Question

我在理解为什么我的Coq代码没有达到我在下面的代码中的预期时遇到了问题。

我试图让这个例子尽可能地简化，但是当我把它变得更简单时，问题就不再出现了。
它正在使用CompCert 1.8文件。
在Coq 8.2-pl2下发生了这件事。

以下是代码：

Require Import Axioms.
Require Import Coqlib.
Require Import Integers.
Require Import Values.
Require Import Asm.

Definition foo (ofs: int) (c: code) : Prop :=
  c <> nil /\ ofs <> Int.zero.

Inductive some_prop: nat -> Prop :=
| some_prop_ctor :
  forall n other_n ofs c lo hi ofs_ra ofs_link,
    some_prop n ->
    foo ofs c ->
    find_instr (Int.unsigned ofs) c <> Some (Pallocframe lo hi ofs_ra ofs_link) ->
    find_instr (Int.unsigned ofs) c <> Some (Pfreeframe lo hi ofs_ra ofs_link) ->
    some_prop other_n
.

Lemma simplified:
  forall n other_n ofs c,
  some_prop n ->
  foo ofs c ->
  find_instr (Int.unsigned ofs) c = Some Pret ->
  some_prop other_n.
Proof.
  intros.

这不起作用：

  eapply some_prop_ctor
    with (lo:=0) (hi:=0) (ofs_ra:=Int.zero) (ofs_link:=Int.zero);
      eauto; rewrite H1; discriminate.

在rewrite H1上失败：

Error:
Found no subterm matching "find_instr (Int.unsigned ofs) c" in the current goal.

但这有效：

  eapply some_prop_ctor
    with (lo:=0) (hi:=0) (ofs_ra:=Int.zero) (ofs_link:=Int.zero);
      eauto.
  rewrite H1; discriminate.
  rewrite H1; discriminate.
Qed.

此外，在eauto之后，我的目标如下：

2 subgoals
n : nat
other_n : nat
ofs : int
c : code
H : some_prop n
H0 : foo ofs c
H1 : find_instr (Int.unsigned ofs) c = Some Pret
______________________________________(1/2)
find_instr (Int.unsigned ofs) c <> Some (Pallocframe 0 0 Int.zero Int.zero)


______________________________________(2/2)
find_instr (Int.unsigned ofs) c <> Some (Pfreeframe 0 0 Int.zero Int.zero)

因此，rewrite H1; discriminate两次有效，但使用分号在eauto之后“管道”它不起作用。

我希望这个问题至少有意义。谢谢！

完整代码：

Require Import Axioms.
Require Import Coqlib.
Require Import Integers.
Require Import Values.
Require Import Asm.

Definition foo (ofs: int) (c: code) : Prop :=
  c <> nil /\ ofs <> Int.zero.

Inductive some_prop: nat -> Prop :=
| some_prop_ctor :
  forall n other_n ofs c lo hi ofs_ra ofs_link,
    some_prop n ->
    foo ofs c ->
    find_instr (Int.unsigned ofs) c <> Some (Pallocframe lo hi ofs_ra ofs_link) ->
    find_instr (Int.unsigned ofs) c <> Some (Pfreeframe lo hi ofs_ra ofs_link) ->
    some_prop other_n
.

Lemma simplified:
  forall n other_n ofs c,
  some_prop n ->
  foo ofs c ->
  find_instr (Int.unsigned ofs) c = Some Pret ->
  some_prop other_n.
Proof.
  intros.
(*** This does not work:
  eapply some_prop_ctor
    with (lo:=0) (hi:=0) (ofs_ra:=Int.zero) (ofs_link:=Int.zero);
      eauto; rewrite H1; discriminate.
***)
  eapply some_prop_ctor
    with (lo:=0) (hi:=0) (ofs_ra:=Int.zero) (ofs_link:=Int.zero);
      eauto.    
  rewrite H1; discriminate.
  rewrite H1; discriminate.
Qed.

Answer 1

所以，这可能是我自己问题的答案（感谢#coq IRC频道上的某人）：

可能是存在变量的统一直到.才会发生的情况。因此，通过分号，我可能会阻止ofs和c统一。

我发现虽然写作...; eauto; subst; rewrite H1; discriminate.会起作用。在这种情况下，subst会强制存在变量的统一，从而解锁重写的能力。

Coq中分号的奇怪行为

1 个答案: