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2title = "2k: Queue Logic"

3weight = 14

4template = "doc.html"

5+++

6### `++to`

9Queue operations

11Container arm for queue operation arms. The contained arms inherit `a`, its

12sample queue.

14#### Accepts

16`a` is a tree.

18#### Source

20```

21 ++ to

22 |_ a=(tree)

23```

25#### Discussion

27`tree` is the generic tree-shape mold. Maps, sets, and queues all share that

28shape, but they put their elements in different places and have different

29interfaces. `to` is the interface core for `qeu`; it's not generic across all

30the different containers that use `tree`.

32---

33### `+-bal:to`

35Balance

37Vertically rebalances queue `a`.

39#### Accepts

41`a` is a queue.

43#### Produces

45A queue.

47#### Source

49```

50 +- bal

51 |- ^+ a

52 ?~ a ~

53 ?. |(?=($~ l.a) (vor n.a n.l.a))

54 $(a [n.l.a l.l.a $(a [n.a r.l.a r.a])])

55 ?. |(?=($~ r.a) (vor n.a n.r.a))

56 $(a [n.r.a $(a [n.a l.a l.r.a]) r.r.a])

57 a

58```

60#### Examples

62```

63 > `(qeu tape)`["a" ~ "b" ~ "c" ~ "d" ~ "e" ~ "f" ~ "g" ~ ~]

64 {"a" "b" "c" "d" "e" "f" "g"}

66 > `*`["a" ~ "b" ~ "c" ~ "d" ~ "e" ~ "f" ~ "g" ~ ~]

67 [[97 0] 0 [98 0] 0 [99 0] 0 [100 0] 0 [101 0] 0 [102 0] 0 [103 0] 0 0]

69 > ~(bal to `(qeu tape)`["a" ~ "b" ~ "c" ~ "d" ~ "e" ~ "f" ~ "g" ~ ~])

70 [n=[i='d' t=""] l={"a" "b" "c"} r={"e" "f" "g"}]

72 > `*`~(bal to `(qeu tape)`["a" ~ "b" ~ "c" ~ "d" ~ "e" ~ "f" ~ "g" ~ ~])

73 [[100 0] [[99 0] [[98 0] [[97 0] 0 0] 0] 0] [101 0] 0 [102 0] 0 [103 0] 0 0]

74```

76---

77### `+-dep:to`

79Maximum Depth

81Produces the maximum depth of leaves (`r.a` and `l.a`) in queue `a`.

83#### Accepts

85`a` is a queue.

87#### Produces

89An atom.

91#### Source

93```

94 +- dep

95 |- ^- @

96 ?~ a 0

97 +((max $(a l.a) $(a r.a)))

98```

100#### Examples

101

102```

103 > =a (~(gas to `(qeu @)`~) `(list @)`[1 2 3 4 5 6 7 ~])

104 > ~(dep to a)

105 4

106

107 > =a (~(gas to `(qeu @)`~) `(list @)`[1 2 3 4 ~])

108 > ~(dep to a)

109 3

110

111 > =a (~(gas to `(qeu @)`~) `(list @)`[1 2 ~])

112 > ~(dep to a)

113 2

114

115 > ~(dep to `(qeu tape)`["a" ~ "b" ~ "c" ~ "d" ~ "e" ~ "f" ~ "g" ~ ~])

116 7

117

118 > ~(dep to ~(bal to `(qeu tape)`["a" ~ "b" ~ "c" ~ "d" ~ "e" ~ "f" ~ "g" ~ ~]))

119 4

120```

121

122---

123### `+-gas:to`

124

125Push list

126

127Push all elements of list `b` into the queue `a`.

129#### Accepts

131`a` is a queue.

133`b` is a list.

135#### Produces

137A queue.

139#### Source

141```

142 +- gas

143 |= b=(list _?>(?=(^ a) n.a))

144 |- ^+ a

145 ?~(b a $(b t.b, a (put i.b)))

146```

147

148

149#### Examples

150

151```

152 > `(qeu)`(~(gas to `(qeu @)`~) [1 2 3 ~])

153 {3 2 1}

154

155 > =a (~(gas to `(qeu @)`~) [1 2 3 ~])

156 > =b [4 5 6 ~]

157 > `(qeu)`(~(gas to a) b)

158 {6 5 4 3 2 1}

159```

160---

161### `+-get:to`

162

163Head-tail pair

164

165Produces the head and tail queue of `a`.

167#### Accepts

169`a` is a queue.

171#### Produces

173A cell of the last element in `a` along with the rest of queue `a`.

174

175#### Source

176

177```

178 +- get

179 |- ^+ ?>(?=(^ a) [p=n.a q=*(tree _n.a)])

180 ?~ a

181 !!

182 ?~ r.a

183 [n.a l.a]

184 =+ b=$(a r.a)

185 :- p.b

186 ?: |(?=($~ q.b) (vor n.a n.q.b))

187 [n.a l.a q.b]

188 [n.q.b [n.a l.a l.q.b] r.q.b]

189```

190

191#### Examples

192

193```

194 > =s (~(gas to *(tree @)) `(list @)`~[1 2 3])

195 > ~(get to s)

196 [n=2 l={3} r={1}]

197

198 > ~(get to ~)

199 ! exit

200```

201

202---

203### `+-nap:to`

204

205Remove head

206

207Removes the head of queue `a`, producing the resulting queue.

209#### Accepts

211`a` is a queue.

213#### Produces

215A queue.

217#### Source

219```

220 +- nap

221 ?> ?=(^ a)

222 ?~ l.a r.a

223 =+ b=get(a l.a)

224 bal(a ^+(a [p.b q.b r.a]))

225```

226

227#### Examples

228

229```

230 > =a (~(gas to `(qeu @)`~) `(list @)`[1 2 3 4 5 6 ~])

231 > -.a

232 n=6

233

234 > =b ~(nap to a)

235 > -.b

236 n=2

237

238 > a

239 [n=6 l={} r={5 4 3 2 1}]

240

241 > b

242 [n=2 l=[n=4 l={5} r={3}] r=[n=1 l={} r={}]]

243

244 > `(qeu)`b

245 {5 4 3 2 1}

246

247 > `(qeu)`a

248 {6 5 4 3 2 1}

249```

250

251---

252### `+-nip:to`

253

254Removes the root of queue `a`, producing the resulting queue.

256#### Accepts

258`a` is a queue.

260#### Produces

262A queue.

264#### Source

266```

267 +- nip

268 |- ^+ a

269 ?~ a ~

270 ?~ l.a r.a

271 ?~ r.a l.a

272 ?: (vor n.l.a n.r.a)

273 [n.l.a l.l.a $(l.a r.l.a)]

274 [n.r.a $(r.a l.r.a) r.r.a]

275```

276

277#### Examples

278

279```

280 > =a (~(gas to `(qeu @)`~) `(list @)`[1 2 3 4 5 6 ~])

281 > a

282 [n=6 l={} r={5 4 3 2 1}]

283

284 > ~(nip to a)

285 [n=2 l=[n=4 l={5} r={3}] r=[n=1 l={} r={}]]

286```

287

288---

289### `+-put:to`

290

291Insert

292

293Accept any noun `b` and adds to queue `a` as the head, producing the

294resulting queue.

296#### Accepts

298`a` is a queue.

300`b` is any noun.

302#### Produces

304A queue.

306#### Source

308```

309 +- put

310 |* b=*

311 |- ^+ a

312 ?~ a

313 [b ~ ~]

314 bal(a a(l $(a l.a)))

315```

316

317#### Examples

318

319```

320 > =a (~(gas to `(qeu @)`~) `(list @)`[3 1 2 4 5 6 ~])

321 > `(qeu)`(~(put to a) 7)

322 {7 6 5 4 2 1 3}

323```

324

325---

326### `+-tap:to`

327

328Queue to list

329

330Produces queue `a` as a list from front to back.

332#### Accepts

334`a` is a queue.

336#### Produces

338A list.

340#### Source

342```

343 +- tap

344 =| b=(list _?>(?=(^ a) n.a))

345 |- ^+ b

346 =+ 0 :: hack for jet match

347 ?~ a

348 b

349 $(a r.a, b [n.a $(a l.a)])

350```

351

352#### Examples

353

354```

355 > =a (~(gas to `(qeu @)`~) [3 1 2 4 5 6 ~])

356 > `*`a

357 [6 0 2 [4 [5 0 0] 0] 1 0 3 0 0]

358 > ~(tap to a)

359 ~[3 1 2 4 5 6]

360```

361

362---

363### `+-top:to`

364

365Produce head

366

367Produces the head of queue `a` as a `unit`.

369#### Accepts

371`a` is a queue.

373#### Produces

375A unit.

377#### Source

379```

380 +- top

381 |- ^- (unit _?>(?=(^ a) n.a))

382 ?~ a ~

383 ?~(r.a [~ n.a] $(a r.a))

384```

385

386#### Examples

387

388```

389 > =a (~(gas to `(qeu @)`~) `(list @)`[1 2 3 4 5 6 ~])

390 > ~(top to a)

391 [~ u=1]

392```

393

394#### Discussion

395

396An empty queue has no head.

397

398---