Commit 3ba59838 authored by Robbert Krebbers's avatar Robbert Krebbers
Browse files

Some ectx_language properties.

(which are useful in Amin's logical relations development).
parent a0dfafa6
......@@ -65,6 +65,10 @@ Section ectx_language.
e1 = fill K e1' e2 = fill K e2'
head_step e1' σ1 e2' σ2 efs prim_step e1 σ1 e2 σ2 efs.
Lemma Ectx_step' K e1 σ1 e2 σ2 efs :
head_step e1 σ1 e2 σ2 efs prim_step (fill K e1) σ1 (fill K e2) σ2 efs.
Proof. econstructor; eauto. Qed.
Lemma val_prim_stuck e1 σ1 e2 σ2 efs :
prim_step e1 σ1 e2 σ2 efs to_val e1 = None.
Proof. intros [??? -> -> ?]; eauto using fill_not_val, val_stuck. Qed.
......@@ -46,6 +46,9 @@ Section ectxi_language.
Definition fill (K : ectx) (e : expr) : expr := fold_right fill_item e K.
Lemma fill_app (K1 K2 : ectx) e : fill (K1 ++ K2) e = fill K1 (fill K2 e).
Proof. apply fold_right_app. Qed.
Instance fill_inj K : Inj (=) (=) (fill K).
Proof. red; induction K as [|Ki K IH]; naive_solver. Qed.
......@@ -78,7 +81,7 @@ Section ectxi_language.
fixed fields of different records, even when I did not. *)
Build_EctxLanguage expr val ectx state of_val to_val [] (++) fill head_step _ _ _ _ _ _ _ _ _.
Solve Obligations with eauto using to_of_val, of_to_val, val_stuck,
fill_not_val, step_by_val, fold_right_app, app_eq_nil.
fill_not_val, fill_app, step_by_val, fold_right_app, app_eq_nil.
Global Instance ectxi_lang_ctx_item Ki :
LanguageCtx (ectx_lang expr) (fill_item Ki).
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