10Now we know enough to write two quick examples: the Sieve of
11Eratosthenes (a naive prime sieve) and a tic-tac-toe engine.
13(Note that these are not examples of perfect Hoon code; they are
14meant for teaching. They err, more than usual for Hoon, on the
15side of simple manual construction over high-octane FP.)
17## `sieve`: code in basic style
19A function that produces the list of primes less than or equal to
24:var field/(set atom) (silt (gulf 2 thru)) :: 3
28 (sort (~(tap in field) ~) lth) :: 7
31 :var factor/atom 2 :: 10
32 :loop :like ..main :: 11
33 :if (gth (mul factor factor) thru) :: 12
35 :moar(factor +(factor), ..main (reap factor)) :: 14
38 :gate factor/atom :: 17
39 :var count/atom (mul 2 factor) :: 18
40 :loop :like ..reap :: 19
41 :if (gth count thru) :: 20
44 count (add count factor) :: 23
45 field (~(del in field) count) :: 24
50## `sieve`: explanation
55:var field/(set atom) (silt (gulf 2 thru)) :: 3
58Line `1`: we are building a gate (function) whose sample
59(argument) is `thru`, an atom.
61Line `2`: the product of this gate is a list of atoms.
63Line `3`: we introduce a variable `field`, whose type is a set of
64atoms. The `silt` function converts a list to a set. The `gulf`
65function creates the range `2` through `thru` inclusive, as a
68Line `4`: below, we introduce a core which does our work. With
69reverse flow, we compute `main` on this core, then `abet` on the
70product of `main`. (`abet:main` means `:rap(abet main)`.)
72The core is a state machine; `main` produces the core itself,
73with the computation completed. `abet` then extracts the result.
78 (sort (~(tap in field) ~) lth) :: 7
81Line `5`: we wrap a core around our existing subject. The
82`field` and `thru` atoms are within the payload and of course
85Lines `6` and `7`: the `abet` arm, which produces the field as a
86sorted list. `in` is the set core; `tap` is an arm which
87produces a gate that exports the set as a list, prepending it to
88a tail which is nil in this case (and most cases). We sort this
89list in ascending order with `lth` (less-than).
93 :var factor/atom 2 :: 10
94 :loop :like ..main :: 11
97Line `9`: the `main` arm, which performs the main calculation.
99Line `10`: we declare a counter, `factor`, which will iterate
100up through the factors we're removing.
102Line `11`: we start a loop. The product of the loop is cast to
103`..main`, which is the core we're in (`+1.main`).
106 :if (gth (mul factor factor) thru) :: 12
108 :moar(factor +(factor), ..main (reap factor)) :: 14
111Lines `12` and `13`: we terminate the loop, returning `..main`,
112if the square of the counter exceeds the range.
114Line `14`: repeats the loop, incrementing the counter, and
115replacing the core with a version sieved by `reap`.
119 :gate factor/atom :: 17
120 :var count/atom (mul 2 factor) :: 18
123Lines `16` and `17`: the `reap` arm, which produces a gate that
124removes multiples of a factor from the field (set of possible
125primes). The sample of this gate is the factor to remove.
127Line `18`: we declare a variable `count`, an atom, with the
128initial value `(mul 2 factor)`.
131 :loop :like ..reap :: 19
132 :if (gth count thru) :: 20
135 count (add count factor) :: 23
136 field (~(del in field) count) :: 24
141Line `19`: we enter a loop. This loop produces the core itself.
143Lines `20` and `21`: we are done if the counter is out of range.
145Lines `22` to `25`: repeat the loop, stepping `count` to the next
146multiple of `factor`, and deleting it from `field`.
148## `sieve`: code in kernel style
150Finally, the same code transliterated into runes (and in a more
151concise "kernel" style).
156=+ fed=(silt (gulf 2 top))
159++ abet (sort (~(tap in fed)) lth)
163 ?: (gth (mul fac fac) top)
165 $(fac +(fac), ..main (reap fac))
173 $(cot (add cot fac), fed (~(del in fed) cot))
177### `toe`: tic-tac-toe engine
179The `toe` tic-tac-toe engine applies a list of events to a game
180state, producing a list of game actions. Events are tic-tac-toe
181moves (`move)`; actions are tic-tac-toe results (`fact`).
184:rap :gate feed/(list move) :: 1
186 :loop :cast (list fact) :: 3
188 :sip this/(unit fact) :: 5
190 (~(do go game) i.feed) :: 7
191 :var rest/(list fact) :moar(feed t.feed) :: 8
192 :ifno(this rest [u.this rest]) :: 9
196 ++ spot {x/atom y/atom} :: 13
197 ++ fact :book {$tie $~} :: 14
200 ++ move :book {$x p/spot} :: 17
204 ++ game :bank w/? :: 21
211 :door half/side :: 28
212 ++ bit :gate(a/atom =(1 (cut 0 [a 1] half))) :: 29
213 ++ off :gate(a/spot (add x.a (mul 3 y.a))) :: 30
214 ++ get :gate(a/spot (bit (off a))) :: 31
215 ++ set :gate(a/spot (con half (bex (off a)))) :: 32
216 ++ win :calt lien :: 33
217 (rip 4 0wl04h0.4A0Aw.4A00s.0e070) :: 34
218 :gate(a/atom =(a (dis a half))) :: 35
221 :door game/game :: 38
224 :cast {(unit fact) ^game} :: 41
226 {$x *} :sure(w.game ~(mo on p.act)) :: 43
227 {$o *} :deny(w.game ~(mo on p.act)) :: 44
231 ++ nu :like(game [& 0 0]) :: 48
233 :door here/spot :: 50
234 ++ is :or (~(get bo a.game) here) :: 51
235 (~(get bo z.game) here) :: 52
237 ++ mo :cast {(unit fact) ^game} :: 54
239 :var next/side (~(set bo a.game) here) :: 56
240 :if ~(win bo next) :: 57
241 [[~ %win ?:(w.game %x %o)] nu] :: 58
242 [~ game(w !w.game, a z.game, z next)] :: 59
248### `toe`: explanation
251:rap :gate feed/(list move) :: 1
253 :loop :cast (list fact) :: 3
257Line `1` wraps a conclusion around a stack of cores. The cores
258at `11` and `26` are the data structures and functions of the
259engine; the conclusion is the interface and top-level logic. It
260produces a gate whose sample is `feed`, a list of `move`.
262Line `2` declares a blank new variable named `game`, whose type
263is the `game` mold (tic-tac-toe game state) defined on line `21`.
264Under line `2`, `game` pulls the variable and `^game` the mold.
266Line `3` enters a loop producing a list of game events, `fact`.
268Line `4` produces nil, `~`, if `feed` is empty.
271 :sip this/(unit fact) :: 5
273 (~(do go game) i.feed) :: 7
276Lines `5` through `7` apply the move. We open a `go` core on the
277current game state, produce a `do` gate, and call that gate on
278the move. The product of the `do` gate is a pair; the head is
279`(unit fact)`, either `~` or `[~ fact]`; the tail is a new
280`game`. The `:sip` twig declares the head as a new variable,
281`this`; it modifies the subject by setting `game` to the tail.
284 :var rest/(list fact) :moar(feed t.feed) :: 8
285 :ifno(this rest [u.this rest]) :: 9
288Line `8` declares a new variable, `rest`, which is all the facts
289generated by the moves in `t.feed`, the tail of the move list.
290(Yes, this is gratuitous head recursion.) Line `9` produces
291`rest` if the `i.feed` move produced no fact; otherwise it
292prepends the new fact to `rest`.
297 ++ spot {x/atom y/atom} :: 13
300Line `11` wraps a library core around a data structure core, a
301common pattern. (You could put the molds and the gates in the
302same core, but the compiler couldn't constant-fold gate samples
303that use these molds, an efficiency cost.)
305Line `12` defines the `side` mold, an alias for `atom` (`@`).
306A side is a half of the board, as a marked/unmarked bitfield.
308Line `13` defines the `spot` mold, a 2D coordinate.
311 ++ fact :book {$tie $~} :: 14
316Lines `14` to `16` define the `fact` mold, a game event (i.e.,
317output action), as a book (tagged union). There are two forms of
318`fact`: `[%tie ~]` (reporting a tie), and `[%win cord]`
319(reporting that `'X'` or `'O'` won a game.
322 ++ move :book {$x p/spot} :: 17
328Lines `17` to `20` define the `move` mold, a game move. This is
329either `[%x spot]`, `[%o spot]`, or `[%z ~]` to reset the board.
332 ++ game :bank w/? :: 21
339Lines `21` to `23` define the `game` mold, the game state. This
340is an `a` side, the next side to move; a `z` side, the other
341side; and `w`, which is `&` (yes) if `a` is X and `b` is O; `|`
342otherwise. (Obviously, we swap `a` and `z` on every move.)
347 :door half/side :: 28
348 ++ bit :gate(a/atom =(1 (cut 0 [a 1] half))) :: 29
349 ++ off :gate(a/spot (add x.a (mul 3 y.a))) :: 30
350 ++ get :gate(a/spot (bit (off a))) :: 31
351 ++ set :gate(a/spot (con half (bex (off a)))) :: 32
354Line `26` introduces the library core, which contains the doors
355`bo` (for `side` bitfields) and `go` (for game state).
357Lines `27` to `28` begin the `bo` core, a door around `half`, a
360Line `29` is the `bit` gate, which tests a bit in `half`.
362Line `30` is the `off` gate, which maps from a `spot` (coordinate)
365Line `31` is the `get` gate, which produces the bit at a `spot`.
367Line `32` is the `set` gate, which produces a new side with the
368bit at a `spot` set. It works by ORing (`con`) `half` with the
369binary exponent (`bex`) of the offset (`off`) of the spot.
372 ++ win :calt lien :: 33
373 (rip 4 0wl04h0.4A0Aw.4A00s.0e070) :: 34
374 :gate(a/atom =(a (dis a half))) :: 35
378Lines `33` to `35` are a victory test. It calls the
379standard `lien` function, which iterates a boolean gate over a
380list and produces `&` (yes) if any item tests as true, against a
381list of magic bitfields (expanded from a base64 constant), each
382of which must equal itself when ANDed (`dis`) with `half`.
386 :door game/game :: 38
389 :cast {(unit fact) ^game} :: 41
392Lines `37` to `38` begin the `go` core, a door around a `game`.
393Again we name the sample `game`. (This is a legitimate style,
396Lines `40` to `42` begin the `do` gate, whose sample is `act`, a
397move. The product is cast to a pair of `(unit fact)` and a new
398game state, written `^game` to skip to the second binding.
402 {$x *} :sure(w.game ~(mo on p.act)) :: 43
403 {$o *} :deny(w.game ~(mo on p.act)) :: 44
409Lines `42` through `46` switch on the form of `act`. If it's an
410`%x` or `%o` move, we assert that it's the right turn, then use
411the `mo` door to apply the move. If it's a `%z` move, we clear
415 ++ nu :like(game [& 0 0]) :: 48
417 :door here/spot :: 50
418 ++ is :or (~(get bo a.game) here) :: 51
419 (~(get bo z.game) here) :: 52
423Line `48` is the `nu` arm, which produces a blank game state.
425Lines `49` to `50` begin the `on` door, a door around `here`, a
426`spot`. Just as we have multiple computed attributes against the
427game state, we have multiple computed attributes (`is` and `mo`)
428against the combination of game state and coordinate.
430Lines `51` to `53` define the `is` arm, which is `&` (yes) iff
431either `a` or `z` has played `here`.
434 ++ mo :cast {(unit fact) ^game} :: 54
436 :var next/side (~(set bo a.game) here) :: 56
437 :if ~(win bo next) :: 57
438 [[~ %win ?:(w.game %x %o)] nu] :: 58
439 [~ game(w !w.game, a z.game, z next)] :: 59
445Line `54` begins the `mo` arm, which produces (with a
446nonessential cast) a pair of `(unit fact)` and game state.
447Again we see `^game` to pull the mold, since `game` is the
448current game state in the `go` core.
450Line `55` asserts that no one has yet played `here`.
452Line `56` declares a variable `next`, as game side `a` with
455Lines `57` and `58` test if `a` has won with this move. If so,
456we produce the win fact and a blank game state.
458Line `59` produces no fact (since nothing has happened), but
459inverts the `w` turn indicator, replaces side `a` with the other
460side `z`, and replaces `z` with `next`.
462### `toe`: code, kernel style
469 =^ did/(unit fact) mag (~(do go mag) i.fed)
471 ?~(did res [u.did res])
478 ++ move $% {$x p/spot}
490 ++ bit |=(a/atom =(1 (cut 0 [a 1] haf)))
491 ++ get |=(a/spot (bit (off a)))
492 ++ off |=(a/spot (add x.a (mul 3 y.a)))
493 ++ set |=(a/spot (con haf (bex (off a))))
495 (rip 4 0wl04h0.4A0Aw.4A00s.0e070)
496 |=(a/atom =(a (dis a haf)))
502 ^- {(unit fact) game}
504 {$x *} ?>(w.mag ~(mo on p.act))
505 {$o *} ?<(w.mag ~(mo on p.act))
513 ++ is ?| (~(get bo a.mag) her)
514 (~(get bo z.mag) her)
516 ++ mo ^- {(unit fact) game}
518 =+ next=(~(set bo a.mag) her)
520 [[~ %win ?:(w.mag %x %o)] nu]
521 [~ mag(w !w.mag, a z.mag, z next)]
529++ atom @ :: just an atom
530++ axis @ :: tree address
531++ bean ? :: 0=&=yes, 1=|=no
532++ bloq @ :: blockclass
533++ char @tD :: UTF-8 byte
534++ cord @t :: text atom (UTF-8)
535++ gate $-(* *) :: general gate
536++ knot @ta :: ASCII text
538++ null $~ :: null, nil, etc
539++ time @da :: galactic time
540++ path (list knot) :: eg, fs location
541++ tang (list tank) :: error trace
543 $% {$leaf p/tape} :: printing formats
544 $: $palm :: backstep list
545 p/{p/tape q/tape r/tape s/tape} ::
548 $: $rose :: flat list
549 p/{p/tape q/tape r/tape} :: mid open close
553++ tanq :: future tank
554 $? {$~ p/(list tanq)} :: list of printables
555 {$~ $~ p/tape} :: simple string
556 (pair @tas tanq) :: captioned
558++ tape (list char) :: string as list
559++ term @tas :: ascii symbol
560++ wall (list tape) :: text lines (no \n)
561++ wain (list cord) :: text lines (no \n)
566++ tree |* a/gate :: binary tree
567 $@($~ {n/a l/(tree a) r/(tree a)}) ::
568++ trap |*(a/_* _|?(*a)) :: makes perfect sense
569++ trel |* {a/gate b/gate c/gate} :: just a triple
571++ each |* {a/gate b/gate} :: either a or b
572 $%({$& p/a} {$| p/b}) :: a default
574++ qual |* {a/gate b/gate c/gate d/gate} :: just a quadruple
576++ pair |*({a/gate b/gate} {p/a q/b}) :: just a pair
577++ quid |*({a/gate b/*} {a _b}) :: for =^
578++ quip |*({a/gate b/*} {(list a) _b}) :: for =^
579++ unit |* a/gate :: maybe
581++ list |* a/gate :: null-term list
582 $@($~ {i/a t/(list a)}) ::
583++ lone |*(a/gate p/a) :: just one thing
587++ map |* {a/gate b/gate} :: associative tree
588 $@($~ {n/{p/a q/b} l/(map a b) r/(map a b)}) ::
589++ qeu |* a/gate :: queue
590 $@($~ {n/a l/(qeu a) r/(qeu a)}) ::
591++ set |* a/gate :: set
592 $@($~ {n/a l/(set a) r/(set a)}) ::
593++ jar |*({a/gate b/gate} (map a (list b))) :: map of lists
594++ jug |*({a/gate b/gate} (map a (set b))) :: map of sets
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