thread_id -> na_inv_pool_name

base_logic/lib/na_invariants.v

@@ -5,7 +5,7 @@ Import uPred.
 
 (* Non-atomic ("thread-local") invariants. *)
 
-Definition thread_id := gname.
+Definition na_inv_pool_name := gname.
 
 Class na_invG Σ :=
   tl_inG :> inG Σ (prodR coPset_disjR (gset_disjR positive)).
@@ -13,12 +13,12 @@ Class na_invG Σ :=
 Section defs.
   Context `{invG Σ, na_invG Σ}.
 
-  Definition na_own (tid : thread_id) (E : coPset) : iProp Σ :=
-    own tid (CoPset E, ∅).
+  Definition na_own (p : na_inv_pool_name) (E : coPset) : iProp Σ :=
+    own p (CoPset E, ∅).
 
-  Definition na_inv (tid : thread_id) (N : namespace) (P : iProp Σ) : iProp Σ :=
+  Definition na_inv (p : na_inv_pool_name) (N : namespace) (P : iProp Σ) : iProp Σ :=
     (∃ i, ⌜i ∈ ↑N⌝ ∧
-          inv N (P ∗ own tid (∅, GSet {[i]}) ∨ na_own tid {[i]}))%I.
+          inv N (P ∗ own p (∅, GSet {[i]}) ∨ na_own p {[i]}))%I.
 End defs.
 
 Instance: Params (@na_inv) 3.
@@ -27,36 +27,36 @@ Typeclasses Opaque na_own na_inv.
 Section proofs.
   Context `{invG Σ, na_invG Σ}.
 
-  Global Instance na_own_timeless tid E : TimelessP (na_own tid E).
+  Global Instance na_own_timeless p E : TimelessP (na_own p E).
   Proof. rewrite /na_own; apply _. Qed.
 
-  Global Instance na_inv_ne tid N n : Proper (dist n ==> dist n) (na_inv tid N).
+  Global Instance na_inv_ne p N n : Proper (dist n ==> dist n) (na_inv p N).
   Proof. rewrite /na_inv. solve_proper. Qed.
-  Global Instance na_inv_proper tid N : Proper ((≡) ==> (≡)) (na_inv tid N).
+  Global Instance na_inv_proper p N : Proper ((≡) ==> (≡)) (na_inv p N).
   Proof. apply (ne_proper _). Qed.
 
-  Global Instance na_inv_persistent tid N P : PersistentP (na_inv tid N P).
+  Global Instance na_inv_persistent p N P : PersistentP (na_inv p N P).
   Proof. rewrite /na_inv; apply _. Qed.
 
-  Lemma na_alloc : (|==> ∃ tid, na_own tid ⊤)%I.
+  Lemma na_alloc : (|==> ∃ p, na_own p ⊤)%I.
   Proof. by apply own_alloc. Qed.
 
-  Lemma na_own_disjoint tid E1 E2 : na_own tid E1 -∗ na_own tid E2 -∗ ⌜E1 ⊥ E2⌝.
+  Lemma na_own_disjoint p E1 E2 : na_own p E1 -∗ na_own p E2 -∗ ⌜E1 ⊥ E2⌝.
   Proof.
     apply wand_intro_r.
     rewrite /na_own -own_op own_valid -coPset_disj_valid_op. by iIntros ([? _]).
   Qed.
 
-  Lemma na_own_union tid E1 E2 :
-    E1 ⊥ E2 → na_own tid (E1 ∪ E2) ⊣⊢ na_own tid E1 ∗ na_own tid E2.
+  Lemma na_own_union p E1 E2 :
+    E1 ⊥ E2 → na_own p (E1 ∪ E2) ⊣⊢ na_own p E1 ∗ na_own p E2.
   Proof.
     intros ?. by rewrite /na_own -own_op pair_op left_id coPset_disj_union.
   Qed.
 
-  Lemma na_inv_alloc tid E N P : ▷ P ={E}=∗ na_inv tid N P.
+  Lemma na_inv_alloc p E N P : ▷ P ={E}=∗ na_inv p N P.
   Proof.
     iIntros "HP".
-    iMod (own_empty (prodUR coPset_disjUR (gset_disjUR positive)) tid) as "Hempty".
+    iMod (own_empty (prodUR coPset_disjUR (gset_disjUR positive)) p) as "Hempty".
     iMod (own_updateP with "Hempty") as ([m1 m2]) "[Hm Hown]".
     { apply prod_updateP'. apply cmra_updateP_id, (reflexivity (R:=eq)).
       apply (gset_disj_alloc_empty_updateP_strong' (λ i, i ∈ ↑N)).
@@ -71,14 +71,14 @@ Section proofs.
     iNext. iLeft. by iFrame.
   Qed.
 
-  Lemma na_inv_open tid E F N P :
+  Lemma na_inv_open p E F N P :
     ↑N ⊆ E → ↑N ⊆ F →
-    na_inv tid N P -∗ na_own tid F ={E}=∗ ▷ P ∗ na_own tid (F∖↑N) ∗
-                       (▷ P ∗ na_own tid (F∖↑N) ={E}=∗ na_own tid F).
+    na_inv p N P -∗ na_own p F ={E}=∗ ▷ P ∗ na_own p (F∖↑N) ∗
+                       (▷ P ∗ na_own p (F∖↑N) ={E}=∗ na_own p F).
   Proof.
     rewrite /na_inv. iIntros (??) "#Htlinv Htoks".
     iDestruct "Htlinv" as (i) "[% Hinv]".
-    rewrite [F as X in na_own tid X](union_difference_L (↑N) F) //.
+    rewrite [F as X in na_own p X](union_difference_L (↑N) F) //.
     rewrite [X in (X ∪ _)](union_difference_L {[i]} (↑N)) ?na_own_union; [|set_solver..].
     iDestruct "Htoks" as "[[Htoki $] $]".
     iInv N as "[[$ >Hdis]|>Htoki2]" "Hclose".