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Loop Invariants

Loop invariants describe facts about the loop that are always true, regardless of how many times it executes. CN checks that loop invariants are true before the loop executes and during every possible iteration, and then uses them to prove things about the rest of the code downstream.

Loop invariants always start with the inv keyword.

Syntax Explanation

inv
 condition;
 condition;

 One or more conditions that are always true before, during, and after loop execution.

Warning

Loop invariants only work with for and while loops. They are not implemented yet for do-while loops.

Here's an example. Suppose we want to prove memory safety of an array search – that is, verifying that we always index within the bounds of the array, and that the returned index is either within the bounds of the array or -1, indicating the searched-for element is not found.

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int find(int k, int arr[], int len)
/*@
  requires
    take arr_in = each (i32 j; 0i32 <= j && j < len) {
      Owned(arr + j)
    };
    0i32 <= len;

  ensures
    take arr_out = each (i32 j; 0i32 <= j && j < len) {
      Owned(arr + j)
    };
    0i32 <= return && return < len || return == -1i32;
@*/
{
  for (int i = 0; i < len; i++)
  /*@
    inv
      0i32 <= i && i <= len;

      {arr} unchanged;
      {len} unchanged;
      {k} unchanged;

      take arr_inv = each (i32 j; 0i32 <= j && j < len) {
        Owned(arr + j)
      };
  @*/
  {
    /*@ extract Owned<int>, i; @*/
    if (arr[i] == k)
    {
      return i;
    }
  }

  return -1;
}

The array invariant (lines 17 – 28) establishes a few facts:

  • The index i is at least zero less than or equal to len. Note the "or equal to" part – the invariant holds before, during, and after the loop. After the loop, i == len.
  • arr, len, and k are not modified in the loop.
  • Memory ownership is preserved throughout the loop.

Together, these facts let CN prove that the return value is either a valid index in the array or -1.

Info

You might wonder – can't CN figure out which variables are unchanged?

We think so, and we're working to make that happen. In the meantime, you'll need to indicate variables that are unchanged in the loop.