Make lock and counter consistent with spawn.

heap_lang/lib/counter.v

@@ -20,20 +20,20 @@ Instance inGF_counterG `{H : inGFs heap_lang Σ counterGF} : counterG Σ.
 Proof. destruct H; split; apply _. Qed.
 
 Section proof.
-Context `{!heapG Σ, !counterG Σ}.
+Context `{!heapG Σ, !counterG Σ} (N : namespace).
 Local Notation iProp := (iPropG heap_lang Σ).
 
 Definition counter_inv (l : loc) (n : mnat) : iProp := (l ↦ #n)%I.
 
 Definition counter (l : loc) (n : nat) : iProp :=
-  (∃ N γ, heapN ⊥ N ∧ heap_ctx ∧
-          auth_ctx γ N (counter_inv l) ∧ auth_own γ (n:mnat))%I.
+  (∃ γ, heapN ⊥ N ∧ heap_ctx ∧
+        auth_ctx γ N (counter_inv l) ∧ auth_own γ (n:mnat))%I.
 
 (** The main proofs. *)
 Global Instance counter_persistent l n : PersistentP (counter l n).
 Proof. apply _. Qed.
 
-Lemma newcounter_spec N (R : iProp) Φ :
+Lemma newcounter_spec (R : iProp) Φ :
   heapN ⊥ N →
   heap_ctx ★ (∀ l, counter l 0 -★ Φ #l) ⊢ WP newcounter #() {{ Φ }}.
 Proof.
@@ -47,7 +47,7 @@ Lemma inc_spec l j (Φ : val → iProp) :
   counter l j ★ (counter l (S j) -★ Φ #()) ⊢ WP inc #l {{ Φ }}.
 Proof.
   iIntros "[Hl HΦ]". iLöb as "IH". wp_rec.
-  iDestruct "Hl" as (N γ) "(% & #? & #Hγ & Hγf)".
+  iDestruct "Hl" as (γ) "(% & #? & #Hγ & Hγf)".
   wp_focus (! _)%E.
   iApply (auth_fsa (counter_inv l) (wp_fsa _) _ N); auto with fsaV.
   iIntros "{$Hγ $Hγf}"; iIntros (j') "[% Hl] /="; rewrite {2}/counter_inv.
@@ -62,7 +62,7 @@ Proof.
     rewrite {2}/counter_inv !mnat_op_max (Nat.max_l (S _)); last abstract lia.
     rewrite Nat2Z.inj_succ -Z.add_1_l.
     iIntros "{$Hl} Hγf". wp_if.
-    iPvsIntro; iApply "HΦ"; iExists N, γ; repeat iSplit; eauto.
+    iPvsIntro; iApply "HΦ"; iExists γ; repeat iSplit; eauto.
     iApply (auth_own_mono with "Hγf"). apply mnat_included. abstract lia.
   - wp_cas_fail; first (rewrite !mnat_op_max; by intros [= ?%Nat2Z.inj]).
     iPvsIntro. iExists j; iSplit; [done|iIntros "{$Hl} Hγf"].
@@ -73,7 +73,7 @@ Lemma read_spec l j (Φ : val → iProp) :
   counter l j ★ (∀ i, ■ (j ≤ i)%nat → counter l i -★ Φ #i)
   ⊢ WP read #l {{ Φ }}.
 Proof.
-  iIntros "[Hc HΦ]". iDestruct "Hc" as (N γ) "(% & #? & #Hγ & Hγf)".
+  iIntros "[Hc HΦ]". iDestruct "Hc" as (γ) "(% & #? & #Hγ & Hγf)".
   rewrite /read. wp_let.
   iApply (auth_fsa (counter_inv l) (wp_fsa _) _ N); auto with fsaV.
   iIntros "{$Hγ $Hγf}"; iIntros (j') "[% Hl] /=".

heap_lang/lib/lock.v

@@ -18,18 +18,18 @@ Instance inGF_lockG `{H : inGFs heap_lang Σ lockGF} : lockG Σ.
 Proof. destruct H. split. apply: inGF_inG. Qed.
 
 Section proof.
-Context `{!heapG Σ, !lockG Σ}.
+Context `{!heapG Σ, !lockG Σ} (N : namespace).
 Local Notation iProp := (iPropG heap_lang Σ).
 
 Definition lock_inv (γ : gname) (l : loc) (R : iProp) : iProp :=
   (∃ b : bool, l ↦ #b ★ if b then True else own γ (Excl ()) ★ R)%I.
 
 Definition is_lock (l : loc) (R : iProp) : iProp :=
-  (∃ N γ, heapN ⊥ N ∧ heap_ctx ∧ inv N (lock_inv γ l R))%I.
+  (∃ γ, heapN ⊥ N ∧ heap_ctx ∧ inv N (lock_inv γ l R))%I.
 
 Definition locked (l : loc) (R : iProp) : iProp :=
-  (∃ N γ, heapN ⊥ N ∧ heap_ctx ∧
-          inv N (lock_inv γ l R) ∧ own γ (Excl ()))%I.
+  (∃ γ, heapN ⊥ N ∧ heap_ctx ∧
+        inv N (lock_inv γ l R) ∧ own γ (Excl ()))%I.
 
 Global Instance lock_inv_ne n γ l : Proper (dist n ==> dist n) (lock_inv γ l).
 Proof. solve_proper. Qed.
@@ -43,9 +43,9 @@ Global Instance is_lock_persistent l R : PersistentP (is_lock l R).
 Proof. apply _. Qed.
 
 Lemma locked_is_lock l R : locked l R ⊢ is_lock l R.
-Proof. rewrite /is_lock. iDestruct 1 as (N γ) "(?&?&?&_)"; eauto. Qed.
+Proof. rewrite /is_lock. iDestruct 1 as (γ) "(?&?&?&_)"; eauto. Qed.
 
-Lemma newlock_spec N (R : iProp) Φ :
+Lemma newlock_spec (R : iProp) Φ :
   heapN ⊥ N →
   heap_ctx ★ R ★ (∀ l, is_lock l R -★ Φ #l) ⊢ WP newlock #() {{ Φ }}.
 Proof.
@@ -54,13 +54,13 @@ Proof.
   iPvs (own_alloc (Excl ())) as (γ) "Hγ"; first done.
   iPvs (inv_alloc N _ (lock_inv γ l R) with "[-HΦ]") as "#?"; first done.
   { iIntros ">". iExists false. by iFrame. }
-  iPvsIntro. iApply "HΦ". iExists N, γ; eauto.
+  iPvsIntro. iApply "HΦ". iExists γ; eauto.
 Qed.
 
 Lemma acquire_spec l R (Φ : val → iProp) :
   is_lock l R ★ (locked l R -★ R -★ Φ #()) ⊢ WP acquire #l {{ Φ }}.
 Proof.
-  iIntros "[Hl HΦ]". iDestruct "Hl" as (N γ) "(%&#?&#?)".
+  iIntros "[Hl HΦ]". iDestruct "Hl" as (γ) "(%&#?&#?)".
   iLöb as "IH". wp_rec. wp_focus (CAS _ _ _)%E.
   iInv N as ([]) "[Hl HR]".
   - wp_cas_fail. iPvsIntro; iSplitL "Hl".
@@ -68,13 +68,13 @@ Proof.
     + wp_if. by iApply "IH".
   - wp_cas_suc. iPvsIntro. iDestruct "HR" as "[Hγ HR]". iSplitL "Hl".
     + iNext. iExists true; eauto.
-    + wp_if. iApply ("HΦ" with "[-HR] HR"). iExists N, γ; eauto.
+    + wp_if. iApply ("HΦ" with "[-HR] HR"). iExists γ; eauto.
 Qed.
 
 Lemma release_spec R l (Φ : val → iProp) :
   locked l R ★ R ★ Φ #() ⊢ WP release #l {{ Φ }}.
 Proof.
-  iIntros "(Hl&HR&HΦ)"; iDestruct "Hl" as (N γ) "(% & #? & #? & Hγ)".
+  iIntros "(Hl&HR&HΦ)"; iDestruct "Hl" as (γ) "(% & #? & #? & Hγ)".
   rewrite /release. wp_let. iInv N as (b) "[Hl _]".
   wp_store. iPvsIntro. iFrame "HΦ". iNext. iExists false. by iFrame.
 Qed.