Partially revert "Explicit namespaces for counter, lock and spawn."

In order to improve flexibility, I have reverted the changes in commit
5cabd278 to counter, lock and spawn because an explicit namespace may be in
the way of modularity, for example, if the interfaces of these libraries will
expose namespaces through view shifts in the future.

Exposure of namespaces in the case of par is very unlikely, so to that end,
par remains to use an explicit namespace.

heap_lang/lib/counter.v

@@ -5,8 +5,6 @@ From iris.proofmode Require Import invariants ghost_ownership coq_tactics.
 From iris.heap_lang Require Import proofmode notation.
 Import uPred.
 
-Definition counterN : namespace := nroot .@ "counter".
-
 Definition newcounter : val := λ: <>, ref #0.
 Definition inc : val :=
   rec: "inc" "l" :=
@@ -28,17 +26,19 @@ 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 :=
-  (∃ γ, heap_ctx ∧ auth_ctx γ counterN (counter_inv l) ∧ auth_own γ (n:mnat))%I.
+  (∃ N 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 (R : iProp) Φ :
+Lemma newcounter_spec N (R : iProp) Φ :
+  heapN ⊥ N →
   heap_ctx ★ (∀ l, counter l 0 -★ Φ #l) ⊢ WP newcounter #() {{ Φ }}.
 Proof.
-  iIntros "[#Hh HΦ]". rewrite /newcounter. wp_seq. wp_alloc l as "Hl".
-  iPvs (auth_alloc (counter_inv l) counterN _ (O:mnat) with "[Hl]")
+  iIntros (?) "[#Hh HΦ]". rewrite /newcounter. wp_seq. wp_alloc l as "Hl".
+  iPvs (auth_alloc (counter_inv l) N _ (O:mnat) with "[Hl]")
     as (γ) "[#? Hγ]"; try by auto.
   iPvsIntro. iApply "HΦ". rewrite /counter; eauto 10.
 Qed.
@@ -47,13 +47,13 @@ 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 (γ) "(#Hh & #Hγ & Hγf)".
+  iDestruct "Hl" as (N γ) "(% & #? & #Hγ & Hγf)".
   wp_focus (! _)%E.
-  iApply (auth_fsa (counter_inv l) (wp_fsa _) _ counterN); auto with fsaV.
+  iApply (auth_fsa (counter_inv l) (wp_fsa _) _ N); auto with fsaV.
   iIntros "{$Hγ $Hγf}"; iIntros (j') "[% Hl] /="; rewrite {2}/counter_inv.
   wp_load; iPvsIntro; iExists j; iSplit; [done|iIntros "{$Hl} Hγf"].
   wp_let; wp_op. wp_focus (CAS _ _ _).
-  iApply (auth_fsa (counter_inv l) (wp_fsa _) _ counterN); auto with fsaV.
+  iApply (auth_fsa (counter_inv l) (wp_fsa _) _ N); auto with fsaV.
   iIntros "{$Hγ $Hγf}"; iIntros (j'') "[% Hl] /="; rewrite {2}/counter_inv.
   destruct (decide (j `max` j'' = j `max` j')) as [Hj|Hj].
   - wp_cas_suc; first (by do 3 f_equal); iPvsIntro.
@@ -62,7 +62,7 @@ Proof.
     rewrite {2}/counter_inv !mnat_op_max (Nat.max_l (S _)); last abstract lia.
     rewrite Nat2Z.inj_succ -Z.add_1_l.
     iIntros "{$Hl} Hγf". wp_if.
-    iPvsIntro; iApply "HΦ"; iExists γ; repeat iSplit; eauto.
+    iPvsIntro; iApply "HΦ"; iExists N, 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 "{$Hl} Hγf"].
@@ -73,9 +73,9 @@ Lemma read_spec l j (Φ : val → iProp) :
   counter l j ★ (∀ i, ■ (j ≤ i)%nat → counter l i -★ Φ #i)
   ⊢ WP read #l {{ Φ }}.
 Proof.
-  iIntros "[Hc HΦ]". iDestruct "Hc" as (γ) "(#Hh & #Hγ & Hγf)".
+  iIntros "[Hc HΦ]". iDestruct "Hc" as (N γ) "(% & #? & #Hγ & Hγf)".
   rewrite /read. wp_let.
-  iApply (auth_fsa (counter_inv l) (wp_fsa _) _ counterN); auto with fsaV.
+  iApply (auth_fsa (counter_inv l) (wp_fsa _) _ N); auto with fsaV.
   iIntros "{$Hγ $Hγf}"; iIntros (j') "[% Hl] /=".
   wp_load; iPvsIntro; iExists (j `max` j'); iSplit.
   { iPureIntro; apply mnat_local_update; abstract lia. }

heap_lang/lib/lock.v

@@ -3,8 +3,6 @@ From iris.proofmode Require Import invariants ghost_ownership.
 From iris.heap_lang Require Import proofmode notation.
 Import uPred.
 
-Definition lockN : namespace := nroot .@ "lock".
-
 Definition newlock : val := λ: <>, ref #false.
 Definition acquire : val :=
   rec: "acquire" "l" :=
@@ -27,10 +25,11 @@ 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 :=
-  (∃ γ, heap_ctx ∧ inv lockN (lock_inv γ l R))%I.
+  (∃ N γ, heapN ⊥ N ∧ heap_ctx ∧ inv N (lock_inv γ l R))%I.
 
 Definition locked (l : loc) (R : iProp) : iProp :=
-  (∃ γ, heap_ctx ∧ inv lockN (lock_inv γ l R) ∧ own γ (Excl ()))%I.
+  (∃ N 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.
@@ -44,38 +43,39 @@ 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 (γ) "(?&?&_)"; eauto. Qed.
+Proof. rewrite /is_lock. iDestruct 1 as (N γ) "(?&?&?&_)"; eauto. Qed.
 
-Lemma newlock_spec (R : iProp) Φ :
+Lemma newlock_spec N (R : iProp) Φ :
+  heapN ⊥ N →
   heap_ctx ★ R ★ (∀ l, is_lock l R -★ Φ #l) ⊢ WP newlock #() {{ Φ }}.
 Proof.
-  iIntros "(#Hh & HR & HΦ)". rewrite /newlock.
+  iIntros (?) "(#Hh & HR & HΦ)". rewrite /newlock.
   wp_seq. wp_alloc l as "Hl".
   iPvs (own_alloc (Excl ())) as (γ) "Hγ"; first done.
-  iPvs (inv_alloc lockN _ (lock_inv γ l R) with "[-HΦ]") as "#?"; 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 γ; eauto.
+  iPvsIntro. iApply "HΦ". iExists N, 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 (γ) "[#Hh #?]".
+  iIntros "[Hl HΦ]". iDestruct "Hl" as (N γ) "(%&#?&#?)".
   iLöb as "IH". wp_rec. wp_focus (CAS _ _ _)%E.
-  iInv lockN as ([]) "[Hl HR]".
+  iInv N as ([]) "[Hl HR]".
   - wp_cas_fail. iPvsIntro; iSplitL "Hl".
     + iNext. iExists true; eauto.
     + 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 γ; eauto.
+    + wp_if. iApply ("HΦ" with "[-HR] HR"). iExists N, 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 (γ) "(#Hh & #? & Hγ)".
-  rewrite /release. wp_let. iInv lockN as (b) "[Hl _]".
+  iIntros "(Hl&HR&HΦ)"; iDestruct "Hl" as (N γ) "(% & #? & #? & Hγ)".
+  rewrite /release. wp_let. iInv N as (b) "[Hl _]".
   wp_store. iPvsIntro. iFrame "HΦ". iNext. iExists false. by iFrame.
 Qed.
 End proof.

heap_lang/lib/par.v

@@ -2,6 +2,8 @@ From iris.heap_lang Require Export spawn.
 From iris.heap_lang Require Import proofmode notation.
 Import uPred.
 
+Definition parN : namespace := nroot .@ "par".
+
 Definition par : val :=
   λ: "fs",
     let: "handle" := spawn (Fst "fs") in
@@ -23,7 +25,7 @@ Lemma par_spec (Ψ1 Ψ2 : val → iProp) e (f1 f2 : val) (Φ : val → iProp) :
 Proof.
   iIntros (?) "(#Hh&Hf1&Hf2&HΦ)".
   rewrite /par. wp_value. iPvsIntro. wp_let. wp_proj.
-  wp_apply spawn_spec; try wp_done. iFrame "Hf1 Hh".
+  wp_apply (spawn_spec parN); try wp_done; try solve_ndisj; iFrame "Hf1 Hh".
   iIntros (l) "Hl". wp_let. wp_proj. wp_focus (f2 _).
   iApply wp_wand_l; iFrame "Hf2"; iIntros (v) "H2". wp_let.
   wp_apply join_spec; iFrame "Hl". iIntros (w) "H1".

heap_lang/lib/spawn.v

@@ -3,8 +3,6 @@ From iris.proofmode Require Import invariants ghost_ownership.
 From iris.heap_lang Require Import proofmode notation.
 Import uPred.
 
-Definition spawnN : namespace := nroot .@ "spawn".
-
 Definition spawn : val :=
   λ: "f",
     let: "c" := ref NONE in
@@ -30,7 +28,7 @@ Proof. destruct H as (?&?). split. apply: inGF_inG. Qed.
 
 (** Now we come to the Iris part of the proof. *)
 Section proof.
-Context `{!heapG Σ, !spawnG Σ}.
+Context `{!heapG Σ, !spawnG Σ} (N : namespace).
 Local Notation iProp := (iPropG heap_lang Σ).
 
 Definition spawn_inv (γ : gname) (l : loc) (Ψ : val → iProp) : iProp :=
@@ -38,7 +36,8 @@ Definition spawn_inv (γ : gname) (l : loc) (Ψ : val → iProp) : iProp :=
                    ∃ v, lv = SOMEV v ★ (Ψ v ∨ own γ (Excl ()))))%I.
 
 Definition join_handle (l : loc) (Ψ : val → iProp) : iProp :=
-  (∃ γ, heap_ctx ★ own γ (Excl ()) ★ inv spawnN (spawn_inv γ l Ψ))%I.
+  (heapN ⊥ N ★ ∃ γ, heap_ctx ★ own γ (Excl ()) ★
+                    inv N (spawn_inv γ l Ψ))%I.
 
 Typeclasses Opaque join_handle.
 
@@ -52,18 +51,19 @@ Proof. solve_proper. Qed.
 (** The main proofs. *)
 Lemma spawn_spec (Ψ : val → iProp) e (f : val) (Φ : val → iProp) :
   to_val e = Some f →
+  heapN ⊥ N →
   heap_ctx ★ WP f #() {{ Ψ }} ★ (∀ l, join_handle l Ψ -★ Φ #l)
   ⊢ WP spawn e {{ Φ }}.
 Proof.
-  iIntros (<-%of_to_val) "(#Hh & Hf & HΦ)". rewrite /spawn.
+  iIntros (<-%of_to_val ?) "(#Hh & Hf & HΦ)". rewrite /spawn.
   wp_let. wp_alloc l as "Hl". wp_let.
   iPvs (own_alloc (Excl ())) as (γ) "Hγ"; first done.
-  iPvs (inv_alloc spawnN _ (spawn_inv γ l Ψ) with "[Hl]") as "#?"; first done.
+  iPvs (inv_alloc N _ (spawn_inv γ l Ψ) with "[Hl]") as "#?"; first done.
   { iNext. iExists NONEV. iFrame; eauto. }
   wp_apply wp_fork. iSplitR "Hf".
   - iPvsIntro. wp_seq. iPvsIntro. iApply "HΦ". rewrite /join_handle. eauto.
   - wp_focus (f _). iApply wp_wand_l. iFrame "Hf"; iIntros (v) "Hv".
-    iInv spawnN as (v') "[Hl _]".
+    iInv N as (v') "[Hl _]".
     wp_store. iPvsIntro. iSplit; [iNext|done].
     iExists (SOMEV v). iFrame. eauto.
 Qed.
@@ -71,8 +71,8 @@ Qed.
 Lemma join_spec (Ψ : val → iProp) l (Φ : val → iProp) :
   join_handle l Ψ ★ (∀ v, Ψ v -★ Φ v) ⊢ WP join #l {{ Φ }}.
 Proof.
-  rewrite /join_handle; iIntros "[H Hv]". iDestruct "H" as (γ) "(#?&Hγ&#?)".
-  iLöb as "IH". wp_rec. wp_focus (! _)%E. iInv spawnN as (v) "[Hl Hinv]".
+  rewrite /join_handle; iIntros "[[% H] Hv]". iDestruct "H" as (γ) "(#?&Hγ&#?)".
+  iLöb as "IH". wp_rec. wp_focus (! _)%E. iInv N as (v) "[Hl Hinv]".
   wp_load. iDestruct "Hinv" as "[%|Hinv]"; subst.
   - iPvsIntro; iSplitL "Hl"; [iNext; iExists _; iFrame; eauto|].
     wp_match. iApply ("IH" with "Hγ Hv").