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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_range(t,0,n-1);
@ ensures Sorted(t,0,n-1);
@*/
void insert_sort(int t[], int n) {
int i,j;
int mv;
if (n <= 1) return;
/*@ loop invariant 0 <= i <= n;
@ loop invariant Sorted(t,0,i);
@ loop variant n-i;
@*/
for (i=1; i<n; i++) {
// assuming t[0..i-1] is sorted, insert t[i] at the right place
mv = t[i];
/*@ loop invariant 0 <= j <= i;
@ loop invariant j == i ==> Sorted(t,0,i);
@ loop invariant j < i ==> Sorted(t,0,i+1);
@ loop invariant \forall integer k; j <= k < i ==> t[k] > mv;
@ loop variant j;
@*/
// look for the right index j to put t[i]
for (j=i; j > 0; j--) {
if (t[j-1] <= mv) break;
t[j] = t[j-1];
}
t[j] = mv;
}
}
/*
Local Variables:
compile-command: "make insertion_sort.why3ml"
End:
*/
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