zlib.bend source
zlib.bend on the hub · documented module
# DEFLATE, gzip, and zlib decoding (RFC 1951, 1952, 1950) over byte strings.import Base# Bytes are one Char per octet (0..255), as everywhere in bend-net.def byte(h: Char) -> U32: Chr{c} = h cdef bits(+n: U32) -> Nat: U32.to_nat(n)def mask(+n: U32) -> U32: (U32.shln(1, bits(n)) - 1 : U32)# Bit reader. over counts bytes read past the end; any over means the input was cut short.type Br is Data: Br{s: String, buf: U32, cnt: U32, over: U32}def br.new(s: String) -> Br: Br{s, 0, 0, 0}def br.pull(b: Br) -> Br: Br{s, +buf, +cnt, +over} = b match s: case SNil{}: Br{SNil{}, buf, (cnt + 8 : U32), (over + 1 : U32)} case SCon{h, t}: Br{t, U32.or(buf, U32.shln(byte(h), bits(cnt))), (cnt + 8 : U32), over}def br.pull.if(b: Br, short: Bool) -> Br: match short: case True{}: br.pull(b) case False{}: bdef br.short(+b: Br, +n: U32) -> Bool: Br{s, buf, +cnt, over} = b U32.is_lt(cnt, n)# n is at most 16, so three bytes always fill the buffer.def br.fill(fuel: Nat, +b: Br, +n: U32) -> Br: match fuel: case 0n: b case 1n+f: br.fill(f, br.pull.if(b, br.short(b, n)), n)def br.cut(b: Br, +n: U32) -> Br & U32: Br{s, +buf, cnt, over} = b (Br{s, U32.shrn(buf, bits(n)), (cnt - n : U32), over}, U32.and(buf, mask(n)))def br.take(b: Br, +n: U32) -> Br & U32: br.cut(br.fill(3n, b, n), n)def br.drop.of(r: Br & U32) -> Br: (b, v) = r bdef br.drop(b: Br, +n: U32) -> Br: br.drop.of(br.cut(b, n))# RFC 1951 §3.2.4: a stored block starts on a byte boundary.def br.align(+b: Br) -> Br: Br{s, buf, +cnt, over} = b br.drop(b, U32.mod(cnt, 8))def br.ok(+b: Br) -> Bool: Br{s, buf, cnt, +over} = b U32.is_eq(over, 0)def br.bytes(k: Nat, +buf: U32) -> String: match k: case 0n: SNil{} case 1n+p: SCon{Chr{U32.and(buf, 255)}, br.bytes(p, U32.shrn(buf, 8n))}def br.rest.of(b: Br) -> String: Br{s, +buf, +cnt, over} = b br.bytes(bits(U32.div(cnt, 8)), buf) ++ s# Whole bytes still in the buffer go back in front of the unread input.def br.rest(+b: Br) -> String: br.rest.of(br.align(b))# Huffman codes as a trie: one step per bit. A read bit picks o (1) or z (0).# Bad: two codes collided, so the code set was over-subscribed.type Ht is Data: HtNone{} HtBad{} HtLeaf{sym: U32} HtNode{z: Ht, o: Ht}def ht.left(t: Ht) -> Ht: match t: case HtNode{z, o}: z case HtNone{}: HtNone{} case HtBad{}: HtBad{} case HtLeaf{s}: HtBad{}def ht.right(t: Ht) -> Ht: match t: case HtNode{z, o}: o case HtNone{}: HtNone{} case HtBad{}: HtBad{} case HtLeaf{s}: HtBad{}def ht.leaf(t: Ht, +sym: U32) -> Ht: match t: case HtNone{}: HtLeaf{sym} case HtBad{}: HtBad{} case HtLeaf{s}: HtBad{} case HtNode{z, o}: HtBad{}def ht.ins(path: List<&2, Bool>, +t: Ht, +sym: U32) -> Ht: match path: case Nil{}: ht.leaf(t, sym) case Con{b, rest}: match b: case True{}: HtNode{ht.left(t), ht.ins(rest, ht.right(t), sym)} case False{}: HtNode{ht.ins(rest, ht.left(t), sym), ht.right(t)}# The code's bits, most significant first: the order the stream sends them.def ht.path(n: Nat, +code: U32, acc: List<&2, Bool>) -> List<&2, Bool>: match n: case 0n: acc case 1n+p: ht.path(p, U32.shr(code), Con{U32.is_eq(U32.and(code, 1), 1), acc})# Canonical codes (RFC 1951 §3.2.2): count lengths, find each length's first code, then assign in symbol order.def cnt.add(ar: Array<U32> & U32, +len: U32) -> Array<U32>: (a, v) = ar Array.set(U32, a, len, (v + 1 : U32))def cnt.go(xs: List<&2, U32>, a: Array<U32>) -> Array<U32>: match xs: case Nil{}: a case Con{+l, t}: cnt.go(t, cnt.add(Array.get(U32, a, l), l))def nx.set(+i: U32, cv: Array<U32> & U32, n: Array<U32>, +code: U32) -> Array<U32> & Array<U32> & U32: (c, v) = cv +code2 = U32.shl((code + Bool.pick(U32, U32.is_eq(i, 1), 0, v) : U32)) (c, Array.set(U32, n, i, code2), code2)def nx.step(+i: U32, st: Array<U32> & Array<U32> & U32) -> Array<U32> & Array<U32> & U32: (c, n, code) = st nx.set(i, Array.get(U32, c, (i - 1 : U32)), n, code)def nx.go(k: Nat, +i: U32, st: Array<U32> & Array<U32> & U32) -> Array<U32> & Array<U32> & U32: match k: case 0n: st case 1n+f: nx.go(f, (i + 1 : U32), nx.step(i, st))def as.put(+l: U32, +sym: U32, nv: Array<U32> & U32, t: Ht) -> Array<U32> & Ht: (n, +code) = nv (Array.set(U32, n, l, (code + 1 : U32)), ht.ins(ht.path(bits(l), code, Nil{}), t, sym))def as.one.nz(+l: U32, +sym: U32, n: Array<U32>, t: Ht, zero: Bool) -> Array<U32> & Ht: match zero: case True{}: (n, t) case False{}: as.put(l, sym, Array.get(U32, n, l), t)def as.one(+l: U32, +sym: U32, st: Array<U32> & Ht) -> Array<U32> & Ht: (n, t) = st as.one.nz(l, sym, n, t, U32.is_zero(l))def as.go(xs: List<&2, U32>, +sym: U32, st: Array<U32> & Ht) -> Array<U32> & Ht: match xs: case Nil{}: st case Con{+l, t}: as.go(t, (sym + 1 : U32), as.one(l, sym, st))def ht.of(st: Array<U32> & Ht) -> Ht: (n, t) = st tdef ht.assign(xs: List<&2, U32>, st: Array<U32> & Array<U32> & U32) -> Ht: (c, n, code) = st ht.of(as.go(xs, 0, (n, HtNone{})))# lens[i] is the code length of symbol i; 0 means the symbol is unused.def ht.build(+lens: List<&2, U32>) -> Ht: ht.assign(lens, nx.go(15n, 1, (cnt.go(lens, Array.new(U32, 4n, 0)), Array.new(U32, 4n, 0), 0)))# No code: 9999, never a symbol.def ht.step(z: Ht, o: Ht, bv: Br & U32) -> Ht & Br: (b, +v) = bv (Bool.pick(Ht, U32.is_eq(v, 1), o, z), b)# A code is at most 15 bits (§3.2.7), so 16 steps always reach a leaf or a miss.def ht.dec(fuel: Nat, st: Ht & Br) -> Br & U32: match fuel: case 0n: (t, b) = st (b, 9999) case 1n+f: (t, b) = st match t: case HtLeaf{s}: (b, s) case HtNone{}: (b, 9999) case HtBad{}: (b, 9999) case HtNode{z, o}: ht.dec(f, ht.step(z, o, br.take(b, 1)))def ht.decode(t: Ht, b: Br) -> Br & U32: ht.dec(16n, (t, b))def nth(xs: List<&2, U32>, +i: U32) -> U32: match xs: case Nil{}: 0 case Con{h, t}: Bool.pick(U32, U32.is_zero(i), h, nth(t, (i - 1 : U32)))def rep(k: Nat, +v: U32, acc: List<&2, U32>) -> List<&2, U32>: match k: case 0n: acc case 1n+p: rep(p, v, Con{v, acc})def take.n(k: Nat, xs: List<&2, U32>) -> List<&2, U32>: match k: case 0n: Nil{} case 1n+p: match xs: case Nil{}: Nil{} case Con{h, t}: Con{h, take.n(p, t)}def drop.n(k: Nat, xs: List<&2, U32>) -> List<&2, U32>: match k: case 0n: xs case 1n+p: match xs: case Nil{}: Nil{} case Con{h, t}: drop.n(p, t)# RFC 1951 §3.2.5def len.base() -> List<&2, U32>: [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]def len.extra() -> List<&2, U32>: [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]def dist.base() -> List<&2, U32>: [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]def dist.extra() -> List<&2, U32>: [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]# RFC 1951 §3.2.6def fixed.lit() -> Ht: ht.build(rep(144n, 8, rep(112n, 9, rep(24n, 7, rep(8n, 8, Nil{})))))def fixed.dist() -> Ht: ht.build(rep(30n, 5, Nil{}))# Output: the 32 KiB window (indexes wrap), the write position, the byte count, and the bytes, reversed.type Ow is Data: Ow{w: U32, n: U32, racc: String}def out.put(win: Array<U32>, +c: U32, o: Ow) -> Array<U32> & Ow: Ow{+w, +n, racc} = o (Array.set(U32, win, w, c), Ow{(w + 1 : U32), (n + 1 : U32), SCon{Chr{c}, racc}})type Mo is Data: MoHead{} MoCodes{lit: Ht, dist: Ht} MoDone{} MoBad{}type Is is Data: Is{br: Br, o: Ow, mode: Mo, last: Bool}def inf.next(last: Bool) -> Mo: match last: case True{}: MoDone{} case False{}: MoHead{}def inf.bad(win: Array<U32>, b: Br, o: Ow) -> Array<U32> & Is: (win, Is{b, o, MoBad{}, True{}})# Stored block (§3.2.4): LEN, then NLEN (its complement), then LEN raw bytes.def sb.put2(p: Array<U32> & Ow, b: Br) -> Array<U32> & Br & Ow: (a, o) = p (a, b, o)def sb.put(win: Array<U32>, bv: Br & U32, o: Ow) -> Array<U32> & Br & Ow: (b, +c) = bv sb.put2(out.put(win, c, o), b)def sb.byte(st: Array<U32> & Br & Ow) -> Array<U32> & Br & Ow: (win, b, o) = st sb.put(win, br.take(b, 8), o)def sb.go(k: Nat, st: Array<U32> & Br & Ow) -> Array<U32> & Br & Ow: match k: case 0n: st case 1n+f: sb.go(f, sb.byte(st))def sb.done(t: Array<U32> & Br & Ow, +last: Bool) -> Array<U32> & Is: (win, b, o) = t (win, Is{b, o, inf.next(last), last})def sb.ok(win: Array<U32>, b: Br, +len: U32, o: Ow, +last: Bool, ok: Bool) -> Array<U32> & Is: match ok: case False{}: inf.bad(win, b, o) case True{}: sb.done(sb.go(bits(len), (win, b, o)), last)def sb.nlen(win: Array<U32>, bv: Br & U32, +len: U32, o: Ow, +last: Bool) -> Array<U32> & Is: (b, +nlen) = bv sb.ok(win, b, len, o, last, U32.is_eq(U32.xor(len, 65535), nlen))def sb.len(win: Array<U32>, bv: Br & U32, o: Ow, +last: Bool) -> Array<U32> & Is: (b, +len) = bv sb.nlen(win, br.take(b, 16), len, o, last)def inf.stored(win: Array<U32>, b: Br, o: Ow, +last: Bool) -> Array<U32> & Is: sb.len(win, br.take(br.align(b), 16), o, last)# Dynamic block (§3.2.7): code lengths for the code-length code, then the lengths themselves.# cl.slot[i]: where symbol i's length sits in the order the stream sends them.def cl.slot() -> List<&2, U32>: [3, 17, 15, 13, 11, 9, 7, 5, 4, 6, 8, 10, 12, 14, 16, 18, 0, 1, 2]def cl.place(xs: List<&2, U32>, +vals: List<&2, U32>) -> List<&2, U32>: match xs: case Nil{}: Nil{} case Con{+i, t}: Con{nth(vals, i), cl.place(t, vals)}def cl.push(bv: Br & U32, acc: List<&2, U32>) -> Br & List<&2, U32>: (b, v) = bv (b, Con{v, acc})def cl.one(st: Br & List<&2, U32>) -> Br & List<&2, U32>: (b, acc) = st cl.push(br.take(b, 3), acc)def cl.read(k: Nat, st: Br & List<&2, U32>) -> Br & List<&2, U32>: match k: case 0n: st case 1n+f: cl.read(f, cl.one(st))# Lengths so far (reversed), how many, the last one (for code 16), and whether it went wrong.type Cd is Data: Cd{br: Br, acc: List<&2, U32>, n: U32, prev: U32, bad: Bool}def cd.fill(+b: Br, +acc: List<&2, U32>, +n: U32, +v: U32, +cnt: U32, +total: U32) -> Cd: 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{}})def cd.rep(bv: Br & U32, +v: U32, +base: U32, acc: List<&2, U32>, +n: U32, +total: U32) -> Cd: (b, +e) = bv cd.fill(b, acc, n, v, (base + e : U32), total)def cd.prev(b: Br, acc: List<&2, U32>, +n: U32, +prev: U32, +total: U32, ok: Bool) -> Cd: match ok: case False{}: Cd{b, acc, n, prev, True{}} case True{}: cd.rep(br.take(b, 2), prev, 3, acc, n, total)def cd.z18(b: Br, acc: List<&2, U32>, +n: U32, +total: U32, ok: Bool) -> Cd: match ok: case True{}: cd.rep(br.take(b, 7), 0, 11, acc, n, total) case False{}: Cd{b, acc, n, 0, True{}}def cd.z17(b: Br, acc: List<&2, U32>, +n: U32, +s: U32, +total: U32, ok: Bool) -> Cd: match ok: case True{}: cd.rep(br.take(b, 3), 0, 3, acc, n, total) case False{}: cd.z18(b, acc, n, total, U32.is_eq(s, 18))def cd.c16(b: Br, acc: List<&2, U32>, +n: U32, +prev: U32, +s: U32, +total: U32, ok: Bool) -> Cd: match ok: case True{}: cd.prev(b, acc, n, prev, total, U32.is_lt(0, n)) case False{}: cd.z17(b, acc, n, s, total, U32.is_eq(s, 17))def cd.lit(b: Br, acc: List<&2, U32>, +n: U32, +prev: U32, +s: U32, +total: U32, ok: Bool) -> Cd: match ok: case True{}: Cd{b, Con{s, acc}, (n + 1 : U32), s, False{}} case False{}: cd.c16(b, acc, n, prev, s, total, U32.is_eq(s, 16))def cd.sym(bv: Br & U32, acc: List<&2, U32>, +n: U32, +prev: U32, +total: U32) -> Cd: (b, +s) = bv cd.lit(b, acc, n, prev, s, total, U32.is_lt(s, 16))def cd.step.go(+cl: Ht, +total: U32, stop: Bool, cs: Cd) -> Cd: match stop: case False{}: Cd{b, acc, +n, +prev, bad} = cs cd.sym(ht.decode(cl, b), acc, n, prev, total) case True{}: Cd{b, acc, n, prev, bad} = cs Cd{b, acc, n, prev, bad}def cd.stop(+st: Cd, +total: U32) -> Bool: Cd{b, acc, +n, prev, +bad} = st Bool.or(bad, U32.is_le(total, n))# Each step adds at least one length, so total steps suffice.def cd.go(k: Nat, +cl: Ht, +total: U32, +st: Cd) -> Cd: match k: case 0n: st case 1n+f: cd.go(f, cl, total, cd.step.go(cl, total, cd.stop(st, total), st))def dyn.tables(b: Br, +lens: List<&2, U32>, +hlit: U32, bad: Bool) -> Br & Mo: match bad: case True{}: (b, MoBad{}) case False{}: (b, MoCodes{ht.build(take.n(bits(hlit), lens)), ht.build(drop.n(bits(hlit), lens))})def dyn.done(st: Cd, +hlit: U32, +total: U32) -> Br & Mo: Cd{b, acc, +n, prev, +bad} = st dyn.tables(b, List.reverse(&2, U32, acc), hlit, Bool.or(bad, Bool.not(U32.is_eq(n, total))))def dyn.lens(st: Br & List<&2, U32>, +hlit: U32, +hdist: U32) -> Br & Mo: (b, acc) = st +total = (hlit + hdist : U32) +clens = cl.place(cl.slot(), List.reverse(&2, U32, acc)) dyn.done(cd.go(bits(total), ht.build(clens), total, Cd{b, Nil{}, 0, 0, False{}}), hlit, total)def dyn.clen(bv: Br & U32, +hlit: U32, +hdist: U32) -> Br & Mo: (b, +hclen) = bv dyn.lens(cl.read(bits((hclen + 4 : U32)), (b, Nil{})), hlit, hdist)def dyn.hdist(bv: Br & U32, +hlit: U32) -> Br & Mo: (b, +hd) = bv dyn.clen(br.take(b, 4), hlit, (hd + 1 : U32))def dyn.hlit(bv: Br & U32) -> Br & Mo: (b, +hl) = bv dyn.hdist(br.take(b, 5), (hl + 257 : U32))def dyn.read(b: Br) -> Br & Mo: dyn.hlit(br.take(b, 5))# A match copies len bytes from d back; the window's indexes wrap, so w - d needs no mask.def cp.put(av: Array<U32> & U32, o: Ow) -> Array<U32> & Ow: (a, +c) = av out.put(a, c, o)def cp.one(+d: U32, st: Array<U32> & Ow) -> Array<U32> & Ow: (win, o) = st Ow{+w, n, racc} = o cp.put(Array.get(U32, win, (w - d : U32)), Ow{w, n, racc})def cp.go(k: Nat, +d: U32, st: Array<U32> & Ow) -> Array<U32> & Ow: match k: case 0n: st case 1n+f: cp.go(f, d, cp.one(d, st))def inf.codes(p: Array<U32> & Ow, b: Br, +lit: Ht, +dist: Ht, +last: Bool) -> Array<U32> & Is: (win, o) = p (win, Is{b, o, MoCodes{lit, dist}, last})def ow.n(+o: Ow) -> U32: Ow{w, +n, racc} = o n# RFC 1951 §3.2.5: a distance may not reach before the first byte out.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: match ok: case False{}: inf.bad(win, b, o) case True{}: inf.codes(cp.go(bits(len), d, (win, o)), b, lit, dist, last)def inf.dx(win: Array<U32>, bv: Br & U32, +db: U32, +len: U32, +o: Ow, +lit: Ht, +dist: Ht, +last: Bool) -> Array<U32> & Is: (b, +e) = bv +d = (db + e : U32) inf.far(win, b, o, len, d, lit, dist, last, U32.is_le(d, ow.n(o)))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: match ok: case False{}: inf.bad(win, b, o) case True{}: inf.dx(win, br.take(b, nth(dist.extra(), ds)), nth(dist.base(), ds), len, o, lit, dist, last)def inf.d(win: Array<U32>, bv: Br & U32, +len: U32, +o: Ow, +lit: Ht, +dist: Ht, +last: Bool) -> Array<U32> & Is: (b, +ds) = bv inf.ds(win, b, ds, len, o, lit, dist, last, U32.is_lt(ds, 30))def inf.lx(win: Array<U32>, bv: Br & U32, +lb: U32, +o: Ow, +lit: Ht, +dist: Ht, +last: Bool) -> Array<U32> & Is: (b, +e) = bv inf.d(win, ht.decode(dist, b), (lb + e : U32), o, lit, dist, last)def inf.ls(win: Array<U32>, b: Br, +s: U32, +o: Ow, +lit: Ht, +dist: Ht, +last: Bool, ok: Bool) -> Array<U32> & Is: match ok: case False{}: inf.bad(win, b, o) case True{}: +i = (s - 257 : U32) inf.lx(win, br.take(b, nth(len.extra(), i)), nth(len.base(), i), o, lit, dist, last)def inf.end(win: Array<U32>, b: Br, +s: U32, +o: Ow, +lit: Ht, +dist: Ht, +last: Bool, eob: Bool) -> Array<U32> & Is: match eob: case True{}: (win, Is{b, o, inf.next(last), last}) case False{}: inf.ls(win, b, s, o, lit, dist, last, U32.is_le(s, 285))def inf.lit(win: Array<U32>, b: Br, +s: U32, +o: Ow, +lit: Ht, +dist: Ht, +last: Bool, ok: Bool) -> Array<U32> & Is: match ok: case True{}: inf.codes(out.put(win, s, o), b, lit, dist, last) case False{}: inf.end(win, b, s, o, lit, dist, last, U32.is_eq(s, 256))def inf.sym(win: Array<U32>, bv: Br & U32, +o: Ow, +lit: Ht, +dist: Ht, +last: Bool) -> Array<U32> & Is: (b, +s) = bv inf.lit(win, b, s, o, lit, dist, last, U32.is_lt(s, 256))def inf.dyn(win: Array<U32>, bm: Br & Mo, o: Ow, +last: Bool) -> Array<U32> & Is: (b, m) = bm (win, Is{b, o, m, last})def inf.t2(win: Array<U32>, b: Br, o: Ow, +last: Bool, is2: Bool) -> Array<U32> & Is: match is2: case True{}: inf.dyn(win, dyn.read(b), o, last) case False{}: inf.bad(win, b, o)def inf.t1(win: Array<U32>, b: Br, o: Ow, +last: Bool, +t: U32, is1: Bool) -> Array<U32> & Is: match is1: case True{}: (win, Is{b, o, MoCodes{fixed.lit(), fixed.dist()}, last}) case False{}: inf.t2(win, b, o, last, U32.is_eq(t, 2))def inf.t0(win: Array<U32>, b: Br, o: Ow, +last: Bool, +t: U32, is0: Bool) -> Array<U32> & Is: match is0: case True{}: inf.stored(win, b, o, last) case False{}: inf.t1(win, b, o, last, t, U32.is_eq(t, 1))# §3.2.3: BFINAL, then BTYPE.def inf.head(win: Array<U32>, bv: Br & U32, o: Ow) -> Array<U32> & Is: (b, +v) = bv +t = U32.shr(v) inf.t0(win, b, o, U32.is_eq(U32.and(v, 1), 1), t, U32.is_zero(t))# Every step reads at least one bit, so 8 steps per input byte always finish a valid stream.def inf.go(k: Nat, st: Array<U32> & Is) -> Array<U32> & Is: match k: case 0n: st case 1n+f: (win, ist) = st Is{b, o, mode, +last} = ist match mode: case MoHead{}: inf.go(f, inf.head(win, br.take(b, 3), o)) case MoCodes{+lit, +dist}: inf.go(f, inf.sym(win, ht.decode(lit, b), o, lit, dist, last)) case MoDone{}: (win, Is{b, o, MoDone{}, last}) case MoBad{}: (win, Is{b, o, MoBad{}, last})# out: the bytes; rest: the input after the stream; n: len(out) mod 2^32.type Inflated is Data: Inflated{out: String, rest: String, n: U32}def inf.fin(ok: Bool, b: Br, o: Ow) -> Maybe<&2, Inflated>: match ok: case False{}: None{} case True{}: Ow{w, n, racc} = o Some{Inflated{String.reverse(racc), br.rest(b), n}}def inf.result(st: Array<U32> & Is) -> Maybe<&2, Inflated>: (win, ist) = st Is{+b, o, mode, last} = ist match mode: case MoDone{}: inf.fin(br.ok(b), b, o) case MoHead{}: None{} case MoCodes{l, d}: None{} case MoBad{}: None{}def inflate.rest(+s: String) -> Maybe<&2, Inflated>: 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{}})))def inflate.out(m: Maybe<&2, Inflated>) -> Maybe<&2, String>: match m: case None{}: None{} case Some{Inflated{out, rest, n}}: Some{out}# Raw DEFLATE. None: malformed or cut short.def inflate(+s: String) -> Maybe<&2, String>: inflate.out(inflate.rest(s))# CRC-32 (RFC 1952 §8), reflected, polynomial 0xEDB88320.def crc.bit(+c: U32) -> U32: Bool.pick(U32, U32.is_eq(U32.and(c, 1), 1), U32.xor(U32.shr(c), 3988292384), U32.shr(c))def crc.bits(k: Nat, +c: U32) -> U32: match k: case 0n: c case 1n+p: crc.bits(p, crc.bit(c))def crc.fill(k: Nat, +i: U32, a: Array<U32>) -> Array<U32>: match k: case 0n: a case 1n+p: crc.fill(p, (i + 1 : U32), Array.set(U32, a, i, crc.bits(8n, i)))def crc.table() -> Array<U32>: crc.fill(256n, 0, Array.new(U32, 8n, 0))def crc.mix(av: Array<U32> & U32, +c: U32) -> Array<U32> & U32: (a, +t) = av (a, U32.xor(t, U32.shrn(c, 8n)))def crc.step(st: Array<U32> & U32, +b: U32) -> Array<U32> & U32: (a, +c) = st crc.mix(Array.get(U32, a, U32.and(U32.xor(c, b), 255)), c)def crc.go(s: String, st: Array<U32> & U32) -> Array<U32> & U32: match s: case SNil{}: st case SCon{h, t}: crc.go(t, crc.step(st, byte(h)))def crc.of(st: Array<U32> & U32) -> U32: (a, +c) = st U32.xor(c, 4294967295)def crc32(s: String) -> U32: crc.of(crc.go(s, (crc.table(), 4294967295)))# Adler-32 (RFC 1950 §9).def adler.go(s: String, +a: U32, +b: U32) -> U32: match s: case SNil{}: U32.or(U32.shln(b, 16n), a) case SCon{h, t}: +a2 = U32.mod((a + byte(h) : U32), 65521) adler.go(t, a2, U32.mod((b + a2 : U32), 65521))def adler32(s: String) -> U32: adler.go(s, 1, 0)# Little- and big-endian 32-bit words at the front of s.def le32(s: String) -> Maybe<&2, U32>: match s: case SCon{Chr{+a}, SCon{Chr{+b}, SCon{Chr{+c}, SCon{Chr{+d}, t}}}}: Some{U32.or(U32.or(a, U32.shln(b, 8n)), U32.or(U32.shln(c, 16n), U32.shln(d, 24n)))} case SNil{}: None{} case SCon{x, y}: None{}def be32(s: String) -> Maybe<&2, U32>: match s: case SCon{Chr{+a}, SCon{Chr{+b}, SCon{Chr{+c}, SCon{Chr{+d}, t}}}}: Some{U32.or(U32.or(U32.shln(a, 24n), U32.shln(b, 16n)), U32.or(U32.shln(c, 8n), d))} case SNil{}: None{} case SCon{x, y}: None{}def flag(+f: U32, +bit: U32) -> Bool: Bool.not(U32.is_zero(U32.and(f, bit)))def check(ok: Bool, +out: String) -> Maybe<&2, String>: match ok: case True{}: Some{out} case False{}: None{}# RFC 1952 §2.3: after the fixed 10 bytes, optional FEXTRA, FNAME, FCOMMENT, FHCRC.# hit: the byte just read was the terminating zero.def gz.zstr(s: String, hit: Bool) -> Maybe<&2, String>: match s: case SNil{}: match hit: case True{}: Some{SNil{}} case False{}: None{} case SCon{Chr{+c}, t}: match hit: case True{}: Some{SCon{Chr{c}, t}} case False{}: gz.zstr(t, U32.is_zero(c))def gz.skip(k: Nat, s: String) -> Maybe<&2, String>: match k: case 0n: Some{s} case 1n+p: match s: case SNil{}: None{} case SCon{h, t}: gz.skip(p, t)def gz.extra.len(s: String) -> Maybe<&2, String>: match s: case SCon{Chr{+a}, SCon{Chr{+b}, t}}: gz.skip(bits(U32.or(a, U32.shln(b, 8n))), t) case SNil{}: None{} case SCon{x, y}: None{}def gz.fextra(on: Bool, +s: String) -> Maybe<&2, String>: match on: case True{}: gz.extra.len(s) case False{}: Some{s}def gz.fstr(on: Bool, +s: String) -> Maybe<&2, String>: match on: case True{}: gz.zstr(s, False{}) case False{}: Some{s}def gz.fhcrc(on: Bool, +s: String) -> Maybe<&2, String>: match on: case True{}: gz.skip(2n, s) case False{}: Some{s}def gz.flags(+f: U32, s: String) -> Maybe<&2, String>: do Maybe<&2, String>: s1 : String <- gz.fextra(flag(f, 4), s) s2 : String <- gz.fstr(flag(f, 8), s1) s3 : String <- gz.fstr(flag(f, 16), s2) gz.fhcrc(flag(f, 2), s3)def gz.head(s: String) -> Maybe<&2, String>: match s: case SCon{Chr{+id1}, SCon{Chr{+id2}, SCon{Chr{+cm}, SCon{Chr{+f}, t}}}}: 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{}) case SNil{}: None{} case SCon{x, y}: None{}def gz.trail2(+out: String, +n: U32, crc: Maybe<&2, U32>, size: Maybe<&2, U32>) -> Maybe<&2, String>: do Maybe<&2, String>: c : U32 <- crc z : U32 <- size check(Bool.and(U32.is_eq(c, crc32(out)), U32.is_eq(z, n)), out)def gz.trail(m: Maybe<&2, Inflated>) -> Maybe<&2, String>: match m: case None{}: None{} case Some{Inflated{+out, +rest, +n}}: gz.trail2(out, n, le32(rest), le32(String.drop(rest, 4n)))def gz.body(m: Maybe<&2, String>) -> Maybe<&2, String>: match m: case None{}: None{} case Some{+s}: gz.trail(inflate.rest(s))# One gzip member; the CRC-32 and ISIZE must match. None: malformed, cut short, or corrupt.# ponytail: bytes after the first member are ignored; loop over members if a server concatenates them.def gunzip(s: String) -> Maybe<&2, String>: gz.body(gz.head(s))# RFC 1950: CMF and FLG, then DEFLATE, then Adler-32, big-endian.def zl.sum(+out: String, a: Maybe<&2, U32>) -> Maybe<&2, String>: match a: case None{}: None{} case Some{+v}: check(U32.is_eq(v, adler32(out)), out)def zl.trail(m: Maybe<&2, Inflated>) -> Maybe<&2, String>: match m: case None{}: None{} case Some{Inflated{+out, +rest, n}}: zl.sum(out, be32(rest))def zl.ok(+cmf: U32, +flg: U32) -> Bool: 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))))def unzlib(s: String) -> Maybe<&2, String>: match s: case SCon{Chr{+cmf}, SCon{Chr{+flg}, +t}}: Bool.pick(Maybe<&2, String>, zl.ok(cmf, flg), zl.trail(inflate.rest(t)), None{}) case SNil{}: None{} case SCon{x, y}: None{}