Invariants over states in WP and get rid of heap_ctx.

The WP construction now takes an invariant on states as a parameter
(part of the irisG class) and no longer builds in the authoritative
ownership of the entire state. When instantiating WP with a concrete
language on can choose its state invariant. For example, for heap_lang
we directly use `auth (gmap loc (frac * dec_agree val))`, and avoid
the indirection through invariants entirely.

As a result, we no longer have to carry `heap_ctx` around.

tests/list_reverse.v

@@ -26,11 +26,11 @@ Definition rev : val :=
     end.
 
 Lemma rev_acc_wp hd acc xs ys (Φ : val → iProp Σ) :
-  heap_ctx ∗ is_list hd xs ∗ is_list acc ys ∗
+  is_list hd xs ∗ is_list acc ys ∗
     (∀ w, is_list w (reverse xs ++ ys) -∗ Φ w)
   ⊢ WP rev hd acc {{ Φ }}.
 Proof.
-  iIntros "(#Hh & Hxs & Hys & HΦ)".
+  iIntros "(Hxs & Hys & HΦ)".
   iLöb as "IH" forall (hd acc xs ys Φ). wp_rec. wp_let.
   destruct xs as [|x xs]; iSimplifyEq.
   - wp_match. by iApply "HΦ".
@@ -42,11 +42,11 @@ Proof.
 Qed.
 
 Lemma rev_wp hd xs (Φ : val → iProp Σ) :
-  heap_ctx ∗ is_list hd xs ∗ (∀ w, is_list w (reverse xs) -∗ Φ w)
+  is_list hd xs ∗ (∀ w, is_list w (reverse xs) -∗ Φ w)
   ⊢ WP rev hd (InjL #()) {{ Φ }}.
 Proof.
-  iIntros "(#Hh & Hxs & HΦ)".
-  iApply (rev_acc_wp hd NONEV xs [] with "[- $Hh $Hxs]").
+  iIntros "[Hxs HΦ]".
+  iApply (rev_acc_wp hd NONEV xs [] with "[- $Hxs]").
   iSplit; first done. iIntros (w). rewrite right_id_L. iApply "HΦ".
 Qed.
 End list_reverse.

tests/one_shot.v

@@ -29,18 +29,18 @@ Instance subG_one_shotΣ {Σ} : subG one_shotΣ Σ → one_shotG Σ.
 Proof. intros [?%subG_inG _]%subG_inv. split; apply _. Qed.
 
 Section proof.
-Context `{!heapG Σ, !one_shotG Σ} (N : namespace) (HN : heapN ⊥ N).
+Context `{!heapG Σ, !one_shotG Σ} (N : namespace).
 
 Definition one_shot_inv (γ : gname) (l : loc) : iProp Σ :=
   (l ↦ NONEV ∗ own γ Pending ∨ ∃ n : Z, l ↦ SOMEV #n ∗ own γ (Shot n))%I.
 
 Lemma wp_one_shot (Φ : val → iProp Σ) :
-  heap_ctx ∗ (∀ f1 f2 : val,
+  (∀ f1 f2 : val,
     (∀ n : Z, □ WP f1 #n {{ w, ⌜w = #true⌝ ∨ ⌜w = #false⌝ }}) ∗
     □ WP f2 #() {{ g, □ WP g #() {{ _, True }} }} -∗ Φ (f1,f2)%V)
   ⊢ WP one_shot_example #() {{ Φ }}.
 Proof.
-  iIntros "[#? Hf] /=".
+  iIntros "Hf /=".
   rewrite -wp_fupd /one_shot_example /=. wp_seq. wp_alloc l as "Hl". wp_let.
   iMod (own_alloc Pending) as (γ) "Hγ"; first done.
   iMod (inv_alloc N _ (one_shot_inv γ l) with "[Hl Hγ]") as "#HN".
@@ -83,14 +83,13 @@ Proof.
 Qed.
 
 Lemma ht_one_shot (Φ : val → iProp Σ) :
-  heap_ctx ⊢ {{ True }} one_shot_example #()
+  {{ True }} one_shot_example #()
     {{ ff,
       (∀ n : Z, {{ True }} Fst ff #n {{ w, ⌜w = #true⌝ ∨ ⌜w = #false⌝ }}) ∗
       {{ True }} Snd ff #() {{ g, {{ True }} g #() {{ _, True }} }}
     }}.
 Proof.
-  iIntros "#? !# _". iApply wp_one_shot. iSplit; first done.
-  iIntros (f1 f2) "[#Hf1 #Hf2]"; iSplit.
+  iIntros "!# _". iApply wp_one_shot. iIntros (f1 f2) "[#Hf1 #Hf2]"; iSplit.
   - iIntros (n) "!# _". wp_proj. iApply "Hf1".
   - iIntros "!# _". wp_proj.
     iApply (wp_wand with "Hf2"). by iIntros (v) "#? !# _".

tests/tree_sum.v

@@ -34,11 +34,10 @@ Definition sum' : val := λ: "t",
   !"l".
 
 Lemma sum_loop_wp `{!heapG Σ} v t l (n : Z) (Φ : val → iProp Σ) :
-  heap_ctx ∗ l ↦ #n ∗ is_tree v t
-    ∗ (l ↦ #(sum t + n) -∗ is_tree v t -∗ Φ #())
+  l ↦ #n ∗ is_tree v t ∗ (l ↦ #(sum t + n) -∗ is_tree v t -∗ Φ #())
   ⊢ WP sum_loop v #l {{ Φ }}.
 Proof.
-  iIntros "(#Hh & Hl & Ht & HΦ)".
+  iIntros "(Hl & Ht & HΦ)".
   iLöb as "IH" forall (v t l n Φ). wp_rec. wp_let.
   destruct t as [n'|tl tr]; simpl in *.
   - iDestruct "Ht" as "%"; subst.
@@ -55,12 +54,11 @@ Proof.
 Qed.
 
 Lemma sum_wp `{!heapG Σ} v t Φ :
-  heap_ctx ∗ is_tree v t ∗ (is_tree v t -∗ Φ #(sum t))
-  ⊢ WP sum' v {{ Φ }}.
+  is_tree v t ∗ (is_tree v t -∗ Φ #(sum t)) ⊢ WP sum' v {{ Φ }}.
 Proof.
-  iIntros "(#Hh & Ht & HΦ)". rewrite /sum' /=.
+  iIntros "[Ht HΦ]". rewrite /sum' /=.
   wp_let. wp_alloc l as "Hl". wp_let.
-  wp_apply (sum_loop_wp with "[- $Hh $Ht $Hl]").
+  wp_apply (sum_loop_wp with "[- $Ht $Hl]").
   rewrite Z.add_0_r.
   iIntros "Hl Ht". wp_seq. wp_load. by iApply "HΦ".
 Qed.