ACSL specification of a function that appends a string to a dynamic character array

Question

I am working on writing an ACSL specification for a function that appends a given string to the end of a dynamic character array.

Here is what I have so far:

#include <stddef.h>
#include <stdint.h>
#include <stdlib.h>
#include <string.h>

#ifndef SIZE_MAX
#define SIZE_MAX ((size_t)-1)
#endif

#undef MAX
#define MAX(a, b) ((a) > (b) ? (a) : (b))

struct st_char_vector {
  char *buf;
  size_t capacity;
  size_t length;
};

/*@ predicate valid_char_vector(struct st_char_vector *vec) =
  @   \valid_read(vec) &&
  @   vec->capacity > 0 &&
  @   \valid(vec->buf + (0..vec->capacity - 1)) &&
  @   vec->length <= vec->capacity;
  @*/


/*@ requires valid_char_vector(vec);
  @ requires new_capacity >= vec->capacity;
  @ ensures valid_char_vector(vec);
  @ ensures \old(vec->length) == vec->length;
  @ ensures memcmp{Pre,Post}(vec->buf, vec->buf, vec->length) == 0;
  @ behavior err:
  @   ensures !\result;
  @   ensures \old(vec->buf) == vec->buf;
  @   ensures \old(vec->capacity) == vec->capacity;
  @ behavior ok:
  @   ensures \result;
  @   ensures vec->capacity >= new_capacity;
  @ complete behaviors;
  @ disjoint behaviors;
  @*/
static int char_vector_reallocate(struct st_char_vector *vec, size_t new_capacity);

/*@ requires valid_char_vector(vec);
  @ requires \valid_read(str + (0..str_length - 1));
  @ requires string_separated_from_extra_capacity:
  @   \separated(str + (0..str_length - 1), vec->buf + (vec->length..vec->capacity - 1));
  @ ensures valid_char_vector(vec);
  @ ensures old_content_unchanged: memcmp{Pre,Post}(vec->buf, vec->buf, \old(vec->length)) == 0;
  @ ensures \forall integer i; 0 <= i && i < \old(vec->length) ==> \old(vec->buf[i]) == vec->buf[i];
  @ behavior err:
  @   ensures !\result;
  @   ensures buf_unchanged: \old(vec->buf) == vec->buf;
  @   ensures capacity_unchanged: \old(vec->capacity) == vec->capacity;
  @   ensures length_unchanged: \old(vec->length) == vec->length;
  @ behavior ok:
  @   ensures \result;
  @   ensures str_length_added_to_length: vec->length == \old(vec->length) + str_length;
  @   ensures string_appended: memcmp{Post,Post}(vec->buf + \at(vec->length, Pre), str, str_length) == 0;
  @ complete behaviors;
  @ disjoint behaviors;
  @*/
int char_vector_append(struct st_char_vector *vec, const char *str, size_t str_length) {
  if (SIZE_MAX - str_length < vec->capacity) {
    return 0;
  }

  if (vec->capacity < (vec->length + str_length)) {
    if (!char_vector_reallocate(vec, vec->capacity + str_length)) {
      //@ assert \at(vec->length, Pre) == \at(vec->length, Here);
      return 0;
    }
  }

  memcpy(vec->buf + vec->length, str, str_length);
  vec->length += str_length;

  return 1;
}

Because verification of dynamic memory allocation is not yet supported, I have added a placeholder function char_vector_reallocate() and ACSL specification without showing the implementation.

Using Frama-C Sodium-20150201 and the WP plugin, I have been unable to verify 6 properties:

• typed_char_vector_append_disjoint_ok_err
• typed_char_vector_append_err_post
• typed_char_vector_append_err_post_length_unchanged
• typed_char_vector_append_ok_post
• typed_char_vector_append_ok_post_str_length_added_to_length
• typed_char_vector_append_ok_post_string_appended

I was not expecting to experience any difficulty with verifying the first 5 properties.

How can I fix the ACSL so that char_vector_append() can be verified?

(As a sidenote, is there an example ACSL specification for a dynamic array that I could refer to as a guide?)

Answer 1

You're lacking assumes clauses that will allow WP to discriminate between your ok and err cases. A good witness of that is the fact that you cannot prove the disjoint clause of the contract. Basically, the function will fail if

• the sum of the sizes of the buffer and the string is too large, or
• the buffer is too small to hold the string, and
• there is not enough memory left

In order to model the third point, I'd suggest to use a ghost variable indicating whether there is enough free memory to extend the vector. In your case, as there is only one allocation, a simple boolean flag will do the trick, e.g. //@ ghost int mem_full.

Of course, you need to adapt the spec of char_vector_reallocate accordingly: it should assigns mem_full and its behaviors should have assumes clauses based on the initial value of mem_full.

Finally, there is an issue with your first argument of memcmp in the ensures clause of char_vector_reallocate and in old_content_unchanged: the argument itself should be evaluated in the Pre-state. Otherwise, you're saying that whatever was pointed at by vec->buf (in the Post-state) in the Pre-state compares equal to was is pointed at by vec->buf (again in the Post-state) in the Post-state. Namely, the evaluation of the arguments to memcmp occurs in the current state, regardless of the labels given in parameter.

Below is a version for which everything is proved by Alt-Ergo

#include "stdlib.h"
#include "string.h"

#ifndef SIZE_MAX
#define SIZE_MAX ((size_t)-1)
#endif

#undef MAX
#define MAX(a, b) ((a) > (b) ? (a) : (b))

struct st_char_vector {
  char *buf;
  size_t capacity;
  size_t length;
};

/*@ predicate valid_char_vector(struct st_char_vector *vec) =
  @   \valid_read(vec) &&
  @   vec->capacity > 0 &&
  @   \valid(vec->buf + (0..vec->capacity - 1)) &&
  @   vec->length <= vec->capacity;
  @*/

//@ ghost extern int mem_full;

/*@ requires valid_char_vector(vec);
  @ requires new_capacity >= vec->capacity;
  @ assigns mem_full;
  @ ensures valid_char_vector(vec);
  @ ensures \old(vec->length) == vec->length;
  @ ensures valid_char_vector(vec);
  @ ensures memcmp{Pre,Post}(\at(vec->buf,Pre), vec->buf, vec->length) == 0;
  @ behavior err:
      assumes mem_full;
  @   ensures !\result;
  @   ensures \old(vec->buf) == vec->buf;
  @   ensures \old(vec->capacity) == vec->capacity;
  @ behavior ok:
      assumes !mem_full;
  @   ensures \result;
  @   ensures vec->capacity >= new_capacity;
  @ complete behaviors;
  @ disjoint behaviors;
  @*/
static int char_vector_reallocate(struct st_char_vector *vec, size_t new_capacity);

/*@ requires valid_char_vector(vec);
  @ requires \valid_read(str + (0..str_length - 1));
  @ requires string_separated_from_extra_capacity:
  @   \separated(str + (0..str_length - 1), vec->buf + (vec->length..vec->capacity - 1));
  @ ensures valid_char_vector(vec);
  @ ensures old_content_unchanged: memcmp{Pre,Post}(\at(vec->buf,Pre), vec->buf, \old(vec->length)) == 0;
  @ ensures \forall integer i; 0 <= i && i < \old(vec->length) ==> \old(vec->buf[i]) == vec->buf[i];
  @ behavior err:
      assumes vec->capacity+str_length>SIZE_MAX || 
      (vec->length+str_length>vec->capacity && mem_full);
  @   ensures !\result;
  @   ensures buf_unchanged: \old(vec->buf) == vec->buf;
  @   ensures capacity_unchanged: \old(vec->capacity) == vec->capacity;
  @   ensures length_unchanged: \old(vec->length) == vec->length;
  @ behavior ok:
      assumes vec->capacity+str_length<=SIZE_MAX && 
      (vec->length+str_length<=vec->capacity || !mem_full);
  @   ensures \result;
  @   ensures str_length_added_to_length: vec->length == \old(vec->length) + str_length;
  @   ensures string_appended: memcmp{Post,Post}(vec->buf + \at(vec->length, Pre), str, str_length) == 0;
  @ complete behaviors;
  @ disjoint behaviors;
  @*/
int char_vector_append(struct st_char_vector *vec, const char *str, size_t str_length) {
  if (SIZE_MAX - str_length < vec->capacity) {
    return 0;
  }

  if (vec->capacity < (vec->length + str_length)) {
    if (!char_vector_reallocate(vec, vec->capacity + str_length)) {
      return 0;
    }
  }
   memcpy(vec->buf + vec->length, str, str_length);
  vec->length += str_length;

  return 1;
}