 : Result<&1, &1, U32 & String, String> <- IO.get_env("AWS_ENDPOINT_URL_S3")
512	    e : Result<&1, &1, U32 & String, String> <- IO.get_env("AWS_ENDPOINT_URL")
513	    return from_env.of(env(a), env(s), env(t), or(env(r), or(env(dr), "us-east-1")), or(env(e3), env(e)))
514	
515	# ---- XML
516	
517	# One closed element: its parent's name, its name, and its own text, entities decoded. Names drop any namespace prefix.
518	type Leaf is Data:
519	  Leaf{parent: String, name: String, text: String}
520	
521	# Where the lexer is: text; after '<'; a start tag's name; its attributes, outside or in "..." or '...'; after '/'
522	# in a start tag; an end tag's name; <?...?>, after '?'; after '<!'; a comment, after one or two '-'; <![CDATA[ up
523	# to its '['; CDATA, after one or two ']'; an entity; <!DOCTYPE ...>.
524	type Lx is Data:
525	  LText{}
526	  LOpen{}
527	  LName{}
528	  LAttr{}
529	  LDq{}
530	  LSq{}
531	  LSelf{}
532	  LEnd{}
533	  LPi{}
534	  LPiQ{}
535	  LBang{}
536	  LCom{}
537	  LCom1{}
538	  LCom2{}
539	  LCdHead{}
540	  LCd{}
541	  LCd1{}
542	  LCd2{}
543	  LEnt{}
544	  LDecl{}
545	
546	# stack: open names, innermost first. txt and nm: text and the name or entity so far, reversed. out: leaves, last first.
547	# ok turns False at a mismatched end tag or an unknown entity.
548	type St is Data:
549	  St{stack: List<&2, String>, txt: String, nm: String, out: List<&2, Leaf>, ok: Bool}
550	
551	def first(xs: List<&2, String>) -> String:
552	  match xs:
553	    case Nil{}:
554	      ""
555	    case Con{h, t}:
556	      h
557	
558	def local.go(s: String, acc: String) -> String:
559	  match s:
560	    case SNil{}:
561	      String.reverse(acc)
562	    case SCon{Chr{58}, t}:
563	      local.go(t, SNil{})
564	    case SCon{c, t}:
565	      local.go(t, SCon{c, acc})
566	
567	# The name after its namespace prefix, as Key for s3:Key.
568	def local(s: String) -> String:
569	  local.go(s, SNil{})
570	
571	def st.txt(st: St, c: Char) -> St:
572	  St{a, x, n, o, k} = st
573	  St{a, SCon{c, x}, n, o, k}
574	
575	def st.nm(st: St, c: Char) -> St:
576	  St{a, x, n, o, k} = st
577	  St{a, x, SCon{c, n}, o, k}
578	
579	def st.nm0(st: St) -> St:
580	  St{a, x, n, o, k} = st
581	  St{a, x, "", o, k}
582	
583	def st.open(st: St) -> St:
584	  St{a, x, n, o, k} = st
585	  St{Con{local(String.reverse(n)), a}, "", "", o, k}
586	
587	def st.shut(stack: List<&2, String>, txt: String, out: List<&2, Leaf>, ok: Bool, +name: String) -> St:
588	  match stack:
589	    case Nil{}:
590	      St{Nil{}, "", "", out, False{}}
591	    case Con{+top, +rest}:
592	      St{rest, "", "", Con{Leaf{first(rest), top, String.reverse(txt)}, out}, Bool.and(ok, String.eq(top, name))}
593	
594	def st.close(st: St) -> St:
595	  St{a, x, n, o, k} = st
596	  st.shut(a, x, o, k, local(String.reverse(n)))
597	
598	def st.close.top(st: St) -> St:
599	  St{+a, x, n, o, k} = st
600	  st.shut(a, x, o, k, first(a))
601	
602	def hex.digit(+c: U32) -> Maybe<&2, U32>:
603	  Bool.pick(Maybe<&2, U32>, Bool.and(U32.is_le(48, c), U32.is_le(c, 57)), Some{(c - 48 : U32)},
604	    Bool.pick(Maybe<&2, U32>, Bool.and(U32.is_le(97, c), U32.is_le(c, 102)), Some{(c - 87 : U32)},
605	      Bool.pick(Maybe<&2, U32>, Bool.and(U32.is_le(65, c), U32.is_le(c, 70)), Some{(c - 55 : U32)}, None{})))
606	
607	def hex.step(m: Maybe<&2, U32>, +acc: U32) -> Maybe<&2, U32>:
608	  match m:
609	    case None{}:
610	      None{}
611	    case Some{d}:
612	      Some{(acc * 16 + d : U32)}
613	
614	# ponytail: no overflow check; a reference past U+10FFFF wraps and decodes to junk rather than failing.
615	def hex(s: String, m: Maybe<&2, U32>) -> Maybe<&2, U32>:
616	  match s:
617	    case SNil{}:
618	      m
619	    case SCon{Chr{c}, t}:
620	      match m:
621	        case None{}:
622	          None{}
623	        case Some{acc}:
624	          hex(t, hex.step(hex.digit(c), acc))
625	
626	def ent.num(+s: String) -> Maybe<&2, U32>:
627	  Bool.pick(Maybe<&2, U32>, String.starts_with(s, "x"), hex(String.drop(s, 1n), Some{0}), U32.read(s))
628	
629	# The five XML entities and &#NN; / &#xHH;. None for any other.
630	def ent(+e: String) -> Maybe<&2, U32>:
631	  Bool.pick(Maybe<&2, U32>, String.eq(e, "lt"), Some{60},
632	    Bool.pick(Maybe<&2, U32>, String.eq(e, "gt"), Some{62},
633	      Bool.pick(Maybe<&2, U32>, String.eq(e, "amp"), Some{38},
634	        Bool.pick(Maybe<&2, U32>, String.eq(e, "quot"), Some{34},
635	          Bool.pick(Maybe<&2, U32>, String.eq(e, "apos"), Some{39},
636	            Bool.pick(Maybe<&2, U32>, Bool.and(String.starts_with(e, "#"), Nat.is_lt(1n, String.length(e))), ent.num(String.drop(e, 1n)), None{}))))))
637	
638	def st.ent.of(m: Maybe<&2, U32>, st: St) -> St:
639	  match m:
640	    case None{}:
641	      St{a, x, n, o, k} = st
642	      St{a, x, n, o, False{}}
643	    case Some{c}:
644	      st.txt(st, Chr{c})
645	
646	def st.ent(st: St) -> St:
647	  St{a, x, n, o, k} = st
648	  st.ent.of(ent(String.reverse(n)), St{a, x, "", o, k})
649	
650	def lx.idle(m: Lx) -> Bool:
651	  match m:
652	    case LText{}:
653	      True{}
654	    case _:
655	      False{}
656	
657	def st.end(m: Lx, st: St) -> St:
658	  St{a, x, n, o, k} = st
659	  St{a, x, n, o, Bool.and(k, lx.idle(m))}
660	
661	# One pass over the text. Each step takes one char, so it ends.
662	def lex(s: String, m: Lx, st: St) -> St:
663	  match s:
664	    case SNil{}:
665	      st.end(m, st)
666	    case SCon{h, t}:
667	      match h m:
668	        case '<' LText{}:
669	          lex(t, LOpen{}, st.nm0(st))
670	        case '&' LText{}:
671	          lex(t, LEnt{}, st.nm0(st))
672	        case c LText{}:
673	          lex(t, LText{}, st.txt(st, c))
674	        case '/' LOpen{}:
675	          lex(t, LEnd{}, st)
676	        case '?' LOpen{}:
677	          lex(t, LPi{}, st)
678	        case '!' LOpen{}:
679	          lex(t, LBang{}, st)
680	        case c LOpen{}:
681	          lex(t, LName{}, st.nm(st, c))
682	        case '>' LName{}:
683	          lex(t, LText{}, st.open(st))
684	        case '/' LName{}:
685	          lex(t, LSelf{}, st.open(st))
686	        case ' ' LName{}:
687	          lex(t, LAttr{}, st.open(st))
688	        case Chr{9} LName{}:
689	          lex(t, LAttr{}, st.open(st))
690	        case Chr{10} LName{}:
691	          lex(t, LAttr{}, st.open(st))
692	        case Chr{13} LName{}:
693	          lex(t, LAttr{}, st.open(st))
694	        case c LName{}:
695	          lex(t, LName{}, st.nm(st, c))
696	        case '"' LAttr{}:
697	          lex(t, LDq{}, st)
698	        case Chr{39} LAttr{}:
699	          lex(t, LSq{}, st)
700	        case '>' LAttr{}:
701	          lex(t, LText{}, st)
702	        case '/' LAttr{}:
703	          lex(t, LSelf{}, st)
704	        case c LAttr{}:
705	          lex(t, LAttr{}, st)
706	        case '"' LDq{}:
707	          lex(t, LAttr{}, st)
708	        case c LDq{}:
709	          lex(t, LDq{}, st)
710	        case Chr{39} LSq{}:
711	          lex(t, LAttr{}, st)
712	        case c LSq{}:
713	          lex(t, LSq{}, st)
714	        case '>' LSelf{}:
715	          lex(t, LText{}, st.close.top(st))
716	        case c LSelf{}:
717	          lex(t, LAttr{}, st)
718	        case '>' LEnd{}:
719	          lex(t, LText{}, st.close(st))
720	        case ' ' LEnd{}:
721	          lex(t, LEnd{}, st)
722	        case Chr{9} LEnd{}:
723	          lex(t, LEnd{}, st)
724	        case Chr{10} LEnd{}:
725	          lex(t, LEnd{}, st)
726	        case Chr{13} LEnd{}:
727	          lex(t, LEnd{}, st)
728	        case c LEnd{}:
729	          lex(t, LEnd{}, st.nm(st, c))
730	        case '?' LPi{}:
731	          lex(t, LPiQ{}, st)
732	        case c LPi{}:
733	          lex(t, LPi{}, st)
734	        case '>' LPiQ{}:
735	          lex(t, LText{}, st)
736	        case '?' LPiQ{}:
737	          lex(t, LPiQ{}, st)
738	        case c LPiQ{}:
739	          lex(t, LPi{}, st)
740	        case '-' LBang{}:
741	          lex(t, LCom{}, st)
742	        case '[' LBang{}:
743	          lex(t, LCdHead{}, st)
744	        case c LBang{}:
745	          lex(t, LDecl{}, st)
746	        case '-' LCom{}:
747	          lex(t, LCom1{}, st)
748	        case c LCom{}:
749	          lex(t, LCom{}, st)
750	        case '-' LCom1{}:
751	          lex(t, LCom2{}, st)
752	        case c LCom1{}:
753	          lex(t, LCom{}, st)
754	        case '>' LCom2{}:
755	          lex(t, LText{}, st)
756	        case '-' LCom2{}:
757	          lex(t, LCom2{}, st)
758	        case c LCom2{}:
759	          lex(t, LCom{}, st)
760	        case '[' LCdHead{}:
761	          lex(t, LCd{}, st)
762	        case c LCdHead{}:
763	          lex(t, LCdHead{}, st)
764	        case ']' LCd{}:
765	          lex(t, LCd1{}, st)
766	        case c LCd{}:
767	          lex(t, LCd{}, st.txt(st, c))
768	        case ']' LCd1{}:
769	          lex(t, LCd2{}, st)
770	        case c LCd1{}:
771	          lex(t, LCd{}, st.txt(st.txt(st, ']'), c))
772	        case '>' LCd2{}:
773	          lex(t, LText{}, st)
774	        case ']' LCd2{}:
775	          lex(t, LCd2{}, st.txt(st, ']'))
776	        case c LCd2{}:
777	          lex(t, LCd{}, st.txt(st.txt(st.txt(st, ']'), ']'), c))
778	        case ';' LEnt{}:
779	          lex(t, LText{}, st.ent(st))
780	        case c LEnt{}:
781	          lex(t, LEnt{}, st.nm(st, c))
782	        case '>' LDecl{}:
783	          lex(t, LText{}, st)
784	        case c LDecl{}:
785	          lex(t, LDecl{}, st)
786	
787	def xml.if(ok: Bool, out: List<&2, Leaf>) -> Maybe<&2, List<&2, Leaf>>:
788	  match ok:
789	    case True{}:
790	      Some{List.reverse(&2, Leaf, out)}
791	    case False{}:
792	      None{}
793	
794	def closed(xs: List<&2, String>) -> Bool:
795	  match xs:
796	    case Nil{}:
797	      True{}
798	    case Con{h, t}:
799	      False{}
800	
801	def xml.fin(st: St) -> Maybe<&2, List<&2, Leaf>>:
802	  St{a, x, n, o, k} = st
803	  xml.if(Bool.and(k, closed(a)), o)
804	
805	# The closed elements of a document in document order, or None when it is not well formed.
806	# ponytail: no DTD internal subsets, and no check of names or attribute syntax; S3 sends neither.
807	def xml(s: String) -> Maybe<&2, List<&2, Leaf>>:
808	  xml.fin(lex(s, LText{}, St{Nil{}, "", "", Nil{}, True{}}))
809	
810	# ---- responses
811	
812	# S3's <Error><Code>..</Code><Message>..</Message></Error>.
813	def fault.scan(ls: List<&2, Leaf>, code: String, msg: String) -> String & String:
814	  match ls:
815	    case Nil{}:
816	      (code, msg)
817	    case Con{Leaf{+p, +n, +x}, t}:
818	      +err = String.eq(p, "Error")
819	      fault.scan(t, Bool.pick(String, Bool.and(err, String.eq(n, "Code")), x, code),
820	        Bool.pick(String, Bool.and(err, String.eq(n, "Message")), x, msg))
821	
822	def fault.of(+status: U32, cm: String & String) -> Err:
823	  (code, msg) = cm
824	  ErrS3{status, code, msg}
825	
826	def fault(+status: U32, m: Maybe<&2, List<&2, Leaf>>) -> Err:
827	  match m:
828	    case None{}:
829	      ErrS3{status, "", ""}
830	    case Some{ls}:
831	      fault.of(status, fault.scan(ls, "", ""))
832	
833	def ok(+s: U32) -> Bool:
834	  Bool.and(U32.is_le(200, s), U32.is_lt(s, 300))
835	
836	def judge.res(good: Bool, +status: U32, h: Map<&2, List<&2, String>>, b: Bytes.Bytes) -> Result<&1, &1, Err, Http.Res>:
837	  match good:
838	    case True{}:
839	      Done{Http.Res{status, h, b}}
840	    case False{}:
841	      Fail{fault(status, xml(Enc.utf8.decode(b)))}
842	
843	def judge(r: Result<&1, &1, Http.Err, Http.Res>) -> Result<&1, &1, Err, Http.Res>:
844	  match r:
845	    case Fail{e}:
846	      Fail{ErrNet{e}}
847	    case Done{res}:
848	      Http.Res{+status, h, b} = res
849	      judge.res(ok(status), status, h, b)
850	
851	# ---- requests
852	
853	def stamp.of(m: Maybe<&2, Time.DateTime>) -> String:
854	  match m:
855	    case None{}:
856	      ""
857	    case Some{Time.DateTime{Time.Date{y, mo, d}, h, mi, s, n}}:
858	      String.concat([Time.pad(y, 4n), Time.pad(mo, 2n), Time.pad(d, 2n), "T", Time.pad(h, 2n), Time.pad(mi, 2n), Time.pad(s, 2n), "Z"])
859	
860	# Now as YYYYMMDDTHHMMSSZ. "" only outside years 0 to 9999, which S3 then refuses.
861	def stamp() -> IO(String):
862	  do IO<String>:
863	    now : Time.Instant <- Time.now()
864	    return stamp.of(Time.DateTime.of_instant(now))
865	
866	# origin: scheme://host field. host: the Host field, as Http sends it. path: the wire path.
867	type Where is Data:
868	  Where{origin: String, host: String, path: String}
869	
870	# "" for the bucket itself.
871	def seg(+key: String) -> String:
872	  Bool.pick(String, String.is_empty(key), "", "/" ++ encode(key, True{}))
873	
874	def loc.at(style: Style, +bucket: String, +key: String, a: Url.Abs) -> Where:
875	  match style:
876	    case Path{}:
877	      Url.Abs{+scheme, host, port, t} = a
878	      +field = Url.host_field(Url.Abs{scheme, host, port, "/"})
879	      Where{scheme ++ "://" ++ field, field, "/" ++ bucket ++ seg(key)}
880	    case Virtual{}:
881	      Url.Abs{+scheme, host, port, t} = a
882	      +field = Url.host_field(Url.Abs{scheme, bucket ++ "." ++ host, port, "/"})
883	      Where{scheme ++ "://" ++ field, field, or(seg(key), "/")}
884	
885	def loc(style: Style, +bucket: String, +key: String, m: Maybe<&2, Url.Abs>) -> Maybe<&2, Where>:
886	  match m:
887	    case None{}:
888	      None{}
889	    case Some{a}:
890	      Some{loc.at(style, bucket, key, a)}
891	
892	def token(c: Credentials) -> String:
893	  Credentials{a, s, t} = c
894	  t
895	
896	def with.token(+token: String, +h: Map<&2, List<&2, String>>) -> Map<&2, List<&2, String>>:
897	  Bool.pick(Map<&2, List<&2, String>>, String.is_empty(token), h, Http.set(h, "x-amz-security-token", token))
898	
899	# extra, and the headers the signature covers. Host is Http's own, from the same URL.
900	def request.signed(extra: Map<&2, List<&2, String>>, date: String, +token: String, got: String & String) -> Map<&2, List<&2, String>>:
901	  (auth, hash) = got
902	  with.token(token, Http.set(Http.set(Http.set(Http.set(extra, "x-amz-date", date), "x-amz-content-sha256", hash), "authorization", auth), "accept-encoding", "identity"))
903	
904	def url(origin: String, path: String, +query: String) -> String:
905	  origin ++ path ++ Bool.pick(String, String.is_empty(query), "", "?" ++ query)
906	
907	def call.done(cfg: Config, x: Hairpin.Client & Result<&1, &1, Http.Err, Http.Res>) -> Client & Result<&1, &1, Err, Http.Res>:
908	  (h, r) = x
909	  (Client{cfg, h}, judge(r))
910	
911	# Hairpin.request with the codings "identity": Http then leaves a stored Content-Encoding (gzip, br, ..) as sent,
912	# so GET returns the object's bytes and HEAD's size matches. ponytail: Http still undoes x-gzip, which S3 rarely stores.
913	def send(c: Hairpin.Client, +method: String, url: String, headers: Map<&2, List<&2, String>>, body: Bytes.Bytes) ->
914	    IO(Hairpin.Client & Result<&1, &1, Http.Err, Http.Res>):
915	  Hairpin.Client{+o, p, j} = c
916	  Hairpin.Opts{b, +h, ms, mode, +n, cert} = o
917	  Hairpin.request.go(o, n, "identity", p, j, method, Hairpin.target.abs(Some{url}), Hairpin.merge(h, headers), body)
918	
919	def call.send(s: Result<&1, &1, U32 & String, String & String>, cfg: Config, http: Hairpin.Client, +method: String, url: String,
920	    extra: Map<&2, List<&2, String>>, date: String, token: String, body: Bytes.Bytes) -> IO(Client & Result<&1, &1, Err, Http.Res>):
921	  match s:
922	    case Fail{e}:
923	      (code, why) = e
924	      IO.pure(Client & Result<&1, &1, Err, Http.Res>, (Client{cfg, http}, Fail{ErrSign{code, why}}))
925	    case Done{got}:
926	      do IO<Client & Result<&1, &1, Err, Http.Res>>:
927	        x : Hairpin.Client & Result<&1, &1, Http.Err, Http.Res> <- send(http, method, url, request.signed(extra, date, token, got), body)
928	        return call.done(cfg, x)
929	
930	# The signer hashes one copy of the body; the other goes on the wire.
931	def call.sign(got: Where, +endpoint: String, +region: String, +style: Style, +creds: Credentials,
932	    http: Hairpin.Client, +method: String, +query: String, extra: Map<&2, List<&2, String>>, +date: String,
933	    b: Bytes.Bytes & Bytes.Bytes) -> IO(Client & Result<&1, &1, Err, Http.Res>):
934	  Where{origin, host, +path} = got
935	  (keep, copy) = b
936	  do IO<Client & Result<&1, &1, Err, Http.Res>>:
937	    s : Result<&1, &1, U32 & String, String & String> <- authorize(creds, region, "s3", date, method, path, query, host, copy)
938	    call.send(s, Config{endpoint, region, style, creds}, http, method, url(origin, path, query), extra, date, token(creds), keep)
939	
940	def call.at(w: Maybe<&2, Where>, +endpoint: String, +region: String, +style: Style, +creds: Credentials,
941	    http: Hairpin.Client, +method: String, +query: String, extra: Map<&2, List<&2, String>>, +date: String, body: Bytes.Bytes) ->
942	    IO(Client & Result<&1, &1, Err, Http.Res>):
943	  match w:
944	    case None{}:
945	      IO.pure(Client & Result<&1, &1, Err, Http.Res>, (Client{Config{endpoint, region, style, creds}, http}, Fail{ErrConfig{"bad endpoint: " ++ endpoint}}))
946	    case Some{got}:
947	      call.sign(got, endpoint, region, style, creds, http, method, query, extra, date, Bytes.slice(body, 0, 4294967295))
948	
949	# Object calls require a bucket and a key. ListObjectsV2 targets the bucket with list-type=2.
950	# The absolute URL bypasses base resolution, so '.' and '..' in object keys survive.
951	def call.run(c: Client, +method: String, +bucket: String, +key: String, +query: String, extra: Map<&2, List<&2, String>>,
952	    body: Bytes.Bytes) -> IO(Client & Result<&1, &1, Err, Http.Res>):
953	  Client{cfg, http} = c
954	  Config{+endpoint, +region, +style, +creds} = cfg
955	  do IO<Client & Result<&1, &1, Err, Http.Res>>:
956	    date : String <- stamp()
957	    call.at(loc(style, bucket, key, Url.absolute(endpoint)), endpoint, region, style, creds, http, method, query, extra, date, body)
958	
959	def call.guard(bad: Bool, c: Client, +method: String, +bucket: String, +key: String, +query: String,
960	    extra: Map<&2, List<&2, String>>, body: Bytes.Bytes) -> IO(Client & Result<&1, &1, Err, Http.Res>):
961	  match bad:
962	    case True{}:
963	      IO.pure(Client & Result<&1, &1, Err, Http.Res>, (c, Fail{ErrConfig{"bucket and object key must not be empty"}}))
964	    case False{}:
965	      call.run(c, method, bucket, key, query, extra, body)
966	
967	def call(c: Client, +method: String, +bucket: String, +key: String, +query: String, extra: Map<&2, List<&2, String>>,
968	    body: Bytes.Bytes) -> IO(Client & Result<&1, &1, Err, Http.Res>):
969	  call.guard(Bool.or(String.is_empty(bucket), Bool.and(String.is_empty(key), String.is_empty(query))),
970	    c, method, bucket, key, query, extra, body)
971	
972	# ---- operations
973	
974	def etag.of(r: Result<&1, &1, Err, Http.Res>) -> Result<&1, &1, Err, String>:
975	  match r:
976	    case Fail{e}:
977	      Fail{e}
978	    case Done{res}:
979	      Http.Res{s, +h, b} = res
980	      Done{Http.header(h, "etag")}
981	
982	def put.done(x: Client & Result<&1, &1, Err, Http.Res>) -> Client & Result<&1, &1, Err, String>:
983	  (c, r) = x
984	  (c, etag.of(r))
985	
986	# PutObject. mime: Content-Type, "" for none. The ETag comes back.
987	def put(c: Client, bucket: String, key: String, +mime: String, body: Bytes.Bytes) -> IO(Client & Result<&1, &1, Err, String>):
988	  +h = Bool.pick(Map<&2, List<&2, String>>, String.is_empty(mime), Http.empty(), Http.set(Http.empty(), "content-type", mime))
989	  do IO<Client & Result<&1, &1, Err, String>>:
990	    x : Client & Result<&1, &1, Err, Http.Res> <- call(c, "PUT", bucket, key, "", h, body)
991	    return put.done(x)
992	
993	def xgzip.values(xs: List<&2, String>) -> Bool:
994	  match xs:
995	    case Nil{}:
996	      False{}
997	    case Con{v, t}:
998	      Bool.or(String.eq(String.to_lower(String.trim(v)), "x-gzip"), xgzip.values(t))
999	
1000	def xgzip.fields(xs: List<&2, String>) -> Bool:
1001	  match xs:
1002	    case Nil{}:
1003	      False{}
1004	    case Con{v, t}:
1005	      Bool.or(xgzip.values(String.split(v, ',')), xgzip.fields(t))
1006	
1007	def body.encoding(gzip: Bool, b: Bytes.Bytes) -> Result<&1, &1, Err, Bytes.Bytes>:
1008	  match gzip:
1009	    case True{}:
1010	      Fail{ErrConfig{"Hairpin decodes x-gzip objects; their stored bytes are unavailable"}}
1011	    case False{}:
1012	      Done{b}
1013	
1014	def body.of(r: Result<&1, &1, Err, Http.Res>) -> Result<&1, &1, Err, Bytes.Bytes>:
1015	  match r:
1016	    case Fail{e}:
1017	      Fail{e}
1018	    case Done{res}:
1019	      Http.Res{s, h, b} = res
1020	      body.encoding(xgzip.fields(Http.fields(h, "content-encoding")), b)
1021	
1022	def get.done(x: Client & Result<&1, &1, Err, Http.Res>) -> Client & Result<&1, &1, Err, Bytes.Bytes>:
1023	  (c, r) = x
1024	  (c, body.of(r))
1025	
1026	# GetObject: the object's bytes. A missing key is ErrS3{404, "NoSuchKey", ..}.
1027	# ponytail: Hairpin decodes x-gzip; reject it rather than return bytes that differ from the stored object.
1028	def get(c: Client, bucket: String, key: String) -> IO(Client & Result<&1, &1, Err, Bytes.Bytes>):
1029	  do IO<Client & Result<&1, &1, Err, Bytes.Bytes>>:
1030	    x : Client & Result<&1, &1, Err, Http.Res> <- call(c, "GET", bucket, key, "", Http.empty(), Bytes.new(0))
1031	    return get.done(x)
1032	
1033	def nat(s: String) -> Nat:
1034	  Maybe.default(&2, Nat, Nat.read(s), 0n)
1035	
1036	def meta.of(r: Result<&1, &1, Err, Http.Res>) -> Result<&1, &1, Err, Meta>:
1037	  match r:
1038	    case Fail{e}:
1039	      Fail{e}
1040	    case Done{res}:
1041	      Http.Res{s, +h, b} = res
1042	      Done{Meta{nat(Http.header(h, "content-length")), Http.header(h, "etag"), Http.header(h, "content-type"), Http.header(h, "last-modified")}}
1043	
1044	def head.done(x: Client & Result<&1, &1, Err, Http.Res>) -> Client & Result<&1, &1, Err, Meta>:
1045	  (c, r) = x
1046	  (c, meta.of(r))
1047	
1048	# HeadObject. A missing key is ErrS3{404, "", ""}: HEAD has no error body.
1049	def head(c: Client, bucket: String, key: String) -> IO(Client & Result<&1, &1, Err, Meta>):
1050	  do IO<Client & Result<&1, &1, Err, Meta>>:
1051	    x : Client & Result<&1, &1, Err, Http.Res> <- call(c, "HEAD", bucket, key, "", Http.empty(), Bytes.new(0))
1052	    return head.done(x)
1053	
1054	def unit.of(r: Result<&1, &1, Err, Http.Res>) -> Result<&1, &1, Err, Unit>:
1055	  match r:
1056	    case Fail{e}:
1057	      Fail{e}
1058	    case Done{res}:
1059	      Done{Unit{}}
1060	
1061	def delete.done(x: Client & Result<&1, &1, Err, Http.Res>) -> Client & Result<&1, &1, Err, Unit>:
1062	  (c, r) = x
1063	  (c, unit.of(r))
1064	
1065	# DeleteObject. S3 answers 204 for a key that was never there too.
1066	def delete(c: Client, bucket: String, key: String) -> IO(Client & Result<&1, &1, Err, Unit>):
1067	  do IO<Client & Result<&1, &1, Err, Unit>>:
1068	    x : Client & Result<&1, &1, Err, Http.Res> <- call(c, "DELETE", bucket, key, "", Http.empty(), Bytes.new(0))
1069	    return delete.done(x)
1070	
1071	# ---- ListObjectsV2
1072	
1073	# cur: the <Contents> being read. Leaves come in document order, so a Contents closes after its fields.
1074	type Acc is Data:
1075	  Acc{cur: Object, objs: List<&2, Object>, pre: List<&2, String>, cut: Bool, next: String}
1076	
1077	def blank() -> Object:
1078	  Object{"", 0n, "", ""}
1079	
1080	def obj.set(o: Object, +n: String, +x: String) -> Object:
1081	  Object{+k, +sz, +e, +mo} = o
1082	  Object{Bool.pick(String, String.eq(n, "Key"), x, k), Bool.pick(Nat, String.eq(n, "Size"), nat(x), sz),
1083	    Bool.pick(String, String.eq(n, "ETag"), x, e), Bool.pick(String, String.eq(n, "LastModified"), x, mo)}
1084	
1085	def page.leaf(a: Acc, +p: String, +n: String, +x: String) -> Acc:
1086	  Acc{+cur, +objs, +pre, +cut, +next} = a
1087	  +top = String.eq(p, "ListBucketResult")
1088	  +done = Bool.and(top, String.eq(n, "Contents"))
1089	  Acc{Bool.pick(Object, done, blank(), Bool.pick(Object, String.eq(p, "Contents"), obj.set(cur, n, x), cur)),
1090	    Bool.pick(List<&2, Object>, done, Con{cur, objs}, objs),
1091	    Bool.pick(List<&2, String>, Bool.and(String.eq(p, "CommonPrefixes"), String.eq(n, "Prefix")), Con{x, pre}, pre),
1092	    Bool.pick(Bool, Bool.and(top, String.eq(n, "IsTruncated")), String.eq(x, "true"), cut),
1093	    Bool.pick(String, Bool.and(top, String.eq(n, "NextContinuationToken")), x, next)}
1094	
1095	def page.scan(ls: List<&2, Leaf>, a: Acc) -> Acc:
1096	  match ls:
1097	    case Nil{}:
1098	      a
1099	    case Con{Leaf{p, n, x}, t}:
1100	      page.scan(t, page.leaf(a, p, n, x))
1101	
1102	def page.fin(a: Acc) -> Page:
1103	  Acc{cur, objs, pre, +cut, +next} = a
1104	  Page{List.reverse(&2, Object, objs), List.reverse(&2, String, pre),
1105	    Bool.pick(Maybe<&2, String>, Bool.and(cut, Bool.not(String.is_empty(next))), Some{next}, None{})}
1106	
1107	def page.root.last(ls: List<&2, Leaf>, +n: String) -> String:
1108	  match ls:
1109	    case Nil{}:
1110	      n
1111	    case Con{Leaf{p, +m, x}, t}:
1112	      page.root.last(t, m)
1113	
1114	def page.if(good: Bool, s: String, ls: List<&2, Leaf>) -> Result<&1, &1, Err, Page>:
1115	  match good:
1116	    case True{}:
1117	      Done{page.fin(page.scan(ls, Acc{blank(), Nil{}, Nil{}, False{}, ""}))}
1118	    case False{}:
1119	      Fail{ErrXml{s}}
1120	
1121	def page.doc(+s: String, m: Maybe<&2, List<&2, Leaf>>) -> Result<&1, &1, Err, Page>:
1122	  match m:
1123	    case None{}:
1124	      Fail{ErrXml{s}}
1125	    case Some{+ls}:
1126	      page.if(String.eq(page.root.last(ls, ""), "ListBucketResult"), s, ls)
1127	
1128	def page.of(r: Result<&1, &1, Err, Http.Res>) -> Result<&1, &1, Err, Page>:
1129	  match r:
1130	    case Fail{e}:
1131	      Fail{e}
1132	    case Done{res}:
1133	      Http.Res{s, h, b} = res
1134	      +text = Enc.utf8.decode(b)
1135	      page.doc(text, xml(text))
1136	
1137	def list.done(x: Client & Result<&1, &1, Err, Http.Res>) -> Client & Result<&1, &1, Err, Page>:
1138	  (c, r) = x
1139	  (c, page.of(r))
1140	
1141	def q.kv(k: String, +v: String) -> String:
1142	  k ++ "=" ++ encode(v, False{})
1143	
1144	def q.opt(k: String, +v: String, +rest: List<&2, String>) -> List<&2, String>:
1145	  Bool.pick(List<&2, String>, String.is_empty(v), rest, Con{q.kv(k, v), rest})
1146	
1147	def q.token(t: Maybe<&2, String>, rest: List<&2, String>) -> List<&2, String>:
1148	  match t:
1149	    case None{}:
1150	      rest
1151	    case Some{v}:
1152	      Con{q.kv("continuation-token", v), rest}
1153	
1154	def q.max(+n: U32) -> List<&2, String>:
1155	  Bool.pick(List<&2, String>, U32.is_eq(n, 0), Nil{}, ["max-keys=" ++ U32.show(n)])
1156	
1157	# In the signer's order: continuation-token, delimiter, list-type, max-keys, prefix.
1158	def list.query(prefix: String, delim: String, +max: U32, t: Maybe<&2, String>) -> String:
1159	  String.join(q.token(t, q.opt("delimiter", delim, Con{"list-type=2", List.append(&2, String, q.max(max), q.opt("prefix", prefix, Nil{}))})), "&")
1160	
1161	# One page of ListObjectsV2. prefix, delim: "" for none. max: keys per page, 0 for S3's 1000. token: a page's next.
1162	def list(c: Client, +bucket: String, prefix: String, delim: String, +max: U32, token: Maybe<&2, String>) ->
1163	    IO(Client & Result<&1, &1, Err, Page>):
1164	  do IO<Client & Result<&1, &1, Err, Page>>:
1165	    x : Client & Result<&1, &1, Err, Http.Res> <- call(c, "GET", bucket, "", list.query(prefix, delim, max, token), Http.empty(), Bytes.new(0))
1166	    return list.done(x)
1167	
1168	def all.merge(objs: List<&2, Object>, pre: List<&2, String>, r: Result<&1, &1, Err, Page>) -> Result<&1, &1, Err, Page>:
1169	  match r:
1170	    case Fail{e}:
1171	      Fail{e}
1172	    case Done{Page{os, ps, next}}:
1173	      Done{Page{List.append(&2, Object, objs, os), List.append(&2, String, pre, ps), next}}
1174	
1175	# f: pages left. When they run out, next holds the token to go on from.
1176	def all.go(f: Nat, +bucket: String, +prefix: String, +delim: String, +max: U32, objs: List<&2, Object>, pre: List<&2, String>,
1177	    x: Client & Result<&1, &1, Err, Page>) -> IO(Client & Result<&1, &1, Err, Page>):
1178	  match f:
1179	    case 0n:
1180	      (c, r) = x
1181	      IO.pure(Client & Result<&1, &1, Err, Page>, (c, all.merge(objs, pre, r)))
1182	    case 1n+g:
1183	      (c, r) = x
1184	      match r:
1185	        case Fail{e}:
1186	          IO.pure(Client & Result<&1, &1, Err, Page>, (c, Fail{e}))
1187	        case Done{Page{os, ps, next}}:
1188	          match next:
1189	            case None{}:
1190	              IO.pure(Client & Result<&1, &1, Err, Page>, (c, Done{Page{List.append(&2, Object, objs, os), List.append(&2, String, pre, ps), None{}}}))
1191	            case Some{tok}:
1192	              do IO<Client & Result<&1, &1, Err, Page>>:
1193	                y : Client & Result<&1, &1, Err, Page> <- list(c, bucket, prefix, delim, max, Some{tok})
1194	                all.go(g, bucket, prefix, delim, max, List.append(&2, Object, objs, os), List.append(&2, String, pre, ps), y)
1195	
1196	# Every page, following NextContinuationToken, up to 100000 pages.
1197	def list.all(c: Client, +bucket: String, +prefix: String, +delim: String, +max: U32) -> IO(Client & Result<&1, &1, Err, Page>):
1198	  do IO<Client & Result<&1, &1, Err, Page>>:
1199	    x : Client & Result<&1, &1, Err, Page> <- list(c, bucket, prefix, delim, max, None{})
1200	    all.go(U32.to_nat(100000), bucket, prefix, delim, max, Nil{}, Nil{}, x)