Fixes #319

Gregory Malecha authored 5 years ago and Robbert Krebbers committed 5 years ago

- remove "odd" comment
- move atomic triples to bi_scope

The general idea is to first import/export modules which are further
than the current one, and then import/export modules which are close
dependencies.

This commit tries to use the same order of imports for every file, and
describes the convention in ProofGuide.md. There is one exception,
where we do not follow said convention: in program_logic/weakestpre.v,
using that order would break printing of texan triples (??).

The new adequacy statement unifies `wp_strong_adequacy`, `wp_strong_all_adequacy`,
and `wp_invariance`.

Thanks @jtassaro.

This commit extends the state interpretation with an additional parameter to
talk about the number of forked-off threads, and a fixed postcondition for each
forked-off thread:

    state_interp : Λstate → list Λobservation → nat → iProp Σ;
    fork_post : iProp Σ;

This way, instead of having `True` as the post-condition of `Fork`, one can
have any post-condition, which is then recorded in the state interpretation.
The point of keeping track of the postconditions of forked-off threads, is that
we get an (additional) stronger adequacy theorem:

    Theorem wp_strong_all_adequacy Σ Λ `{invPreG Σ} s e σ1 v vs σ2 φ :
       (∀ `{Hinv : invG Σ} κs,
         (|={⊤}=> ∃
             (stateI : state Λ → list (observation Λ) → nat → iProp Σ)
             (fork_post : iProp Σ),
           let _ : irisG Λ Σ := IrisG _ _ _ Hinv stateI fork_post in
           stateI σ1 κs 0 ∗ WP e @ s; ⊤ {{ v,
             let m := length vs in
             stateI σ2 [] m -∗ [∗] replicate m fork_post ={⊤,∅}=∗ ⌜ φ v ⌝ }})%I) →
      rtc erased_step ([e], σ1) (of_val <$> v :: vs, σ2) →
      φ v.

The difference with the ordinary adequacy theorem is that this one only applies
once all threads terminated. In this case, one gets back the post-conditions
`[∗] replicate m fork_post` of all forked-off threads.

In Iron we showed that we can use this mechanism to make sure that all
resources are disposed of properly in the presence of fork-based concurrency.

Use explicit names in some scripts, re-organize fupd plainly derived laws, adjust wsat import/export.

Modify adequacy proof to not break the 'fancy update' abstraction. Modify fupd plainly interface and add new derived results.

Marianna Rapoport authored 6 years ago and Ralf Jung committed 6 years ago

- Removing head of list of observations after each reduction step in definition of wp
- Adding support for observations to state_interp and world
- Applying Ralf's suggestions to previous commit (e.g. replacing /\ and -> with unicode characters)

We already used the following naming convention: `wp_value'` is stated in
terms of `of_val` and `wp_value` is stated in terms of `IntoVal`. This
commit applies this convention to `wp_value_inv` as well.