1	# DEFLATE, gzip, and zlib encoding and decoding (RFC 1951, 1952, 1950) over byte strings, plus gzip, zstd, and brotli through the C libraries. Source: https://github.com/paymog/bend-kit/tree/main/zlib
2	import Base
3	import bend-kit-hash@0.1.0.0/hash.bend as Hash
4	
5	# Bytes are one Char per octet (0..255), as everywhere in bend-kit.
6	
7	def byte(h: Char) -> U32:
8	  Chr{c} = h
9	  c
10	
11	def bits(+n: U32) -> Nat:
12	  U32.to_nat(n)
13	
14	def mask(+n: U32) -> U32:
15	  (U32.shln(1, bits(n)) - 1 : U32)
16	
17	# Bit reader. over counts bytes read past the end; any over means the input was cut short.
18	type Br is Data:
19	  Br{s: String, buf: U32, cnt: U32, over: U32}
20	
21	def br.new(s: String) -> Br:
22	  Br{s, 0, 0, 0}
23	
24	def br.pull(b: Br) -> Br:
25	  Br{s, +buf, +cnt, +over} = b
26	  match s:
27	    case SNil{}:
28	      Br{SNil{}, buf, (cnt + 8 : U32), (over + 1 : U32)}
29	    case SCon{h, t}:
30	      Br{t, U32.or(buf, U32.shln(byte(h), bits(cnt))), (cnt + 8 : U32), over}
31	
32	def br.pull.if(b: Br, short: Bool) -> Br:
33	  match short:
34	    case True{}:
35	      br.pull(b)
36	    case False{}:
37	      b
38	
39	def br.short(+b: Br, +n: U32) -> Bool:
40	  Br{s, buf, +cnt, over} = b
41	  U32.is_lt(cnt, n)
42	
43	# n is at most 16, so three bytes always fill the buffer.
44	def br.fill(fuel: Nat, +b: Br, +n: U32) -> Br:
45	  match fuel:
46	    case 0n:
47	      b
48	    case 1n+f:
49	      br.fill(f, br.pull.if(b, br.short(b, n)), n)
50	
51	def br.cut(b: Br, +n: U32) -> Br & U32:
52	  Br{s, +buf, cnt, over} = b
53	  (Br{s, U32.shrn(buf, bits(n)), (cnt - n : U32), over}, U32.and(buf, mask(n)))
54	
55	def br.take(b: Br, +n: U32) -> Br & U32:
56	  br.cut(br.fill(3n, b, n), n)
57	
58	def br.drop.of(r: Br & U32) -> Br:
59	  (b, v) = r
60	  b
61	
62	def br.drop(b: Br, +n: U32) -> Br:
63	  br.drop.of(br.cut(b, n))
64	
65	# RFC 1951 §3.2.4: a stored block starts on a byte boundary.
66	def br.align(+b: Br) -> Br:
67	  Br{s, buf, +cnt, over} = b
68	  br.drop(b, U32.mod(cnt, 8))
69	
70	def br.ok(+b: Br) -> Bool:
71	  Br{s, buf, cnt, +over} = b
72	  U32.is_eq(over, 0)
73	
74	def br.bytes(k: Nat, +buf: U32) -> String:
75	  match k:
76	    case 0n:
77	      SNil{}
78	    case 1n+p:
79	      SCon{Chr{U32.and(buf, 255)}, br.bytes(p, U32.shrn(buf, 8n))}
80	
81	def br.rest.of(b: Br) -> String:
82	  Br{s, +buf, +cnt, over} = b
83	  br.bytes(bits(U32.div(cnt, 8)), buf) ++ s
84	
85	# Whole bytes still in the buffer go back in front of the unread input.
86	def br.rest(+b: Br) -> String:
87	  br.rest.of(br.align(b))
88	
89	# Huffman codes as a trie: one step per bit. A read bit picks o (1) or z (0).
90	# Bad: two codes collided, so the code set was over-subscribed.
91	type Ht is Data:
92	  HtNone{}
93	  HtBad{}
94	  HtLeaf{sym: U32}
95	  HtNode{z: Ht, o: Ht}
96	
97	def ht.left(t: Ht) -> Ht:
98	  match t:
99	    case HtNode{z, o}:
100	      z
101	    case HtNone{}:
102	      HtNone{}
103	    case HtBad{}:
104	      HtBad{}
105	    case HtLeaf{s}:
106	      HtBad{}
107	
108	def ht.right(t: Ht) -> Ht:
109	  match t:
110	    case HtNode{z, o}:
111	      o
112	    case HtNone{}:
113	      HtNone{}
114	    case HtBad{}:
115	      HtBad{}
116	    case HtLeaf{s}:
117	      HtBad{}
118	
119	def ht.leaf(t: Ht, +sym: U32) -> Ht:
120	  match t:
121	    case HtNone{}:
122	      HtLeaf{sym}
123	    case HtBad{}:
124	      HtBad{}
125	    case HtLeaf{s}:
126	      HtBad{}
127	    case HtNode{z, o}:
128	      HtBad{}
129	
130	def ht.ins(path: List<&2, Bool>, +t: Ht, +sym: U32) -> Ht:
131	  match path:
132	    case Nil{}:
133	      ht.leaf(t, sym)
134	    case Con{b, rest}:
135	      match b:
136	        case True{}:
137	          HtNode{ht.left(t), ht.ins(rest, ht.right(t), sym)}
138	        case False{}:
139	          HtNode{ht.ins(rest, ht.left(t), sym), ht.right(t)}
140	
141	# The code's bits, most significant first: the order the stream sends them.
142	def ht.path(n: Nat, +code: U32, acc: List<&2, Bool>) -> List<&2, Bool>:
143	  match n:
144	    case 0n:
145	      acc
146	    case 1n+p:
147	      ht.path(p, U32.shr(code), Con{U32.is_eq(U32.and(code, 1), 1), acc})
148	
149	# Canonical codes (RFC 1951 §3.2.2): count lengths, find each length's first code, then assign in symbol order.
150	def cnt.add(ar: Array<U32> & U32, +len: U32) -> Array<U32>:
151	  (a, v) = ar
152	  Array.set(U32, a, len, (v + 1 : U32))
153	
154	def cnt.go(xs: List<&2, U32>, a: Array<U32>) -> Array<U32>:
155	  match xs:
156	    case Nil{}:
157	      a
158	    case Con{+l, t}:
159	      cnt.go(t, cnt.add(Array.get(U32, a, l), l))
160	
161	def nx.set(+i: U32, cv: Array<U32> & U32, n: Array<U32>, +code: U32) -> Array<U32> & Array<U32> & U32:
162	  (c, v) = cv
163	  +code2 = U32.shl((code + Bool.pick(U32, U32.is_eq(i, 1), 0, v) : U32))
164	  (c, Array.set(U32, n, i, code2), code2)
165	
166	def nx.step(+i: U32, st: Array<U32> & Array<U32> & U32) -> Array<U32> & Array<U32> & U32:
167	  (c, n, code) = st
168	  nx.set(i, Array.get(U32, c, (i - 1 : U32)), n, code)
169	
170	def nx.go(k: Nat, +i: U32, st: Array<U32> & Array<U32> & U32) -> Array<U32> & Array<U32> & U32:
171	  match k:
172	    case 0n:
173	      st
174	    case 1n+f:
175	      nx.go(f, (i + 1 : U32), nx.step(i, st))
176	
177	def as.put(+l: U32, +sym: U32, nv: Array<U32> & U32, t: Ht) -> Array<U32> & Ht:
178	  (n, +code) = nv
179	  (Array.set(U32, n, l, (code + 1 : U32)), ht.ins(ht.path(bits(l), code, Nil{}), t, sym))
180	
181	def as.one.nz(+l: U32, +sym: U32, n: Array<U32>, t: Ht, zero: Bool) -> Array<U32> & Ht:
182	  match zero:
183	    case True{}:
184	      (n, t)
185	    case False{}:
186	      as.put(l, sym, Array.get(U32, n, l), t)
187	
188	def as.one(+l: U32, +sym: U32, st: Array<U32> & Ht) -> Array<U32> & Ht:
189	  (n, t) = st
190	  as.one.nz(l, sym, n, t, U32.is_zero(l))
191	
192	def as.go(xs: List<&2, U32>, +sym: U32, st: Array<U32> & Ht) -> Array<U32> & Ht:
193	  match xs:
194	    case Nil{}:
195	      st
196	    case Con{+l, t}:
197	      as.go(t, (sym + 1 : U32), as.one(l, sym, st))
198	
199	def ht.of(st: Array<U32> & Ht) -> Ht:
200	  (n, t) = st
201	  t
202	
203	def ht.assign(xs: List<&2, U32>, st: Array<U32> & Array<U32> & U32) -> Ht:
204	  (c, n, code) = st
205	  ht.of(as.go(xs, 0, (n, HtNone{})))
206	
207	# lens[i] is the code length of symbol i; 0 means the symbol is unused.
208	def ht.build(+lens: List<&2, U32>) -> Ht:
209	  ht.assign(lens, nx.go(15n, 1, (cnt.go(lens, Array.new(U32, 4n, 0)), Array.new(U32, 4n, 0), 0)))
210	
211	# No code: 9999, never a symbol.
212	def ht.step(z: Ht, o: Ht, bv: Br & U32) -> Ht & Br:
213	  (b, +v) = bv
214	  (Bool.pick(Ht, U32.is_eq(v, 1), o, z), b)
215	
216	# A code is at most 15 bits (§3.2.7), so 16 steps always reach a leaf or a miss.
217	def ht.dec(fuel: Nat, st: Ht & Br) -> Br & U32:
218	  match fuel:
219	    case 0n:
220	      (t, b) = st
221	      (b, 9999)
222	    case 1n+f:
223	      (t, b) = st
224	      match t:
225	        case HtLeaf{s}:
226	          (b, s)
227	        case HtNone{}:
228	          (b, 9999)
229	        case HtBad{}:
230	          (b, 9999)
231	        case HtNode{z, o}:
232	          ht.dec(f, ht.step(z, o, br.take(b, 1)))
233	
234	def ht.decode(t: Ht, b: Br) -> Br & U32:
235	  ht.dec(16n, (t, b))
236	
237	def nth(xs: List<&2, U32>, +i: U32) -> U32:
238	  match xs:
239	    case Nil{}:
240	      0
241	    case Con{h, t}:
242	      Bool.pick(U32, U32.is_zero(i), h, nth(t, (i - 1 : U32)))
243	
244	def rep(k: Nat, +v: U32, acc: List<&2, U32>) -> List<&2, U32>:
245	  match k:
246	    case 0n:
247	      acc
248	    case 1n+p:
249	      rep(p, v, Con{v, acc})
250	
251	def take.n(k: Nat, xs: List<&2, U32>) -> List<&2, U32>:
252	  match k:
253	    case 0n:
254	      Nil{}
255	    case 1n+p:
256	      match xs:
257	        case Nil{}:
258	          Nil{}
259	        case Con{h, t}:
260	          Con{h, take.n(p, t)}
261	
262	def drop.n(k: Nat, xs: List<&2, U32>) -> List<&2, U32>:
263	  match k:
264	    case 0n:
265	      xs
266	    case 1n+p:
267	      match xs:
268	        case Nil{}:
269	          Nil{}
270	        case Con{h, t}:
271	          drop.n(p, t)
272	
273	# RFC 1951 §3.2.5
274	def len.base() -> List<&2, U32>:
275	  [3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 17, 19, 23, 27, 31, 35, 43, 51, 59, 67, 83, 99, 115, 131, 163, 195, 227, 258]
276	
277	def len.extra() -> List<&2, U32>:
278	  [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 0]
279	
280	def dist.base() -> List<&2, U32>:
281	  [1, 2, 3, 4, 5, 7, 9, 13, 17, 25, 33, 49, 65, 97, 129, 193, 257, 385, 513, 769, 1025, 1537, 2049, 3073, 4097, 6145, 8193, 12289, 16385, 24577]
282	
283	def dist.extra() -> List<&2, U32>:
284	  [0, 0, 0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13]
285	
286	# RFC 1951 §3.2.6
287	def fixed.lit() -> Ht:
288	  ht.build(rep(144n, 8, rep(112n, 9, rep(24n, 7, rep(8n, 8, Nil{})))))
289	
290	def fixed.dist() -> Ht:
291	  ht.build(rep(30n, 5, Nil{}))
292	
293	# Output: the 32 KiB window (indexes wrap), the write position, the byte count, and the bytes, reversed.
294	type Ow is Data:
295	  Ow{w: U32, n: U32, racc: String}
296	
297	def out.put(win: Array<U32>, +c: U32, o: Ow) -> Array<U32> & Ow:
298	  Ow{+w, +n, racc} = o
299	  (Array.set(U32, win, w, c), Ow{(w + 1 : U32), (n + 1 : U32), SCon{Chr{c}, racc}})
300	
301	type Mo is Data:
302	  MoHead{}
303	  MoCodes{lit: Ht, dist: Ht}
304	  MoDone{}
305	  MoBad{}
306	
307	type Is is Data:
308	  Is{br: Br, o: Ow, mode: Mo, last: Bool}
309	
310	def inf.next(last: Bool) -> Mo:
311	  match last:
312	    case True{}:
313	      MoDone{}
314	    case False{}:
315	      MoHead{}
316	
317	def inf.bad(win: Array<U32>, b: Br, o: Ow) -> Array<U32> & Is:
318	  (win, Is{b, o, MoBad{}, True{}})
319	
320	# Stored block (§3.2.4): LEN, then NLEN (its complement), then LEN raw bytes.
321	def sb.put2(p: Array<U32> & Ow, b: Br) -> Array<U32> & Br & Ow:
322	  (a, o) = p
323	  (a, b, o)
324	
325	def sb.put(win: Array<U32>, bv: Br & U32, o: Ow) -> Array<U32> & Br & Ow:
326	  (b, +c) = bv
327	  sb.put2(out.put(win, c, o), b)
328	
329	def sb.byte(st: Array<U32> & Br & Ow) -> Array<U32> & Br & Ow:
330	  (win, b, o) = st
331	  sb.put(win, br.take(b, 8), o)
332	
333	def sb.go(k: Nat, st: Array<U32> & Br & Ow) -> Array<U32> & Br & Ow:
334	  match k:
335	    case 0n:
336	      st
337	    case 1n+f:
338	      sb.go(f, sb.byte(st))
339	
340	def sb.done(t: Array<U32> & Br & Ow, +last: Bool) -> Array<U32> & Is:
341	  (win, b, o) = t
342	  (win, Is{b, o, inf.next(last), last})
343	
344	def sb.ok(win: Array<U32>, b: Br, +len: U32, o: Ow, +last: Bool, ok: Bool) -> Array<U32> & Is:
345	  match ok:
346	    case False{}:
347	      inf.bad(win, b, o)
348	    case True{}:
349	      sb.done(sb.go(bits(len), (win, b, o)), last)
350	
351	def sb.nlen(win: Array<U32>, bv: Br & U32, +len: U32, o: Ow, +last: Bool) -> Array<U32> & Is:
352	  (b, +nlen) = bv
353	  sb.ok(win, b, len, o, last, U32.is_eq(U32.xor(len, 65535), nlen))
354	
355	def sb.len(win: Array<U32>, bv: Br & U32, o: Ow, +last: Bool) -> Array<U32> & Is:
356	  (b, +len) = bv
357	  sb.nlen(win, br.take(b, 16), len, o, last)
358	
359	def inf.stored(win: Array<U32>, b: Br, o: Ow, +last: Bool) -> Array<U32> & Is:
360	  sb.len(win, br.take(br.align(b), 16), o, last)
361	
362	# Dynamic block (§3.2.7): code lengths for the code-length code, then the lengths themselves.
363	# cl.slot[i]: where symbol i's length sits in the order the stream sends them.
364	def cl.slot() -> List<&2, U32>:
365	  [3, 17, 15, 13, 11, 9, 7, 5, 4, 6, 8, 10, 12, 14, 16, 18, 0, 1, 2]
366	
367	def cl.place(xs: List<&2, U32>, +vals: List<&2, U32>) -> List<&2, U32>:
368	  match xs:
369	    case Nil{}:
370	      Nil{}
371	    case Con{+i, t}:
372	      Con{nth(vals, i), cl.place(t, vals)}
373	
374	def cl.push(bv: Br & U32, acc: List<&2, U32>) -> Br & List<&2, U32>:
375	  (b, v) = bv
376	  (b, Con{v, acc})
377	
378	def cl.one(st: Br & List<&2, U32>) -> Br & List<&2, U32>:
379	  (b, acc) = st
380	  cl.push(br.take(b, 3), acc)
381	
382	def cl.read(k: Nat, st: Br & List<&2, U32>) -> Br & List<&2, U32>:
383	  match k:
384	    case 0n:
385	      st
386	    case 1n+f:
387	      cl.read(f, cl.one(st))
388	
389	# Lengths so far (reversed), how many, the last one (for code 16), and whether it went wrong.
390	type Cd is Data:
391	  Cd{br: Br, acc: List<&2, U32>, n: U32, prev: U32, bad: Bool}
392	
393	def cd.fill(+b: Br, +acc: List<&2, U32>, +n: U32, +v: U32, +cnt: U32, +total: U32) -> Cd:
394	  Bool.pick(Cd, U32.is_lt(total, (n + cnt : U32)), Cd{b, acc, n, v, True{}}, Cd{b, rep(bits(cnt), v, acc), (n + cnt : U32), v, False{}})
395	
396	def cd.rep(bv: Br & U32, +v: U32, +base: U32, acc: List<&2, U32>, +n: U32, +total: U32) -> Cd:
397	  (b, +e) = bv
398	  cd.fill(b, acc, n, v, (base + e : U32), total)
399	
400	def cd.prev(b: Br, acc: List<&2, U32>, +n: U32, +prev: U32, +total: U32, ok: Bool) -> Cd:
401	  match ok:
402	    case False{}:
403	      Cd{b, acc, n, prev, True{}}
404	    case True{}:
405	      cd.rep(br.take(b, 2), prev, 3, acc, n, total)
406	
407	def cd.z18(b: Br, acc: List<&2, U32>, +n: U32, +total: U32, ok: Bool) -> Cd:
408	  match ok:
409	    case True{}:
410	      cd.rep(br.take(b, 7), 0, 11, acc, n, total)
411	    case False{}:
412	      Cd{b, acc, n, 0, True{}}
413	
414	def cd.z17(b: Br, acc: List<&2, U32>, +n: U32, +s: U32, +total: U32, ok: Bool) -> Cd:
415	  match ok:
416	    case True{}:
417	      cd.rep(br.take(b, 3), 0, 3, acc, n, total)
418	    case False{}:
419	      cd.z18(b, acc, n, total, U32.is_eq(s, 18))
420	
421	def cd.c16(b: Br, acc: List<&2, U32>, +n: U32, +prev: U32, +s: U32, +total: U32, ok: Bool) -> Cd:
422	  match ok:
423	    case True{}:
424	      cd.prev(b, acc, n, prev, total, U32.is_lt(0, n))
425	    case False{}:
426	      cd.z17(b, acc, n, s, total, U32.is_eq(s, 17))
427	
428	def cd.lit(b: Br, acc: List<&2, U32>, +n: U32, +prev: U32, +s: U32, +total: U32, ok: Bool) -> Cd:
429	  match ok:
430	    case True{}:
431	      Cd{b, Con{s, acc}, (n + 1 : U32), s, False{}}
432	    case False{}:
433	      cd.c16(b, acc, n, prev, s, total, U32.is_eq(s, 16))
434	
435	def cd.sym(bv: Br & U32, acc: List<&2, U32>, +n: U32, +prev: U32, +total: U32) -> Cd:
436	  (b, +s) = bv
437	  cd.lit(b, acc, n, prev, s, total, U32.is_lt(s, 16))
438	
439	def cd.step.go(+cl: Ht, +total: U32, stop: Bool, cs: Cd) -> Cd:
440	  match stop:
441	    case False{}:
442	      Cd{b, acc, +n, +prev, bad} = cs
443	      cd.sym(ht.decode(cl, b), acc, n, prev, total)
444	    case True{}:
445	      Cd{b, acc, n, prev, bad} = cs
446	      Cd{b, acc, n, prev, bad}
447	
448	def cd.stop(+st: Cd, +total: U32) -> Bool:
449	  Cd{b, acc, +n, prev, +bad} = st
450	  Bool.or(bad, U32.is_le(total, n))
451	
452	# Each step adds at least one length, so total steps suffice.
453	def cd.go(k: Nat, +cl: Ht, +total: U32, +st: Cd) -> Cd:
454	  match k:
455	    case 0n:
456	      st
457	    case 1n+f:
458	      cd.go(f, cl, total, cd.step.go(cl, total, cd.stop(st, total), st))
459	
460	def dyn.tables(b: Br, +lens: List<&2, U32>, +hlit: U32, bad: Bool) -> Br & Mo:
461	  match bad:
462	    case True{}:
463	      (b, MoBad{})
464	    case False{}:
465	      (b, MoCodes{ht.build(take.n(bits(hlit), lens)), ht.build(drop.n(bits(hlit), lens))})
466	
467	def dyn.done(st: Cd, +hlit: U32, +total: U32) -> Br & Mo:
468	  Cd{b, acc, +n, prev, +bad} = st
469	  dyn.tables(b, List.reverse(&2, U32, acc), hlit, Bool.or(bad, Bool.not(U32.is_eq(n, total))))
470	
471	def dyn.lens(st: Br & List<&2, U32>, +hlit: U32, +hdist: U32) -> Br & Mo:
472	  (b, acc) = st
473	  +total = (hlit + hdist : U32)
474	  +clens = cl.place(cl.slot(), List.reverse(&2, U32, acc))
475	  dyn.done(cd.go(bits(total), ht.build(clens), total, Cd{b, Nil{}, 0, 0, False{}}), hlit, total)
476	
477	def dyn.clen(bv: Br & U32, +hlit: U32, +hdist: U32) -> Br & Mo:
478	  (b, +hclen) = bv
479	  dyn.lens(cl.read(bits((hclen + 4 : U32)), (b, Nil{})), hlit, hdist)
480	
481	def dyn.hdist(bv: Br & U32, +hlit: U32) -> Br & Mo:
482	  (b, +hd) = bv
483	  dyn.clen(br.take(b, 4), hlit, (hd + 1 : U32))
484	
485	def dyn.hlit(bv: Br & U32) -> Br & Mo:
486	  (b, +hl) = bv
487	  dyn.hdist(br.take(b, 5), (hl + 257 : U32))
488	
489	def dyn.read(b: Br) -> Br & Mo:
490	  dyn.hlit(br.take(b, 5))
491	
492	# A match copies len bytes from d back; the window's indexes wrap, so w - d needs no mask.
493	def cp.put(av: Array<U32> & U32, o: Ow) -> Array<U32> & Ow:
494	  (a, +c) = av
495	  out.put(a, c, o)
496	
497	def cp.one(+d: U32, st: Array<U32> & Ow) -> Array<U32> & Ow:
498	  (win, o) = st
499	  Ow{+w, n, racc} = o
500	  cp.put(Array.get(U32, win, (w - d : U32)), Ow{w, n, racc})
501	
502	def cp.go(k: Nat, +d: U32, st: Array<U32> & Ow) -> Array<U32> & Ow:
503	  match k:
504	    case 0n:
505	      st
506	    case 1n+f:
507	      cp.go(f, d, cp.one(d, st))
508	
509	def inf.codes(p: Array<U32> & Ow, b: Br, +lit: Ht, +dist: Ht, +last: Bool) -> Array<U32> & Is:
510	  (win, o) = p
511	  (win, Is{b, o, MoCodes{lit, dist}, last})
512	
513	def ow.n(+o: Ow) -> U32:
514	  Ow{w, +n, racc} = o
515	  n
516	
517	# RFC 1951 §3.2.5: a distance may not reach before the first byte out.
518	def inf.far(win: Array<U32>, b: Br, +o: Ow, +len: U32, +d: U32, +lit: Ht, +dist: Ht, +last: Bool, ok: Bool) -> Array<U32> & Is:
519	  match ok:
520	    case False{}:
521	      inf.bad(win, b, o)
522	    case True{}:
523	      inf.codes(cp.go(bits(len), d, (win, o)), b, lit, dist, last)
524	
525	def inf.dx(win: Array<U32>, bv: Br & U32, +db: U32, +len: U32, +o: Ow, +lit: Ht, +dist: Ht, +last: Bool) -> Array<U32> & Is:
526	  (b, +e) = bv
527	  +d = (db + e : U32)
528	  inf.far(win, b, o, len, d, lit, dist, last, U32.is_le(d, ow.n(o)))
529	
530	def inf.ds(win: Array<U32>, b: Br, +ds: U32, +len: U32, +o: Ow, +lit: Ht, +dist: Ht, +last: Bool, ok: Bool) -> Array<U32> & Is:
531	  match ok:
532	    case False{}:
533	      inf.bad(win, b, o)
534	    case True{}:
535	      inf.dx(win, br.take(b, nth(dist.extra(), ds)), nth(dist.base(), ds), len, o, lit, dist, last)
536	
537	def inf.d(win: Array<U32>, bv: Br & U32, +len: U32, +o: Ow, +lit: Ht, +dist: Ht, +last: Bool) -> Array<U32> & Is:
538	  (b, +ds) = bv
539	  inf.ds(win, b, ds, len, o, lit, dist, last, U32.is_lt(ds, 30))
540	
541	def inf.lx(win: Array<U32>, bv: Br & U32, +lb: U32, +o: Ow, +lit: Ht, +dist: Ht, +last: Bool) -> Array<U32> & Is:
542	  (b, +e) = bv
543	  inf.d(win, ht.decode(dist, b), (lb + e : U32), o, lit, dist, last)
544	
545	def inf.ls(win: Array<U32>, b: Br, +s: U32, +o: Ow, +lit: Ht, +dist: Ht, +last: Bool, ok: Bool) -> Array<U32> & Is:
546	  match ok:
547	    case False{}:
548	      inf.bad(win, b, o)
549	    case True{}:
550	      +i = (s - 257 : U32)
551	      inf.lx(win, br.take(b, nth(len.extra(), i)), nth(len.base(), i), o, lit, dist, last)
552	
553	def inf.end(win: Array<U32>, b: Br, +s: U32, +o: Ow, +lit: Ht, +dist: Ht, +last: Bool, eob: Bool) -> Array<U32> & Is:
554	  match eob:
555	    case True{}:
556	      (win, Is{b, o, inf.next(last), last})
557	    case False{}:
558	      inf.ls(win, b, s, o, lit, dist, last, U32.is_le(s, 285))
559	
560	def inf.lit(win: Array<U32>, b: Br, +s: U32, +o: Ow, +lit: Ht, +dist: Ht, +last: Bool, ok: Bool) -> Array<U32> & Is:
561	  match ok:
562	    case True{}:
563	      inf.codes(out.put(win, s, o), b, lit, dist, last)
564	    case False{}:
565	      inf.end(win, b, s, o, lit, dist, last, U32.is_eq(s, 256))
566	
567	def inf.sym(win: Array<U32>, bv: Br & U32, +o: Ow, +lit: Ht, +dist: Ht, +last: Bool) -> Array<U32> & Is:
568	  (b, +s) = bv
569	  inf.lit(win, b, s, o, lit, dist, last, U32.is_lt(s, 256))
570	
571	def inf.dyn(win: Array<U32>, bm: Br & Mo, o: Ow, +last: Bool) -> Array<U32> & Is:
572	  (b, m) = bm
573	  (win, Is{b, o, m, last})
574	
575	def inf.t2(win: Array<U32>, b: Br, o: Ow, +last: Bool, is2: Bool) -> Array<U32> & Is:
576	  match is2:
577	    case True{}:
578	      inf.dyn(win, dyn.read(b), o, last)
579	    case False{}:
580	      inf.bad(win, b, o)
581	
582	def inf.t1(win: Array<U32>, b: Br, o: Ow, +last: Bool, +t: U32, is1: Bool) -> Array<U32> & Is:
583	  match is1:
584	    case True{}:
585	      (win, Is{b, o, MoCodes{fixed.lit(), fixed.dist()}, last})
586	    case False{}:
587	      inf.t2(win, b, o, last, U32.is_eq(t, 2))
588	
589	def inf.t0(win: Array<U32>, b: Br, o: Ow, +last: Bool, +t: U32, is0: Bool) -> Array<U32> & Is:
590	  match is0:
591	    case True{}:
592	      inf.stored(win, b, o, last)
593	    case False{}:
594	      inf.t1(win, b, o, last, t, U32.is_eq(t, 1))
595	
596	# §3.2.3: BFINAL, then BTYPE.
597	def inf.head(win: Array<U32>, bv: Br & U32, o: Ow) -> Array<U32> & Is:
598	  (b, +v) = bv
599	  +t = U32.shr(v)
600	  inf.t0(win, b, o, U32.is_eq(U32.and(v, 1), 1), t, U32.is_zero(t))
601	
602	# Every step reads at least one bit, so 8 steps per input byte always finish a valid stream.
603	def inf.go(k: Nat, st: Array<U32> & Is) -> Array<U32> & Is:
604	  match k:
605	    case 0n:
606	      st
607	    case 1n+f:
608	      (win, ist) = st
609	      Is{b, o, mode, +last} = ist
610	      match mode:
611	        case MoHead{}:
612	          inf.go(f, inf.head(win, br.take(b, 3), o))
613	        case MoCodes{+lit, +dist}:
614	          inf.go(f, inf.sym(win, ht.decode(lit, b), o, lit, dist, last))
615	        case MoDone{}:
616	          (win, Is{b, o, MoDone{}, last})
617	        case MoBad{}:
618	          (win, Is{b, o, MoBad{}, last})
619	
620	# out: the bytes; rest: the input after the stream; n: len(out) mod 2^32.
621	type Inflated is Data:
622	  Inflated{out: String, rest: String, n: U32}
623	
624	def inf.fin(ok: Bool, b: Br, o: Ow) -> Maybe<&2, Inflated>:
625	  match ok:
626	    case False{}:
627	      None{}
628	    case True{}:
629	      Ow{w, n, racc} = o
630	      Some{Inflated{String.reverse(racc), br.rest(b), n}}
631	
632	def inf.result(st: Array<U32> & Is) -> Maybe<&2, Inflated>:
633	  (win, ist) = st
634	  Is{+b, o, mode, last} = ist
635	  match mode:
636	    case MoDone{}:
637	      inf.fin(br.ok(b), b, o)
638	    case MoHead{}:
639	      None{}
640	    case MoCodes{l, d}:
641	      None{}
642	    case MoBad{}:
643	      None{}
644	
645	def inflate.rest(+s: String) -> Maybe<&2, Inflated>:
646	  inf.result(inf.go(Nat.add(Nat.mul(String.length(s), 8n), 8n), (Array.new(U32, 15n, 0), Is{br.new(s), Ow{0, 0, ""}, MoHead{}, False{}})))
647	
648	def inflate.out(m: Maybe<&2, Inflated>) -> Maybe<&2, String>:
649	  match m:
650	    case None{}:
651	      None{}
652	    case Some{Inflated{out, rest, n}}:
653	      Some{out}
654	
655	# Raw DEFLATE. None: malformed or cut short.
656	def inflate(+s: String) -> Maybe<&2, String>:
657	  inflate.out(inflate.rest(s))
658	
659	# Checksum views for byte strings; hash owns the algorithms.
660	def crc32(s: String) -> U32:
661	  Hash.crc32.str(s)
662	
663	def adler32(s: String) -> U32:
664	  Hash.adler32.str(s)
665	
666	# Little- and big-endian 32-bit words at the front of s.
667	def le32(s: String) -> Maybe<&2, U32>:
668	  match s:
669	    case SCon{Chr{+a}, SCon{Chr{+b}, SCon{Chr{+c}, SCon{Chr{+d}, t}}}}:
670	      Some{U32.or(U32.or(a, U32.shln(b, 8n)), U32.or(U32.shln(c, 16n), U32.shln(d, 24n)))}
671	    case SNil{}:
672	      None{}
673	    case SCon{x, y}:
674	      None{}
675	
676	def be32(s: String) -> Maybe<&2, U32>:
677	  match s:
678	    case SCon{Chr{+a}, SCon{Chr{+b}, SCon{Chr{+c}, SCon{Chr{+d}, t}}}}:
679	      Some{U32.or(U32.or(U32.shln(a, 24n), U32.shln(b, 16n)), U32.or(U32.shln(c, 8n), d))}
680	    case SNil{}:
681	      None{}
682	    case SCon{x, y}:
683	      None{}
684	
685	def flag(+f: U32, +bit: U32) -> Bool:
686	  Bool.not(U32.is_zero(U32.and(f, bit)))
687	
688	def check(ok: Bool, +out: String) -> Maybe<&2, String>:
689	  match ok:
690	    case True{}:
691	      Some{out}
692	    case False{}:
693	      None{}
694	
695	# RFC 1952 §2.3: after the fixed 10 bytes, optional FEXTRA, FNAME, FCOMMENT, FHCRC.
696	# hit: the byte just read was the terminating zero.
697	def gz.zstr(s: String, hit: Bool) -> Maybe<&2, String>:
698	  match s:
699	    case SNil{}:
700	      match hit:
701	        case True{}:
702	          Some{SNil{}}
703	        case False{}:
704	          None{}
705	    case SCon{Chr{+c}, t}:
706	      match hit:
707	        case True{}:
708	          Some{SCon{Chr{c}, t}}
709	        case False{}:
710	          gz.zstr(t, U32.is_zero(c))
711	
712	def gz.skip(k: Nat, s: String) -> Maybe<&2, String>:
713	  match k:
714	    case 0n:
715	      Some{s}
716	    case 1n+p:
717	      match s:
718	        case SNil{}:
719	          None{}
720	        case SCon{h, t}:
721	          gz.skip(p, t)
722	
723	def gz.extra.len(s: String) -> Maybe<&2, String>:
724	  match s:
725	    case SCon{Chr{+a}, SCon{Chr{+b}, t}}:
726	      gz.skip(bits(U32.or(a, U32.shln(b, 8n))), t)
727	    case SNil{}:
728	      None{}
729	    case SCon{x, y}:
730	      None{}
731	
732	def gz.fextra(on: Bool, +s: String) -> Maybe<&2, String>:
733	  match on:
734	    case True{}:
735	      gz.extra.len(s)
736	    case False{}:
737	      Some{s}
738	
739	def gz.fstr(on: Bool, +s: String) -> Maybe<&2, String>:
740	  match on:
741	    case True{}:
742	      gz.zstr(s, False{})
743	    case False{}:
744	      Some{s}
745	
746	def gz.fhcrc(on: Bool, +s: String) -> Maybe<&2, String>:
747	  match on:
748	    case True{}:
749	      gz.skip(2n, s)
750	    case False{}:
751	      Some{s}
752	
753	def gz.flags(+f: U32, s: String) -> Maybe<&2, String>:
754	  do Maybe<&2, String>:
755	    s1 : String <- gz.fextra(flag(f, 4), s)
756	    s2 : String <- gz.fstr(flag(f, 8), s1)
757	    s3 : String <- gz.fstr(flag(f, 16), s2)
758	    gz.fhcrc(flag(f, 2), s3)
759	
760	def gz.head(s: String) -> Maybe<&2, String>:
761	  match s:
762	    case SCon{Chr{+id1}, SCon{Chr{+id2}, SCon{Chr{+cm}, SCon{Chr{+f}, t}}}}:
763	      Bool.pick(Maybe<&2, String>, Bool.and(Bool.and(U32.is_eq(id1, 31), U32.is_eq(id2, 139)), U32.is_eq(cm, 8)), gz.flags(f, String.drop(t, 6n)), None{})
764	    case SNil{}:
765	      None{}
766	    case SCon{x, y}:
767	      None{}
768	
769	def gz.trail2(+out: String, +n: U32, crc: Maybe<&2, U32>, size: Maybe<&2, U32>) -> Maybe<&2, String>:
770	  do Maybe<&2, String>:
771	    c : U32 <- crc
772	    z : U32 <- size
773	    check(Bool.and(U32.is_eq(c, crc32(out)), U32.is_eq(z, n)), out)
774	
775	def gz.trail(m: Maybe<&2, Inflated>) -> Maybe<&2, String>:
776	  match m:
777	    case None{}:
778	      None{}
779	    case Some{Inflated{+out, +rest, +n}}:
780	      gz.trail2(out, n, le32(rest), le32(String.drop(rest, 4n)))
781	
782	def gz.body(m: Maybe<&2, String>) -> Maybe<&2, String>:
783	  match m:
784	    case None{}:
785	      None{}
786	    case Some{+s}:
787	      gz.trail(inflate.rest(s))
788	
789	# One gzip member; the CRC-32 and ISIZE must match. None: malformed, cut short, or corrupt.
790	# ponytail: bytes after the first member are ignored; loop over members if a server concatenates them.
791	def gunzip(s: String) -> Maybe<&2, String>:
792	  gz.body(gz.head(s))
793	
794	# RFC 1950: CMF and FLG, then DEFLATE, then Adler-32, big-endian.
795	def zl.sum(+out: String, a: Maybe<&2, U32>) -> Maybe<&2, String>:
796	  match a:
797	    case None{}:
798	      None{}
799	    case Some{+v}:
800	      check(U32.is_eq(v, adler32(out)), out)
801	
802	def zl.trail(m: Maybe<&2, Inflated>) -> Maybe<&2, String>:
803	  match m:
804	    case None{}:
805	      None{}
806	    case Some{Inflated{+out, +rest, n}}:
807	      zl.sum(out, be32(rest))
808	
809	def zl.ok(+cmf: U32, +flg: U32) -> Bool:
810	  Bool.and(Bool.and(U32.is_eq(U32.and(cmf, 15), 8), U32.is_le(U32.shrn(cmf, 4n), 7)), Bool.and(U32.is_zero(U32.mod((cmf * 256 + flg : U32), 31)), Bool.not(flag(flg, 32))))
811	
812	def unzlib(s: String) -> Maybe<&2, String>:
813	  match s:
814	    case SCon{Chr{+cmf}, SCon{Chr{+flg}, +t}}:
815	      Bool.pick(Maybe<&2, String>, zl.ok(cmf, flg), zl.trail(inflate.rest(t)), None{})
816	    case SNil{}:
817	      None{}
818	    case SCon{x, y}:
819	      None{}
820	
821	# DEFLATE encoding: LZ77 over hash chains, then one final fixed-Huffman block (RFC 1951 §3.2.6).
822	# ponytail: fixed Huffman only; dynamic trees would cut text output further.
823	
824	# Bit writer: bits wait in buf, least significant first; racc holds the bytes out, reversed.
825	type Bw is Data:
826	  Bw{buf: U32, cnt: U32, racc: String}
827	
828	def bw.emit(w: Bw) -> Bw:
829	  Bw{+buf, cnt, racc} = w
830	  Bw{U32.shrn(buf, 8n), (cnt - 8 : U32), SCon{Chr{U32.and(buf, 255)}, racc}}
831	
832	def bw.emit.if(w: Bw, full: Bool) -> Bw:
833	  match full:
834	    case True{}:
835	      bw.emit(w)
836	    case False{}:
837	      w
838	
839	def bw.full(+w: Bw) -> Bool:
840	  Bw{buf, +cnt, racc} = w
841	  U32.is_le(8, cnt)
842	
843	# A put adds at most 16 bits to at most 7, so two emits drain every whole byte.
844	def bw.drain(fuel: Nat, +w: Bw) -> Bw:
845	  match fuel:
846	    case 0n:
847	      w
848	    case 1n+f:
849	      bw.drain(f, bw.emit.if(w, bw.full(w)))
850	
851	def bw.put(w: Bw, +v: U32, +n: U32) -> Bw:
852	  Bw{buf, +cnt, racc} = w
853	  bw.drain(2n, Bw{U32.or(buf, U32.shln(v, bits(cnt))), (cnt + n : U32), racc})
854	
855	def bw.out(w: Bw) -> String:
856	  Bw{buf, cnt, racc} = w
857	  String.reverse(racc)
858	
859	# Seven zero bits push out a partial last byte.
860	def bw.done(w: Bw) -> String:
861	  bw.out(bw.put(w, 0, 7))
862	
863	# A Huffman code goes out most significant bit first, so it is reversed before the put.
864	def rev(k: Nat, +v: U32, +acc: U32) -> U32:
865	  match k:
866	    case 0n:
867	      acc
868	    case 1n+p:
869	      rev(p, U32.shr(v), U32.or(U32.shl(acc), U32.and(v, 1)))
870	
871	def bw.code(w: Bw, cl: U32 & U32) -> Bw:
872	  (+c, +l) = cl
873	  bw.put(w, rev(bits(l), c, 0), l)
874	
875	# RFC 1951 §3.2.6: the fixed code of literal/length symbol s, and its length.
876	def fx.hi(+s: U32, lo: Bool) -> U32 & U32:
877	  match lo:
878	    case True{}:
879	      ((s - 256 : U32), 7)
880	    case False{}:
881	      ((s - 88 : U32), 8)
882	
883	def fx.mid(+s: U32, lo: Bool) -> U32 & U32:
884	  match lo:
885	    case True{}:
886	      ((s + 256 : U32), 9)
887	    case False{}:
888	      fx.hi(s, U32.is_lt(s, 280))
889	
890	def fx.low(+s: U32, lo: Bool) -> U32 & U32:
891	  match lo:
892	    case True{}:
893	      ((s + 48 : U32), 8)
894	    case False{}:
895	      fx.mid(s, U32.is_lt(s, 256))
896	
897	def fx.lit(+s: U32) -> U32 & U32:
898	  fx.low(s, U32.is_lt(s, 144))
899	
900	# The last index whose base is at most v, with that base and its extra-bit count; bases ascend.
901	type Cx is Data:
902	  Cx{i: U32, base: U32, extra: U32}
903	
904	def cx.go(bs: List<&2, U32>, es: List<&2, U32>, +v: U32, +i: U32, +best: Cx) -> Cx:
905	  match bs:
906	    case Nil{}:
907	      best
908	    case Con{+b, bt}:
909	      match es:
910	        case Nil{}:
911	          best
912	        case Con{+e, et}:
913	          cx.go(bt, et, v, (i + 1 : U32), Bool.pick(Cx, U32.is_le(b, v), Cx{i, b, e}, best))
914	
915	def em.len(w: Bw, +len: U32, c: Cx) -> Bw:
916	  Cx{+i, +b, +e} = c
917	  bw.put(bw.code(w, fx.lit((i + 257 : U32))), (len - b : U32), e)
918	
919	def em.dist(w: Bw, +d: U32, c: Cx) -> Bw:
920	  Cx{+i, +b, +e} = c
921	  bw.put(bw.put(w, rev(5n, i, 0), 5), (d - b : U32), e)
922	
923	def em.match(w: Bw, +len: U32, +d: U32) -> Bw:
924	  em.dist(em.len(w, len, cx.go(len.base(), len.extra(), len, 0, Cx{0, 3, 0})), d, cx.go(dist.base(), dist.extra(), d, 0, Cx{0, 1, 0}))
925	
926	def em.lit(w: Bw, +c: U32) -> Bw:
927	  bw.code(w, fx.lit(c))
928	
929	# Match finder: the input, the newest position + 1 per hash, and per position the previous one with its hash (0: none).
930	type Lz is Type:
931	  Lz{src: Array<U32>, head: Array<U32>, prev: Array<U32>}
932	
933	def lz.at.of(r: Array<U32> & U32, head: Array<U32>, prev: Array<U32>) -> Lz & U32:
934	  (src, v) = r
935	  (Lz{src, head, prev}, v)
936	
937	def lz.at(z: Lz, +i: U32) -> Lz & U32:
938	  Lz{src, head, prev} = z
939	  lz.at.of(Array.get(U32, src, i), head, prev)
940	
941	def lz.drop(r: Lz & U32) -> Lz:
942	  (z, v) = r
943	  z
944	
945	def lz.h3(r: Lz & U32, +a: U32, +b: U32) -> Lz & U32:
946	  (z, +c) = r
947	  (z, U32.and(U32.xor(U32.xor(U32.shln(a, 10n), U32.shln(b, 5n)), c), 32767))
948	
949	def lz.h2(r: Lz & U32, +i: U32, +a: U32) -> Lz & U32:
950	  (z, +b) = r
951	  lz.h3(lz.at(z, (i + 2 : U32)), a, b)
952	
953	def lz.h1(r: Lz & U32, +i: U32) -> Lz & U32:
954	  (z, +a) = r
955	  lz.h2(lz.at(z, (i + 1 : U32)), i, a)
956	
957	def lz.hash(z: Lz, +i: U32) -> Lz & U32:
958	  lz.h1(lz.at(z, i), i)
959	
960	def lz.link(r: Array<U32> & U32, +i: U32, +h: U32, src: Array<U32>, prev: Array<U32>) -> Lz & U32:
961	  (head, +old) = r
962	  (Lz{src, Array.set(U32, head, h, (i + 1 : U32)), Array.set(U32, prev, U32.and(i, 32767), old)}, old)
963	
964	def lz.ins.of(r: Lz & U32, +i: U32) -> Lz & U32:
965	  (z, +h) = r
966	  Lz{src, head, prev} = z
967	  lz.link(Array.get(U32, head, h), i, h, src, prev)
968	
969	# Links position i into the chain for its next three bytes; answers the chain's previous head.
970	def lz.insert(z: Lz, +i: U32) -> Lz & U32:
971	  lz.ins.of(lz.hash(z, i), i)
972	
973	# Match length: bytes at a + k and b + k compared so far, and whether the last pair was equal.
974	type Ml is Type:
975	  Ml{z: Lz, a: U32, b: U32, k: U32, eq: Bool}
976	
977	def ml.cmp(r: Lz & U32, +a: U32, +b: U32, +k: U32, +x: U32) -> Ml:
978	  (z, +y) = r
979	  Ml{z, a, b, (k + 1 : U32), U32.is_eq(x, y)}
980	
981	def ml.read(r: Lz & U32, +a: U32, +b: U32, +k: U32) -> Ml:
982	  (z, +x) = r
983	  ml.cmp(lz.at(z, (b + k : U32)), a, b, k, x)
984	
985	def ml.len(+k: U32, eq: Bool) -> U32:
986	  match eq:
987	    case True{}:
988	      k
989	    case False{}:
990	      (k - 1 : U32)
991	
992	# Counts equal bytes from a and from b, up to fuel.
993	def ml.go(fuel: Nat, st: Ml) -> Lz & U32:
994	  match fuel:
995	    case 0n:
996	      Ml{z, a, b, +k, eq} = st
997	      (z, ml.len(k, eq))
998	    case 1n+f:
999	      Ml{z, +a, +b, +k, eq} = st
1000	      match eq:
1001	        case True{}:
1002	          ml.go(f, ml.read(lz.at(z, (a + k : U32)), a, b, k))
1003	        case False{}:
1004	          (z, (k - 1 : U32))
1005	
1006	# Chain walk at i: candidate c (position + 1), the longest match so far, and whether to go on.
1007	type Ch is Type:
1008	  Ch{z: Lz, i: U32, c: U32, max: U32, blen: U32, bdist: U32, go: Bool}
1009	
1010	# RFC 1951 §3.2.5: a distance is at most 32768.
1011	def ch.ok(+i: U32, +c: U32, +max: U32, +blen: U32) -> Bool:
1012	  Bool.and(Bool.and(U32.is_lt(0, c), U32.is_lt((i - c : U32), 32768)), U32.is_lt(blen, max))
1013	
1014	def ch.next(r: Array<U32> & U32, src: Array<U32>, head: Array<U32>, +i: U32, +max: U32, +blen: U32, +bdist: U32) -> Ch:
1015	  (prev, +c) = r
1016	  Ch{Lz{src, head, prev}, i, c, max, blen, bdist, ch.ok(i, c, max, blen)}
1017	
1018	def ch.best(r: Lz & U32, +i: U32, +p: U32, +max: U32, +blen: U32, +bdist: U32) -> Ch:
1019	  (z, +len) = r
1020	  Lz{src, head, prev} = z
1021	  +more = U32.is_lt(blen, len)
1022	  ch.next(Array.get(U32, prev, U32.and(p, 32767)), src, head, i, max, Bool.pick(U32, more, len, blen), Bool.pick(U32, more, (i - p : U32), bdist))
1023	
1024	def ch.go(fuel: Nat, st: Ch) -> Ch:
1025	  match fuel:
1026	    case 0n:
1027	      st
1028	    case 1n+f:
1029	      Ch{z, +i, +c, +max, +blen, +bdist, go} = st
1030	      match go:
1031	        case True{}:
1032	          +p = (c - 1 : U32)
1033	          ch.go(f, ch.best(ml.go(bits(max), Ml{z, i, p, 0, True{}}), i, p, max, blen, bdist))
1034	        case False{}:
1035	          Ch{z, i, c, max, blen, bdist, False{}}
1036	
1037	# Encoder: match finder, bit writer, position, input length, and whether bytes are left.
1038	type Es is Type:
1039	  Es{z: Lz, w: Bw, i: U32, n: U32, more: Bool}
1040	
1041	def es.lit.of(r: Lz & U32, w: Bw, +i: U32, +n: U32) -> Es:
1042	  (z, +c) = r
1043	  +j = (i + 1 : U32)
1044	  Es{z, em.lit(w, c), j, n, U32.is_lt(j, n)}
1045	
1046	def es.lit(z: Lz, w: Bw, +i: U32, +n: U32) -> Es:
1047	  es.lit.of(lz.at(z, i), w, i, n)
1048	
1049	def ins.one(ok: Bool, z: Lz, +j: U32) -> Lz:
1050	  match ok:
1051	    case True{}:
1052	      lz.drop(lz.insert(z, j))
1053	    case False{}:
1054	      z
1055	
1056	# Positions inside a match join their chains too, when three bytes remain.
1057	def ins.go(k: Nat, z: Lz, +j: U32, +n: U32) -> Lz:
1058	  match k:
1059	    case 0n:
1060	      z
1061	    case 1n+f:
1062	      ins.go(f, ins.one(U32.is_le((j + 3 : U32), n), z, j), (j + 1 : U32), n)
1063	
1064	def es.emit(hit: Bool, z: Lz, w: Bw, +i: U32, +n: U32, +blen: U32, +bdist: U32) -> Es:
1065	  match hit:
1066	    case True{}:
1067	      +j = (i + blen : U32)
1068	      Es{ins.go(bits((blen - 1 : U32)), z, (i + 1 : U32), n), em.match(w, blen, bdist), j, n, U32.is_lt(j, n)}
1069	    case False{}:
1070	      es.lit(z, w, i, n)
1071	
1072	def es.pick(st: Ch, w: Bw, +n: U32) -> Es:
1073	  Ch{z, +i, c, max, +blen, +bdist, go} = st
1074	  es.emit(U32.is_le(3, blen), z, w, i, n, blen, bdist)
1075	
1076	# ponytail: greedy parse, 32 chain steps; lazy matching would compress text further.
1077	def es.chain(r: Lz & U32, w: Bw, +i: U32, +n: U32) -> Es:
1078	  (z, +c) = r
1079	  +room = (n - i : U32)
1080	  +max = Bool.pick(U32, U32.is_lt(room, 258), room, 258)
1081	  es.pick(ch.go(32n, Ch{z, i, c, max, 0, 0, ch.ok(i, c, max, 0)}), w, n)
1082	
1083	def es.find(short: Bool, z: Lz, w: Bw, +i: U32, +n: U32) -> Es:
1084	  match short:
1085	    case True{}:
1086	      es.lit(z, w, i, n)
1087	    case False{}:
1088	      es.chain(lz.insert(z, i), w, i, n)
1089	
1090	# Each step consumes at least one byte, so n steps finish.
1091	def es.go(fuel: Nat, st: Es) -> Es:
1092	  match fuel:
1093	    case 0n:
1094	      st
1095	    case 1n+f:
1096	      Es{z, w, +i, +n, more} = st
1097	      match more:
1098	        case True{}:
1099	          es.go(f, es.find(U32.is_lt((n - i : U32), 3), z, w, i, n))
1100	        case False{}:
1101	          Es{z, w, i, n, False{}}
1102	
1103	def es.out(st: Es) -> String:
1104	  Es{z, w, i, n, more} = st
1105	  bw.done(em.lit(w, 256))
1106	
1107	def slen(s: String, +n: U32) -> U32:
1108	  match s:
1109	    case SNil{}:
1110	      n
1111	    case SCon{h, t}:
1112	      slen(t, (n + 1 : U32))
1113	
1114	def src.fill(s: String, +i: U32, a: Array<U32>) -> Array<U32>:
1115	  match s:
1116	    case SNil{}:
1117	      a
1118	    case SCon{h, t}:
1119	      src.fill(t, (i + 1 : U32), Array.set(U32, a, i, byte(h)))
1120	
1121	# The smallest depth whose 2^depth slots hold n.
1122	def depth(k: Nat, +d: Nat, +n: U32) -> Nat:
1123	  match k:
1124	    case 0n:
1125	      d
1126	    case 1n+f:
1127	      Bool.pick(Nat, U32.is_le(n, U32.shln(1, d)), d, depth(f, 1n+d, n))
1128	
1129	# Raw DEFLATE. The header bits are BFINAL = 1 and BTYPE = 01.
1130	def deflate(+s: String) -> String:
1131	  +n = slen(s, 0)
1132	  src = src.fill(s, 0, Array.new(U32, depth(31n, 0n, n), 0))
1133	  es.out(es.go(bits(n), Es{Lz{src, Array.new(U32, 15n, 0), Array.new(U32, 15n, 0)}, Bw{3, 3, ""}, 0, n, U32.is_lt(0, n)}))
1134	
1135	def str.of(xs: List<&2, U32>, t: String) -> String:
1136	  match xs:
1137	    case Nil{}:
1138	      t
1139	    case Con{c, r}:
1140	      SCon{Chr{c}, str.of(r, t)}
1141	
1142	def le32.put(+v: U32, t: String) -> String:
1143	  str.of([U32.and(v, 255), U32.and(U32.shrn(v, 8n), 255), U32.and(U32.shrn(v, 16n), 255), U32.shrn(v, 24n)], t)
1144	
1145	def be32.put(+v: U32, t: String) -> String:
1146	  str.of([U32.shrn(v, 24n), U32.and(U32.shrn(v, 16n), 255), U32.and(U32.shrn(v, 8n), 255), U32.and(v, 255)], t)
1147	
1148	# One gzip member (RFC 1952): no flags, mtime 0, OS unknown.
1149	def gzip(+s: String) -> String:
1150	  str.of([31, 139, 8, 0, 0, 0, 0, 0, 0, 255], deflate(s) ++ le32.put(crc32(s), le32.put(slen(s, 0), "")))
1151	
1152	# RFC 1950: CMF 0x78 (32 KiB window), FLG 0x01 (fastest), then DEFLATE, then Adler-32.
1153	def zlib(+s: String) -> String:
1154	  str.of([120, 1], deflate(s) ++ be32.put(adler32(s), ""))
1155	
1156	# Zstandard frames (RFC 8878) through libzstd, as (len, words) like Wire.recv.words.
1157	# Fails with EFBIG when the output passes max bytes, and ENOENT without libzstd.
1158	def zstd.words(max: U32, len: U32, words: Array<U32>) ->
1159	  IO(Result<&1, &1, U32 & String, U32 & Array<U32>>):
1160	  import "./effs/zlib.c"
1161	  import "./effs/zlib.js"
1162	
1163	# gzip, zlib, or raw DEFLATE data through libz, selected from the first two bytes. Every gzip member is decoded in turn, as gzip -d does.
1164	# Fails with EFBIG when the output passes max bytes, and ENOENT without libz.
1165	def inflate.words(max: U32, len: U32, words: Array<U32>) ->
1166	  IO(Result<&1, &1, U32 & String, U32 & Array<U32>>):
1167	  import "./effs/zlib.c"
1168	  import "./effs/zlib.js"
1169	
1170	# One raw DEFLATE stream through libz. Trailing bytes, truncated input and output above max fail.
1171	def inflate.raw.words(max: U32, len: U32, words: Array<U32>) ->
1172	  IO(Result<&1, &1, U32 & String, U32 & Array<U32>>):
1173	  import "./effs/zlib.c"
1174	  import "./effs/zlib.js"
1175	
1176	# One gzip member at level 6 through libz.
1177	def gzip.words(len: U32, words: Array<U32>) ->
1178	  IO(Result<&1, &1, U32 & String, U32 & Array<U32>>):
1179	  import "./effs/zlib.c"
1180	  import "./effs/zlib.js"
1181	
1182	# Brotli (RFC 7932) through libbrotlidec. Fails as zstd.words does.
1183	def brotli.words(max: U32, len: U32, words: Array<U32>) ->
1184	  IO(Result<&1, &1, U32 & String, U32 & Array<U32>>):
1185	  import "./effs/zlib.c"
1186	  import "./effs/zlib.js"
1187	
1188	# A live native decoder. Call dec.finish even after a failed feed to release it.
1189	type Decoder is Type:
1190	  Decoder{id: U32}
1191	
1192	def dec.open(kind: U32) -> IO(Result<&1, &1, U32 & String, U32>):
1193	  import "./effs/zlib.c"
1194	  import "./effs/zlib.js"
1195	
1196	def dec.new.got(r: Result<&1, &1, U32 & String, U32>) -> Result<&1, &1, U32 & String, Decoder>:
1197	  match r:
1198	    case Fail{e}:
1199	      Fail{e}
1200	    case Done{+id}:
1201	      Done{Decoder{id}}
1202	
1203	def dec.new(+kind: U32) -> IO(Result<&1, &1, U32 & String, Decoder>):
1204	  do IO<Result<&1, &1, U32 & String, Decoder>>:
1205	    r : Result<&1, &1, U32 & String, U32> <- dec.open(kind)
1206	    return dec.new.got(r)
1207	
1208	def inflate.new() -> IO(Result<&1, &1, U32 & String, Decoder>):
1209	  dec.new(0)
1210	
1211	def brotli.new() -> IO(Result<&1, &1, U32 & String, Decoder>):
1212	  dec.new(1)
1213	
1214	def zstd.new() -> IO(Result<&1, &1, U32 & String, Decoder>):
1215	  dec.new(2)
1216	
1217	def dec.feed(id: U32, max: U32, len: U32, words: Array<U32>) ->
1218	  IO(Result<&1, &1, U32 & String, U32 & Array<U32>>):
1219	  import "./effs/zlib.c"
1220	  import "./effs/zlib.js"
1221	
1222	# max caps the output of this call, not the total output of the stream.
1223	def dec.feed.words(d: Decoder, +max: U32, +len: U32, words: Array<U32>) ->
1224	  IO(Decoder & Result<&1, &1, U32 & String, U32 & Array<U32>>):
1225	  Decoder{+id} = d
1226	  do IO<Decoder & Result<&1, &1, U32 & String, U32 & Array<U32>>>:
1227	    r : Result<&1, &1, U32 & String, U32 & Array<U32>> <- dec.feed(id, max, len, words)
1228	    return (Decoder{id}, r)
1229	
1230	def dec.finish.id(id: U32) -> IO(Result<&1, &1, U32 & String, Unit>):
1231	  import "./effs/zlib.c"
1232	  import "./effs/zlib.js"
1233	
1234	# Finish validates the end marker and always releases the decoder.
1235	def dec.finish(d: Decoder) -> IO(Result<&1, &1, U32 & String, Unit>):
1236	  Decoder{+id} = d
1237	  dec.finish.id(id)