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/**************************************************************************/
/* */
/* 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). */
/* */
/**************************************************************************/
//@ lemma mean1 : (\forall integer x y ; x <= y ==> x <= (x + y) / 2) ;
//@ lemma mean2 : (\forall integer x y ; x < y ==> (x + y) / 2 < y) ;
//@ type intset ;
//@ predicate In(int n, intset s) ;
//@ logic intset emptyset() ;
//@ logic intset union(intset s1, intset s2) ;
//@ logic intset singleton(int n) ;
/*@ axiom union_empty_left :
@ \forall intset s ; union(emptyset(),s) == s;
@*/
/*@ axiom In_emptyset :
@ \forall int n ; ! In(n,emptyset()) ;
@*/
/*@ axiom In_singleton :
@ \forall int n k ;
@ In(n,singleton(k)) <==> n==k ;
@*/
/*@ axiom In_union :
@ \forall intset s1 s2, int n ;
@ In(n,union(s1,s2)) <==> In(n,s1) || In(n,s2) ;
@*/
/*@ axiom intset_ext :
@ \forall intset s1 s2;
@ (\forall int n ; In(n,s1) <==> In(n,s2)) ==> s1==s2 ;
@*/
/*@ predicate array_models(intset s, int t[], integer i, integer j) {
@ t != null &&
@ 0 <= i && j < t.length &&
@ (\forall int n; In(n,s) <==>
@ (\exists int k; i <= k <= j && n==t[k]))
@ }
@*/
/*@ predicate IntSetModelField_models(intset s, IntSetModelField i) {
@ i != null &&
@ array_models(s,i.t,0,i.size-1)
@ }
@*/
public class IntSetModelField {
int size;
int t[];
/*@ invariant private_inv:
@ t != null && 0 <= size <= t.length &&
@ (\forall integer i j; 0 <= i <= j < size ==> t[i] <= t[j]);
@*/
//@ model intset my_model;
//@ invariant repr_inv: IntSetModelField_models(this.my_model,this);
/*@ assigns my_model;
@ ensures my_model == emptyset();
@*/
IntSetModelField () {
t = new int[10];
size = 0;
}
/*@ assigns \nothing;
@ ensures
@ 0 <= \result <= size &&
@ (\forall integer i; 0 <= i < \result ==> t[i] < n) &&
@ (\forall integer i; \result <= i < size ==> t[i] >= n) ;
@*/
public int index(int n) {
int a = 0, b = size, m;
/*@ loop_invariant
@ 0 <= a <= b <= size &&
@ (\forall integer i; 0 <= i < a ==> t[i] < n) &&
@ (\forall integer i; b <= i < size ==> t[i] >= n) ;
@ decreases b-a;
@*/
while (a<b) {
m = (a+b)/2;
if (t[m] < n) a=m+1; else b=m;
}
return a;
}
/*@ assigns \nothing;
@ ensures \result == true <==> In(n,my_model);
@*/
public boolean mem(int n) {
int i = index(n);
return (i < size && t[i] == n);
}
/* add with intermediate annotations for automatic
* proof with simplify
*/
/*@ assigns t,size, my_model; // t[..], syntax error ?
@ ensures my_model == union(\old(my_model),singleton(n));
@*/
public void add(int n) {
int i = index(n);
if (i < size && t[i] == n) return;
/* @ // assigns t; // ,t[*]; syntax error ?
ensures (\forall int j; 0 <= j && j < i; t[j]==\old(t[j]))
&& (\forall int j; i+1 <= j && j < size + 1; t[j]==\old(t[j-1]))
&& (\forall int j; i <= j && j < size; \old(t[j])==t[j+1])
&& t !=null && t[i]==n && size < t.length && t instanceof int[];
*/
{if (size < t.length) {
copy(t,t,i,size-1,i+1);
}
else {
int old[] = t;
t = new int[2*size+1];
copy(old,t,0,i-1,0);
copy(old,t,i,size-1,i+1);
}
t[i] = n;};
size++;
}
/*@ ensures \result == true;
@*/
public static boolean test() {
IntSetModelField s = new IntSetModelField();
s.add(1);
s.add(2);
//@ assert s.my_model == union(singleton(1),singleton(2));
return s.mem(1);
}
/*
copy(src,dest,a,b,c) copies src[a..b] to dest[c..c+b-a]
if src and dest are the same, c is assumed greater than or equal to a.
*/
/*@ requires src != null && dest != null &&
@ 0 <= a && a-1 <= b < src.length && 0 <= c &&
@ c+b-a < dest.length && (dest == src ==> c >= a);
@ assigns dest[c..c+b-a];
@ ensures \forall integer i; c <= i <= c+b-a ==> dest[i] == \old(src[i+a-c]);
@*/
public static void copy(int src[], int dest[],int a, int b, int c) {
/*@ loop_invariant
@ a-1 <= j <= b &&
@ \forall integer i; j < i <= b ==> dest[i+c-a] == \old(src[i]) &&
@ \forall integer i; c <= i <= j+c-a ==> dest[i] == \old(dest[i]);
@ decreases j;
@*/
for (int j = b; j >= a; j--) {
dest[j+c-a] = src[j];
}
}
}
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