aboutsummaryrefslogtreecommitdiffhomepage
path: root/plugins/micromega/mutils.ml
blob: b4c6d032bfc0cc64cba28c4f38ba513a3ae95261 (plain)
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
(************************************************************************)
(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
(* <O___,, *   INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016     *)
(*   \VV/  **************************************************************)
(*    //   *      This file is distributed under the terms of the       *)
(*         *       GNU Lesser General Public License Version 2.1        *)
(************************************************************************)
(*                                                                      *)
(* Micromega: A reflexive tactic using the Positivstellensatz           *)
(*                                                                      *)
(* ** Utility functions **                                              *)
(*                                                                      *)
(* - Modules CoqToCaml, CamlToCoq                                       *)
(* - Modules Cmp, Tag, TagSet                                           *)
(*                                                                      *)
(*  Frédéric Besson (Irisa/Inria) 2006-2008                             *)
(*                                                                      *)
(************************************************************************)

let debug = false

let rec pp_list f o l =
  match l with
    | [] -> ()
    | e::l -> f o e ; output_string o ";" ; pp_list f o l


let finally f rst =
  try
    let res = f () in
      rst () ; res
  with reraise ->
    (try rst ()
    with any -> raise reraise
    ); raise reraise

let map_option f x =
  match x with
    | None -> None
    | Some v -> Some (f v)

let from_option = function
  | None -> failwith "from_option"
  | Some v -> v

let rec try_any l x =
 match l with
  | [] -> None
  | (f,s)::l -> match f x with
     | None -> try_any l x
     | x -> x

let iteri f l =
 let rec xiter i l =
  match l with
   | [] -> ()
   | e::l -> f i e ; xiter (i+1) l in
  xiter 0 l

let all_sym_pairs f l = 
  let pair_with acc e l = List.fold_left (fun acc x -> (f e x) ::acc) acc l in

  let rec xpairs acc l = 
    match l with
      | [] -> acc
      | e::l -> xpairs (pair_with acc e l) l in
    xpairs [] l

let all_pairs f l = 
  let pair_with acc e l = List.fold_left (fun acc x -> (f e x) ::acc) acc l in

  let rec xpairs acc l = 
    match l with
      | [] -> acc
      | e::lx -> xpairs (pair_with acc e l) lx in
    xpairs [] l



let rec map3 f l1 l2 l3 =
  match l1 , l2 ,l3 with
    | [] , [] , [] -> []
    | e1::l1 , e2::l2 , e3::l3 -> (f e1 e2 e3)::(map3 f l1 l2 l3)
    |      _   -> invalid_arg "map3"

let rec is_sublist f l1 l2 =
  match l1 ,l2 with
    | [] ,_ -> true
    | e::l1', [] -> false
    | e::l1' , e'::l2' ->
	if f e e' then is_sublist f l1' l2'
	else is_sublist f l1 l2'

let list_try_find f =
  let rec try_find_f = function
    | [] -> failwith "try_find"
    | h::t -> try f h with Failure _ -> try_find_f t
  in
  try_find_f

let list_fold_right_elements f l =
  let rec aux = function
    | [] -> invalid_arg "list_fold_right_elements"
    | [x] -> x
    | x::l -> f x (aux l) in
  aux l

let interval n m =
  let rec interval_n (l,m) =
    if n > m then l else interval_n (m::l,pred m)
  in
  interval_n ([],m)

let extract pred l = 
  List.fold_left (fun (fd,sys) e -> 
		    match fd with
		    | None -> 
			begin
			  match pred e with
			  | None -> fd, e::sys
			  | Some v -> Some(v,e) , sys
			end
		    |  _   -> (fd, e::sys)
		 ) (None,[]) l

open Num
open Big_int

let ppcm x y =
 let g = gcd_big_int x y in
 let x' = div_big_int x g in
 let y' = div_big_int y g in
  mult_big_int g (mult_big_int x' y')

let denominator = function
 | Int _ | Big_int _ -> unit_big_int
 | Ratio r -> Ratio.denominator_ratio r

let numerator = function
 | Ratio r -> Ratio.numerator_ratio r
 | Int i -> Big_int.big_int_of_int i
 | Big_int i -> i

let rec ppcm_list c l =
 match l with
  | [] -> c
  | e::l -> ppcm_list (ppcm c (denominator e)) l

let rec rec_gcd_list c l  =
 match l with
  | [] -> c
  | e::l -> rec_gcd_list (gcd_big_int  c (numerator e)) l

let gcd_list l =
 let res = rec_gcd_list zero_big_int l in
  if Int.equal (compare_big_int res zero_big_int) 0
  then unit_big_int else res

let rats_to_ints l =
 let c = ppcm_list unit_big_int l in
  List.map (fun x ->  (div_big_int (mult_big_int (numerator x) c)
			(denominator x))) l

(* Nasty reordering of lists - useful to trim certificate down *)
let mapi f l =
 let rec xmapi i l =
  match l with
   | []   -> []
   | e::l ->  (f e i)::(xmapi (i+1) l) in
  xmapi 0 l

let concatMapi f l = List.rev (mapi (fun e i -> (i,f e)) l)

(* assoc_pos j [a0...an] = [j,a0....an,j+n],j+n+1 *)
let assoc_pos j l = (mapi (fun e i -> e,i+j) l, j + (List.length l))

let assoc_pos_assoc l =
 let rec xpos i l =
  match l with
   | [] -> []
   | (x,l) ::rst -> let (l',j) = assoc_pos i l in
		     (x,l')::(xpos j rst) in
  xpos 0 l

let filter_pos f l =
 (* Could sort ... take care of duplicates... *)
 let rec xfilter l =
  match l with
   | []  -> []
   | (x,e)::l ->
      if List.exists (fun ee -> List.mem ee f) (List.map snd e)
      then (x,e)::(xfilter l)
      else xfilter l in
  xfilter l

let  select_pos lpos l =
 let rec xselect i lpos l =
  match lpos with
   | [] -> []
   | j::rpos ->
      match l with
       | []   -> failwith "select_pos"
       | e::l ->
	  if Int.equal i j
	  then e:: (xselect (i+1) rpos l)
	  else xselect (i+1) lpos l in
  xselect 0 lpos l

(**
  * MODULE: Coq to Caml data-structure mappings
  *)

module CoqToCaml =
struct
 open Micromega

 let rec nat = function
  | O -> 0
  | S n -> (nat n) + 1


 let rec positive p =
  match p with
   | XH -> 1
   | XI p -> 1+ 2*(positive p)
   | XO p -> 2*(positive p)

 let n nt =
  match nt with
   | N0 -> 0
   | Npos p -> positive p

 let rec index i = (* Swap left-right ? *)
  match i with
   | XH -> 1
   | XI i -> 1+(2*(index i))
   | XO i -> 2*(index i)

 let z x =
  match x with
   | Z0 -> 0
   | Zpos p -> (positive p)
   | Zneg p -> - (positive p)

 open Big_int

 let rec positive_big_int p =
  match p with
   | XH -> unit_big_int
   | XI p -> add_int_big_int 1 (mult_int_big_int 2 (positive_big_int p))
   | XO p -> (mult_int_big_int 2 (positive_big_int p))

 let z_big_int x =
  match x with
   | Z0 -> zero_big_int
   | Zpos p -> (positive_big_int p)
   | Zneg p -> minus_big_int (positive_big_int p)

 let num x = Num.Big_int (z_big_int x)

 let q_to_num {qnum = x ; qden = y} =
  Big_int (z_big_int x) // (Big_int (z_big_int (Zpos y)))

end


(**
  * MODULE: Caml to Coq data-structure mappings
  *)

module CamlToCoq =
struct
 open Micromega

 let rec nat = function
  | 0 -> O
  | n -> S (nat (n-1))


 let rec positive n =
  if Int.equal n 1 then XH
  else if Int.equal (n land 1) 1 then XI (positive (n lsr 1))
  else  XO (positive (n lsr 1))

 let n nt =
  if nt < 0
  then assert false
  else if Int.equal nt 0 then N0
  else Npos (positive nt)

 let rec index  n =
  if Int.equal n 1 then XH
  else if Int.equal (n land 1) 1 then XI (index (n lsr 1))
  else  XO (index (n lsr 1))


 let z x =
  match compare x 0 with
   | 0 -> Z0
   | 1 -> Zpos (positive x)
   | _ -> (* this should be -1 *)
      Zneg (positive (-x))

 open Big_int

 let positive_big_int n =
  let two = big_int_of_int 2 in
  let rec _pos n =
   if eq_big_int n unit_big_int then XH
   else
    let (q,m) = quomod_big_int n two  in
     if eq_big_int unit_big_int m
     then XI (_pos q)
     else XO (_pos q) in
   _pos n

 let bigint x =
  match sign_big_int x with
   | 0 -> Z0
   | 1 -> Zpos (positive_big_int x)
   | _ -> Zneg (positive_big_int (minus_big_int x))

 let q n =
  {Micromega.qnum = bigint (numerator n) ;
   Micromega.qden = positive_big_int (denominator n)}

end

(**
  * MODULE: Comparisons on lists: by evaluating the elements in a single list,
  * between two lists given an ordering, and using a hash computation
  *)

module Cmp =
struct

 let rec compare_lexical l =
  match l with
   | [] -> 0 (* Equal *)
   | f::l ->
      let cmp = f () in
       if Int.equal cmp 0 then compare_lexical l else cmp

 let rec compare_list cmp l1 l2 =
  match l1 , l2 with
   | []  , [] -> 0
   | []  , _  -> -1
   | _   , [] -> 1
   | e1::l1 , e2::l2 ->
      let c = cmp e1 e2 in
       if Int.equal c 0 then compare_list cmp l1 l2 else c

(**
  * hash_list takes a hash function and a list, and computes an integer which
  * is the hash value of the list.
  *)
 let hash_list hash l =
  let rec _hash_list l h =
   match l with
    | []  -> h lxor (Hashtbl.hash [])
    | e::l -> _hash_list l ((hash e) lxor h) 
  in _hash_list l 0

end

(**
  * MODULE: Labels for atoms in propositional formulas. 
  * Tags are used to identify unused atoms in CNFs, and propagate them back to
  * the original formula. The translation back to Coq then ignores these
  * superfluous items, which speeds the translation up a bit.
  *)

module type Tag =
sig

  type t

  val from : int -> t
  val next : t -> t
  val pp : out_channel -> t -> unit
  val compare : t -> t -> int

end

module Tag : Tag =
struct

  type t = int

  let from i = i
  let next i = i + 1
  let pp o i = output_string o (string_of_int i)
  let compare : int -> int -> int = Int.compare

end

(**
  * MODULE: Ordered sets of tags.
  *)

module TagSet = Set.Make(Tag)

(** As for Unix.close_process, our Unix.waipid will ignore all EINTR *)

let rec waitpid_non_intr pid =
  try snd (Unix.waitpid [] pid)
  with Unix.Unix_error (Unix.EINTR, _, _) -> waitpid_non_intr pid

(**
  * Forking routine, plumbing the appropriate pipes where needed.
  *)

let command exe_path args vl =
  (* creating pipes for stdin, stdout, stderr *)
  let (stdin_read,stdin_write) = Unix.pipe ()
  and (stdout_read,stdout_write) = Unix.pipe ()
  and (stderr_read,stderr_write) = Unix.pipe () in

  (* Create the process *)
  let pid = Unix.create_process exe_path args stdin_read stdout_write stderr_write in

  (* Write the data on the stdin of the created process *)
  let outch = Unix.out_channel_of_descr stdin_write in
    output_value outch vl ;
    flush outch ;

  (* Wait for its completion *)
    let status = waitpid_non_intr pid in

      finally
        (* Recover the result *)
	(fun () ->
	  match status with
	    | Unix.WEXITED 0 ->
		let inch = Unix.in_channel_of_descr stdout_read in
		begin
                  try Marshal.from_channel inch
                  with any ->
                    failwith
                      (Printf.sprintf "command \"%s\" exited %s" exe_path
                         (Printexc.to_string any))
                end
	    | Unix.WEXITED i   ->
                failwith (Printf.sprintf "command \"%s\" exited %i" exe_path i)
	    | Unix.WSIGNALED i ->
                failwith (Printf.sprintf "command \"%s\" killed %i" exe_path i)
	    | Unix.WSTOPPED i  ->
                failwith (Printf.sprintf "command \"%s\" stopped %i" exe_path i))
        (* Cleanup  *)
	(fun () ->
	  List.iter (fun x -> try Unix.close x with any -> ())
            [stdin_read; stdin_write;
             stdout_read; stdout_write;
             stderr_read; stderr_write])

(* Local Variables: *)
(* coding: utf-8 *)
(* End: *)