Commit ac0d54da authored by Ralf Jung's avatar Ralf Jung

rename sub_values -> sub_redexes_are_values

parent 0582920d
......@@ -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.
......
......@@ -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].
......
......@@ -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.
......
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