anil.recoil.org
My working unpac repository
1(**************************************************************************)
2(* *)
3(* OCaml *)
4(* *)
5(* Xavier Leroy, projet Cristal, INRIA Rocquencourt *)
6(* *)
7(* Copyright 1996 Institut National de Recherche en Informatique et *)
8(* en Automatique. *)
9(* *)
10(* All rights reserved. This file is distributed under the terms of *)
11(* the GNU Lesser General Public License version 2.1, with the *)
12(* special exception on linking described in the file LICENSE. *)
13(* *)
14(**************************************************************************)
15
16module type OrderedType =
17 sig
18 type t
19 val compare: t -> t -> int
20 end
21
22module type S =
23 sig
24 type key
25 type !+'a t
26 val empty: 'a t
27 val add: key -> 'a -> 'a t -> 'a t
28 val add_to_list: key -> 'a -> 'a list t -> 'a list t
29 val update: key -> ('a option -> 'a option) -> 'a t -> 'a t
30 val singleton: key -> 'a -> 'a t
31 val remove: key -> 'a t -> 'a t
32 val merge:
33 (key -> 'a option -> 'b option -> 'c option) ->
34 'a t -> 'b t -> 'c t
35 val union: (key -> 'a -> 'a -> 'a option) -> 'a t -> 'a t -> 'a t
36 val cardinal: 'a t -> int
37 val bindings: 'a t -> (key * 'a) list
38 val min_binding: 'a t -> (key * 'a)
39 val min_binding_opt: 'a t -> (key * 'a) option
40 val max_binding: 'a t -> (key * 'a)
41 val max_binding_opt: 'a t -> (key * 'a) option
42 val choose: 'a t -> (key * 'a)
43 val choose_opt: 'a t -> (key * 'a) option
44 val find: key -> 'a t -> 'a
45 val find_opt: key -> 'a t -> 'a option
46 val find_first: (key -> bool) -> 'a t -> key * 'a
47 val find_first_opt: (key -> bool) -> 'a t -> (key * 'a) option
48 val find_last: (key -> bool) -> 'a t -> key * 'a
49 val find_last_opt: (key -> bool) -> 'a t -> (key * 'a) option
50 val iter: (key -> 'a -> unit) -> 'a t -> unit
51 val fold: (key -> 'a -> 'b -> 'b) -> 'a t -> 'b -> 'b
52 val map: ('a -> 'b) -> 'a t -> 'b t
53 val mapi: (key -> 'a -> 'b) -> 'a t -> 'b t
54 val filter: (key -> 'a -> bool) -> 'a t -> 'a t
55 val filter_map: (key -> 'a -> 'b option) -> 'a t -> 'b t
56 val partition: (key -> 'a -> bool) -> 'a t -> 'a t * 'a t
57 val split: key -> 'a t -> 'a t * 'a option * 'a t
58 val is_empty: 'a t -> bool
59 val is_singleton: 'a t -> bool
60 val mem: key -> 'a t -> bool
61 val equal: ('a -> 'a -> bool) -> 'a t -> 'a t -> bool
62 val compare: ('a -> 'a -> int) -> 'a t -> 'a t -> int
63 val for_all: (key -> 'a -> bool) -> 'a t -> bool
64 val exists: (key -> 'a -> bool) -> 'a t -> bool
65 val to_list : 'a t -> (key * 'a) list
66 val of_list : (key * 'a) list -> 'a t
67 val to_seq : 'a t -> (key * 'a) Seq.t
68 val to_rev_seq : 'a t -> (key * 'a) Seq.t
69 val to_seq_from : key -> 'a t -> (key * 'a) Seq.t
70 val add_seq : (key * 'a) Seq.t -> 'a t -> 'a t
71 val of_seq : (key * 'a) Seq.t -> 'a t
72 end
73
74module Make(Ord: OrderedType) = struct
75
76 type key = Ord.t
77
78 type 'a t =
79 Empty
80 | Node of {l:'a t; v:key; d:'a; r:'a t; h:int}
81
82 let height = function
83 Empty -> 0
84 | Node {h} -> h
85
86 let create l x d r =
87 let hl = height l and hr = height r in
88 Node{l; v=x; d; r; h=(if hl >= hr then hl + 1 else hr + 1)}
89
90 let singleton x d = Node{l=Empty; v=x; d; r=Empty; h=1}
91
92 let bal l x d r =
93 let hl = match l with Empty -> 0 | Node {h} -> h in
94 let hr = match r with Empty -> 0 | Node {h} -> h in
95 if hl > hr + 2 then begin
96 match l with
97 Empty -> invalid_arg "Map.bal"
98 | Node{l=ll; v=lv; d=ld; r=lr} ->
99 if height ll >= height lr then
100 create ll lv ld (create lr x d r)
101 else begin
102 match lr with
103 Empty -> invalid_arg "Map.bal"
104 | Node{l=lrl; v=lrv; d=lrd; r=lrr}->
105 create (create ll lv ld lrl) lrv lrd (create lrr x d r)
106 end
107 end else if hr > hl + 2 then begin
108 match r with
109 Empty -> invalid_arg "Map.bal"
110 | Node{l=rl; v=rv; d=rd; r=rr} ->
111 if height rr >= height rl then
112 create (create l x d rl) rv rd rr
113 else begin
114 match rl with
115 Empty -> invalid_arg "Map.bal"
116 | Node{l=rll; v=rlv; d=rld; r=rlr} ->
117 create (create l x d rll) rlv rld (create rlr rv rd rr)
118 end
119 end else
120 Node{l; v=x; d; r; h=(if hl >= hr then hl + 1 else hr + 1)}
121
122 let empty = Empty
123
124 let is_empty = function Empty -> true | _ -> false
125
126 let is_singleton = function
127 | Node{l=Empty; r=Empty} -> true
128 | Empty | Node _ -> false
129
130 let rec add x data = function
131 Empty ->
132 Node{l=Empty; v=x; d=data; r=Empty; h=1}
133 | Node {l; v; d; r; h} as m ->
134 let c = Ord.compare x v in
135 if c = 0 then
136 if d == data then m else Node{l; v=x; d=data; r; h}
137 else if c < 0 then
138 let ll = add x data l in
139 if l == ll then m else bal ll v d r
140 else
141 let rr = add x data r in
142 if r == rr then m else bal l v d rr
143
144 let rec find x = function
145 Empty ->
146 raise Not_found
147 | Node {l; v; d; r} ->
148 let c = Ord.compare x v in
149 if c = 0 then d
150 else find x (if c < 0 then l else r)
151
152 let rec find_first_aux v0 d0 f = function
153 Empty ->
154 (v0, d0)
155 | Node {l; v; d; r} ->
156 if f v then
157 find_first_aux v d f l
158 else
159 find_first_aux v0 d0 f r
160
161 let rec find_first f = function
162 Empty ->
163 raise Not_found
164 | Node {l; v; d; r} ->
165 if f v then
166 find_first_aux v d f l
167 else
168 find_first f r
169
170 let rec find_first_opt_aux v0 d0 f = function
171 Empty ->
172 Some (v0, d0)
173 | Node {l; v; d; r} ->
174 if f v then
175 find_first_opt_aux v d f l
176 else
177 find_first_opt_aux v0 d0 f r
178
179 let rec find_first_opt f = function
180 Empty ->
181 None
182 | Node {l; v; d; r} ->
183 if f v then
184 find_first_opt_aux v d f l
185 else
186 find_first_opt f r
187
188 let rec find_last_aux v0 d0 f = function
189 Empty ->
190 (v0, d0)
191 | Node {l; v; d; r} ->
192 if f v then
193 find_last_aux v d f r
194 else
195 find_last_aux v0 d0 f l
196
197 let rec find_last f = function
198 Empty ->
199 raise Not_found
200 | Node {l; v; d; r} ->
201 if f v then
202 find_last_aux v d f r
203 else
204 find_last f l
205
206 let rec find_last_opt_aux v0 d0 f = function
207 Empty ->
208 Some (v0, d0)
209 | Node {l; v; d; r} ->
210 if f v then
211 find_last_opt_aux v d f r
212 else
213 find_last_opt_aux v0 d0 f l
214
215 let rec find_last_opt f = function
216 Empty ->
217 None
218 | Node {l; v; d; r} ->
219 if f v then
220 find_last_opt_aux v d f r
221 else
222 find_last_opt f l
223
224 let rec find_opt x = function
225 Empty ->
226 None
227 | Node {l; v; d; r} ->
228 let c = Ord.compare x v in
229 if c = 0 then Some d
230 else find_opt x (if c < 0 then l else r)
231
232 let rec mem x = function
233 Empty ->
234 false
235 | Node {l; v; r} ->
236 let c = Ord.compare x v in
237 c = 0 || mem x (if c < 0 then l else r)
238
239 let rec min_binding = function
240 Empty -> raise Not_found
241 | Node {l=Empty; v; d} -> (v, d)
242 | Node {l} -> min_binding l
243
244 let rec min_binding_opt = function
245 Empty -> None
246 | Node {l=Empty; v; d} -> Some (v, d)
247 | Node {l}-> min_binding_opt l
248
249 let rec max_binding = function
250 Empty -> raise Not_found
251 | Node {v; d; r=Empty} -> (v, d)
252 | Node {r} -> max_binding r
253
254 let rec max_binding_opt = function
255 Empty -> None
256 | Node {v; d; r=Empty} -> Some (v, d)
257 | Node {r} -> max_binding_opt r
258
259 let rec remove_min_binding = function
260 Empty -> invalid_arg "Map.remove_min_elt"
261 | Node {l=Empty; r} -> r
262 | Node {l; v; d; r} -> bal (remove_min_binding l) v d r
263
264 let merge t1 t2 =
265 match (t1, t2) with
266 (Empty, t) -> t
267 | (t, Empty) -> t
268 | (_, _) ->
269 let (x, d) = min_binding t2 in
270 bal t1 x d (remove_min_binding t2)
271
272 let rec remove x = function
273 Empty ->
274 Empty
275 | (Node {l; v; d; r} as m) ->
276 let c = Ord.compare x v in
277 if c = 0 then merge l r
278 else if c < 0 then
279 let ll = remove x l in if l == ll then m else bal ll v d r
280 else
281 let rr = remove x r in if r == rr then m else bal l v d rr
282
283 let rec update x f = function
284 Empty ->
285 begin match f None with
286 | None -> Empty
287 | Some data -> Node{l=Empty; v=x; d=data; r=Empty; h=1}
288 end
289 | Node {l; v; d; r; h} as m ->
290 let c = Ord.compare x v in
291 if c = 0 then begin
292 match f (Some d) with
293 | None -> merge l r
294 | Some data ->
295 if d == data then m else Node{l; v=x; d=data; r; h}
296 end else if c < 0 then
297 let ll = update x f l in
298 if l == ll then m else bal ll v d r
299 else
300 let rr = update x f r in
301 if r == rr then m else bal l v d rr
302
303 let add_to_list x data m =
304 let add = function None -> Some [data] | Some l -> Some (data :: l) in
305 update x add m
306
307 let rec iter f = function
308 Empty -> ()
309 | Node {l; v; d; r} ->
310 iter f l; f v d; iter f r
311
312 let rec map f = function
313 Empty ->
314 Empty
315 | Node {l; v; d; r; h} ->
316 let l' = map f l in
317 let d' = f d in
318 let r' = map f r in
319 Node{l=l'; v; d=d'; r=r'; h}
320
321 let rec mapi f = function
322 Empty ->
323 Empty
324 | Node {l; v; d; r; h} ->
325 let l' = mapi f l in
326 let d' = f v d in
327 let r' = mapi f r in
328 Node{l=l'; v; d=d'; r=r'; h}
329
330 let rec fold f m accu =
331 match m with
332 Empty -> accu
333 | Node {l; v; d; r} ->
334 fold f r (f v d (fold f l accu))
335
336 let rec for_all p = function
337 Empty -> true
338 | Node {l; v; d; r} -> p v d && for_all p l && for_all p r
339
340 let rec exists p = function
341 Empty -> false
342 | Node {l; v; d; r} -> p v d || exists p l || exists p r
343
344 (* Beware: those two functions assume that the added k is *strictly*
345 smaller (or bigger) than all the present keys in the tree; it
346 does not test for equality with the current min (or max) key.
347
348 Indeed, they are only used during the "join" operation which
349 respects this precondition.
350 *)
351
352 let rec add_min_binding k x = function
353 | Empty -> singleton k x
354 | Node {l; v; d; r} ->
355 bal (add_min_binding k x l) v d r
356
357 let rec add_max_binding k x = function
358 | Empty -> singleton k x
359 | Node {l; v; d; r} ->
360 bal l v d (add_max_binding k x r)
361
362 (* Same as create and bal, but no assumptions are made on the
363 relative heights of l and r. *)
364
365 let rec join l v d r =
366 match (l, r) with
367 (Empty, _) -> add_min_binding v d r
368 | (_, Empty) -> add_max_binding v d l
369 | (Node{l=ll; v=lv; d=ld; r=lr; h=lh},
370 Node{l=rl; v=rv; d=rd; r=rr; h=rh}) ->
371 if lh > rh + 2 then bal ll lv ld (join lr v d r) else
372 if rh > lh + 2 then bal (join l v d rl) rv rd rr else
373 create l v d r
374
375 (* Merge two trees l and r into one.
376 All elements of l must precede the elements of r.
377 No assumption on the heights of l and r. *)
378
379 let concat t1 t2 =
380 match (t1, t2) with
381 (Empty, t) -> t
382 | (t, Empty) -> t
383 | (_, _) ->
384 let (x, d) = min_binding t2 in
385 join t1 x d (remove_min_binding t2)
386
387 let concat_or_join t1 v d t2 =
388 match d with
389 | Some d -> join t1 v d t2
390 | None -> concat t1 t2
391
392 let rec split x = function
393 Empty ->
394 (Empty, None, Empty)
395 | Node {l; v; d; r} ->
396 let c = Ord.compare x v in
397 if c = 0 then (l, Some d, r)
398 else if c < 0 then
399 let (ll, pres, rl) = split x l in (ll, pres, join rl v d r)
400 else
401 let (lr, pres, rr) = split x r in (join l v d lr, pres, rr)
402
403 let rec merge f s1 s2 =
404 match (s1, s2) with
405 (Empty, Empty) -> Empty
406 | (Node {l=l1; v=v1; d=d1; r=r1; h=h1}, _) when h1 >= height s2 ->
407 let (l2, d2, r2) = split v1 s2 in
408 concat_or_join (merge f l1 l2) v1 (f v1 (Some d1) d2) (merge f r1 r2)
409 | (_, Node {l=l2; v=v2; d=d2; r=r2}) ->
410 let (l1, d1, r1) = split v2 s1 in
411 concat_or_join (merge f l1 l2) v2 (f v2 d1 (Some d2)) (merge f r1 r2)
412 | _ ->
413 assert false
414
415 let rec union f s1 s2 =
416 match (s1, s2) with
417 | (Empty, s) | (s, Empty) -> s
418 | (Node {l=l1; v=v1; d=d1; r=r1; h=h1},
419 Node {l=l2; v=v2; d=d2; r=r2; h=h2}) ->
420 if h1 >= h2 then
421 let (l2, d2, r2) = split v1 s2 in
422 let l = union f l1 l2 and r = union f r1 r2 in
423 match d2 with
424 | None -> join l v1 d1 r
425 | Some d2 -> concat_or_join l v1 (f v1 d1 d2) r
426 else
427 let (l1, d1, r1) = split v2 s1 in
428 let l = union f l1 l2 and r = union f r1 r2 in
429 match d1 with
430 | None -> join l v2 d2 r
431 | Some d1 -> concat_or_join l v2 (f v2 d1 d2) r
432
433 let rec filter p = function
434 Empty -> Empty
435 | Node {l; v; d; r} as m ->
436 (* call [p] in the expected left-to-right order *)
437 let l' = filter p l in
438 let pvd = p v d in
439 let r' = filter p r in
440 if pvd then if l==l' && r==r' then m else join l' v d r'
441 else concat l' r'
442
443 let rec filter_map f = function
444 Empty -> Empty
445 | Node {l; v; d; r} ->
446 (* call [f] in the expected left-to-right order *)
447 let l' = filter_map f l in
448 let fvd = f v d in
449 let r' = filter_map f r in
450 begin match fvd with
451 | Some d' -> join l' v d' r'
452 | None -> concat l' r'
453 end
454
455 let rec partition p = function
456 Empty -> (Empty, Empty)
457 | Node {l; v; d; r} ->
458 (* call [p] in the expected left-to-right order *)
459 let (lt, lf) = partition p l in
460 let pvd = p v d in
461 let (rt, rf) = partition p r in
462 if pvd
463 then (join lt v d rt, concat lf rf)
464 else (concat lt rt, join lf v d rf)
465
466 type 'a enumeration = End | More of key * 'a * 'a t * 'a enumeration
467
468 let rec cons_enum m e =
469 match m with
470 Empty -> e
471 | Node {l; v; d; r} -> cons_enum l (More(v, d, r, e))
472
473 let compare cmp m1 m2 =
474 let rec compare_aux e1 e2 =
475 match (e1, e2) with
476 (End, End) -> 0
477 | (End, _) -> -1
478 | (_, End) -> 1
479 | (More(v1, d1, r1, e1), More(v2, d2, r2, e2)) ->
480 let c = Ord.compare v1 v2 in
481 if c <> 0 then c else
482 let c = cmp d1 d2 in
483 if c <> 0 then c else
484 compare_aux (cons_enum r1 e1) (cons_enum r2 e2)
485 in compare_aux (cons_enum m1 End) (cons_enum m2 End)
486
487 let equal cmp m1 m2 =
488 let rec equal_aux e1 e2 =
489 match (e1, e2) with
490 (End, End) -> true
491 | (End, _) -> false
492 | (_, End) -> false
493 | (More(v1, d1, r1, e1), More(v2, d2, r2, e2)) ->
494 Ord.compare v1 v2 = 0 && cmp d1 d2 &&
495 equal_aux (cons_enum r1 e1) (cons_enum r2 e2)
496 in equal_aux (cons_enum m1 End) (cons_enum m2 End)
497
498 let rec cardinal = function
499 Empty -> 0
500 | Node {l; r} -> cardinal l + 1 + cardinal r
501
502 let rec bindings_aux accu = function
503 Empty -> accu
504 | Node {l; v; d; r} -> bindings_aux ((v, d) :: bindings_aux accu r) l
505
506 let bindings s =
507 bindings_aux [] s
508
509 let choose = min_binding
510
511 let choose_opt = min_binding_opt
512
513 let to_list = bindings
514 let of_list bs = List.fold_left (fun m (k, v) -> add k v m) empty bs
515
516 let add_seq i m =
517 Seq.fold_left (fun m (k,v) -> add k v m) m i
518
519 let of_seq i = add_seq i empty
520
521 let rec seq_of_enum_ c () = match c with
522 | End -> Seq.Nil
523 | More (k,v,t,rest) -> Seq.Cons ((k,v), seq_of_enum_ (cons_enum t rest))
524
525 let to_seq m =
526 seq_of_enum_ (cons_enum m End)
527
528 let rec snoc_enum s e =
529 match s with
530 Empty -> e
531 | Node{l; v; d; r} -> snoc_enum r (More(v, d, l, e))
532
533 let rec rev_seq_of_enum_ c () = match c with
534 | End -> Seq.Nil
535 | More (k,v,t,rest) ->
536 Seq.Cons ((k,v), rev_seq_of_enum_ (snoc_enum t rest))
537
538 let to_rev_seq c =
539 rev_seq_of_enum_ (snoc_enum c End)
540
541 let to_seq_from low m =
542 let rec aux low m c = match m with
543 | Empty -> c
544 | Node {l; v; d; r; _} ->
545 begin match Ord.compare v low with
546 | 0 -> More (v, d, r, c)
547 | n when n<0 -> aux low r c
548 | _ -> aux low l (More (v, d, r, c))
549 end
550 in
551 seq_of_enum_ (aux low m End)
552end