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
|
/**************************************************************************/
/* */
/* 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). */
/* */
/**************************************************************************/
//@+ CheckArithOverflow = no
//@ logic integer num_of_pos{L}(integer i,integer j,int t[]) reads t[i..j] ;
/*@ axiom num_of_pos_empty{L} :
@ \forall integer i j, int t[];
@ i > j ==> num_of_pos(i,j,t) == 0;
@*/
/*@ axiom num_of_pos_true_case{L} :
@ \forall integer i j k, int t[];
@ i <= j && t[j] > 0 ==>
@ num_of_pos(i,j,t) == num_of_pos(i,j-1,t) + 1;
@*/
/*@ axiom num_of_pos_false_case{L} :
@ \forall integer i j k, int t[];
@ i <= j && ! (t[j] > 0) ==>
@ num_of_pos(i,j,t) == num_of_pos(i,j-1,t);
@*/
/*@ axiom num_of_pos_strictly_increasing{L} :
@ \forall integer i j k l, int t[];
@ j < k && k <= l && t[k] > 0 ==>
@ num_of_pos(i,j,t) < num_of_pos(i,l,t);
@*/
public class Muller {
/*@ requires t!=null;
@*/
public static int[] m(int t[]) {
int count = 0;
/*@ loop_invariant
@ 0 <= i && i <= t.length &&
@ 0 <= count && count <= i &&
@ count == num_of_pos(0,i-1,t) ;
@ decreases t.length - i;
@*/
for (int i=0 ; i < t.length; i++) if (t[i] > 0) count++;
int u[] = new int[count];
count = 0;
/*@ loop_invariant
@ 0 <= i && i <= t.length &&
@ 0 <= count && count <= i &&
@ count == num_of_pos(0,i-1,t);
@ decreases t.length - i;
@*/
for (int i=0 ; i < t.length; i++) {
if (t[i] > 0) u[count++] = t[i];
}
return u;
}
}
/*
Local Variables:
compile-command: "make Muller"
End:
*/
|
