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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. */
/* */
/**************************************************************************/
// RUNSIMPLIFY: will ask regtests to run Simplify on this program
#pragma JessieIntegerModel(math)
#include "sorting.h"
/*@ requires \valid(t+i) && \valid(t+j);
@ assigns t[i],t[j];
@ ensures Swap{Old,Here}(t,i,j);
@*/
void swap(int t[], int i, int j) {
int tmp = t[i];
t[i] = t[j];
t[j] = tmp;
}
/*@ requires \valid_range(t,0,n-1);
@ behavior sorted:
@ ensures Sorted(t,0,n);
@ behavior permutation:
@ ensures Permut{Old,Here}(t,0,n-1);
@*/
void sel_sort(int t[], int n) {
int i,j;
int mi,mv;
if (n <= 0) return;
/*@ loop invariant 0 <= i < n;
@ for sorted:
@ loop invariant
@ Sorted(t,0,i) &&
@ (\forall integer k1, k2 ;
@ 0 <= k1 < i <= k2 < n ==> t[k1] <= t[k2]) ;
@ for permutation:
@ loop invariant Permut{Pre,Here}(t,0,n-1);
@ loop variant n-i;
@*/
for (i=0; i<n-1; i++) {
// look for minimum value among t[i..n-1]
mv = t[i]; mi = i;
/*@ loop invariant i < j && i <= mi < n;
@ for sorted:
@ loop invariant
@ mv == t[mi] &&
@ (\forall integer k; i <= k < j ==> t[k] >= mv);
@ for permutation:
@ loop invariant
@ Permut{Pre,Here}(t,0,n-1);
@ loop variant n-j;
@*/
for (j=i+1; j < n; j++) {
if (t[j] < mv) {
mi = j ; mv = t[j];
}
}
L:
swap(t,i,mi);
//@ assert Permut{L,Here}(t,0,n-1);
}
}
/*
Local Variables:
compile-command: "frama-c -jessie selection_sort.c"
End:
*/
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