将字符串附加到动态字符数组的函数的 ACSL 规范

Question

我正在为将给定字符串附加到动态字符数组末尾的函数编写 ACSL 规范。

这是我目前的情况：

#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;
}

因为还不支持动态内存分配的验证，所以我添加了一个占位符函数char_vector_reallocate()和ACSL规范，但没有显示实现。

使用 Frama-C Sodium-20150201 和 WP 插件，我无法验证 6 个属性：

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

我没想到在验证前 5 个属性时会遇到任何困难。

如何修复 ACSL 以便 char_vector_append() 可以被验证？

（作为旁注，是否有动态数组的 ACSL 规范示例，我可以将其作为指南参考？）

Answer 1

您缺少允许 WP 区分您的 ok 和 err 案例的 assumes 条款。一个很好的证据就是你无法证明合同的 disjoint 条款。基本上，如果

函数将失败

缓冲区和字符串的总和太大，或
缓冲区太小，无法容纳字符串，和
剩余内存不足

为了对第三点进行建模，我建议使用一个幽灵变量来指示是否有足够的空闲内存来扩展向量。在你的情况下，因为只有一个分配，一个简单的布尔标志就可以了，例如//@ ghost int mem_full.

当然，您需要相应地调整 char_vector_reallocate 的规范：它应该 assigns mem_full 并且它的 behavior 应该有 assumes 基于初始值的子句mem_full.

最后，char_vector_reallocate 的 ensures 子句和 old_content_unchanged 中 memcmp 的第一个参数存在问题：参数本身应在Pre 状态。否则，您是说 vec->buf（在 Post 状态下）在 Pre 状态下所指向的内容比较等于 vec->buf 所指向的内容（再次处于 Post-状态）处于 Post-状态。即，memcmp 的参数求值发生在 当前状态 ，而不管参数中给定的标签。

以下是Alt-Ergo证明一切的版本

#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;
}

将字符串附加到动态字符数组的函数的 ACSL 规范

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

c

dynamic-arrays

frama-c

formal-verification

acsl