package fmlib_std

  1. Overview
  2. Docs

Source file array.ml

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
include Stdlib.Array


type 'a t = 'a array

let is_empty (xs: 'a t): bool =
    length xs = 0


let valid_index (i: int) (xs: 'a t): bool =
    0 <= i && i < length xs


let has_some (xs: 'a t): bool =
    0 < length xs


let first (xs: 'a t): 'a =
    assert (has_some xs);
    get xs 0


let last (xs: 'a t): 't =
    let len = length xs in
    assert (0 < len);
    get xs (len - 1)



let foldi_left (f: 'a -> int -> 'b -> 'a) (start: 'a) (xs: 'b t): 'a =
    fold_left
        (fun (start, idx) e -> f start idx e, idx + 1)
        (start, 0)
        xs
    |>
    fst


let push (x: 'a) (xs: 'a array): 'a array =
    let len = length xs in
    let xs_new = make (len + 1) x in
    blit xs 0 xs_new 0 len;
    xs_new


let push_front (x: 'a) (xs: 'a array): 'a array =
    let len = length xs in
    let xs_new = make (len + 1) x in
    blit xs 0 xs_new 1 len;
    xs_new


let insert (i: int) (x: 'a) (xs: 'a array): 'a array =
    assert (0 <= i);
    assert (i <= length xs);
    (* 0 1 ... (i-1)   i ... (len-1)
                     ^ insert here
    *)
    let len = length xs in
    let arr = make (len + 1) x in
    blit xs 0 arr 0 i;
    blit xs i arr (i + 1) (len - i);
    arr


let replace (i: int) (x: 'a) (xs: 'a array): 'a array =
    assert (0 <= i);
    assert (i < length xs);
    (* 0 1 ... i ... (len-1)
               ^ replace
    *)
    if get xs i == x then
        xs
    else begin
        let arr = copy xs in
        set arr i x;
        arr
    end



let remove (i: int) (xs: 'a array): 'a array =
    assert (0 <= i);
    assert (i < length xs);
    (* 0 1 ... i  (i + 1) ... (len-1)
               ^ remove
    *)
    let len = length xs in
    assert (0 < len);
    let arr = make (len - 1) (get xs 0) in
    blit xs 0 arr 0 i;
    blit xs (i + 1) arr i (len - (i + 1));
    arr


let remove_first (xs: 'a array): 'a array =
    let len = length xs in
    assert (0 < len);
    sub xs 1 (len - 1)



let remove_last (xs: 'a array): 'a array =
    let len = length xs in
    assert (0 < len);
    sub xs 0 (len - 1)



let find (p: 'a -> bool) (arr: 'a array): int option =
    let len = length arr
    in
    let rec find_from i =
        if i = len then
            None
        else if p (get arr i) then
            Some i
        else
            find_from (i + 1)
    in
    find_from 0


let binsearch
        (compare: 'key -> 'key -> int)
        (key_of: 'a -> 'key)
        (key: 'key)
        (arr: 'a array)
    : int * bool =
    (* Search the position of [key] in [arr] which is sorted without
       duplicates.

        Result: i, exact_flag with [key <= project arr.(i)]

        If [exact_flag] is set, the key in position [i] is exactly [key],
        otherwise the key in position [i] is strictly greater than [key].

        Corner case: [i = length arr, exact_flag = false]. This corresponds to a
        fictitious key of [+ infinity] at position [length arr].

        Precondition:
            The array must be sorted and does not contain duplicates.
    *)
    let len = length arr
    in
    if len = 0 then
        len, false
    else if len = 1 then
        let cmp = compare key (get arr 0 |> key_of) in
        if cmp <= 0 then
            0, cmp = 0
        else
            len, false
    else
        let rec search lower upper =
            (* Invariant:

                0 <= lower < upper < len
                arr.(lower) < key < arr.(upper)
            *)
            if lower + 1 = upper then
                upper, false
            else
                let mid = lower + (upper - lower) / 2 in
                assert (lower < mid);
                assert (mid < upper);
                let cmp = compare key (get arr mid |> key_of) in
                if cmp = 0 then
                    mid, true
                else if cmp < 0 then
                    search lower mid
                else
                    search mid upper
        in
        let lower, upper = 0, len - 1 in
        let cmp = compare key (get arr lower |> key_of) in
        if cmp <= 0 then
            (* key is less or equal the first element *)
            lower, cmp = 0
        else
            (* key is greater than the first element *)
            let cmp = compare key (get arr upper |> key_of) in
            if cmp < 0 then
                (* invariant for [search] satisfied. *)
                search lower upper
            else if cmp = 0 then
                (* exact match with the last element *)
                upper, true
            else
                (* key is greater than all elements *)
                len, false






module Map (Key: Interfaces.SORTABLE) =
struct
    type key = Key.t

    type 'a t = (Key.t * 'a) array


    let cardinal (map: 'a t): int =
        length map


    let is_empty (map: 'a t): bool =
        cardinal map = 0


    let bindings (map: 'a t): (Key.t * 'a) list =
        to_list map


    let fold_left (f: 'a -> Key.t -> 'b -> 'a) (start: 'a) (map: 'b t): 'a =
        Stdlib.Array.fold_left
            (fun a (key, value) -> f a key value)
            start
            map

    let fold_right (f: 'a -> Key.t -> 'b -> 'a) (start: 'a) (map: 'b t) =
        Stdlib.Array.fold_right
            (fun (key, value) result -> f result key value)
            map
            start


    let index_of (key: Key.t) (map: 'a t): int option =
        let len = length map in
        let i, exact = binsearch Key.compare fst key map in
        if i = len || not exact then
            None
        else
            Some i

    let pair (i: int) (map: 'a t): Key.t * 'a =
        assert (i < cardinal map);
        get map i


    let find_opt (key: Key.t) (map: 'a t): 'a option =
        Option.map
            (fun i -> snd (get map i))
            (index_of key map)


    let mem (key: Key.t) (map: 'a t): bool =
        index_of key map <> None


    let empty: 'a t =
        [||]


    let singleton (key: Key.t) (value: 'a): 'a t =
        [| key, value |]



    let add (key: Key.t) (value: 'a) (map: 'a t): 'a t =
        let i,exact = binsearch Key.compare fst key map in
        if exact then
            replace i (key, value) map
        else
            insert i (key, value) map



    let update (key: Key.t) (f: 'a option -> 'a option) (map: 'a t): 'a t =
        let i, exact = binsearch Key.compare fst key map in
        if exact then
            match f (Some (get map i |> snd)) with
            | None ->
                remove i map
            | Some value ->
                replace i (key, value) map
        else
            match f None with
            | None ->
                map
            | Some value ->
                insert i (key, value) map


    let remove (key: Key.t) (map: 'a t): 'a t =
        let i, exact = binsearch Key.compare fst key map in
        if exact then
            remove i map
        else
            map
end





module Set (Key: Interfaces.SORTABLE) =
struct
    module M =  Map (Key)

    type item = Key.t

    type t = unit M.t

    let cardinal (set: t): int =
        M.cardinal set


    let is_empty = M.is_empty


    let fold_left (f: 'a -> Key.t -> 'a) (start: 'a) (set: t): 'a =
        M.fold_left
            (fun res key _ -> f res key)
            start
            set


    let fold_right (f: 'a -> Key.t -> 'a) (start: 'a) (set: t): 'a =
        M.fold_right
            (fun res key _ -> f res key)
            start
            set


    let elements (set: t): Key.t list =
        fold_right
            (fun lst key -> key :: lst)
            []
            set


    let element (i: int) (set: t): Key.t =
        assert (0 <= i);
        assert (i < cardinal set);
        M.pair i set |> fst


    let index_of = M.index_of


    let empty = M.empty


    let singleton (e: Key.t): t =
        M.singleton e ()


    let mem = M.mem


    let add (e: Key.t) (set: t): t =
        M.add e () set


    let remove = M.remove
end










(* Unit Tests
 * ==========
 *)


(* Binary search *)
let%test _ =
    binsearch Int.compare Fun.id 100 [||] = (0, false)



let%test _ =
    binsearch Int.compare Fun.id 99 [|100|] = (0, false)



let%test _ =
    binsearch Int.compare Fun.id 100 [|100|] = (0, true)



let%test _ =
    binsearch Int.compare Fun.id 101 [|100|] = (1, false)





(* Set *)
module SetInt = Set (Int)

let insert_downward (lower: int) (beyond: int) (set: SetInt.t): SetInt.t =
    let rec insert i set =
        if i = lower then
            set
        else
            let i = i - 1 in
            insert i (SetInt.add i set)
    in
    insert beyond set

let insert_upward (lower: int) (beyond: int) (set: SetInt.t): SetInt.t =
    let rec insert i set =
        if i = beyond then
            set
        else
            insert (i + 1) (SetInt.add i set)
    in
    insert lower set



let%test _ =
    insert_upward 0 3 SetInt.empty = [|0,(); 1,(); 2,()|]


let%test _ =
    insert_downward 0 3 SetInt.empty = [|0,(); 1,(); 2,()|]


let%test _ =
    insert_downward 0 3 SetInt.empty |> SetInt.remove 1 = [|0,(); 2,()|]


let%test _ =
    insert_downward 0 3 SetInt.empty  |> SetInt.remove 4 = [|0,(); 1,(); 2,()|]


let%test _ =
    (insert_upward 0 3 SetInt.empty |> insert_downward 0 3)
    =
    [|0,(); 1,(); 2,()|]


let%test _ =
    (insert_upward 0 3 SetInt.empty |> insert_downward 3 6)
    =
    [|0,(); 1,(); 2,(); 3,(); 4,(); 5,()|]


let%test _ =
    (insert_downward 0 3 SetInt.empty |> SetInt.remove 0)
    =
    [|1,(); 2,()|]


let%test _ =
    let set = insert_downward 0 3 SetInt.empty in
    SetInt.index_of 3 set = None


let%test _ =
    let set = insert_downward 0 3 SetInt.empty in
    SetInt.index_of 0 set = Some 0
OCaml

Innovation. Community. Security.