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我的简单程序是vars.c：

int pure0 ()
{
    return 0;
}

int get0(int* arr)
{
    int z = pure0();
    return z;
}

我开始证明（文件verif_vars.c）：

Require Import floyd.proofauto.
Require Import vars.

Local Open Scope logic.
Local Open Scope Z.

Definition get0_spec :=
  DECLARE _get0
    WITH sh : share, arr : Z->val, varr : val
    PRE [_arr OF (tptr tint)]
        PROP ()
        LOCAL (`(eq varr) (eval_id _arr);
               `isptr (eval_id _arr))
        SEP (`(array_at tint sh arr 0 100) (eval_id _arr))
    POST [tint] `(array_at tint sh arr 0 100 varr) &&
                 local(`(eq (Vint (Int.repr 0))) retval).

Definition pure0_spec :=
  DECLARE _pure0
    WITH sh : share
    PRE []
        PROP ()
        LOCAL ()
        SEP ()
    POST [tint] local(`(eq (Vint (Int.repr 0))) retval).

Definition Vprog : varspecs := nil.
Definition Gprog : funspecs := get0_spec :: pure0_spec ::nil.

Lemma body_pure0: semax_body Vprog Gprog f_pure0 pure0_spec.
Proof.
  start_function.
  forward.
Qed.


Lemma body_get0: semax_body Vprog Gprog f_get0 get0_spec.
Proof.
  start_function.
  name arrarg _arr.
  name zloc _z.
  name zloc' _z'.
  forward_call (sh).
  entailer!.
  auto with closed.
  after_call.
  forward.
  entailer!.

最后有两个子目标：

  Espec : OracleKind
  sh : share
  arr : Z -> val
  Struct_env := abbreviate : type_id_env.type_id_env
  Delta := abbreviate : tycontext
  zloc0 : val
  arrarg : val
  zloc : int
  TC : is_pointer_or_null arrarg
  Parrarg : isptr arrarg
  ============================
   Int.repr 0 = zloc

subgoal 2 (ID 1273) is:
 !!(Int.repr 0 = zloc) |-- emp
  • 第一个直接来自pure0_spec后置条件。但是我怎么能告诉 Coq 呢？
  • 第二个目标可以简化（由admit. entailer.）为TT |-- emp。这似乎又是微不足道的，但仍然如何证明它（SearchAbout derives并且SearchAbout emp不显示任何一般引理）？

我使用：VST 1.5（2014-10-02 时为 6834P）、CompCert 2.4、Coq 8.4pl3（Jan'14）和 OCaml 4.01.0。

4

1 回答 1

1

First: offhand, without attempting to reproduce this myself-- is it possible that using entailer! is too "risky", because (as documented) entailer! can sometimes turn a provable goal into an unprovable one. Try with entailer without the bang, and see if it looks better.

Second, TT |-- emp is not true. TT applies to any heap, and emp applies only to empty heaps. You can fix this by changing the postcondition the pure function to,

POST [tint] local(`(eq (Vint (Int.repr 0))) retval) && emp.
于 2015-01-18T19:13:06.660 回答