mirror of
https://github.com/achlipala/frap.git
synced 2024-11-10 00:07:51 +00:00
Some ModelChecking improvements
This commit is contained in:
parent
b0ad93e6a4
commit
712aacf9de
2 changed files with 11 additions and 7 deletions
|
@ -173,7 +173,9 @@ Proof.
|
|||
assumption.
|
||||
Qed.
|
||||
|
||||
(* A trivial fact about union and singleton sets. *)
|
||||
(* A trivial fact about union and singleton sets.
|
||||
* Note that we model sets as functions that are passed elements, deciding in
|
||||
* each case whether that element belongs to the set. *)
|
||||
Theorem singleton_in : forall {A} (x : A) rest,
|
||||
({x} \cup rest) x.
|
||||
Proof.
|
||||
|
@ -264,7 +266,7 @@ Proof.
|
|||
apply oneStepClosure_empty.
|
||||
simplify.
|
||||
|
||||
(* Now the candidate invariatn is closed under single steps. Let's prove
|
||||
(* Now the candidate invariant is closed under single steps. Let's prove
|
||||
* it. *)
|
||||
apply MscDone.
|
||||
apply prove_oneStepClosure; simplify.
|
||||
|
@ -346,7 +348,9 @@ Ltac model_check := model_check_find_invariant; model_check_finish.
|
|||
(* END CODE THAT WILL NOT BE EXPLAINED IN DETAIL! *)
|
||||
|
||||
(* Now watch this. We can check various instances of factorial
|
||||
* automatically. *)
|
||||
* automatically. Notice that reachable states are printed as we encounter them
|
||||
* in exploration, using [idtac] invocations above. This printing is for the
|
||||
* user's understanding and has no logical meaning. *)
|
||||
|
||||
Theorem factorial_ok_2_snazzy :
|
||||
invariantFor (factorial_sys 2) (fact_correct 2).
|
||||
|
@ -695,7 +699,8 @@ Proof.
|
|||
(* It finds exactly four reachable states. We finish by showing that they all
|
||||
* obey the original invariant. *)
|
||||
|
||||
invert 1.
|
||||
invert 1. (* Note that this [1] means "first premise below the double
|
||||
* line." *)
|
||||
invert H0.
|
||||
simplify.
|
||||
unfold add2_correct.
|
||||
|
@ -960,8 +965,7 @@ Proof.
|
|||
(* We get 7 neat little states, one per program counter. Next, we prove that
|
||||
* each of them implies the original invariant. *)
|
||||
|
||||
invert 1. (* Note that this [1] means "first premise below the double
|
||||
* line." *)
|
||||
invert 1.
|
||||
invert H0.
|
||||
unfold loopy_correct.
|
||||
simplify.
|
||||
|
|
|
@ -1398,7 +1398,7 @@ For our purposes, the key pay-off from this connection is that we may translate
|
|||
If $\angled{S, S_0, \to} \simulate_R \angled{S', S'_0, \to'}$, and if $I$ is an invariant of $\angled{S', S'_0, \to'}$, then $R^{-1}(I)$ is an invariant of $\angled{S, S_0, \to}$.
|
||||
\end{theorem}
|
||||
|
||||
We can apply this theorem to the two example programs from earlier in the section.
|
||||
We can apply this theorem to the two example programs from earlier in the section, now imagining that we run two parallel-thread copies of each program, using last chapter's approach to modeling threads with transition systems.
|
||||
The concrete system can be represented with thread-local states $\{\mathsf{Read}\} \cup \{\mathsf{Write}(n) \mid n \in \mathbb N\}$ and the abstract system with $\{\mathsf{BRead}\} \cup \{\mathsf{BWrite}(b) \mid b \in \mathbb B\}$, for the Booleans $\mathbb B$.
|
||||
We define compatibility between local states.
|
||||
|
||||
|
|
Loading…
Reference in a new issue