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// quicksort_contracts_01
// This test checks the correctness of a quicksort implementation using explicit
// ghost state.
// This test currently fails for a variety of reasons, including:
// (1) Lack of support for quantifiers in ensures statements.
// (2) Lack of support for reading from memory in loop invariants (under some
// circumstances)
#include <assert.h>
#include <stdlib.h>
#include <string.h>
void swap(int *a, int *b)
{
*a ^= *b;
*b ^= *a;
*a ^= *b;
}
int partition(int arr_ghost[], int arr[], int len)
__CPROVER_requires(__CPROVER_forall {
int i;
(0 <= i && i < len) == > arr_ghost[i] == arr[i]
} && len > 0 && 1 == 1)
__CPROVER_ensures(
__CPROVER_forall {
int i;
(0 <= i && i < len) == > __CPROVER_exists
{
int j;
0 <= j &&j < len &&arr_ghost[i] == arr[j]
}
} &&
__CPROVER_forall {
int i;
(0 <= i && i < len) == > __CPROVER_exists
{
int j;
0 <= j &&j < len &&arr[i] == arr_ghost[j]
}
} &&
0 <= __CPROVER_return_value && __CPROVER_return_value < len &&
__CPROVER_forall {
int i;
(0 <= i && i <= __CPROVER_return_value) ==
> arr[i] <= arr[__CPROVER_return_value]
} &&
__CPROVER_forall {
int i;
(__CPROVER_return_value <= i && i < len) ==
> arr[__CPROVER_return_value] <= arr[i]
} &&
1 == 1)
{
int h = len - 1;
int l = 0;
int pivot_idx = len / 2;
int pivot = arr[pivot_idx];
while(h > l)
__CPROVER_loop_invariant(
0 <= l && l <= pivot_idx && pivot_idx <= h && h < len &&
arr[pivot_idx] == pivot &&
__CPROVER_forall {
int i;
(0 <= i && i < l) == > arr[i] <= pivot
} &&
__CPROVER_forall {
int i;
(h < i && i < len) == > pivot <= arr[i]
} &&
1 == 1)
{
if(arr[h] <= pivot && arr[l] >= pivot)
{
swap(arr + h, arr + l);
if(pivot_idx == h)
{
pivot_idx = l;
h--;
}
if(pivot_idx == l)
{
pivot_idx = h;
l++;
}
}
else if(arr[h] <= pivot)
{
l++;
}
else
{
h--;
}
}
return pivot_idx;
}
void quicksort(int arr_ghost[], int arr[], int len)
__CPROVER_requires(__CPROVER_forall {
int i;
(0 <= i && i < len) == > arr_ghost[i] == arr[i]
} && 1 == 1)
__CPROVER_ensures(
__CPROVER_forall {
int i;
(0 <= i && i < len) == > __CPROVER_exists
{
int j;
0 <= j &&j < len &&arr_ghost[i] == arr[j]
}
} &&
__CPROVER_forall {
int i;
(0 <= i && i < len) == > __CPROVER_exists
{
int j;
0 <= j &&j < len &&arr[i] == arr_ghost[j]
}
} &&
__CPROVER_forall {
int i;
(0 <= i && i < len) == > __CPROVER_forall
{
int j;
(i <= j && j < len) == > arr[i] <= arr[j]
}
} &&
1 == 1)
{
if(len <= 1)
{
return;
}
int *new_ghost = malloc(len * sizeof(int));
memcpy(new_ghost, arr, len * sizeof(int));
int pivot_idx = partition(new_ghost, arr, len);
memcpy(new_ghost, arr, len * sizeof(int));
quicksort(new_ghost, arr, pivot_idx);
quicksort(new_ghost, arr + pivot_idx + 1, len - pivot_idx - 1);
free(new_ghost);
}
int main()
{
int arr[5] = {1, 2, 3, 0, 4};
int arr_ghost[5] = {1, 2, 3, 0, 4};
quicksort(arr_ghost, arr, 5);
}
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