Add a very simple lock example.

F_mu_ref_par/examples/lock.v

+From iris.proofmode Require Import invariants ghost_ownership tactics.
+From F_mu_ref_par Require Import lang rules rules_binary.
+Import uPred.
+
+Definition newlock : expr := Alloc (♭ false).
+Definition acquire : expr :=
+  Lam (If (CAS (Var 1) (♭ false) (♭ true)) (Unit) (App (Var 0) (Var 1))).
+Definition release : expr := Lam (Store (Var 1) (♭ false)).
+
+Definition with_lock (e : expr) (l : expr) : expr :=
+  App
+    (Lam
+       (App (Lam (App (Lam (App release (Var 5))) (App e Unit)))
+            (App acquire (Var 1))
+       )
+    )
+    l
+.
+
+Section proof.
+  Context {Σ : gFunctors} {iS : cfgSG Σ}.
+  Context (S : namespace).
+
+  Lemma steps_with_lock N E ρ j K e l P Q :
+    nclose N ⊆ E →
+    (∀ f, e.[f] = e) (* e is a closed term *)
+    →
+    (∃ v, ∀ K', ((Spec_ctx N ρ ★ P ★ j ⤇ (fill K' (App e Unit)))%I)
+            ⊢ |={E}=>(j ⤇ (fill K' (of_val v)) ★ Q)%I)
+    →
+    (((Spec_ctx N ρ ★ P ★ l ↦ₛ (♭v false) ★ j ⤇ (fill K (with_lock e (Loc l))))%I)
+      ⊢ |={E}=>(j ⤇ (fill K (Unit)) ★ Q ★ l ↦ₛ (♭v false))%I).
+  Proof.
+    intros HNE H1 [v H2].
+    iIntros "[#Hspec [HP [Hl Hj]]]".
+    iPvs (step_lam _ _ _ j K _ _ _ _ with "[Hj]") as "Hj"; eauto.
+    iFrame "Hspec Hj"; trivial.
+    asimpl.
+    Unshelve. 3: simpl; auto.
+    iPvs (step_lam _ _ _ j (K ++ [AppRCtx (LamV _)])
+                   _ _ _ _ with "[Hj]") as "Hj"; eauto.
+    rewrite fill_app. simpl.
+    iFrame "Hspec Hj"; trivial.
+    Unshelve. 3: simpl; trivial.
+    asimpl.
+    iPvs (step_cas_suc _ _ _ j (K ++ [AppRCtx (LamV _); IfCtx _ _])
+                       _ _ _ _ _ _ _ _ _ with "[Hj Hl]") as "[Hj Hl]"; trivial.
+    rewrite ?fill_app. simpl.
+    iFrame "Hspec Hj Hl"; trivial.
+    Unshelve. 7: simpl; trivial. 5: simpl; trivial. 4: trivial.
+    iNext; trivial.
+    rewrite fill_app. simpl.
+    iPvs (step_if_true _ _ _ j (K ++ [AppRCtx (LamV _)])
+                       _ _ _ with "[Hj]") as "Hj"; trivial.
+    rewrite ?fill_app. simpl.
+    iFrame "Hspec Hj"; trivial.
+    rewrite fill_app. simpl.
+    Unshelve. all: trivial.
+    iPvs (step_lam _ _ _ j K _ _ _ _ with "[Hj]") as "Hj"; eauto.
+    iFrame "Hspec Hj"; trivial.
+    asimpl.
+    Unshelve. 3: simpl; auto.
+    rewrite H1.
+    iPvs (H2 (K ++ [AppRCtx (LamV _)]) with "[Hj HP]") as "[Hj HQ]"; eauto.
+    rewrite ?fill_app. simpl.
+    iFrame "Hspec Hj"; trivial.
+    rewrite ?fill_app. simpl.
+    iPvs (step_lam _ _ _ j K _ _ _ _ with "[Hj]") as "Hj"; eauto.
+    iFrame "Hspec Hj"; trivial.
+    asimpl.
+    Unshelve. 3: auto using to_of_val.
+    iPvs (step_lam _ _ _ j K _ _ _ _ with "[Hj]") as "Hj"; eauto.
+    iFrame "Hspec Hj"; trivial.
+    asimpl.
+    Unshelve. 3: simpl; auto.
+    iPvs (step_store _ _ _ j K _ _ _ _ _ with "[Hj Hl]") as "[Hj Hl]"; eauto.
+    iFrame "Hspec Hj"; trivial.
+    Unshelve. 3: auto.
+    iPvsIntro. iFrame "HQ Hj Hl"; trivial.
+  Qed.
+
+End proof.
\ No newline at end of file

_CoqProject

@@ -27,4 +27,5 @@ F_mu_ref_par/rules_binary.v
 F_mu_ref_par/logrel_binary.v
 F_mu_ref_par/fundamental_binary.v
 F_mu_ref_par/soundness_unary.v
-F_mu_ref_par/soundness_binary.v
\ No newline at end of file
+F_mu_ref_par/soundness_binary.v
+F_mu_ref_par/examples/lock.v
\ No newline at end of file