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
|
/**************************************************************************/
/* */
/* The Why platform for program certification */
/* Copyright (C) 2002-2008 */
/* Romain BARDOU */
/* Jean-François COUCHOT */
/* Mehdi DOGGUY */
/* Jean-Christophe FILLIÂTRE */
/* Thierry HUBERT */
/* Claude MARCHÉ */
/* Yannick MOY */
/* Christine PAULIN */
/* Yann RÉGIS-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). */
/* */
/**************************************************************************/
//@ type larray
/* [create(x)] returns an array
* where each cell contains [x]
**/
//@ logic larray create(double x);
//@ logic double select(larray t, integer i);
/*@ logic larray
@ store(larray t, integer i, double x);
@*/
/*@ axiom select_store_eq:
@ \forall larray t, integer i, double x;
@ select(store(t,i,x),i) == x;
@*/
/*@ axiom select_store_neq:
@ \forall larray t, integer i j;
@ \forall double x;
@ i != j ==>
@ select(store(t,i,x),j) == select(x,j);
@*/
// public Interface for PArray
interface PArrayInterface {
//@ model larray model_array;
//@ model integer model_length;
/* @ requires n >= 0;
@ ensures
@ this.model_array == create(0.0)
@ && this.model_length == n;
@*/
// PArrayInterface(int n);
/*@ requires 0 <= i < this.model_length;
@ assigns \nothing;
@ ensures \result == select(this.model_array,i);
@*/
double get(int i);
/*@ requires 0 <= i < this.model_length;
@ assigns \nothing;
@ // ensures \fresh(\result);
@ ensures \result.model_array == store(this.model_array,i,x)
@ && \result.model_length == this.model_length;
@*/
PArrayInterface set(int i, double x);
}
abstract class Data {
abstract double get(int i);
abstract PArray set(int i, double x, PArray parent);
}
class Arr extends Data {
double table[];
//@ invariant table_non_null: table != null;
Arr(int n) {
table = new double[n];
}
double get(int i) {
return table[i];
}
PArray set(int i, double x, PArray parent) {
double old = table[i];
table[i] = x;
PArray tmp1 = new PArray(this);
Data tmp2 = new Diff(i,old,tmp1);
parent.contents = tmp2;
return tmp1;
}
public String toString() {
String s = "Arr [";
for (int i = 0; i < table.length; i++)
s += table[i] + "; ";
return (s + "]");
}
}
class Diff extends Data {
private int index;
private double value;
private PArray remaining;
//@ invariant remaining_non_null: remaining != null;
/*@ invariant diff_repr:
@ data_repr(this.remaining.model_length,store(index,value,this.remaining.model_array),this);
@*/
Diff(int i, double x, PArray rem) {
index = i;
value = x;
remaining = rem;
}
double get(int i) {
if (i == index) return value;
return remaining.get(i);
}
PArray set(int i, double x, PArray t) {
Data tmp = new Diff(i,x,t);
return new PArray(tmp);
}
public String toString() {
return "Diff " + index + ", " + value + ", " + remaining;
}
}
public class PArray implements PArrayInterface
{
protected Data contents;
//@ invariant contents_non_null: contents != null;
/*@ invariant data_repr:
@ data_repr(model_length,model_array,contents);
@*/
protected PArray(Data d) {
contents = d;
}
public PArray(int n) {
this(new Arr(n));
}
public double get(int i) {
return contents.get(i);
}
public PArray set(int i, double x) {
return contents.set(i,x,this);
}
public String toString() {
return ("-> " + contents);
}
public static void main(String argv[]) {
PArray t1 = new PArray(4);
PArray t2 = t1.set(0,2.2);
PArray t3 = t2.set(1,3.3);
System.out.println("t1 = " + t1);
System.out.println("t2 = " + t2);
System.out.println("t3 = " + t3);
}
}
/*@ predicate data_repr(integer model_length,
@ larray model_array, Data contents);
@*/
/*@ predicate repr(integer model_length,
@ larray model_array, PArray p);
@*/
/*@ axiom arr_repr :
@ \forall integer model_length, larray model_array, Arr a ;
@ data_repr(model_length, model_array,a)
@ <==>
@ model_length == a.table.length &&
@ \forall integer i;
@ 0 <= i < a.table.length ==> a.table[i] == select(model_array,i) ;
@*/
/*@ axiom diff_repr_1 :
@ \forall integer model_length, larray model_array, Diff d;
@ \forall integer i, double x;
@ repr(model_length, model_array, d.remaining) &&
@ i == d.index && x == d.value
@ ==>
@ data_repr(model_length, store(i,x,model_array),d) ;
@*/
/*@ axiom diff_repr_2 :
@ \forall integer model_length, larray model_array, Diff d ;
@ data_repr(model_length, model_array, d) &&
@ \exists larray a;
@ model_array == store(d.index,d.value,a)
@ &&
@ repr(model_length, a, d.remaining) ;
@*/
|
