Gregory Malecha authored Mar 16, 2020 and Robbert Krebbers committed Mar 16, 2020

- 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 (??).

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.

Marianna Rapoport authored Jul 17, 2018 and Ralf Jung committed Oct 05, 2018

- 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)