7Now we know enough to write two quick examples: the Sieve of
8Eratosthenes (a naive prime sieve) and a tictactoe engine.
10(Note that these are not examples of perfect Hoon code; they are
11meant for teaching. They err, more than usual for Hoon, on the
12side of simple manual construction over high-octane FP.)
14## `sieve`: code in basic style
16A function that produces the list of primes less than or equal to
17than its argument, an atom:
21:var field/(set atom) (silt (gulf 2 thru)) :: 3
25 (sort (~(tap in field) ~) lth) :: 7
28 :var factor/atom 2 :: 10
29 :loop :like ..main :: 11
30 :if (gth (mul factor factor) thru) :: 12
32 :moar(factor +(factor), ..main (reap factor)) :: 14
35 :gate factor/atom :: 17
36 :var count/atom (mul 2 factor) :: 18
37 :loop :like ..reap :: 19
38 :if (gth count thru) :: 20
41 count (add count factor) :: 23
42 field (~(del in field) count) :: 24
47## `sieve`: explanation
49Line `1`: we are building a gate (function) whose sample
50(argument) is `thru`, an atom.
52Line `2`: the product of this gate is a list of atoms.
54Line `3`: we introduce a variable `field`, whose type is a set of
55atoms. The `silt` function converts a list to a set. The `gulf`
56function creates the range `2` through `thru` inclusive, as a
59Line `4`: below, we introduce a core which does our work. With
60reverse flow, we compute `main` on this core, then `abet` on the
61product of `main`. (`abet:main` means `:rap(abet main)`.)
63The core is a state machine; `main` produces the core itself,
64with the computation completed. `abet` then extracts the result.
66Line `5`: we wrap a core around our existing subject. The
67`field` and `thru` atoms are within the payload and of course
70Lines `6` and `7`: the `abet` arm, which produces the field as a
71sorted list. `in` is the set core; `tap` is an arm which
72produces a gate that exports the set as a list, prepending it to
73a tail which is nil in this case (and most cases). We sort this
74list in ascending order with `lth` (less-than).
76Line `9`: the `main` arm, which performs the main calculation.
78Line `10`: we declare a counter, `factor`, which will iterate
79up through the factors we're removing.
81Line `11`: we start a loop. The product of the loop is cast to
82`..main`, which is the core we're in (`+1.main`).
84Lines `12` and `13`: we terminate the loop, returning `..main`,
85if the square of the counter exceeds the range.
87Line `14`: repeats the loop, incrementing the counter, and
88replacing the core with a version sieved by `reap`.
90Lines `16` and `17`: the `reap` arm, which produces a gate that
91removes multiples of a factor from the field (set of possible
92primes). The sample of this gate is the factor to remove.
94Line `18`: we declare a variable `count`, an atom, with the
95initial value `(mul 2 factor)`.
97Line `19`: we enter a loop. This loop produces the core itself.
99Lines `20` and `21`: we are done if the counter is out of range.
101Lines `22` to `25`: repeat the loop, stepping `count` to the next
102multiple of `factor`, and deleting it from `field`.
104## `sieve`: code in kernel style
106Finally, the same code transliterated into runes (and in a more
107concise "kernel" style).
112=+ fed=(silt (gulf 2 top))
115++ abet (sort (~(tap in fed)) lth)
119 ?: (gth (mul fac fac) top)
121 $(fac +(fac), ..main (reap fac))
129 $(cot (add cot fac), fed (~(del in fed) cot))
133### `toe`: tictactoe engine
135The `toe` tictactoe engine applies a list of events to a game
136state, producing a list of game actions. Events are tictactoe
137moves (`move)`; actions are tictactoe results (`fact`).
140:rap :gate feed/(list move) :: 1
142 :loop :cast (list fact) :: 3
144 :sip this/(unit fact) :: 5
146 (~(do go game) i.feed) :: 7
147 :var rest/(list fact) :moar(feed t.feed) :: 8
148 :ifno(this rest [u.this rest]) :: 9
152 ++ spot {x/atom y/atom} :: 13
153 ++ fact :book {$tie $~} :: 14
156 ++ move :book {$x p/spot} :: 17
160 ++ game :bank w/? :: 21
167 :door half/side :: 28
168 ++ bit :gate(a/atom =(1 (cut 0 [a 1] half))) :: 29
169 ++ off :gate(a/spot (add x.a (mul 3 y.a))) :: 30
170 ++ get :gate(a/spot (bit (off a))) :: 31
171 ++ set :gate(a/spot (con half (bex (off a)))) :: 32
172 ++ win :calt lien :: 33
173 (rip 4 0wl04h0.4A0Aw.4A00s.0e070) :: 34
174 :gate(a/atom =(a (dis a half))) :: 35
177 :door game/game :: 38
180 :cast {(unit fact) ^game} :: 41
182 {$x *} :sure(w.game ~(mo on p.act)) :: 43
183 {$o *} :deny(w.game ~(mo on p.act)) :: 44
187 ++ nu :like(game [& 0 0]) :: 48
189 :door here/spot :: 50
190 ++ is :or (~(get bo a.game) here) :: 51
191 (~(get bo z.game) here) :: 52
193 ++ mo :cast {(unit fact) ^game} :: 54
195 :var next/side (~(set bo a.game) here) :: 56
196 :if ~(win bo next) :: 57
197 [[~ %win ?:(w.game %x %o)] nu] :: 58
198 [~ game(w !w.game, a z.game, z next)] :: 59
204### `toe`: explanation
206Line `1` wraps a conclusion around a stack of cores. The cores
207at `11` and `26` are the data structures and functions of the
208engine; the conclusion is the interface and top-level logic. It
209produces a gate whose sample is `feed`, a list of `move`.
211Line `2` declares a blank new variable named `game`, whose type
212is the `game` mold (tictactoe game state) defined on line `21`.
213Under line `2`, `game` pulls the variable and `^game` the mold.
215Line `3` enters a loop producing a list of game events, `fact`.
217Line `4` produces nil, `~`, if `feed` is empty.
219Lines `5` through `7` apply the move. We open a `go` core on the
220current game state, produce a `do` gate, and call that gate on
221the move. The product of the `do` gate is a pair; the head is
222`(unit fact)`, either `~` or `[~ fact]`; the tail is a new
223`game`. The `:sip` twig declares the head as a new variable,
224`this`; it modifies the subject by setting `game` to the tail.
226Line `8` declares a new variable, `rest`, which is all the facts
227generated by the moves in `t.feed`, the tail of the move list.
228(Yes, this is gratuitous head recursion.) Line `9` produces
229`rest` if the `i.feed` move produced no fact; otherwise it
230prepends the new fact to `rest`.
232Line `11` wraps a library core around a data structure core, a
233common pattern. (You could put the molds and the gates in the
234same core, but the compiler couldn't constant-fold gate samples
235that use these molds, an efficiency cost.)
237Line `12` defines the `side` mold, an alias for `atom` (`@`).
238A side is a half of the board, as a marked/unmarked bitfield.
240Line `13` defines the `spot` mold, a 2D coordinate.
242Lines `14` to `16` define the `fact` mold, a game event (ie,
243output action), as a book (tagged union). There are two forms of
244`fact`: `[%tie ~]` (reporting a tie), and `[%win cord]`
245(reporting that `'X'` or `'O'` won a game.
247Lines `17` to `20` define the `move` mold, a game move. This is
248either `[%x spot]`, `[%o spot]`, or `[%z ~]` to reset the board.
250Lines `21` to `23` define the `game` mold, the game state. This
251is an `a` side, the next side to move; a `z` side, the other
252side; and `w`, which is `&` (yes) if `a` is X and `b` is O; `|`
253otherwise. (Obviously, we swap `a` and `z` on every move.)
255Line `26` introduces the library core, which contains the doors
256`bo` (for `side` bitfields) and `go` (for game state).
258Lines `27` to `28` begin the `bo` core, a door around `half`, a
261Line `29` is the `bit` gate, which tests a bit in `half`.
263Line `30` is the `off` gate, which maps from a `spot` (coordinate)
266Line `31` is the `get` gate, which produces the bit at a `spot`.
268Line `32` is the `set` gate, which produces a new side with the
269bit at a `spot` set. It works by ORing (`con`) `half` with the
270binary exponent (`bex`) of the offset (`off`) of the spot.
272Lines `33` to `35` are a victory test. It calls the
273standard `lien` function, which iterates a boolean gate over a
274list and produces `&` (yes) if any item tests as true, against a
275list of magic bitfields (expanded from a base64 constant), each
276of which must equal itself when ANDed (`dis`) with `half`.
278Lines `37` to `38` begin the `go` core, a door around a `game`.
279Again we name the sample `game`. (This is a legitimate style,
282Lines `40` to `42` begin the `do` gate, whose sample is `act`, a
283move. The product is cast to a pair of `(unit fact)` and a new
284game state, written `^game` to skip to the second binding.
286Lines `42` through `46` switch on the form of `act`. If it's an
287`%x` or `%o` move, we assert that it's the right turn, then use
288the `mo` door to apply the move. If it's a `%z` move, we clear
291Line `48` is the `nu` arm, which produces a blank game state.
293Lines `49` to `50` begin the `on` door, a door around `here`, a
294`spot`. Just as we have multiple computed attributes against the
295game state, we have multiple computed attributes (`is` and `mo`)
296against the combination of game state and coordinate.
298Lines `51` to `53` define the `is` arm, which is `&` (yes) iff
299either `a` or `z` has played `here`.
301Line `54` begins the `mo` arm, which produces (with a
302nonessential cast) a pair of `(unit fact)` and game state.
303Again we see `^game` to pull the mold, since `game` is the
304current game state in the `go` core.
306Line `55` asserts that no one has yet played `here`.
308Line `56` declares a variable `next`, as game side `a` with
311Lines `57` and `58` test if `a` has won with this move. If so,
312we produce the win fact and a blank game state.
314Line `59` produces no fact (since nothing has happened), but
315inverts the `w` turn indicator, replaces side `a` with the other
316side `z`, and replaces `z` with `next`.
318### `toe`: code, kernel style
325 =^ did/(unit fact) mag (~(do go mag) i.fed)
327 ?~(did res [u.did res])
334 ++ move $% {$x p/spot}
346 ++ bit |=(a/atom =(1 (cut 0 [a 1] haf)))
347 ++ get |=(a/spot (bit (off a)))
348 ++ off |=(a/spot (add x.a (mul 3 y.a)))
349 ++ set |=(a/spot (con haf (bex (off a))))
351 (rip 4 0wl04h0.4A0Aw.4A00s.0e070)
352 |=(a/atom =(a (dis a haf)))
358 ^- {(unit fact) game}
360 {$x *} ?>(w.mag ~(mo on p.act))
361 {$o *} ?<(w.mag ~(mo on p.act))
369 ++ is ?| (~(get bo a.mag) her)
370 (~(get bo z.mag) her)
372 ++ mo ^- {(unit fact) game}
374 =+ next=(~(set bo a.mag) her)
376 [[~ %win ?:(w.mag %x %o)] nu]
377 [~ mag(w !w.mag, a z.mag, z next)]
385++ atom @ :: just an atom
386++ axis @ :: tree address
387++ bean ? :: 0=&=yes, 1=|=no
388++ bloq @ :: blockclass
389++ char @tD :: UTF-8 byte
390++ cord @t :: text atom (UTF-8)
391++ gate $-(* *) :: general gate
392++ knot @ta :: ASCII text
394++ null $~ :: null, nil, etc
395++ time @da :: galactic time
396++ path (list knot) :: eg, fs location
397++ tang (list tank) :: error trace
399 $% {$leaf p/tape} :: printing formats
400 $: $palm :: backstep list
401 p/{p/tape q/tape r/tape s/tape} ::
404 $: $rose :: flat list
405 p/{p/tape q/tape r/tape} :: mid open close
409++ tanq :: future tank
410 $? {$~ p/(list tanq)} :: list of printables
411 {$~ $~ p/tape} :: simple string
412 (pair @tas tanq) :: captioned
414++ tape (list char) :: string as list
415++ term @tas :: ascii symbol
416++ wall (list tape) :: text lines (no \n)
417++ wain (list cord) :: text lines (no \n)
422++ tree |* a/gate :: binary tree
423 $@($~ {n/a l/(tree a) r/(tree a)}) ::
424++ trap |*(a/_* _|?(*a)) :: makes perfect sense
425++ trel |* {a/gate b/gate c/gate} :: just a triple
427++ each |* {a/gate b/gate} :: either a or b
428 $%({$& p/a} {$| p/b}) :: a default
430++ qual |* {a/gate b/gate c/gate d/gate} :: just a quadruple
432++ pair |*({a/gate b/gate} {p/a q/b}) :: just a pair
433++ quid |*({a/gate b/*} {a _b}) :: for =^
434++ quip |*({a/gate b/*} {(list a) _b}) :: for =^
435++ unit |* a/gate :: maybe
437++ list |* a/gate :: null-term list
438 $@($~ {i/a t/(list a)}) ::
439++ lone |*(a/gate p/a) :: just one thing
443++ map |* {a/gate b/gate} :: associative tree
444 $@($~ {n/{p/a q/b} l/(map a b) r/(map a b)}) ::
445++ qeu |* a/gate :: queue
446 $@($~ {n/a l/(qeu a) r/(qeu a)}) ::
447++ set |* a/gate :: set
448 $@($~ {n/a l/(set a) r/(set a)}) ::
449++ jar |*({a/gate b/gate} (map a (list b))) :: map of lists
450++ jug |*({a/gate b/gate} (map a (set b))) :: map of sets
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