rename sub_values -> sub_redexes_are_values

theories/heap_lang/tactics.v

@@ -195,7 +195,7 @@ Proof.
     destruct e=> //=; repeat (simplify_eq/=; case_match=>//);
       inversion 1; simplify_eq/=; rewrite ?to_of_val; eauto.
     unfold subst'; repeat (simplify_eq/=; case_match=>//); eauto.
-  - apply ectxi_language_sub_values=> /= Ki e' Hfill.
+  - apply ectxi_language_sub_redexes_are_values=> /= Ki e' Hfill.
     destruct e=> //; destruct Ki; repeat (simplify_eq/=; case_match=>//);
       naive_solver eauto using to_val_is_Some.
 Qed.

theories/program_logic/ectx_language.v

@@ -62,7 +62,9 @@ Section ectx_language.
   Definition head_irreducible (e : expr) (σ : state) :=
     ∀ e' σ' efs, ¬head_step e σ e' σ' efs.
 
-  Definition sub_values (e : expr) :=
+  (* All non-value redexes are at the root.  In other words, all sub-redexes are
+     values. *)
+  Definition sub_redexes_are_values (e : expr) :=
     ∀ K e', e = fill K e' → to_val e' = None → K = empty_ectx.
 
   Inductive prim_step (e1 : expr) (σ1 : state)
@@ -103,21 +105,21 @@ Section ectx_language.
   Qed.
 
   Lemma prim_head_reducible e σ :
-    reducible e σ → sub_values e → head_reducible e σ.
+    reducible e σ → sub_redexes_are_values e → head_reducible e σ.
   Proof.
     intros (e'&σ'&efs&[K e1' e2' -> -> Hstep]) ?.
     assert (K = empty_ectx) as -> by eauto 10 using val_stuck.
     rewrite fill_empty /head_reducible; eauto.
   Qed.
   Lemma prim_head_irreducible e σ :
-    head_irreducible e σ → sub_values e → irreducible e σ.
+    head_irreducible e σ → sub_redexes_are_values e → irreducible e σ.
   Proof.
     rewrite -not_reducible -not_head_reducible. eauto using prim_head_reducible.
   Qed.
 
   Lemma ectx_language_atomic e :
     (∀ σ e' σ' efs, head_step e σ e' σ' efs → irreducible e' σ') →
-    sub_values e →
+    sub_redexes_are_values e →
     Atomic e.
   Proof.
     intros Hatomic_step Hatomic_fill σ e' σ' efs [K e1' e2' -> -> Hstep].

theories/program_logic/ectxi_language.v

@@ -90,8 +90,9 @@ Section ectxi_language.
     fill_not_val, fill_app, step_by_val, foldl_app.
   Next Obligation. intros K1 K2 ?%app_eq_nil; tauto. Qed.
 
-  Lemma ectxi_language_sub_values e :
-    (∀ Ki e', e = fill_item Ki e' → is_Some (to_val e')) → sub_values e.
+  Lemma ectxi_language_sub_redexes_are_values e :
+    (∀ Ki e', e = fill_item Ki e' → is_Some (to_val e')) →
+    sub_redexes_are_values e.
   Proof.
     intros Hsub K e' ->. destruct K as [|Ki K _] using @rev_ind=> //=.
     intros []%eq_None_not_Some. eapply fill_val, Hsub. by rewrite /= fill_app.