source: CIVL/examples/verifyThis/pairInsertSort_loop.cvl@ bca19b1

#include <stdio.h>
#pragma PARSE_ACSL
$input int N = 6; // upper bound on n
$input int n; // size of array
$assume(1<=n && n<=N);
$input int LEFT;
$input int RIGHT;
$assume(1<=LEFT && LEFT < RIGHT && RIGHT<n-1);

int main() {
  int a[n];

  // assumption: a[LEFT-1] is less than every thing of right of LEFT:
  $assume($forall (int j : LEFT .. RIGHT) a[j] >= a[LEFT-1]);
  int left = LEFT, right = RIGHT;
  int k;

  /*@ loop invariant left <= right + 2;
    @ loop invariant LEFT <= k && k <= RIGHT+2;
    @ loop invariant \forall int i; LEFT <= i && i <= RIGHT ==>
    @                               a[i] >= a[LEFT-1];
    @ loop invariant \forall int j; LEFT <= j && j < k ==>
    @                               a[j] <= a[j+1];
    @*/
  for (k = left; ++left <= right; k = ++left) {
    int a1 = a[k], a2 = a[left];
    if (a1 < a2) {
      a2 = a1; a1 = a[left];
    }
    /*@ loop invariant LEFT - 1 <= k && k <= left - 1;
      @ loop invariant \forall int i; k < i && i < left - 1 ==> 
      @                                a[i] <= a[i+1];
      @*/
    while (a1 < a[--k]) {
      a[k + 2] = a[k];
    }
    a[++k + 1] = a1;
    /*@ loop invariant LEFT - 1 <= k && k <= left - 1;
      @ loop invariant \forall int i; LEFT <= i && i <= k+1 ==> 
      @                                a[i] <= a[i+1];
      @*/
    while (a2 < a[--k]) {
      a[k + 1] = a[k]; 
    }
    a[k + 1] = a2;
  }
}