Dafny：复制数组区域方法验证 [英] Dafny: copy array region method validation

问题描述

我正在着手比较几种在考虑验证的情况下创建的语言（Whiley，Dafny和Frama-C等）。我得到了该函数的示例，该函数将一个数组的区域复制到另一个数组中的另一个位置在目标数组中。我想出的规范在Dafny中看起来像这样：

I am working on a language comparison of several languages created with verification in mind (Whiley, Dafny and Frama-C etc.) I was given this example of a function which copied a region of one array to another array with different placement within the destination array. The specification I came up with looks like this in Dafny:

method copy( src: array<int>, sStart: nat, dest: array<int>, dStart: nat, len: nat)
    returns (r: array<int>)
  // both arrays cannot be null
   requires dest != null && src != null
  // Source array must contain enough elements to be copied
   requires src.Length >= sStart + len
  // Destination array must have enough space for copied elements
   requires dest.Length >= dStart + len
  // Result is same size as dest
  ensures r != null
  ensures r.Length == dest.Length
  // All elements before copied region are same
   ensures r[..dStart] == dest[..dStart]
  // All elements above copied region are same
   ensures r[dStart + len..] == dest[dStart + len..]
  // All elements in copied region match src
   ensures forall k: nat :: k < len ==> r[dStart + k] == src[sStart + k]

{
    if len == 0 { return dest; }
    assert len > 0;
    var i: nat := 0;
    r := new int[dest.Length];
    while (i < r.Length)
      invariant i <= r.Length
      decreases r.Length - i
      invariant r.Length == dest.Length
      invariant forall k: nat :: k < i ==> r[k] == dest[k]
    {
        r[i] := dest[i];
        i := i + 1;
    }
    assume r[..] == dest[..];
    i := 0;
    while (i < len)
      invariant i <= len
      decreases len - i
      invariant r.Length == dest.Length
      invariant r.Length >= dStart + i
      invariant src.Length >= sStart + i
      invariant r[..dStart] == dest[..dStart]
      invariant r[(dStart + len)..] == dest[(dStart + len)..]
      invariant forall k: nat :: k < i ==> r[dStart + k] == src[sStart + k]
    {
        r[dStart + i] := src[sStart + i];
        i := i + 1;
    }
}

在上面的第二个while循环中可能不需要我试图涵盖所有我能想到的东西。但是，是的，这并没有得到证实，我对为什么感到困惑……

In the second while loop above there may be some unneeded invariants as I have tried to cover everything I can think of. but, yeah, this doesn't verify and I am perplexed as to why...

Dafny/copy.dfy(35,4): Error BP5003: A postcondition might not hold on this return path.
Dafny/copy.dfy(17,11): Related location: This is the postcondition that might not hold.
Execution trace:
    (0,0): anon0
    (0,0): anon19_Else
    Dafny/copy.dfy(24,5): anon20_LoopHead
    (0,0): anon20_LoopBody
    Dafny/copy.dfy(24,5): anon21_Else
    (0,0): anon23_Then
    Dafny/copy.dfy(35,5): anon24_LoopHead
    (0,0): anon24_LoopBody
    Dafny/copy.dfy(35,5): anon25_Else
    (0,0): anon27_Then
Dafny/copy.dfy(43,16): Error BP5005: This loop invariant might not be maintained by the loop.
Execution trace:
    (0,0): anon0
    (0,0): anon19_Else
    Dafny/copy.dfy(24,5): anon20_LoopHead
    (0,0): anon20_LoopBody
    Dafny/copy.dfy(24,5): anon21_Else
    (0,0): anon23_Then
    Dafny/copy.dfy(35,5): anon24_LoopHead
    (0,0): anon24_LoopBody
    Dafny/copy.dfy(35,5): anon25_Else
    Dafny/copy.dfy(35,5): anon27_Else

Dafny program verifier finished with 1 verified, 2 errors

推荐答案

您可以通过添加更多不变变量来验证它

You can get it to verify by adding one more invariant

invariant r[dStart .. dStart + i] == src[sStart .. sStart + i]

如：

while (i < len)
  invariant i <= len
  decreases len - i
  invariant r.Length == dest.Length
  invariant r.Length >= dStart + i
  invariant src.Length >= sStart + i
  invariant r[..dStart] == dest[..dStart]
  invariant r[(dStart + len)..] == dest[(dStart + len)..]
  invariant r[dStart .. dStart + i] == src[sStart .. sStart + i]
  invariant forall k: nat :: k < i ==> r[dStart + k] == src[sStart + k]

顺便说一句，我想你如果想删除

By the way, I think you can remove many of the invariants if you want to

method copy( src: array<int>, sStart: nat, dest: array<int>, dStart: nat, len: nat)
    returns (r: array<int>)
  // both arrays cannot be null
   requires dest != null && src != null
  // Source array must contain enough elements to be copied
   requires src.Length >= sStart + len
  // Destination array must have enough space for copied elements
   requires dest.Length >= dStart + len
  // Result is same size as dest
  ensures r != null
  ensures r.Length == dest.Length
  // All elements before copied region are same
   ensures r[..dStart] == dest[..dStart]
  // All elements above copied region are same
   ensures r[dStart + len..] == dest[dStart + len..]
  // All elements in copied region match src
   ensures forall k: nat :: k < len ==> r[dStart + k] == src[sStart + k]

{
    if len == 0 { return dest; }
    var i: nat := 0;
    r := new int[dest.Length];
    while (i < r.Length)
      invariant i <= r.Length
      invariant r[..i] == dest[..i]
    {
        r[i] := dest[i];
        i := i + 1;
    }

    i := 0;
    while (i < len)
      invariant i <= len
      invariant r[..dStart] == dest[..dStart]
      invariant r[(dStart + len)..] == dest[(dStart + len)..]
      invariant r[dStart .. dStart + i] == src[sStart .. sStart + i]
      {
        r[dStart + i] := src[sStart + i];
        i := i + 1;
    }
}

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