package mopsa

  1. Overview
  2. Docs
package mopsa
Legend:
Page
Library
Module
Module type
Parameter
Class
Class type
Source

Source file dnf.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
(****************************************************************************)
(*                                                                          *)
(* This file is part of MOPSA, a Modular Open Platform for Static Analysis. *)
(*                                                                          *)
(* Copyright (C) 2017-2019 The MOPSA Project.                               *)
(*                                                                          *)
(* This program is free software: you can redistribute it and/or modify     *)
(* it under the terms of the GNU Lesser General Public License as published *)
(* by the Free Software Foundation, either version 3 of the License, or     *)
(* (at your option) any later version.                                      *)
(*                                                                          *)
(* This program is distributed in the hope that it will be useful,          *)
(* but WITHOUT ANY WARRANTY; without even the implied warranty of           *)
(* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the            *)
(* GNU Lesser General Public License for more details.                      *)
(*                                                                          *)
(* You should have received a copy of the GNU Lesser General Public License *)
(* along with this program.  If not, see <http://www.gnu.org/licenses/>.    *)
(*                                                                          *)
(****************************************************************************)

(** Disjunctive normal form. *)

type 'a t = 'a list list


let singleton (a: 'a) : 'a t = [[a]]


let mk_true : 'a t = [[]]


let mk_false : 'a t = []

let is_true a = a = [[]]

let is_false a = a = []

let rec mk_and
    (a: 'a t) (b: 'a t) : 'a t
  =
  if a == b then a else
  if is_true a then b else
  if is_true b then a
  else
    List.fold_left
      (fun acc conj1 ->
         List.fold_left
           (fun acc conj2 ->
              let conj = conj1 @ conj2 in
              mk_or acc [conj]
           ) acc b
      ) mk_false a


and mk_or
    (a: 'a t) (b: 'a t) : 'a t
  =
  if a == b then a else
  if is_false a then b else
  if is_false b then a
  else a @ b


and mk_neg neg (a: 'a t) : 'a t =
  a |> List.fold_left (fun acc conj ->
      mk_and acc (
        conj |>
        List.fold_left (fun acc x ->
            mk_or acc (neg x)
          ) []
      )
    ) [[]]

let is_empty a = is_false a || is_true a

let map
    (f: 'a -> 'b)
    (dnf: 'a t)
    : 'b t =
  match dnf with
  | [] -> []
  | [[x]] -> [[f x]]
  | [[x]; [y]] -> [[f x]; [f y]]
  | _ ->
  List.map (List.map f) dnf

let map_conjunction
    (f:'a list -> 'b list)
    (dnf: 'a t)
  : 'b t =
  List.map (fun conj -> f conj) dnf

let rec to_cnf (dnf:'a t) : 'a list list =
  match dnf with
  | [] -> [[]]
  | conj::tl ->
    let next = to_cnf tl in
    List.fold_left
      (fun acc x ->
         List.fold_left
           (fun acc nexti -> (x::nexti) :: acc)
           acc next
      )
      [] conj

let from_cnf (cnf:'a list list) : 'a t = to_cnf cnf

let map_disjunction
    (f: 'a list -> 'b list)
    (dnf: 'a t)
  : 'b t =
  let cnf = to_cnf dnf in
  let cnf' = List.map f cnf in
  from_cnf cnf'

let iter
    (f:'a -> unit)
    (dnf:'a t)
  : unit
  =
  List.iter (List.iter f) dnf


let reduce
    (f: 'a -> 'b)
    ~(join: 'b -> 'b -> 'b)
    ~(meet: 'b -> 'b -> 'b)
    (dnf: 'a t)
  : 'b =
  let rec apply_conj = function
    | [] -> assert false
    | [e] -> f e
    | e :: tl -> meet (f e) (apply_conj tl)
  in
  let rec apply_disj = function
    | [conj] -> apply_conj conj
    | conj :: tl -> join (apply_conj conj) (apply_disj tl)
    | _ -> assert false
  in
  apply_disj dnf

let fold_reduce
    (f:'a -> 'b -> 'a * 'c)
    ~(join:'c -> 'c -> 'c)
    ~(meet:'c -> 'c -> 'c)
    (init:'a)
    (dnf:'b t) : 'a * 'c =
  match dnf with
  | [] -> assert false
  | [[x]] -> f init x
  | [[x];[y]] ->
     let acc', x = f init x in
     let acc'', y = f acc' y in
     acc'', join x y
  | _ ->
     let rec apply_conj acc = function
       | [e] -> f acc e
       | e :: tl ->
          let acc',x = f acc e in
          let acc'',y = apply_conj acc' tl in
          acc'',meet x y
       | [] -> assert false
     in
     let rec apply_disj acc = function
       | [conj] -> apply_conj acc conj
       | conj :: tl ->
          let acc',x = apply_conj acc conj in
          let acc'',y = apply_disj acc' tl in
          acc'',join x y
       | _ -> assert false
     in
     apply_disj init dnf

let reduce_conjunction
    (f: 'a list -> 'b)
    ~(join: 'b -> 'b -> 'b)
    (dnf: 'a t)
  : 'b =
  let rec apply_disj = function
    | [conj] -> f conj
    | conj :: tl -> join (f conj) (apply_disj tl)
    | _ -> assert false
  in
  apply_disj dnf

let fold_reduce_conjunction
    (f: 'a -> 'b list -> 'a * 'c)
    ~(join: 'c -> 'c -> 'c)
    (init:'a)
    (dnf: 'b t)
  : 'a * 'c =
  let rec apply_disj acc = function
    | [conj] -> f acc conj
    | conj :: tl ->
      let acc',x = f acc conj in
      let acc'',y = apply_disj acc' tl in
      acc', join x y
    | _ -> assert false
  in
  apply_disj init dnf

let reduce_disjunction
    (f: 'a list -> 'b)
    ~(meet: 'b -> 'b -> 'b)
    (dnf: 'a t)
  : 'b =
  let cnf = to_cnf dnf in
  let rec apply_conj = function
    | [disj] -> f disj
    | disj::tl -> meet (f disj) (apply_conj tl)
    | _ -> assert false
  in
  apply_conj cnf

let fold_reduce_disjunction
    (f: 'a -> 'b list -> 'a * 'c)
    ~(meet: 'c -> 'c -> 'c)
    (init:'a)
    (dnf: 'b t)
  : 'a * 'c =
  let cnf = to_cnf dnf in
  let rec apply_conj acc = function
    | [disj] -> f acc disj
    | disj::tl ->
      let acc',x = f acc disj in
      let acc'',y = apply_conj acc' tl in
      acc', meet x y
    | _ -> assert false
  in
  apply_conj init cnf

let bind
    (f: 'a -> 'b t)
    (dnf: 'a t) : 'b t =
  reduce f ~join:mk_or ~meet:mk_and dnf

let fold_bind
    (f: 'a -> 'b -> 'a * 'c t)
    (init:'a)
    (dnf: 'b t) : 'a * 'c t =
  fold_reduce f ~join:mk_or ~meet:mk_and init dnf

let bind_conjunction
    (f: 'a list -> 'b t)
    (dnf: 'a t) : 'b t =
  reduce_conjunction f ~join:mk_or dnf

let fold_bind_conjunction
    (f: 'a -> 'b list -> 'a * 'c t)
    (init:'a)
    (dnf: 'b t) : 'a * 'c t =
  fold_reduce_conjunction f ~join:mk_or init dnf

let bind_disjunction
    (f: 'a list -> 'b t)
    (dnf: 'a t) : 'b t =
  reduce_disjunction f ~meet:mk_and dnf

let fold_bind_disjunction
    (f: 'a -> 'b list -> 'a * 'c t)
    (init:'a)
    (dnf: 'b t) : 'a * 'c t =
  fold_reduce_disjunction f ~meet:mk_and init dnf

let fold
    (f: 'b -> 'a -> 'b)
    (init: 'b)
    (dnf: 'a t)
    : 'b =
  match dnf with
  | [] -> init
  | [[x]] -> f init x
  | [[x]; [y]] -> f (f init x) y
  | _ ->
     List.fold_left (List.fold_left f) init dnf


let partition (f:'a -> bool) (a:'a t) =
  let r1,r2 =
    List.fold_left
      (fun (acc1,acc2) conj ->
         let conj1,conj2 = List.partition f conj in
         let acc1' = if conj1 = [] then acc1 else mk_or acc1 [conj1] in
         let acc2' = if conj2 = [] then acc2 else mk_or acc2 [conj2] in
         acc1',acc2'
      ) (mk_false, mk_false) a in
  if is_false r1 then None,Some a else
  if is_false r2 then Some a, None
  else Some r1, Some r2

let choose (dnf: 'a t) : 'a option =
  match dnf with
  | [] | [[]] -> None
  | (hd :: _) :: _ -> Some hd
  | _ -> assert false


let to_list (dnf: 'a t) : 'a list list = dnf


let from_list (l: 'a list list) : 'a t = l


let print pp fmt (dnf:'a t) =
  let open Format in
  if is_true dnf then pp_print_string fmt "true" else
  if is_false dnf then pp_print_string fmt "false" else
  let l = to_list dnf in
  fprintf fmt "@[<hv 2>%a@]"
  (pp_print_list
     ~pp_sep:(fun fmt () -> Format.fprintf fmt " ∨@;")
     (fun fmt conj ->
        match conj with
        | [] -> ()
        | [e] -> pp fmt e
        | _ ->
          fprintf fmt "(@[<hv 2>@,%a@;@])"
            (pp_print_list
               ~pp_sep:(fun fmt () -> Format.fprintf fmt " ∧@;")
               pp
            )
            conj
     )
  )
  l


let cardinal (dnf:'a t) : int =
  List.fold_left (fun acc conj ->
      List.length conj + acc
    ) 0 dnf
OCaml

Innovation. Community. Security.

GitHub Discord Twitter Peertube RSS
About
Changelog Releases Industrial Users Academic Users Why OCaml
Ecosystem
Packages Community Events OCaml Planet Jobs
Resources
Install OCaml Get Started Platform Tools Language Manual Standard Library API Books Exercises Papers OCaml Playground Logo
Policies
Carbon Footprint Governance Privacy Code of Conduct