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/**************************************************************************/
/* */
/* The Why platform for program certification */
/* */
/* Copyright (C) 2002-2011 */
/* */
/* Jean-Christophe FILLIATRE, CNRS & Univ. Paris-sud 11 */
/* Claude MARCHE, INRIA & Univ. Paris-sud 11 */
/* Yannick MOY, Univ. Paris-sud 11 */
/* Romain BARDOU, Univ. Paris-sud 11 */
/* */
/* Secondary contributors: */
/* */
/* Thierry HUBERT, Univ. Paris-sud 11 (former Caduceus front-end) */
/* Nicolas ROUSSET, Univ. Paris-sud 11 (on Jessie & Krakatoa) */
/* Ali AYAD, CNRS & CEA Saclay (floating-point support) */
/* Sylvie BOLDO, INRIA (floating-point support) */
/* Jean-Francois COUCHOT, INRIA (sort encodings, hyps pruning) */
/* Mehdi DOGGUY, Univ. Paris-sud 11 (Why GUI) */
/* */
/* This software is free software; you can redistribute it and/or */
/* modify it under the terms of the GNU Lesser General Public */
/* License version 2.1, with the special exception on linking */
/* described in file LICENSE. */
/* */
/* 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. */
/* */
/**************************************************************************/
//@+ CheckArithOverflow = no
/* is_max(t,i,l) is true whenever t[i] is the maximum of t[0]..t[l-1]
* l is an integer and not an int, because used as t.length which
* (in the logic) returns an integer and not an int
*/
/*@ predicate is_max{L}(int[] t,int i,integer l) =
@ t != null && 0 <= i < l <= t.length &&
@ (\forall integer j; 0 <= j < l ==> t[j] <= t[i]) ;
@*/
public class Arrays {
/*@ requires t != null && 1 <= t.length <= 32767;
@ behavior max_found:
@ ensures
@ 0 <= \result < t.length &&
@ (\forall integer i;
@ 0 <= i < t.length ==> t[i] <= t[\result]);
@*/
public static short findMax(int[] t) {
int m = t[0];
short r = 0;
/*@ loop_invariant
@ 1 <= i <= t.length && 0 <= r < t.length &&
@ m == t[r] && (\forall integer j; 0 <= j < i ==> t[j] <= m);
@ loop_variant t.length-i;
@*/
for (short i=1; i < t.length; i++) {
if (t[i] > m) {
r = i;
m = t[i];
}
}
return r;
}
/*@ requires t != null && t.length >= 1;
@ behavior max_found:
@ ensures
@ 0 <= \result < t.length &&
@ is_max(t,\result,t.length) ;
@*/
public static int findMax2(int[] t) {
int m = t[0];
int r = 0;
/*@ loop_invariant
@ 1 <= i <= t.length && 0 <= r < t.length &&
@ m == t[r] && is_max(t,r,i) ;
@ loop_variant t.length-i;
@*/
for (int i=1; i < t.length; i++) {
if (t[i] > m) {
r = i;
m = t[i];
}
}
return r;
}
/*@ requires t != null ;
@ ensures
@ \forall integer i; 0 < i < t.length ==> t[i] == \old(t[i-1]);
@*/
public static void arrayShift(int[] t) {
/*@ loop_invariant
@ j < t.length &&
@ (t.length > 0 ==>
@ (0 <= j &&
@ (\forall integer i; 0 <= i <= j ==> t[i] == \at(t[i],Pre)) &&
@ (\forall integer i; j < i < t.length ==> t[i] == \at(t[i-1],Pre))));
@ loop_variant j;
@*/
for (int j = t.length-1 ; j > 0 ; j--) {
t[j] = t[j-1];
}
}
}
/*
Local Variables:
compile-command: "make Arrays.why3ml"
End:
*/
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