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2title = "2h: Set Logic"

3weight = 11

4template = "doc.html"

5+++

7### `++in`

9Set operations

11Core whose arms contain a variety of functions that operate on `set`s. Its

12sample accepts the input `set` to be manipulated.

14#### Accepts

16A `set`.

18#### Source

20```hoon

21 ++ in

22 ~/ %in

23 |_ a=(set)

24```

26#### Examples

28```

29 > ~(. in (sy "asd"))

30 <13.evb [nlr(^$1{@tD $1}) <414.fvk 101.jzo 1.ypj %164>]>

31```

33### `+-all:in`

35Logical AND

37Computes the logical AND on every element in `a` slammed with `b`, producing a

38flag.

40#### Accepts

42`a` is a `set`.

44`b` is a wet gate that accepts a noun and produces a flag.

46#### Produces

48A flag.

50#### Source

52```hoon

53 +- all

54 ~/ %all

55 |* b=$-(* ?)

56 |- ^- ?

57 ?~ a

58 &

59 ?&((b n.a) $(a l.a) $(a r.a))

60```

62#### Examples

64```

65 > =b (sy `(list [@t *])`[['a' 1] ['b' [2 3]] ~])

66 > (~(all in b) |=(a=* ?@(+.a & |)))

67 %.n

69 > =b (sy `(list @t)`['john' 'bonita' 'daniel' 'madeleine' ~])

70 > (~(all in b) |=(a=@t (gte a 100)))

71 %.y

72```

74---

75### `+-any:in`

77Logical OR

79Computes the logical OR on every element of `a` slammed with `b`, producing a

80flag.

82#### Accepts

84`a` is a `set`.

86`b` is a gate that accepts a noun and produces a flag.

88#### Produces

90A flag.

92#### Source

94```hoon

95 +- any

96 ~/ %any

97 |* b=$-(* ?)

98 |- ^- ?

99 ?~ a

100 |

101 ?|((b n.a) $(a l.a) $(a r.a))

102```

103

104#### Examples

105

106```

107 > =b (sy `(list [@t *])`[['a' 1] ['b' [2 3]] ~])

108 > (~(any in b) |=(a/* ?@(+.a & |)))

109 %.y

110

111 > =b (sy `(list @t)`['john' 'bonita' 'daniel' 'madeleine' ~])

112 > (~(any in b) |=(a=@t (lte a 100)))

113 %.n

114```

115

116---

117### `+-apt:in`

118

119Check correctness

120

121Computes whether `a` has a correct horizontal order and a correct vertical

122order, producing a flag.

124#### Accepts

126`a` is a set.

128#### Produces

130A flag.

132#### Source

134```hoon

135 +- apt

136 =| [l=(unit) r=(unit)]

137 |- ^- ?

138 ?~ a &

139 ?& ?~(l & (hor n.a u.l))

140 ?~(r & (hor u.r n.a))

141 ?~(l.a & ?&((vor n.a n.l.a) $(a l.a, l `n.a)))

142 ?~(r.a & ?&((vor n.a n.r.a) $(a r.a, r `n.a)))

143 ==

144```

145

146#### Examples

147

148```

149 > ~(apt in ~)

150 %.y

151

152 > =a (sy [1 2 3 4 5 6 ~])

153 > a

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

155 > ~(apt in a)

156 %.y

157

158 > =z ?~ a ~ a(n 7)

159 > z

160 [n=7 l={5 4} r={1 3 2}]

161 > ~(apt in z)

162 %.n

163```

164

165#### Discussion

166

167See section [`2f`](@/docs/reference/library/2f.md) for more information on noun ordering.

168

169---

170### `+-bif:in`

171

172Bifurcate

173

174Splits set `a` into two sets `l` and `r`, with any noun `b` removed.

176#### Accepts

178`a` is a set.

180`b` is a noun.

182#### Produces

184A cell of two sets.

185

186#### Source

187

188```hoon

189 +- bif

190 ~/ %bif

191 |* b=*

192 ^+ [l=a r=a]

193 =< [+< +>]

194 |- ^+ a

195 ?~ a

196 [b ~ ~]

197 ?: =(b n.a)

198 a

199 ?: (hor b n.a)

200 =+ c=$(a l.a)

201 ?> ?=(^ c)

202 [n.c l.c [n.a r.c r.a]]

203 =+ c=$(a r.a)

204 ?> ?=(^ c)

205 [n.c [n.a l.a l.c] r.c]

206```

207

208#### Examples

209

210```

211 > =a (sy `(list @)`[1 2 3 4 5 6 ~])

212 > a

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

214

215 > (~(bif in a) 6)

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

217

218 > (~(bif in a) 100)

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

220```

221

222---

223### `+-del:in`

224

225Remove noun

226

227Removes `b` from the `set` `a`.

229#### Accepts

231`a` is a set.

233`b` is a noun.

235#### Produces

237A set.

239#### Source

241```hoon

242 +- del

243 ~/ %del

244 |* b=*

245 |- ^+ a

246 ?~ a

247 ~

248 ?. =(b n.a)

249 ?: (hor b n.a)

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

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

252 |- ^- {$?($~ _a)}

253 ?~ l.a r.a

254 ?~ r.a l.a

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

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

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

258```

259

260

261#### Examples

262

263```

264 > =b (sy `(list @t)`['a' 'b' 'c' ~])

265 > (~(del in b) 'a')

266 [n='b' l=[n='c' l={} r={}] r=~]

267

268 > =b (sy `(list @t)`['john' 'bonita' 'daniel' 'madeleine' ~])

269 > (~(del in b) 'john')

270 [n='madeleine' l=[n='daniel' l={} r={'bonita'}] r=~]

271

272 > (~(del in b) 'susan')

273 [n='madeleine' l=[n='daniel' l={} r={'bonita'}] r=[n='john' l={} r={}]]

274```

275

276---

277### `+-dif:in`

278

279Difference

280

281Computes the difference between `a` and `b`, producing the set of items in `a`

282that are not in `b`.

284#### Accepts

286`a` is a set.

288`b` is a set.

290#### Produces

292A set.

294#### Source

296```hoon

297 +- dif

298 ~/ %dif

299 |* b=_a

300 |- ^+ a

301 ?~ b

302 a

303 =+ c=(bif n.b)

304 ?> ?=(^ c)

305 =+ d=$(a l.c, b l.b)

306 =+ e=$(a r.c, b r.b)

307 |- ^- {$?($~ _a)}

308 ?~ e d

309 ?: (vor n.d n.e)

310 [n.d l.d $(d r.d)]

311 [n.e $(e l.e) r.e]

312```

313

314#### Examples

315

316```

317 > =c (sy 1 2 3 ~)

318 > =d (sy 2 3 4 ~)

319 > (~(dif in c) d)

320 [n=1 l=~ r=~]

321

322 > (~(dif in d) c)

323 [n=4 l=~ r=~]

324

325 > `(set @ud)`(~(dif in c) d)

326 {1}

327

328 > `(set @ud)`(~(dif in d) c)

329 {4}

330```

331

332---

333### `+-dig:in`

334

335Address b in a

336

337Produce the tree address of `b` within `a`.

339#### Accepts

341`a` is a set.

343`b` is a noun.

345#### Produces

347The `unit` of an atom.

348

349#### Source

350

351```hoon

352 +- dig

353 |= b=*

354 =+ c=1

355 |- ^- (unit @)

356 ?~ a ~

357 ?: =(b n.a) [~ u=(peg c 2)]

358 ?: (hor b n.a)

359 $(a l.a, c (peg c 6))

360 $(a r.a, c (peg c 7))

361```

362

363

364#### Examples

365

366```

367 > =a (sy `(list @)`[1 2 3 4 5 6 7 ~])

368 > `(set @)`a

369 {5 4 7 6 1 3 2}

370

371 > -.a

372 n=6

373

374 > (~(dig in a) 7)

375 [~ u=12]

376

377 > (~(dig in a) 2)

378 [~ u=14]

379

380 > (~(dig in a) 6)

381 [~ u=2]

382```

383

384#### Discussion

385

386For more on the tree addressing system, see section [1b](@/docs/reference/library/1b.md).

387

388---

389### `+-gas:in`

390

391Concatenate

392

393Insert the elements of a `list` `b` into a `set` `a`.

395#### Accepts

397`a` is a set.

399`b` is a list.

401#### Produces

403A `set`.

405#### Source

407```hoon

408 +- gas

409 ~/ %gas

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

411 |- ^+ a

412 ?~ b

413 a

414 $(b t.b, a (put i.b))

415```

416

417#### Examples

418

419```

420 > =b `(set @t)`(sy `(list @t)`['bonita' 'madeleine' 'rudolf' 'john' ~])

421 > b

422 {'bonita' 'madeleine' 'rudolf' 'john'}

423

424 > (~(gas in b) `(list @t)`['14' 'things' 'number' '1.337' ~])

425 [n='number' l={'1.337' '14'} r={'things' 'bonita' 'madeleine' 'rudolf' 'john'}]

426

427 > =s (sy `(list @t)`['a' 'b' 'c' 'd' 'e' ~])

428 > (~(gas in s) `(list @t)`['1' '2' '3' ~])

429 [n='e' l=[n='1' l={} r={'3' '2'}] r=[n='b' l={'d' 'a' 'c'} r={}]]

430```

431

432---

433### `+-has:in`

434

435b in a?

436

437Checks if `b` is an element of `a`, producing a flag.

439#### Accepts

441`a` is a set.

443`b` is a noun.

445#### Produces

447A flag.

449#### Source

451```hoon

452 +- has

453 ~/ %has

454 |* b=*

455 |- ^- ?

456 ?~ a

457 |

458 ?: =(b n.a)

459 &

460 ?: (hor b n.a)

461 $(a l.a)

462 $(a r.a)

463```

464

465#### Examples

466

467```

468 > =a (~(gas in `(set @t)`~) `(list @t)`['a' 'b' 'c' ~])

469 > (~(has in a) 'a')

470 %.y

471

472 > (~(has in a) 'z')

473 %.n

474```

475

476---

477### `+-int:in`

478

479Intersection

480

481Produces a set of the intersection between two sets of the same type,

482`a` and `b`.

484#### Accepts

486`a` is a set.

488`b` is a set.

490#### Produces

492A `set`.

494#### Source

496```hoon

497 +- int

498 ~/ %int

499 |* b=_a

500 |- ^+ a

501 ?~ b

502 ~

503 ?~ a

504 ~

505 ?. (vor n.a n.b)

506 $(a b, b a)

507 ?: =(n.b n.a)

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

509 ?: (hor n.b n.a)

510 %- uni(a $(a l.a, b [n.b l.b ~])) $(b r.b)

511 %- uni(a $(a r.a, b [n.b ~ r.b])) $(b l.b)

512```

513

514

515#### Examples

516

517```

518 > (~(int in `(set @t)`(sy "acmo")) `(set @t)`(sy "ham"))

519 [n='m' l={'a'} r={}]

520

521 > (~(int in (sy "acmo")) ~)

522 ~

523

524 > (~(int in `(set @t)`(sy "ac")) `(set @t)`(sy "ha"))

525 [n='a' l={} r={}]

526```

527

528---

529### `+-put:in`

530

531Put b in a

532

533Add an element `b` to the set `a`, producing a set.

535#### Accepts

537`a` is a set.

539`b` is a noun.

541#### Produces

543A `set`.

545#### Source

547```hoon

548 +- put

549 ~/ %put

550 |* b=*

551 |- ^+ a

552 ?~ a

553 [b ~ ~]

554 ?: =(b n.a)

555 a

556 ?: (hor b n.a)

557 =+ c=$(a l.a)

558 ?> ?=(^ c)

559 ?: (vor n.a n.c)

560 [n.a c r.a]

561 [n.c l.c [n.a r.c r.a]]

562 =+ c=$(a r.a)

563 ?> ?=(^ c)

564 ?: (vor n.a n.c)

565 [n.a l.a c]

566 [n.c [n.a l.a l.c] r.c]

567```

568

569#### Examples

570

571```

572 > =a (~(gas in `(set @t)`~) `(list @t)`['a' 'b' 'c' ~])

573 > =b (~(put in a) 'd')

574 > `(set @t)`b

575 {'d' 'a' 'c' 'b'}

576

577 > -.l.+.b

578 n='d'

579```

580

581---

582### `+-rep:in`

583

584Accumulate

585

586Accumulate the elements of `a` using a gate `b`.

588#### Accepts

590`a` is a `set`.

592`b` is a gate.

594#### Produces

596A noun.

598#### Source

600```hoon

601 +- rep :: replace by product

602 |* b=_|=([* *] +<+)

603 |-

604 ?~ a +<+.b

605 $(a r.a, +<+.b $(a l.a, +<+.b (b n.a +<+.b)))

606```

607

608#### Examples

609

610```

611 > =a (~(gas in *(set @)) [1 2 3 ~])

612 > `(set @)`a

613 {1 3 2}

614

615 > (~(rep in a) |=([a=@ b=@] (add a b)))

616 b=6

617```

618

619---

620### `+-run:in`

621

622Apply gate to set

623

624Produce a `set` containing the products of gate `b` applied to each element

625in `a`.

627#### Accepts

629`a` is a `set`.

631`b` is a gate.

633#### Produces

635A set.

637#### Source

639```hoon

640 +- run

641 ~/ %run

642 |* b=gate

643 =| c=(set _?>(?=(^ a) (b n.a)))

644 |- ?~ a c

645 =. c (~(put in c) (b n.a))

646 =. c $(a l.a, c c)

647 $(a r.a, c c)

648```

649

650#### Examples

651

652```

653 > =s (sy ~["a" "A" "b" "c"])

654 > `(set tape)`s

655 {"A" "a" "c" "b"}

656

657 > (~(run in s) cuss)

658 {"A" "C" "B"}

659```

660

661---

662### `+-tap:in`

663

664Set to list

665

666Flattens the `set` `a` into a `list`.

668#### Accepts

670`a` is an set.

672#### Produces

674A list.

676#### Source

678```hoon

679 +- tap

680 ~/ %tap

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

682 ^+ b

683 ?~ a

684 b

685 $(a r.a b [n.a $(a l.a)])

686```

687

688

689#### Examples

690

691```

692 > =s (sy `(list @t)`['a' 'b' 'c' 'd' 'e' ~])

693 > s

694 [n='e' l={} r={'d' 'a' 'c' 'b'}]

695

696 > ~(tap in s)

697 ~['b' 'c' 'a' 'd' 'e']

698```

699

700---

701### `+-uni:in`

702

703Union

704

705Produces a set of the union between two sets of the same type, `a` and

706`b`.

708#### Accepts

710`a` is a set.

712`b` is a set.

714#### Produces

716A set.

718#### Source

720```hoon

721 +- uni

722 ~/ %uni

723 |* b=_a

724 ?: =(a b) a

725 |- ^+ a

726 ?~ b

727 a

728 ?~ a

729 b

730 ?: (vor n.a n.b)

731 ?: =(n.b n.a)

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

733 ?: (hor n.b n.a)

734 $(a [n.a $(a l.a, b [n.b l.b ~]) r.a], b r.b)

735 $(a [n.a l.a $(a r.a, b [n.b ~ r.b])], b l.b)

736 ?: =(n.a n.b)

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

738 ?: (hor n.a n.b)

739 $(b [n.b $(b l.b, a [n.a l.a ~]) r.b], a r.a)

740 $(b [n.b l.b $(b r.b, a [n.a ~ r.a])], a l.a)

741 ::

742```

743

744

745#### Examples

746

747```

748 > (~(uni in `(set @t)`(sy "ac")) `(set @)`(sy "ha"))

749 [n='c' l={'a'} r={'h'}]

750

751 > (~(uni in `(set @t)`(sy "acmo")) ~)

752 [n='c' l={'a'} r={'m' 'o'}]

753

754 > (~(uni in `(set @t)`(sy "acmo")) `(set @t)`(sy "ham"))

755 [n='c' l={'a'} r={'m' 'o' 'h'}]

756

757 > (~(uni in `(set @t)`(sy "acmo")) `(set @t)`(sy "lep"))

758 [n='e' l={} r={'a' 'c' 'm' 'l' 'o' 'p'}]

759```

760

761---

762### `+-wyt:in`

763

764Set size

765

766Produces the number of elements in set `a` as an atom.

768#### Accepts

770`a` is an set.

772#### Produces

774An atom.

776#### Source

778```hoon

779 +- wyt :: size of set

780 |- ^- @

781 ?~(a 0 +((add $(a l.a) $(a r.a))))

782 --

783```

784

785

786#### Examples

787

788```

789 > =a (~(put in (~(put in (sy)) 'a')) 'b')

790 > ~(wyt in a)

791 2

792

793 > =b (sy `(list @t)`['john' 'bonita' 'daniel' 'madeleine' ~])

794 > ~(wyt in b)

795 4

796```

797

798---