Make atomic a type class.

theories/heap_lang/tactics.v

@@ -175,7 +175,7 @@ Proof.
     f_equal; eauto using subst_is_closed_nil, is_closed_to_val, eq_sym.
 Qed.
 
-Definition atomic (e : expr) :=
+Definition is_atomic (e : expr) :=
   match e with
   | Alloc e => bool_decide (is_Some (to_val e))
   | Load e => bool_decide (is_Some (to_val e))
@@ -187,7 +187,7 @@ Definition atomic (e : expr) :=
   | App (Rec _ _ (Lit _)) (Lit _) => true
   | _ => false
   end.
-Lemma atomic_correct e : atomic e → language.atomic (to_expr e).
+Lemma is_atomic_correct e : is_atomic e → Atomic (to_expr e).
 Proof.
   intros He. apply ectx_language_atomic.
   - intros σ e' σ' ef Hstep; simpl in *.
@@ -228,13 +228,11 @@ Hint Extern 10 (AsVal _) => solve_to_val : typeclass_instances.
 
 Ltac solve_atomic :=
   match goal with
-  | |- language.atomic ?e =>
-     let e' := W.of_expr e in change (language.atomic (W.to_expr e'));
-     apply W.atomic_correct; vm_compute; exact I
+  | |- Atomic ?e =>
+     let e' := W.of_expr e in change (Atomic (W.to_expr e'));
+     apply W.is_atomic_correct; vm_compute; exact I
   end.
-Hint Extern 10 (language.atomic _) => solve_atomic.
-(* For the side-condition of elim_upd_fupd_wp_atomic *)
-Hint Extern 10 (language.atomic _) => solve_atomic : typeclass_instances.
+Hint Extern 10 (Atomic _) => solve_atomic : typeclass_instances.
 
 (** Substitution *)
 Ltac simpl_subst :=

theories/program_logic/ectx_language.v

@@ -118,7 +118,7 @@ Section ectx_language.
   Lemma ectx_language_atomic e :
     (∀ σ e' σ' efs, head_step e σ e' σ' efs → irreducible e' σ') →
     sub_values e →
-    atomic e.
+    Atomic e.
   Proof.
     intros Hatomic_step Hatomic_fill σ e' σ' efs [K e1' e2' -> -> Hstep].
     assert (K = empty_ectx) as -> by eauto 10 using val_stuck.

theories/program_logic/hoare.v

@@ -58,7 +58,7 @@ Proof.
 Qed.
 
 Lemma ht_atomic E1 E2 P P' Φ Φ' e :
-  atomic e →
+  Atomic e →
   (P ={E1,E2}=> P') ∧ {{ P' }} e @ E2 {{ Φ' }} ∧ (∀ v, Φ' v ={E2,E1}=> Φ v)
   ⊢ {{ P }} e @ E1 {{ Φ }}.
 Proof.

theories/program_logic/language.v

@@ -58,15 +58,15 @@ Section language.
      stronger sense defined below, and we have to be able to open invariants
      around that expression.  See `CasStuckS` in
      [lambdaRust](https://gitlab.mpi-sws.org/FP/LambdaRust-coq/blob/master/theories/lang/lang.v). *)
-  Definition atomic (e : expr Λ) : Prop :=
-    ∀ σ e' σ' efs, prim_step e σ e' σ' efs → irreducible e' σ'.
+  Class Atomic (e : expr Λ) : Prop :=
+    atomic σ e' σ' efs : prim_step e σ e' σ' efs → irreducible e' σ'.
 
   (* To open invariants with a WP that does not ensure safety, we need a
      stronger form of atomicity.  With the above definition, in case `e` reduces
      to a stuck non-value, there is no proof that the invariants have been
      established again. *)
-  Definition strongly_atomic (e : expr Λ) : Prop :=
-    ∀ σ e' σ' efs, prim_step e σ e' σ' efs → is_Some (to_val e').
+  Class StronglyAtomic (e : expr Λ) : Prop :=
+    strongly_atomic σ e' σ' efs : prim_step e σ e' σ' efs → is_Some (to_val e').
 
   Inductive step (ρ1 ρ2 : cfg Λ) : Prop :=
     | step_atomic e1 σ1 e2 σ2 efs t1 t2 :
@@ -87,9 +87,8 @@ Section language.
   Global Instance of_val_inj : Inj (=) (=) (@of_val Λ).
   Proof. by intros v v' Hv; apply (inj Some); rewrite -!to_of_val Hv. Qed.
 
-  Lemma strongly_atomic_atomic e :
-    strongly_atomic e → atomic e.
-  Proof. unfold strongly_atomic, atomic. eauto using val_irreducible. Qed.
+  Lemma strongly_atomic_atomic e : StronglyAtomic e → Atomic e.
+  Proof. unfold StronglyAtomic, Atomic. eauto using val_irreducible. Qed.
 
   Lemma reducible_fill `{LanguageCtx Λ K} e σ :
     to_val e = None → reducible (K e) σ → reducible e σ.

theories/program_logic/weakestpre.v

@@ -147,7 +147,7 @@ Lemma wp_fupd E e Φ : WP e @ E {{ v, |={E}=> Φ v }} ⊢ WP e @ E {{ Φ }}.
 Proof. iIntros "H". iApply (wp_strong_mono E); try iFrame; auto. Qed.
 
 Lemma wp_atomic E1 E2 e Φ :
-  atomic e →
+  Atomic e →
   (|={E1,E2}=> WP e @ E2 {{ v, |={E2,E1}=> Φ v }}) ⊢ WP e @ E1 {{ Φ }}.
 Proof.
   iIntros (Hatomic) "H". rewrite !wp_unfold /wp_pre.
@@ -285,10 +285,8 @@ Section proofmode_classes.
 
   (* lower precedence, if possible, it should persistently pick elim_upd_fupd_wp *)
   Global Instance elim_modal_fupd_wp_atomic E1 E2 e P Φ :
-    atomic e →
+    Atomic e →
     ElimModal (|={E1,E2}=> P) P
             (WP e @ E1 {{ Φ }}) (WP e @ E2 {{ v, |={E2,E1}=> Φ v }})%I | 100.
   Proof. intros. by rewrite /ElimModal fupd_frame_r wand_elim_r wp_atomic. Qed.
 End proofmode_classes.
-
-Hint Extern 0 (atomic _) => assumption : typeclass_instances.

theories/tests/ipm_paper.v

@@ -101,7 +101,7 @@ update modalities (which we did not cover in the paper). Normally we use these
 mask changing update modalities directly in our proofs, but in this file we use
 the first prove the rule as a lemma, and then use that. *)
 Lemma wp_inv_open `{irisG Λ Σ} N E P e Φ :
-  nclose N ⊆ E → atomic e →
+  nclose N ⊆ E → Atomic e →
   inv N P ∗ (▷ P -∗ WP e @ E ∖ ↑N {{ v, ▷ P ∗ Φ v }}) ⊢ WP e @ E {{ Φ }}.
 Proof.
   iIntros (??) "[#Hinv Hwp]".