package dunolint-lib

  1. Overview
  2. Docs

Source file blang.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
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
(* The MIT License

   Copyright (c) 2008--2024 Jane Street Group, LLC
   <opensource-contacts@janestreet.com>

   Permission is hereby granted, free of charge, to any person obtaining a copy
   of this software and associated documentation files (the "Software"), to deal
   in the Software without restriction, including without limitation the rights
   to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
   copies of the Software, and to permit persons to whom the Software is
   furnished to do so, subject to the following conditions:

   The above copyright notice and this permission notice shall be included in
   all copies or substantial portions of the Software.

   THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
   IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
   FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
   AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
   LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
   OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
   SOFTWARE. *)

(* The module [T] serves to enforce the invariant that all Blang.t values are in
   a normal form whereby boolean constants True and False only appear as the
   topmost constructor -- in any other position they are simplified away using
   laws of boolean algebra.

   We also enforce that nested [And]s and [Or]s each lean to the right so that
   [eval] doesn't need so much stack space as it would if they leaned to the
   left. Thought experiment: compare how [eval] works on right-leaning
   [And (a, And (b, And (c, d)))] versus left-leaning
   [And (And (And (a, b), c), d)]. The former is the best case and is enforced.

   Note: this file deviates from the usual pattern of modules with Stable
   interfaces in that the Stable sub-module is not the first thing to be defined
   in the module. The reason for this deviation is so that one can convince
   oneself of the aforementioned invariant after reading only this small amount
   of code. After defining T we then immediately define its Stable interface. *)
module T : sig
  type +'a t = private
    | True
    | False
    | And of 'a t * 'a t
    | Or of 'a t * 'a t
    | Not of 'a t
    | If of 'a t * 'a t * 'a t
    | Base of 'a
  [@@deriving compare, equal, hash]

  val invariant : 'a t -> unit
  val true_ : 'a t
  val false_ : 'a t
  val not_ : 'a t -> 'a t
  val andalso : 'a t -> 'a t -> 'a t
  val orelse : 'a t -> 'a t -> 'a t
  val if_ : 'a t -> 'a t -> 'a t -> 'a t
  val base : 'a -> 'a t
end = struct
  type +'a t =
    | True
    | False
    | And of 'a t * 'a t
    | Or of 'a t * 'a t
    | Not of 'a t
    | If of 'a t * 'a t * 'a t
    | Base of 'a
  [@@deriving compare, equal, hash]

  let invariant =
    let subterms = function
      | True | False | Base _ -> []
      | Not t1 -> [ t1 ]
      | And (t1, t2) | Or (t1, t2) -> [ t1; t2 ]
      | If (t1, t2, t3) -> [ t1; t2; t3 ]
    in
    let rec contains_no_constants = function
      | True | False -> assert false
      | t -> List.iter ~f:contains_no_constants (subterms t)
    in
    fun t -> List.iter ~f:contains_no_constants (subterms t)
  ;;

  let true_ = True
  let false_ = False
  let base v = Base v

  let not_ = function
    | True -> False
    | False -> True
    | Not t -> t
    | t -> Not t
  ;;

  let rec andalso t1 t2 =
    match t1, t2 with
    | _, False | False, _ -> False
    | other, True | True, other -> other
    | And (t1a, t1b), _ ->
      (* nested [And]s lean right -- see comment above *)
      And (t1a, andalso t1b t2)
    | _ -> And (t1, t2)
  ;;

  let rec orelse t1 t2 =
    match t1, t2 with
    | _, True | True, _ -> True
    | other, False | False, other -> other
    | Or (t1a, t1b), _ ->
      (* nested [Or]s lean right -- see comment above *)
      Or (t1a, orelse t1b t2)
    | _ -> Or (t1, t2)
  ;;

  let if_ a b c =
    match a with
    | True -> b
    | False -> c
    | _ ->
      (match b, c with
       | True, _ -> orelse a c
       | _, False -> andalso a b
       | _, True -> orelse (not_ a) b
       | False, _ -> andalso (not_ a) c
       | _ -> If (a, b, c))
  ;;
end

module Raw = struct
  type 'a t = 'a T.t = private
    | True
    | False
    | And of 'a t * 'a t
    | Or of 'a t * 'a t
    | Not of 'a t
    | If of 'a t * 'a t * 'a t
    | Base of 'a
  [@@deriving sexp_of]
end

include T

module Stable = struct
  module V1 : sig
    (* THIS TYPE AND ITS SERIALIZATIONS SHOULD NEVER BE CHANGED - PLEASE SPEAK
       WITH ANOTHER DEVELOPER IF YOU NEED MORE DETAIL *)

    type 'a t = 'a T.t = private
      | True
      | False
      | And of 'a t * 'a t
      | Or of 'a t * 'a t
      | Not of 'a t
      | If of 'a t * 'a t * 'a t
      | Base of 'a
    [@@deriving compare, equal, hash, sexp]

    (* the remainder of this signature consists of functions used in the
       definitions of sexp conversions that are also useful more generally *)

    val and_ : 'a t list -> 'a t
    val or_ : 'a t list -> 'a t
    val gather_conjuncts : 'a t -> 'a t list
    val gather_disjuncts : 'a t -> 'a t list
  end = struct
    type 'a t = 'a T.t = private
      | True
      | False
      | And of 'a t * 'a t
      | Or of 'a t * 'a t
      | Not of 'a t
      | If of 'a t * 'a t * 'a t
      | Base of 'a

    include (
      T :
        sig
          type 'a t [@@deriving compare, equal, hash]
        end
        with type 'a t := 'a t)

    type sexp = Sexp.t =
      | Atom of string
      | List of sexp list

    (* cheap import *)

    (* flatten out nested and's *)
    let gather_conjuncts t =
      let rec loop acc = function
        | True :: ts -> loop acc ts
        | And (t1, t2) :: ts -> loop acc (t1 :: t2 :: ts)
        | t :: ts -> loop (t :: acc) ts
        | [] -> List.rev acc
      in
      loop [] [ t ]
    ;;

    (* flatten out nested or's *)
    let gather_disjuncts t =
      let rec loop acc = function
        | False :: ts -> loop acc ts
        | Or (t1, t2) :: ts -> loop acc (t1 :: t2 :: ts)
        | t :: ts -> loop (t :: acc) ts
        | [] -> List.rev acc
      in
      loop [] [ t ]
    ;;

    (* [and_] and [or_] use [fold_right] instead of [fold_left] to avoid
       quadratic behavior with [andalso] or [orelse], respectively. *)
    let and_ ts = List.fold_right ts ~init:true_ ~f:andalso
    let or_ ts = List.fold_right ts ~init:false_ ~f:orelse
    let of_sexp_error str sexp = raise_s [%sexp (str : string), (sexp : Sexp.t)]

    let unary name args sexp =
      match args with
      | [ x ] -> x
      | _ ->
        let n = List.length args in
        of_sexp_error (Printf.sprintf "%s expects one argument, %d found" name n) sexp
    ;;

    let ternary name args sexp =
      match args with
      | [ x; y; z ] -> x, y, z
      | _ ->
        let n = List.length args in
        of_sexp_error (Printf.sprintf "%s expects three arguments, %d found" name n) sexp
    ;;

    let sexp_of_t sexp_of_value t =
      let rec aux t =
        match t with
        | Base x -> sexp_of_value x
        | True -> Atom "true"
        | False -> Atom "false"
        | Not t -> List [ Atom "not"; aux t ]
        | If (t1, t2, t3) -> List [ Atom "if"; aux t1; aux t2; aux t3 ]
        | And _ as t ->
          let ts = gather_conjuncts t in
          List (Atom "and" :: List.map ~f:aux ts)
        | Or _ as t ->
          let ts = gather_disjuncts t in
          List (Atom "or" :: List.map ~f:aux ts)
      in
      aux t
    ;;

    let t_of_sexp base_of_sexp sexp =
      let base sexp = base (base_of_sexp sexp) in
      let rec aux sexp =
        match sexp with
        | Atom kw ->
          (match String.lowercase kw with
           | "true" -> true_
           | "false" -> false_
           | _ -> base sexp)
        | List (Atom kw :: args) ->
          (match String.lowercase kw with
           | "and" -> and_ (List.map ~f:aux args)
           | "or" -> or_ (List.map ~f:aux args)
           | "not" -> not_ (aux (unary "not" args sexp))
           | "if" ->
             let x, y, z = ternary "if" args sexp in
             if_ (aux x) (aux y) (aux z)
           | _ -> base sexp)
        | _ -> base sexp
      in
      aux sexp
    ;;
  end
end

include (Stable.V1 : module type of Stable.V1 with type 'a t := 'a t)

let constant b = if b then true_ else false_

module type Constructors = sig
  val base : 'a -> 'a t
  val true_ : _ t
  val false_ : _ t
  val constant : bool -> _ t
  val not_ : 'a t -> 'a t
  val and_ : 'a t list -> 'a t
  val or_ : 'a t list -> 'a t
  val if_ : 'a t -> 'a t -> 'a t -> 'a t
end

module O = struct
  include T

  let not = not_
  let and_ = and_
  let or_ = or_
  let constant = constant
  let ( && ) = andalso
  let ( || ) = orelse
  let ( ==> ) a b = (not a) || b
end

let constant_value = function
  | True -> Some true
  | False -> Some false
  | _ -> None
;;

(* [values t] lists the base predicates in [t] from left to right *)
let values t =
  let rec loop acc = function
    | Base v :: ts -> loop (v :: acc) ts
    | True :: ts -> loop acc ts
    | False :: ts -> loop acc ts
    | Not t1 :: ts -> loop acc (t1 :: ts)
    | And (t1, t2) :: ts -> loop acc (t1 :: t2 :: ts)
    | Or (t1, t2) :: ts -> loop acc (t1 :: t2 :: ts)
    | If (t1, t2, t3) :: ts -> loop acc (t1 :: t2 :: t3 :: ts)
    | [] -> List.rev acc
  in
  loop [] [ t ]
;;

module C = Container.Make (struct
    type 'a t = 'a T.t

    let fold t ~init ~f =
      let rec loop acc t pending =
        match t with
        | Base a -> next (f acc a) pending
        | True | False -> next acc pending
        | Not t -> loop acc t pending
        | And (t1, t2) | Or (t1, t2) -> loop acc t1 (t2 :: pending)
        | If (t1, t2, t3) -> loop acc t1 (t2 :: t3 :: pending)
      and next acc = function
        | [] -> acc
        | t :: ts -> loop acc t ts
      in
      (loop init t [] [@nontail])
    ;;

    (* Don't allocate *)
    let rec iter t ~f =
      match t with
      | Base a -> f a
      | True | False -> ()
      | Not t -> iter t ~f
      | And (t1, t2) | Or (t1, t2) ->
        iter t1 ~f;
        iter t2 ~f
      | If (t1, t2, t3) ->
        iter t1 ~f;
        iter t2 ~f;
        iter t3 ~f
    ;;

    let iter = `Custom iter
    let length = `Define_using_fold
  end)

let count = C.count
let sum = C.sum
let exists = C.exists
let find = C.find
let find_map = C.find_map
let fold = C.fold
let for_all = C.for_all
let is_empty = C.is_empty
let iter = C.iter
let length = C.length
let mem = C.mem
let to_array = C.to_array
let to_list = C.to_list
let min_elt = C.min_elt
let max_elt = C.max_elt
let fold_result = C.fold_result
let fold_until = C.fold_until

let rec bind t ~f:k =
  match t with
  | Base v -> k v
  | True -> true_
  | False -> false_
  | Not t1 -> not_ (bind t1 ~f:k)
  (* Unfortunately we need to duplicate some of the short-circuiting from
     [andalso] and friends here. In principle we could do something involving
     [Lazy.t] but the overhead probably wouldn't be worth it. *)
  | And (t1, t2) ->
    (match bind t1 ~f:k with
     | False -> false_
     | other -> andalso other (bind t2 ~f:k))
  | Or (t1, t2) ->
    (match bind t1 ~f:k with
     | True -> true_
     | other -> orelse other (bind t2 ~f:k))
  | If (t1, t2, t3) ->
    (match bind t1 ~f:k with
     | True -> bind t2 ~f:k
     | False -> bind t3 ~f:k
     | other -> if_ other (bind t2 ~f:k) (bind t3 ~f:k))
;;

(* semantics *)

let rec eval t base_eval =
  match t with
  | True -> true
  | False -> false
  | And (t1, t2) -> eval t1 base_eval && eval t2 base_eval
  | Or (t1, t2) -> eval t1 base_eval || eval t2 base_eval
  | Not t -> not (eval t base_eval)
  | If (t1, t2, t3) -> if eval t1 base_eval then eval t2 base_eval else eval t3 base_eval
  | Base x -> base_eval x
;;

let specialize t f =
  bind t ~f:(fun v ->
    match f v with
    | `Known c -> constant c
    | `Unknown -> base v)
  [@nontail]
;;

let eval_set ~universe:all set_of_base t =
  let rec aux (b : _ t) =
    match b with
    | True -> force all
    | False -> Set.Using_comparator.empty ~comparator:(Set.comparator (force all))
    | And (a, b) -> Set.inter (aux a) (aux b)
    | Or (a, b) -> Set.union (aux a) (aux b)
    | Not a -> Set.diff (force all) (aux a)
    | Base a -> set_of_base a
    | If (cond, a, b) ->
      let cond = aux cond in
      Set.union (Set.inter cond (aux a)) (Set.inter (Set.diff (force all) cond) (aux b))
  in
  (aux t [@nontail])
;;

include Monad.Make (struct
    type 'a t = 'a T.t

    let return = base
    let bind = bind
    let map = `Define_using_bind
  end)

module type Monadic = sig
  module M : Monad.S

  val map : 'a t -> f:('a -> 'b M.t) -> 'b t M.t
  val bind : 'a t -> f:('a -> 'b t M.t) -> 'b t M.t
  val eval : 'a t -> f:('a -> bool M.t) -> bool M.t
end

module For_monad (M : Monad.S) : Monadic with module M := M = struct
  open M.Monad_infix

  let rec bind t ~f =
    match t with
    | Base x -> f x
    | True -> M.return true_
    | False -> M.return false_
    | And (a, b) ->
      bind a ~f
      >>= (function
       | False -> M.return false_
       | True -> bind b ~f
       | a -> bind b ~f >>| fun b -> andalso a b)
    | Or (a, b) ->
      bind a ~f
      >>= (function
       | True -> M.return true_
       | False -> bind b ~f
       | a -> bind b ~f >>| fun b -> orelse a b)
    | Not a -> bind a ~f >>| not_
    | If (a, b, c) ->
      bind a ~f
      >>= (function
       | True -> bind b ~f
       | False -> bind c ~f
       | a -> bind b ~f >>= fun b -> bind c ~f >>| fun c -> if_ a b c)
  ;;

  let map t ~f = bind t ~f:(fun x -> f x >>| base)

  let eval t ~f =
    bind t ~f:(fun x ->
      f x
      >>| function
      | true -> true_
      | false -> false_)
    >>| fun t -> eval t Nothing.unreachable_code
  ;;
end
OCaml

Innovation. Community. Security.