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
|
(**************************************************************************)
(* *)
(* The Why platform for program certification *)
(* Copyright (C) 2002-2008 *)
(* Romain BARDOU *)
(* Jean-Franois COUCHOT *)
(* Mehdi DOGGUY *)
(* Jean-Christophe FILLITRE *)
(* Thierry HUBERT *)
(* Claude MARCH *)
(* Yannick MOY *)
(* Christine PAULIN *)
(* Yann RGIS-GIANAS *)
(* Nicolas ROUSSET *)
(* Xavier URBAIN *)
(* *)
(* This software is free software; you can redistribute it and/or *)
(* modify it under the terms of the GNU General Public *)
(* License version 2, as published by the Free Software Foundation. *)
(* *)
(* This software 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 General Public License version 2 for more details *)
(* (enclosed in the file GPL). *)
(* *)
(**************************************************************************)
open Cenv
open Cast
open Clogic
open Info
open Ctypes
let binop = function
| Cast.Bbw_and -> Bbw_and
| Cast.Bbw_or -> Bbw_or
| Cast.Bbw_xor -> Bbw_xor
| Cast.Bshift_right -> Bshift_right
| Cast.Bshift_left -> Bshift_left
| _ -> assert false
let rec term_of_expr (e:texpr) =
{
term_node =
begin
match e.texpr_node with
| TEnop -> assert false
| TEconstant c -> Tconstant c
| TEstring_literal s -> assert false (*TODO*)
| TEvar (Var_info v) ->
Clogic.Tvar v
| TEvar (Fun_info f) -> assert false (*TODO*)
| TEdot (e, v) -> Tdot (term_of_expr e, v)
| TEarrow (e, v) -> Tarrow (term_of_expr e, v)
| TEarrget (e1, e2) -> Tarrget (term_of_expr e1, term_of_expr e2)
| TEseq (e1, e2) -> assert false
| TEassign (e1, e2) -> assert false (*TODO*)
| TEassign_op (e1, b, e2) -> assert false (*TODO*)
| TEunary (Cast.Uplus, e) -> Tunop (Clogic.Uplus, term_of_expr e)
| TEunary (Cast.Uminus, e) -> Tunop (Clogic.Uminus, term_of_expr e)
| TEunary (Cast.Unot, e) -> Tunop (Clogic.Unot,term_of_expr e)
| TEunary (Cast.Ustar, e) -> Tunop (Clogic.Ustar, term_of_expr e)
| TEunary (Cast.Uamp, e) -> Tunop (Clogic.Uamp, term_of_expr e)
| TEunary (Cast.Utilde, e) -> Tunop (Utilde, term_of_expr e)
| TEunary (Cast.Ufloat_of_int, e) ->
Tunop (Ufloat_of_int, term_of_expr e)
| TEunary (Cast.Ufloat_conversion, e) ->
Tunop (Ufloat_conversion, term_of_expr e)
| TEunary (Cast.Uint_of_float, e) ->
Tunop (Uint_of_float, term_of_expr e)
| TEunary (Cast.Uint_conversion, e) ->
(term_of_expr e).term_node
| TEincr (Uprefix_inc,e)| TEincr (Upostfix_inc,e) ->
Tbinop (term_of_expr e, Badd, {
term_node = Tconstant (IntConstant "1");
term_loc = Loc.dummy_position;
term_type = c_int;
})
| TEincr (Uprefix_dec,e) | TEincr (Upostfix_dec,e) ->
Tbinop (term_of_expr e, Bsub, {
term_node = Tconstant (IntConstant "1");
term_loc = Loc.dummy_position;
term_type = c_int;
})
| TEbinary (e1, Badd_pointer_int, e2) | TEbinary (e1,Badd_float _,e2)
| TEbinary (e1, Badd_int _, e2) | TEbinary (e1, Cast.Badd, e2) ->
Tbinop (term_of_expr e1, Badd, term_of_expr e2)
| TEbinary (e1, Bsub_float _, e2)| TEbinary (e1, Bsub_pointer, e2)
| TEbinary (e1, Bsub_int _, e2) | TEbinary (e1, Cast.Bsub, e2) ->
Tbinop (term_of_expr e1, Bsub, term_of_expr e2)
| TEbinary (e1, Bmul_float _, e2)
| TEbinary (e1, Bmul_int _, e2) | TEbinary (e1, Cast.Bmul, e2) ->
Tbinop (term_of_expr e1, Bmul, term_of_expr e2)
| TEbinary (e1, Bdiv_int _, e2) | TEbinary (e1, Cast.Bdiv, e2)
| TEbinary (e1, Bdiv_float _, e2) ->
Tbinop (term_of_expr e1, Bdiv, term_of_expr e2)
| TEbinary (e1, Bmod_int _, e2) | TEbinary (e1, Cast.Bmod, e2) ->
Tbinop (term_of_expr e1, Bmod, term_of_expr e2)
| TEbinary (e1, (Cast.Bbw_and | Cast.Bbw_or | Cast.Bbw_xor |
Cast.Bshift_left | Cast.Bshift_right as op), e2) ->
Tbinop (term_of_expr e1, binop op, term_of_expr e2)
| TEbinary (e1, Blt, e2) | TEbinary (e1, Bgt, e2) ->
assert false
| TEbinary (e1, Ble, e2) | TEbinary (e1, Bge, e2)->
assert false
| TEbinary (e1, Beq, e2) | TEbinary (e1, Bneq, e2) ->
assert false
| TEbinary (e1, Band, e2) | TEbinary (e1, Bor, e2)->
assert false
| TEbinary (e1, Blt_int, e2) ->
if (Ctyping.eval_const_expr e1 < Ctyping.eval_const_expr e2)
then
Tconstant (IntConstant "0")
else
Tconstant (IntConstant "1")
| TEbinary (e1, Ble_int, e2)->
if (Ctyping.eval_const_expr e1 <= Ctyping.eval_const_expr e2)
then
Tconstant (IntConstant "0")
else
Tconstant (IntConstant "1")
| TEbinary (e1, Bgt_int, e2) ->
if (Ctyping.eval_const_expr e1 < Ctyping.eval_const_expr e2)
then
Tconstant (IntConstant "0")
else
Tconstant (IntConstant "1")
| TEbinary (e1, Bge_int, e2)->
if (Ctyping.eval_const_expr e1 >= Ctyping.eval_const_expr e2)
then
Tconstant (IntConstant "0")
else
Tconstant (IntConstant "1")
| TEbinary (e1, Beq_int, e2)->
if (Ctyping.eval_const_expr e1 = Ctyping.eval_const_expr e2)
then
Tconstant (IntConstant "0")
else
Tconstant (IntConstant "1")
| TEbinary (e1, Bneq_int, e2)->
if (Ctyping.eval_const_expr e1 = Ctyping.eval_const_expr e2)
then
Tconstant (IntConstant "1")
else
Tconstant (IntConstant "0")
| TEbinary (e1, Blt_float _, e2) | TEbinary (e1, Bgt_float _, e2)->
assert false
| TEbinary (e1, Ble_float _, e2) | TEbinary (e1, Bge_float _, e2)->
assert false
| TEbinary (e1, Beq_float _, e2) | TEbinary (e1, Bneq_float _, e2) ->
assert false
| TEbinary (e1, Blt_pointer, e2) | TEbinary (e1, Bgt_pointer, e2) ->
assert false
| TEbinary (e1, Ble_pointer, e2) | TEbinary (e1, Bge_pointer, e2) ->
assert false
| TEbinary (e1, Beq_pointer, e2) | TEbinary (e1, Bneq_pointer, e2) ->
assert false
| TEcall (e, l) -> assert false
| TEcond (e1,e2,e3) ->
Tif (term_of_expr e1, term_of_expr e2, term_of_expr e3)
| TEcast ({ctype_node = Tint _},
({texpr_type = {ctype_node = Tfloat _}} as e) ) ->
Tunop (Clogic.Uint_of_float,(term_of_expr e))
| TEcast ({ctype_node = Tfloat _},
({texpr_type = {ctype_node = Tint _}} as e) ) ->
Tunop (Clogic.Ufloat_of_int,(term_of_expr e))
| TEcast (ty,e) -> Tcast (ty, term_of_expr e)
| TEsizeof _ -> assert false
| TEmalloc _ -> assert false
end;
term_loc = e.texpr_loc;
term_type = e.texpr_type;
}
let in_struct v1 v =
{ term_node = Tdot (v1, v);
term_loc = v1.term_loc;
term_type = v.var_type }
let split_decl e ((invs,inits) as acc) =
match e.node with
| Tinvariant (_,p) -> (p :: invs, inits)
| Tdecl (t, v, c) -> (invs, e :: inits)
| _ -> acc
let split_decls d = List.fold_right split_decl d ([],[])
let dummy_pred p = { pred_node = p; pred_loc = Loc.dummy_position }
let rec combine_inv = function
| [] -> dummy_pred Ptrue
| a::[] -> a
| a::l -> { a with pred_node = Pand (a, combine_inv l) }
let noattr loc ty e =
{ term_node = e;
term_type = ty;
term_loc = loc
}
let rec pop_initializer loc t i =
match i with
| [] ->{ term_node =
(match t.ctype_node with
| Tint _ | Tenum _-> Tconstant (IntConstant "0")
| Tfloat _ -> Tconstant (RealConstant "0.0")
| Tpointer _ -> let null = default_var_info "null" in
Cenv.set_var_type (Var_info null) t false;
Clogic.Tvar (null)
| _ -> assert false);
term_type = t;
term_loc = loc
},[]
| (Iexpr e)::l ->
let term = term_of_expr e in
let term =
{ term with term_node =
if t.ctype_node <> term.term_type.ctype_node then
Tcast (t,term)
else
term.term_node} in
term,l
| (Ilist [])::l -> pop_initializer loc t l
| (Ilist l)::l' ->
let e,r = pop_initializer loc t l in e,r@l'
let make_and p1 p2 = match p1.pred_node, p2.pred_node with
| Ptrue, _ -> p2
| _, Ptrue -> p1
| _ -> { p1 with pred_node = Pand (p1, p2) }
let prel (t1, r, t2) = dummy_pred (Prel (t1, r, t2))
let make_implies p1 p2 = match p2.pred_node with
| Ptrue -> { p1 with pred_node = Ptrue }
| _ -> { p1 with pred_node = Pimplies (p1, p2) }
let make_forall q p = match p.pred_node with
| Ptrue -> { p with pred_node = Ptrue }
| _ -> { p with pred_node = Pforall (q, p) }
let rec init_expr loc t lvalue initializers =
match t.ctype_node with
| Tint _ | Tfloat _ | Tpointer _ | Tenum _ ->
let x,l = pop_initializer loc t initializers in
({pred_node = Prel(lvalue,Eq,x);pred_loc = loc}, l)
| Tstruct n ->
begin match tag_type_definition n with
| TTStructUnion (Tstruct (_), fl) ->
List.fold_left
(fun (acc,init) f ->
let block, init' =
init_expr loc f.var_type
(in_struct lvalue f) init
in ({ acc with pred_node = Pand (acc, block)},init'))
(dummy_pred Ptrue,initializers) fl
| _ ->
assert false
end
| Tunion n ->
begin match tag_type_definition n with
| TTStructUnion (Tunion (_), f::_) ->
let block, init' =
init_expr loc f.var_type
(noattr loc f.var_type (Tarrow(lvalue, f)))
initializers
in (block,init')
| _ ->
assert false
end
| Tarray (_,ty,Some t) ->
begin
match initializers with
| [] ->
let i = default_var_info "counter" in
Cenv.set_var_type (Var_info i) c_int false;
let vari = { term_node = Clogic.Tvar i;
term_loc = Loc.dummy_position;
term_type = c_int;
} in
let ts = Cltyping.int_constant (Int64.to_string t) in
let ineq = make_and
(prel (Cltyping.zero, Le, vari))
(prel (vari, Lt,ts)) in
let (b,init') =
match ty.ctype_node with
| Tstruct _ | Tunion _ ->
init_expr loc ty
(noattr loc ty
(Tbinop(lvalue,Badd,vari))) initializers
| _ ->
init_expr loc ty
(noattr loc ty (Tarrget(lvalue,vari))) initializers
in
((make_forall [c_int,i] (make_implies ineq b)), init')
| _ ->
let rec init_cells i (block,init) =
if i >= t then (block,init)
else
let ts = Cltyping.int_constant (Int64.to_string i) in
let (b,init') =
match ty.ctype_node with
| Tstruct _ | Tunion _ ->
init_expr loc ty
(noattr loc ty
(Tbinop(lvalue,Badd,ts))) init
| _ ->
init_expr loc ty
(noattr loc ty (Tarrget(lvalue,ts))) init
in
init_cells (Int64.add i Int64.one)
({ block with pred_node = Pand (block,b)},init')
in
init_cells Int64.zero (dummy_pred Ptrue,initializers)
end
| Tarray (_,ty,None) -> assert false
| Tfun (_, _) -> assert false
| Tvar _ -> assert false
| Tvoid -> dummy_pred Ptrue,initializers
let rec assigns decl =
match decl with
| [] -> dummy_pred Ptrue
| {node = Tdecl (t,v,None); loc = l}::decl ->
Coptions.lprintf "initialization of %s@." v.var_name;
let declar,_ =
init_expr l t (noattr l t (Clogic.Tvar v)) [] in
{declar with pred_node = Pand (declar, assigns decl)}
| {node = Tdecl(t, v, Some c) ; loc = l }:: decl ->
Coptions.lprintf "initialization of %s@." v.var_name;
let declar,_ = init_expr l t (noattr l t (Clogic.Tvar v)) [c] in
{declar with pred_node = Pand (declar, assigns decl) }
| _ -> assert false
let invariants_initially_established_info =
default_fun_info "invariants_initially_established"
let rec reorder l =
match l with
| { node = Tdecl _ }as e ::l -> let decl,other = reorder l in
e::decl,other
| e::l -> let decl,other = reorder l in
decl,e::other
| [] -> [],[]
let user_invariants = ref false
let add_init l =
let (inv,decl) = split_decls l in
if inv = [] then user_invariants := false
else user_invariants := true;
let inv = combine_inv inv in
let init_fun =
Tfundef ({requires = Some (assigns decl);
assigns = None;
ensures = Some inv;
decreases = None},
c_void,
invariants_initially_established_info,
{st_node = TSnop;
st_break = false;
st_continue = false;
st_return = false;
st_term = true;
st_loc = Loc.dummy_position
})
in
let decl,other =
reorder ({ node = init_fun; loc = Loc.dummy_position } :: l) in
decl@other
|
